<%BANNER%>

Diagnostic and Analytical Studies of Laser Induced Plasmas

Permanent Link: http://ufdc.ufl.edu/UFE0041633/00001

Material Information

Title: Diagnostic and Analytical Studies of Laser Induced Plasmas
Physical Description: 1 online resource (261 p.)
Language: english
Creator: Moon, Heh
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2010

Subjects

Subjects / Keywords: laser, libs, plasma
Chemistry -- Dissertations, Academic -- UF
Genre: Chemistry thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: DIAGNOSTIC AND ANALYTICAL STUDIES OF LASER INDUCED PLASMAS Since its early applications, Laser-Induced Breakdown Spectroscopy (LIBS) has been recognized as a useful tool for solid state chemical analysis due to its numerous attractive advantages as an analytical tool: e.g., simultaneous multi-element detection capability, no sample preparation, rapid or real-time analysis, and allowing in situ analysis requiring only optical access to the sample. However, the quantitative accuracy of the technique depends on the complex fundamental processes involved in laser-induced plasma formation, ablation, atomization, excitation and ion recombination. Thus, problems arising from laser target coupling, matrix effects, line interferences, fractionation in target vaporization, the main assumptions of the methods, namely the optically thin emission of spectral lines and the existence of local thermodynamic equilibrium in the plasma should be properly addressed in order to obtain reliable quantitative results. The general scope of this research encompasses two aspects related to the LIBS technique: one aspect is the fundamental study of the plasma characteristics and another is an improved use of the technique in quantitative analysis. The main project is to revisit and investigate some fundamental assumptions such as the existence of local thermodynamic equilibrium (LTE) and optically thin plasma conditions (e.g., free of self-absorption phenomenon) as mentioned above. Moreover, double-pulse LIBS, which is one of the attractive spectroscopic methods for the diagnostics of the laser-induced plasma due to lower detection limits and enhanced and longer sustained emission signals for analysis, was also investigated herein in order to understand the relative importance of the factors related to the intensity increases as well as the underlying physical mechanisms. In general, LIBS signal enhancement is commonly attributed to an increase of ablated mass from the target or to plasma reheating. Furthermore, signals in LIBS measurement are influenced by the presence of spurious signals or noises. Some types of noises are fundamental to a given experiment, and although they may not be entirely eliminated, it is often possible to minimize them if the limiting noise can be determined. The study of noise forms a part of the discussion of errors in analytical measurement. The root mean square (RMS) value of a noise source and the signal-to-noise (S/N) ratio are useful parameters to describe figures of merit of the analytical procedure. In addition, the relative standard deviation (RSD) is also related to the precision of the measurement. The generally useful S/N ratio expression will be discussed with respect to analytical measurements in this study. The noise expression occurring in LIBS measurement will be also explicitly discussed and evaluated with some information about the type of noise present.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Heh Moon.
Thesis: Thesis (Ph.D.)--University of Florida, 2010.
Local: Adviser: Omenetto, Nicolo.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2011-02-28

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2010
System ID: UFE0041633:00001

Permanent Link: http://ufdc.ufl.edu/UFE0041633/00001

Material Information

Title: Diagnostic and Analytical Studies of Laser Induced Plasmas
Physical Description: 1 online resource (261 p.)
Language: english
Creator: Moon, Heh
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2010

Subjects

Subjects / Keywords: laser, libs, plasma
Chemistry -- Dissertations, Academic -- UF
Genre: Chemistry thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: DIAGNOSTIC AND ANALYTICAL STUDIES OF LASER INDUCED PLASMAS Since its early applications, Laser-Induced Breakdown Spectroscopy (LIBS) has been recognized as a useful tool for solid state chemical analysis due to its numerous attractive advantages as an analytical tool: e.g., simultaneous multi-element detection capability, no sample preparation, rapid or real-time analysis, and allowing in situ analysis requiring only optical access to the sample. However, the quantitative accuracy of the technique depends on the complex fundamental processes involved in laser-induced plasma formation, ablation, atomization, excitation and ion recombination. Thus, problems arising from laser target coupling, matrix effects, line interferences, fractionation in target vaporization, the main assumptions of the methods, namely the optically thin emission of spectral lines and the existence of local thermodynamic equilibrium in the plasma should be properly addressed in order to obtain reliable quantitative results. The general scope of this research encompasses two aspects related to the LIBS technique: one aspect is the fundamental study of the plasma characteristics and another is an improved use of the technique in quantitative analysis. The main project is to revisit and investigate some fundamental assumptions such as the existence of local thermodynamic equilibrium (LTE) and optically thin plasma conditions (e.g., free of self-absorption phenomenon) as mentioned above. Moreover, double-pulse LIBS, which is one of the attractive spectroscopic methods for the diagnostics of the laser-induced plasma due to lower detection limits and enhanced and longer sustained emission signals for analysis, was also investigated herein in order to understand the relative importance of the factors related to the intensity increases as well as the underlying physical mechanisms. In general, LIBS signal enhancement is commonly attributed to an increase of ablated mass from the target or to plasma reheating. Furthermore, signals in LIBS measurement are influenced by the presence of spurious signals or noises. Some types of noises are fundamental to a given experiment, and although they may not be entirely eliminated, it is often possible to minimize them if the limiting noise can be determined. The study of noise forms a part of the discussion of errors in analytical measurement. The root mean square (RMS) value of a noise source and the signal-to-noise (S/N) ratio are useful parameters to describe figures of merit of the analytical procedure. In addition, the relative standard deviation (RSD) is also related to the precision of the measurement. The generally useful S/N ratio expression will be discussed with respect to analytical measurements in this study. The noise expression occurring in LIBS measurement will be also explicitly discussed and evaluated with some information about the type of noise present.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Heh Moon.
Thesis: Thesis (Ph.D.)--University of Florida, 2010.
Local: Adviser: Omenetto, Nicolo.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2011-02-28

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2010
System ID: UFE0041633:00001


This item has the following downloads:


Full Text






DIAGNOSTIC AND ANALYTICAL STUDIES OF LASER INDUCED PLASMAS


By

HEH YOUNG MOON















A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA

2010


























2010 Heh Young Moon




























To my parents, my husband (Dooho Park) and my lovely daughter (Suebin Park)









ACKNOWLEDGMENTS

I would like to express my sincere appreciation to my mentor Dr. Nicolo6 Omenetto

for his outstanding guidance and discussion, understanding, patience, and most

importantly, his friendship during my graduate studies at University of Florida. It has

been a wonderful experience to work in Dr. Omenetto lab for that he has always created

the best ever environment for us to conduct scientific experiments under his mentorship

and insightful discussion. I believe he is a wonderful scientist and wonderful person. I

really respect his enthusiasm, eagerness and deep knowledge to the research.

Whenever I felt that I could not go on much longer, he had encouraged me all the time

to not only grow as an experimentalist and a chemist but also as an instructor and an

independent thinker so that I can focus on my research again. For everything you've

done for me, Professor Omenetto, I would like to gratefully and sincerely thank you

again. I would also like to acknowledge to Dr. James D. Winefordner for his all the

insightful comments and support for my research in our regular meeting even thought

he has already retired from the faculty at UF. I am also grateful to Dr. Benjamin W.

Smith for his good guide and advice from his scientific experience and knowledge. He is

also wonderful person and scientist. I think I have been very fortunate to have many

research co-supervisors. I could never have been able to finish my dissertation without

the guidance of them. I also thank my committee members, Dr. Philip Brucat, Dr.

Nicolas Polfer and Dr. David Hahn.

I would like to thank all the previous and current members in our group, especially

Dr. Kathleen Kate Herrera and Daniel Edward Shelby for all insightful discussion on

LIBS and a good friendship. I also thank to Dr. Ben6it Lauly, Jonathan A. Merten and

Richard A. Warren for a good discussion and all the help.









Finally, and most importantly, I would like to thank my family for all of their love

and support without which I could not have managed to complete my dissertation. I

would like to thank my husband, Dooho Park, for understanding and love during the

past few years. His support, encouragement, patience and unwavering faith and love

were in the end what made this dissertation possible. I also would like to thank to my

daughter, Suebin Park (a source of unending joy and love), has been wonderfully

understanding throughout the dissertation process and has been awaiting the day when

I would be finished. Specially, I would also like to thank my parent for taking care of my

daughter during two years in South Korea for helping me focus on my research. My

mother always listened to me on the phone and encouraged me to continue on with the

research whenever I was stressed and feeling down.









TABLE OF CONTENTS

page

A C K N O W LE D G M E N T S ........................................................................................ .... 4

LIST O F TA BLES ............... ................................................................................... 9

LIST O F FIG U R ES ........................................................................................................ 10

LIST O F A B BR EV IA T IO N S .................................................................. ............... 19

LIST OF SYM BOLS AND CONSTANTS.................................................. ............... 21

A B S T R A C T ........................................................................................... 2 8

CHAPTER

1 INTENT A N D SCO PE O F STUDY ..................................................... ............... 30

2 FU N DA M E N TA L O F LIBS ..................................... ......................... ............... 32

In tro d u c tio n ......................................................................................................... .. 3 2
T he D discovery of LIBS ...................................................................................... 32
General Principle of LIBS [1] .............................................................. .............. 36
LIB S D esign (G general) ................. .. .......... ...... ...................................... 37
Basics of Laser-Matter Interaction and Processes in Laser-Induced Plasma... 37

3 FUNDAMENTAL INVESTIGATION OF LASER INDUCED PLASMA.................. 48

In tro d u c tio n ......................................................................................................... .. 4 8
S pectral E m mission from P lasm a ......................................................... ............... 49
W idth and Shape of Spectral Lines [74] ...................................... ............... 51
Determining Electron Densities from Spectral Line Widths ........................... 56
P lasm a O pa city ....................................................... ............. ... .......... 5 7
Thermodynamic Equilibrium and Temperature........................................... 61

4 LINE-TO-CONTINUUM INTENSITY RATIO IN LASER-INDUCED
BREAKDOWN SPECTROSCOPY AS AN EXPERIMENTAL CHECK TO
LOCAL THERMODYNAMIC EQUILIBRIUM..................................................... 72

In tro d u c tio n ......................................................................................................... .. 7 2
Theory [107] ................ ... ....... ........ ................. ......................... 74
Line-to-Continuum Intensity Ratio Method for Determining of Te ................... 74
E x p e rim e n ta l .......................................................................................................... 7 8
R results and D iscussion..................................................................................... 79
E lectron N um ber D ensity (ne) ......................... .......................... ............... 79
Excitation Tem perature (Texc) ......................... .......................... ............... 82


6









E lectron T em perature (T e)................................. ......................... ............... 83
C conclusions ............................................................................ ........ ............... 88

5 ON THE USEFULNESS OF A DUPLICATING MIRROR TO EVALUATE SELF-
ABSORPTION EFFECTS IN LASER-INDUCED BREAKDOWN
S PECTR O SC O PY ................................................................... ..................... 102

Introduction ....................................................................................... ............... 102
The Self-absorption Correction Factor KA ................ ............... 104
E x p e rim e n ta l......................................................................................................... 1 0 9
Results and D discussion .................................................................................... 109
E v a lu a tio n o f R c ......................................................................... ............... 1 0 9
Evaluation of RA ............... ................... ......... ............... 110
Temporal Behavior of KA,corr and DA(A) .......................................... ............... 111
Self-absorption Corrected Saha-Boltzmann Plots........................................ 113
Self-absorption Corrected Calibration Curves.............................................. 114
Conclusions ........................................................................... ..... ............... 115

6 A COMPARISON OF SINGLE VERSUS DOUBLE PULSE LASER-INDUCED
BREAKDOWN SPECTROSCOPY .............. ......................... 134

Introduction .................................................................................... ............... 134
E xpe rim e nta l ......................................................................................................... 136
Laser and Detector System............. ............................. 136
T riggering System ..................................................................................... 139
Results and D discussion .................................................................................... 139
O ptim ization ........................... ............ ..................................... 139
Time-gated, Spectrally Resolved, One-direction Images in Single and
Orthogonal Double Pulse Pre-ablation Scheme........................................ 146
Spectroscopic Study of the Factors Concurring to the Intensity
Enhancement in Double-pulse LIBS ....... ... ..................................... 150
C conclusions ................................................................................... ............... 159

7 CONSIDERATION ON THE SPECTRAL FLUCTUATION APPROACH IN
LASER INDUCED BREAKDOWN SPECTROSCOPY........................................ 195

T h e o ry ................ .. ... ................. ................................................ ............ 1 9 6
Standard Deviation Lim iting Cases ....... ... ...................................... 199
Relative Standard Deviation Lim iting Cases ............................ ............... 203
E x p e rim e n ta l ......................................................................... ......................... 2 0 6
Results and D discussion .................................................................................... 207
C o n c lu s io n s ................................................................................................. 2 1 8
A p p e n d ix ............................................................................................................... 2 4 1
G lo s s a ry ......................................................................................................... 2 4 1

8 CONCLUSION AND FUTURE W ORK .............................................. .............. ...... 243

S u m m a ry .................................................................................................. 2 4 3









F u tu re W o rk ................................................................................................ 2 4 7

LIST O F R EFER ENC ES ........................................................................................ 248

BIO G RA PH ICAL SKETC H ..................................................................................... 261









LIST OF TABLES


Table page

2-1 Significant milestones in the development of LIBS as an analytical technique
applicable to a variety of samples and circumstances [1 ]................................ 46

2-2 Advantages and disadvantages of laser-induced breakdown spectroscopy....... 47

4-1 Selected spectral lines and corresponding spectroscopic information of the
investigated elem ents(a) .............................................................................. 100

4-2 Gating and laser energy parameters used for temporal characteristic and
line-to-continuum intensity ratio method of pure copper metal: (a) at the short
delay times with laser pulse energy 50 5 mJ and (b) at long delay times
with laser pulse energy 90 5 mJ ............... ......................... 101

5-1 Elemental percentage composition of South African aluminum alloy
standards disks (APEX Smelter Co., South Africa) [166]. ............................. 132

5-2 Selected spectral line and corresponding spectroscopic information of the
investigated elem ents(a) [166] ....... ...... .. ....... ..................... 133

6-1 Concentration of several elements in NIST Al SRM 603 and South African Al
alloy standards AA1 and D28 (APEX Smelter Co., South African)................ 190

6-2 Selected spectral lines and corresponding spectroscopic information of the
investigated elem ents(a) .............................................................................. 191

6-3 All parameter values mentioned in Eq. 6-11 at different delay times (pre-
ablation air spark scheme) ................................... 192

6-4 Plasma temperature and electron number density in both single and
orthogonal pre-ablation air spark double-pulse configuration at different delay
tim e s ............................................................................................................ .... 1 9 3

6-5 All parameter values mentioned in Eq. 6-11 at different delay times
(reheating schem e)..................................................................................... 194

6-6 Plasma temperature and electron number density in both single and
orthogonal reheating double-pulse configuration at different delay times......... 194

7-1 Factors affecting quantitative analysis using LIBS................. .................. 239

7-2 Elemental percentage composition of South African aluminum alloy
standards disks (APEX Smelter Co., South Africa) ............................ 240

7-3 Elemental percentage composition of NIST brass standards ........................ 240









LIST OF FIGURES


Figure page

2-1 Diagram of a typical laboratory LIBS apparatus. ........................... ............... 42

2-2 A summary of laser ablation (LA) processes and various mechanisms
occurring during each process. Inserted figure shows the schematic diagram
of expanding laser produced plasma into ambient gas in detail. The plasma
plume is divided into several zones having high-density hot and low-density
cold plasma. The farthest zone from the target has minimum plasma density
and temperature. The laser is absorbed in low-density corona [70]. ................ 43

2-3 Timing of the physical phenomenon observed during the plasma expansion
and two major types of laser absorption wave schemes [68, 71]..................... 44

2-4 (a) Relevant time periods after plasma formation during which emission from
different species predominate. The box represents the time during which the
plasma light is monitored using a gatable detector. (Here, td is the delay time
and tw is the gate pulse width.) (b) Relevant timing periods for a double-pulse
configuration. (Here, At is interpulse delay time between two lasers.) [2]........... 45

3-1 Energy level scheme and associated excitation/de-excitation processes. The
symbols shown above the arrows represent the rate constants for the
transition: i.e., C (/,p): excitation rate coefficient; F(p,/): de-excitation rate
coefficient; A(p,/): Einstein's A coefficient or transition probability for p-*/;
S(/): ionization rate coefficient; a(/): three-body recombination rate coefficient;
13(/): radiative recombination rate coefficient; x(/): ionization potential of level I/
(adapted from ref [90]) .................................................... ............... .......... 68

3-2 Spectral line profile. Here Ao is the central wavelength, A\1 and A2 are the
wavelength whose intensity is half of the maximum intensity I (Ao), and AA is
the full width at half maximum (FWHM) (adapted from [99]). ........................... 69

3-3 Normalized spectral profiles versus relative frequency for pure Doppler (D),
pure Lorentzian (L) distributions of equal full-width at half-maximum (FWHM),
and the resulting Voigt (V) profile (adapted from ref [100])............................... 70

3-4 Spectral line profile as a function of gradually increasing atomic
concentration (a -4h). Note that the center of the line reaches the blackbody
radiation limit at high atom densities (adapted from ref [100]). ........................ 71

4-1 Experim ental LIB S set-up .............................................................. .............. 90

4-2 (a) Line broadening and (b) the electron number density calculated from
Stark-broadened line widths of the Ba II line at 252.84 nm at 905 mJ laser
pulse energy as a function of delay tim e. ...................................... ............... 91









4-3 (a and b) Saha-Boltzmann plots and (c) Boltzmann plot in different delay
times. (d f) Corresponding excitation temperatures versus delay times
show in the figure. .................................................................................... 92

4-4 Electron temperature versus (a -b) free-free bound correction factor and (c-d)
free-bound continuum correction factor as a function of delay time................. 93

4-5 Normalized line profiles of Cu atomic transition at 282.44 nm (a) at 50 ns < td
< 500 ns delays (laser pulse energy 50+5 mJ and gate width 50 ns) and (b)
at 500 ns < td < 15000 ns delays (laser pulse energy 90+5 mJ and gate width
1 0 0 n s ) ..................................................... ...... .............................................. .. 9 4

4-6 (a and c) Temporal evolution of the excitation and electron temperatures at
282.44 nm Cu I line from copper metal. (b and d) The line profile in the
figures corresponds to the Voigt profile fit of the emission lines at different
delays from plasm a creation .......................................................... ............... 95

4-7 (a) Temporal evolution of the excitation temperature and electron
temperature at 296.12 nm Cu I line of Al-alloy sample (Z8). (b) The line
profile in the figures corresponds to the Voigt profile fit of the emission lines
at different delays from plasm a creation ....................................... ............... 96

4-8 Temporal evolution of the excitation temperature and electron temperature
for Cu atomic lines at 282.44, 296.12 and 510.55 nm in a copper metal for (a)
short delay times (100 ns td 500 ns) and (b) long delay time (500 ns td
< 1 5 0 0 0 n s )....................................................................................................... 9 7

4-9 Time-resolved emission spectra from laser-induced plasma of Ba II lines.
The spectra were recorded at 90 + 5 mJ pulse energy and the gate time of
the intensity w as set by 0.1 ps ............................................................... 98

4-10 (a) Temporal evolution of the excitation temperature and electron
temperature at 252.84 nm Ba II line of Al-alloy sample (Z8). (b) The line
profile in the figures corresponds to the Voigt profile fit of the emission lines
at different delays from plasm a creation ....................................... ............... 99

5-1 (a) Scheme of the set-up used, with the addition of an external spherical
mirror; (b) Schematic representation of the plasma images on the slit with
and without the mirror, which is located at a distance from the plasma equal
to its radius of curvature; (c) zero order plasma images obtained with and
w without the m irro r [166 ] ................................................. ............... .......... 118

5-2 Magnesium, copper, and iron compositions in the 9- aluminum alloy samples
used. The insert represents the magnesium composition used to obtain the
ca lib ratio n p lots [16 6 ] ................................................... ................ .......... 1 19









5-3 (a) Observed spectral profile of the copper atomic line at 510.55 nm for
different delay times from the onset of the plasma. (b) Experimental
evaluation of RA and Rc in the case of the copper atomic line at 510.55 nm.
The delay time is 1.0 ps and the gate width 0.1 ps [166]................................ 120

5-4 Experimental ratio (Rc) of the continuum radiation with and without the mirror
observed at different delay times. The measurements refer to the 510.55 nm
Cu line. The average value of Rc over the delay times is 1.60 [166] ............. 121

5-5 Calculated dependence of the correction factor KA,corr as a function of Rc for
different values of RA, e.g., for different degree of self-absorption [166] ........ 122

5-6 (a) Calculated values of RA as a function of wavelength along the line profiles;
(b) Correction factor KA,corras a function of wavelength and self-absorption
corrected line profiles (c) Voigt profile fit of the emission lines obtained with
and without the mirror and after correction for self-absorption. All cases refer
to the Cu I transition at 510.55 nm and to measurements taken at 1.0 ps
delay time. The average value of Rc (1.6) was used here [166] ........ ......... 123

5-7 Temporal behavior of the correction factor KA,corr (evaluated at the line center)
for three Cu atomic lines at 510.55 nm, 324.75nm and 327.40 nm as a
function of different delay times after plasma formation. The error bars
reported were calculated assuming a maximum error of 10 % for each
correction factor (see text for discussion) [166]. .................... ...... ............ 124

5-8 Temporal behavior of the correction factor, KA,corr (evaluated at the line
center) for three Mn lines at 403.08 nm, 403.31 nm and 403.45 nm as a
function of different delay times after plasma formation [166]. ....................... 125

5-9 Cu I emission profiles observed at 510.55 nm with and without the mirror,
together with corresponding calculated duplication factor DA at different delay
tim e s [1 6 6 ]........................................................................................................ 1 2 6

5-10 Saha-Boltzmann plots constructed using atomic and ionic lines of Al and Cu
measured in the spectra of two different alloy samples. The data were
obtained at 1.0 ps delay time. Plots (a) and (c) show all the data while plots
(b) and (d) result after exclusion of the transitions affected by self-absorption
[1 6 6 ] ...................................................... ...... .............................................. ... 1 2 7

5-11 Saha-Boltzmann plot constructed using Fe atomic and ionic lines: (a) 1.0 ps
delay time, and (b) 3.0 delay time. The two slopes result from the data
uncorrected (open squares) and corrected (open circles) for self-absorption.
The lines correspond to the best linear fitting of the data [166]. ..................... 128

5-12 Saha-Boltzmann plot constructed using Cu atomic and ionic lines at 5.0 ps
delay time. The two slopes result from the data uncorrected (open squares)
and corrected (open circles) for self-absorption. The lines correspond to the
best linear fitting of the data. The transitions used (nm) are indicated [166]..... 129









5-13 Experimental calibration plots of Mg using eight Al-alloy standard samples
with and without correction for self-absorption at (a) Ionic line 280.27 nm and
(b) atomic line 285.21 nm. Gate width: 0.1 ps; delay time: 2.0 ps; pulse
energy 905 mJ. The dotted lines connecting the uncorrected data are meant
as a visual aid while those drawn through the corrected data correspond to
the best linear fit [166]. ....................... ........................................................ 130

5-14 Variation of the calculated correction factor KA,corr (evaluated at the line
center) for the Mg atomic (open squares) and ionic (open triangles) lines for
each Al alloy sample measured. The insert indicates the magnesium content
of each sample. The error bars reported were calculated assuming a
maximum error of 10 % for each correction factor (see text for discussion)
[1 6 6 ] ....................................................... ..... ............................................... ... 1 3 1

6-1 Common pulse configurations. (a) Collinear configuration, in which the first
and second laser pulses are both focused on/or into a sample. In orthogonal
configuration, a single ablative pulse is coupled with either (b) a pre-ablation
air spark that is parallel to and up to several millimeters above the sample
surface or (c) a reheating pulse [70]. ...... ... ........................................ 161

6-2 (a) Scheme of the set-up showing LIBS system for both single- and double-
pulse operation ............................................................................ .. ......... 162

(b) Timing and triggering system used for both pre-ablation air spark and
reheating double-pulse schemes ................ .......................... 162

6-3 LIBS signal enhancement at the several different transition lines for the
several elements (Al II, Mg I and II and Cr II) versus the interpulse delay time
(At, up to 100 ps) at several different distances (d, 0.3 2.5 mm) in SRM
6 0 3 s a m p le ....................................................................................................... 1 6 3

6-4 Pre-ablation air spark double-pulse configuration signal enhancement versus
the interpulse delay time (=At) in (a) NIST Al SRM 603 and (c) South African
Al AA1 sample and signal enhancement versus the distance (=d, mm) from
the sample surface to air spark above the sample in (b) NIST Al SRM 603
and (d) South African Al AA1 sample ............................................ 164

6-5 Spectra showing Al II 281.62 nm and Mg I 285.21 nm emission lines of
interest in terms of delay time in Al alloy sample (SRM 603) in both (a)
single-pulse and (b) orthogonal pre-ablation air spark double-pulse
configuration. (c) For each emission line, graphs of LIBS signal enhancement
with use of the double-pulse irradiation versus several delay times from 0.5
p s to 1 0 s ........................................................................................................ 1 6 5

6-6 Signal-to-noise (S/N) ratio as a function of delay times for each Al II and Mg I
e m is s io n lin e ..................................................................................................... 1 6 6









6-7 Triggering scheme for the time-resolved study of plasma evolution in the
reheating double-pulse scheme (a) with short gate width of 0.1 ps and (b)
long gate width of 30 ps (averaged measuring) of plasma in the triggering
system initiated by the Quantel Brillant laser ......................... .................. 167

6-8 LIBS signal enhancement versus interpulse delay in the reheating double-
pulse scheme (a) with short gate width of 0.1 ps and (b) long gate width of
30 ps (averaged measuring) of plasma in the triggering system initiated by
the Q uantel Brillant laser. ....................... .................................................... 168

6-9 Plasma images in (a) double-pulse, (b) single-pulse and (c) only air spark
(without sample plasma) at the center wavelength of 259.09 nm in aluminum
alloy AA1 sample. (d) Intensity enhancement compared to only air spark
(without ablation) laser pulse as well as the LIBS signal from the ablation
lase r pu lse o n ly........................................................................................ 16 9

6-10 (a) Time sequence for the time-resolved study of plasma evolution in the
reheating double-pulse scheme. The acquisition time after the ablating laser
pulse is about 3.0 ps (tw:0.1 ps; td: 1.0 ps; At: 2.0 ps). (b) Peak intensity as a
function of decay time of plasma for selected neutral and ionic lines (tw:0.1
ps; td: 1.0 ps; d:3.0 mm) and inserted figure shows a log-log scale plot of the
s a m e d a ta ......................................................................................................... 1 7 0

6-11 (a) Time sequence of the experimental set-up in the case of the reheating
double-pulse scheme. (b) Timing between laser output pulse and HV gate
pulse (PG-200 Delay Trigger out) at the different delay time td. (c) LIBS
signal enhancement (log-scale) of Al II 281.62 nm as a function of the delay
tim e td ............................................................ ............................................. .. 1 7 1

6-12 LIBS signal enhancement versus the interpulse delay time (=At) at the
several distances (=d, mm) from the air-spark to sample surface in a
selected line (a) Mg II 279.08 nm and (b) Al II 281.62 nm and (c) at the
maximum distance (d = ~ 3.0 mm) for several transition lines in the reheating
double-pulse configuration. .... ............................ 172

6-13 LIBS signal enhancement versus the delay between the two laser pulses At
in the reheating double-pulse scheme for selected neutral and ionic lines
(gate width: 0.1 ps; delay time: 1.0 ps; d: 3.0 mm) ................. .................. 173

6-14 Signal-to-noise (S/N) ratio as a function of delay times for each Al II and Mg I
e m is s io n lin e ..................................................................................................... 1 7 4

6-15 Time-gated, spectrally resolved, one-directional images of the laser-induced
plasma of a Al alloy sample (603), obtained in the single (left images) and in
the orthogonal pre-ablation air spark double-pulse mode (right images). The
gate width and interpulse delays between two laser pulses were kept by
constants (0.1 ps and 30 ps respectively), and the ICCD gate delays were
0.5 (a,g), 1.0 (b,h), 2.0 (c,i), 3.0 (d,j), 5.0 (e,k) and 8.0 (f,l)............................ 175








6-16 Time-gated, spectrally resolved, one-directional images of the laser-induced
plasma of a Al alloy sample (603), obtained in the single (left images) and in
the orthogonal reheating double-pulse mode (right images). The gate width
and ICCD gate delays were kept by constants (0.1 ps and 1.0 ps
respectively), and interpulse delay times (At) between two laser pulses were
0.5 (a,g), 1.0 (b,h), 1.5 (c,i), 2.5 (d,j), 4.0 (e,k) and 6.0 (f,l)............................ 176

6-17 Spatial intensity profiles of atomic and ionic emission lines of Al, Mg, Cr at
different delay times from 0.5 ps to 8.0 ps in the pre-ablation air spark
scheme. The acquisition time (= tw) and interpulse delay time (At) between
two laser pulse was fixed at 0.1 ps and 30ps. ....................... .................. 177

6-18 Spatial intensity profiles of atomic and ionic emission lines of Al, Mg, Cr at
different delay times from 0.5 ps to 6.0 ps in the reheating scheme. The gate
width and ICCD gate delays were kept by constants (tw: 0.1 ps and td: 1.0 ps
re s p e c tiv e ly ). .................................................................................................... 1 7 8

6-19 SEM images of craters produced 50 consecutive samplings of Al alloy
sample (a) in the single-pulse and (b) in the double-pulse (At = 20 ps) using
the orthogonal pre-ablation air spark mode, and (c) in the single-pulse and
(d) in the double-pulse (At = 5.0 ps) using the orthogonal reheating mode...... 179

6-20 Signal enhancement versus delay times at the different Mg atomic (solid
dots) and ionic (open dots) lines (a) In orthogonal pre-ablation air spark and
(b) in reheating schem e LIBS. ...... ........ ........ ..................... 180

6-21 Logarithmic plots of neutral and ionic line enhancements at the different
delay times from (a) 0.5 ps to (i) 10 ps (in the pre-ablation air spark scheme). 181

6-22 (a) LIBS spectra in both single (black color) and double pulse (gray color) at
the different delay times for the pre-ablation air spark scheme (Acenter = 281.5
nm, At = 30 ps and tw = 0.1 ps). .............. .......................... 182

(b) LIBS spectra in both single (black color) and double pulse (gray color) at
the different delay times for the pre-ablation air spark scheme (Acenter = 292
nm, At = 30 ps and tw = 0.1 ps). .............. .......................... 183

6-23 (a) Plasma temperature obtained from Saha-Boltzmann plot, (b) temperature
difference (AT = slope) and intercept (= q) from the logarithm plots of neutral
and ionic line enhancements, (c) electron number density using Stark-
broadening (Al II 281.62 nm) and (d) The enhancement of total number
density of atoms and ions in plasma from Eq. 6-11 at the different delay
tim e s ............................................................................................................ .... 1 8 4

6-24 Saha-Boltzmann plot in both (a) single and (b) orthogonal pre-ablation air
spark double-pulse configuration and (c) single and (d) orthogonal reheating
double-pulse configuration. .... ............................ 185









6-25 SEM images of craters produced 50 consecutive samplings of Al alloy
sample (a) in the single-pulse and (b) in the double-pulse (At = 20 ps) using
a pre-ablation air spark. Spectrally resolved one-directional images of the
laser-induced plasma of a Al alloy sample, obtained (c) in the single and (d)
in the double-pulse ablation mode (td= 2.0 ps; tw = 0.1 ps; At = 30 ps)......... 186

6-26 Logarithmic plots of neutral and ionic line enhancements at the different
delay times from (a) 0.5 ps to (f) 9.0 ps (in the reheating scheme). ............... 187

6-27 (a) LIBS spectra in both single (black color) and double pulse (gray color) at
the different delay times for the reheating scheme (Acenter = 281.5 nm, td = 1.0
p s a n d tw = 0 .1 p s) ....................................................... ................ .......... 18 8

(b) LIBS spectra in both single (black color) and double pulse (gray color) at
the different delay times for the reheating scheme (Acenter = 292 nm, td = 1.0
p s a n d tw = 0 .1 p s) ....................................................... ................ .......... 18 8

6-28 (a) Plasma temperature obtained from Saha-Boltzmann plot, (b) temperature
difference (AT = slope) and intercept (= q) from the logarithm plots of neutral
and ionic line enhancements, (c) electron number density using Stark-
broadening (Al II 281.62 nm) and (d) The enhancement of total number
density of atoms and ions in plasma from Eq. 6-11 at the different delay
tim e s ............................................................................................................ .... 1 8 9

7-1 An example of the description of net signal: i.e., the simplest signal
measurement consists of the peak intensity (Sneto ) at the central wavelength
of the analyte line and an off-peak measurement of the background at a
single position (B ,off peak) ............................................. ............................... 221

7-2 In standard deviation (SD) limiting cases, simulated shapes of the plot SD
ve rsus w ave le ngth ........................................................ ............... .......... 222

7-3 In relative standard deviation (RSD) limiting cases, simulated shapes of the
plot RSD versus wavelength....... ......... ........ ..................... 223

7-4 (a) 3D LIBS spectra for 55 laser shots in an Al-alloy (D28) sample and (b) a
55-shot ensemble-averaged LIBS spectrum (black line) with both associated
standard deviation (red line) and relative standard deviation (blue line). Used
gate delay time and gate width are 2.0 ps and 0.1 ps, respectively. .............. 224

7-5 Zn and Cu atomic emission lines for both (a and c) 55 single-shot ensemble-
averaged spectra and (b and d) associated standard deviation curves at the
same spectral range in Al alloy sample (D28) and NIST brass standard
(1113), respectively. In both samples, the settings on the detection system
were 2.0 us and 0.1 ps for the gate delay time and gate width, respectively.
Each full width at half maximum value of Cu I resonance line at 324.7 nm
was obtained by fitting a Voigt profile (see the blue arrows).......................... 225









7-6 (a and b) 55 single-shot LIBS spectra at the peak of Zn I 330.3 nm in both Al-
alloy sample (D28) and NIST brass standard (1113), respectively. (The used
gate delay time and gate width were 2.0 ps and 0.1 ps, respectively.) Each
correlation factor 0 between two major noise sources was calculated at the
peak of Zn I 330.3 nm by using Eq. 7-7. In Al-alloy sample (D28), 0 is 0.527,
while in NIST brass standard (1113), 0 is 0.871 ................... .................. 226

7-7 (a and b) LIBS spectra for the several Mg compositions in Al-alloy samples
(Square box indicates the region for zoom-in) and (c and d) experimentally
calculated correlation factor as a function of both concentration and standard
deviation of the background measured near Mg I 285.21 nm, respectively.
Either a single pixel or 20 pixels measurement was used for the
determination of the standard deviation of the background measured .......... 227

7-8 (a) LIBS spectra (ensemble-averaged) showing the Mg I and II lines and Al II
line and (b) standard deviation curves for 50 laser shots in 6 Al-alloys
samples. (c) Relative standard deviation (RSD) curves as calculated from the
quotient of the standard deviation (square box indicates the region for zoom-
in). (d) RSD curves showing the increase of Mg composition. ....................... 228

7-9 (a) LIBS spectra (ensemble-averaged) showing the Cu I and Zn I lines and
(b) standard deviation curves for 50 laser shots in 7 NIST brass standards.
(c) Relative standard deviation (RSD) curves as calculated from the quotient
of the standard deviation (square box indicates the region for zoom-in). (d)
RSD curves showing the increase of Cu composition. ............................... 229

7-10 (a and b) LIBS spectra and standard deviation curves as a function of
wavelength for different delay times at Mn II 259.37 nm in Al-alloy (AA1)
sample. (c) The plot of correlation factor 0 versus delay time....................... 230

7-11 The plot of a relative standard deviation versus wavelength for different delay
times at Mn II 259.37 nm in Al-alloy (603) sample................. .................. 231

7-12 (a and b) The ensemble-averaged spectra for Ba II in BaCI2 pallet at 0.5 us
and 3.0 us delay times, respectively with each RSD curve and (c and d)
associated SD curves .................................................................. .............. 232

7-13 The ensemble-averaged spectra for several elements in Al-alloy (S5) sample
at (a) 0.5 us and (c) 5.0 us delay times, respectively with each RSD curve
(blue line) and (c and d) associated SD curves. .................... ...... ............ 233

7-14 (a) LIBS spectrum at 2.0 us delay time in Al-alloy (AA1) sample including
0.540 % of Mn and (b) the standard deviation curve only near Mn II 259.37
nm line. (c) LIBS spectrum showing Mn ionic emission line at 259.37 nm. The
region A, B, C and D indicate the region selected for RMS noise calculation.
(d) Experimental values of the correlation factor 0 as a function of standard









deviation of the background measured by 10 pixels (the region A,B ,C and D:
black squares) and single pixel (the region A~C, blue dots)......................... 234

7-15 Experimental percent RSD of the net signal (% RSDnet) as a function of the
analyte concentration (a) at Mg I 285.21 nm line in 7 Al-alloy samples an (b)
at Zn I 330.26 nm line in 6 NIST brass standards.................. .................. 235

7-16 The log of the signal-to-noise (S/N) ratio as a function of the log of net-signal
for (a) Mg I 285.21 nm in 5 Al-alloy samples and (b) Zn I 330.26 nm in 7
NIST brass standards .................................................................. .............. 236

7-17 (a and c) LIBS spectra and (c and d) associated SD curves at both 0.5 us
and 3.0 ps delay times, respectively in Al-alloy (SM10) sample.................... 237

7-18 (a and b) LIBS spectra and associated SD curves at Mg I 285.21 nm in the
samples containing two extreme concentrations such as Al-alloy D28
(0.004 % of Mg) and S11 (1.11 % of Mg). .................................... 238









LIST OF ABBREVIATIONS

AAS Atomic Absorption Spectrometry

AES Atomic Emission Spectroscopy

BK Blank signal

CCD Charge Coupled Device

DP Double-Pulse

FWHM Full Width at Half Maximum

fs femtosecond

IB Inverse Bremsstrahlung

ICCD Intensified Charge Coupled Device

ICP-AES Inductively-Coupled Plasma Atomic Emission Spectrometry

ICP-MS Inductively Coupled Plasma Mass Spectrometry

IR Infrared

LA Laser Ablation

LIBS Laser Induced Breakdown Spectroscopy

LIF Laser Induced Fluorescence

LIPS Laser Induced Plasma Spectroscopy

LOD Limit of Detection

LSC Laser Supported Combustion

LSD Laser Supported Detonation (waves)

LSR Laser Supported Radiation

LTE Local Thermodynamic Equilibrium

LTSD Lens-to-Surface Distance

mJ milli-Joule

Nd:YAG Neodymium Yttrium Aluminum Garnet









NIST National Institute of Standards and Technology

nm nanometer

ns nanosecond

P/B Peak-to-Base

PC Personal Computer

PMT Photomultiplier Tube

ps picoseconds

RMS Root Mean Square

RSD Relative Standard Deviation

S/B Signal-to-Background Ratio

S/N Signal-to-Noise Ratio

SP Single-Pulse

SEM Scanning Electron Microscopy

TE Thermodynamic Equilibrium

ps microsecond









LIST OF SYMBOLS AND CONSTANTS


Roman Symbols

A Analyte (element) in plasma, e.g. A Mn,

A,, Einstein transition probability of spontaneous emission between
upper level (u) and lower level (1), s-1

A Einstein transition probability of spontaneous emission between
upper excitation level (j) and lower excitation level (i) of the ion ,
S-1

a0 First Bohr radius, nm

a(r,t) Line damping parameter, dimensionless

B~b Blackbody spectral radiance, J s-1 cm-2 sr1 nm-1

Bpl nk Blackbody radiation distribution or Planck's distribution function, W
cm-2 sr' nm-1

Bwe Blackbody radiation distribution or Wien's distribution function, W
cm-2 sr' nm-1

C(u,1) Excitation rate coefficient, cm3 S-1

DA Duplication factor, dimensionless

d Sample-to-lens distance

E, Energy of lower level 1, eV

E Energy of upper level u, eV

E Excitation energy of lower level 1 of the ionic line, eV

E Ionization potential of the neutral species in its ground state, eV

Ej Excitation energy of lower level u of the ionic line, eV

Es, Energy separation between level u and 1, eV

AE Energy difference, eV









AEon Correction of ionization energy (or lowering correction parameter),
eV

F Electric field strength of the plasma microfield, kg m s-3A-1

F(u,1) De-excitation rate coefficient, cm3 S-1

f Focal length of the spectrometer, mm or cm

f Oscillator strength for transition 1 -* u

fet Detection function, cm3.counts-photon-l-s

fexc Excitation/ionization function leading to atomic/ionic emission

nf Initial interaction function between the sample and the laser leading
to ablation/vaporization of solid material

Ial The calibration function, which describes the plasma characteristics
in terms of optical depth

G Free-free Gaunt factor, dimensionless

G reflection and absorption losses of the duplication mirror

g1 Statistical weight of lower level 1, dimensionless

g. Statistical weight of upper level u, dimensionless

I, or I, Integrated line intensity, photons cm-3 S-1

Iv0 Intensity at the center of the line profile v0, photons cm-3 s-1

IDPsp integrated net intensity fI(A)dA

J Total angular momentum

K,.corr Self-absorption correction factor, dimensionless

klon Ionization rate coefficient, cm3 s-1

kz Absorption coefficient, cm-'










Net absorption coefficient, cm-1


1

M

mN


N1 pxel





n D

ne
e

nDPorSP

n

nneutral or n

n~onc, n, or n'"

A,plasma



plasma
DP or SP



R

Rc


Rneutral K 'DP
S iSP neutral


(277nekBT) 2U .o. (T) E / kBT
h3 U neutral,A (T)

Optical path length, cm

Atomic or molecular weight, g molf or amu

Quantum number representing the z -component of the total
angular momentum J

Number of column pixels on ICCD camera

Boltzmann distribution/ or population density for analyte A in the
excited level u

Number of particles in the Debye sphere, cm-3

Electron number density, cm-3

Electron number density in DP or SP, cm-3

Number density in the excited state u, cm-3

Number density of neutral atomic species, cm-3

Number density of single ionized species, cm-3

Total number density of atoms and ions for the analyte A in the
plasma, cm-3

Total number density of atoms and ions in the plasma in DP and
SP, cm-3

Ratio of two emission intensities

Ratio of continuum radiation with and without duplicating mirror


Double pulse/single pulse intensity ratio for neutral lines










R IDP
\ SP / ionic

AR

r

Snet

net

S

S (2)A

TDP or SP

Te

Texc

Tion

AT

td

t

U(T)

uneutral,A or U on.c,A


plasm a
V
Vexc

AV

Zif

Z


Double pulse/single pulse intensity ratio for ionic lines


Uncertainty associated with the ratio of two emission intensities

Radial coordinate of particle in the plasma, cm

Analytical net-signal, counts

Ensemble-average net signal, counts

Slit width, upm

Spectral profile of the line, cm-1

Plasma excitation temperature in SP and DP, K

Electron temperature, K

Excitation temperature, K

Ionization temperature, K

Temperature difference, K

Delay time, s

Gate width, s

Partition function, dimensionless

Partition function of the analyte in neutral or singly ionized state

plasma volume, cm3

the excitation volume seen by a detector, cm-3

Lennard-Jones potential ( ~ 1/r6)

Nuclear charge which acts on the optical electron

Spectroscopic symbol










z-1

Greek Symbols

a

neutral,A
DPorSP

ionicA
aDPorSP




c or E

0 or O^p


k(A)

A

AA or Av


AAsarkx

AAFWHM


O-B

OBK

-D




o-

7


iDPorSP


V


Ionization stage


ion broadening parameter

Neutral fraction of the atoms of the analyte in the plasma

Singly ionized fraction of the atoms of the analyte in the plasma

Emission coefficient

Continuum emission coefficient

Correlation factor between major noise sources in a LIBS
measurement

Absorption coefficient, cm-1

Wavelength, nm

Instrumental spectral bandwidth, nm

Stark line width, nm

Stark line width at FWHM of the experimental spectral line, nm


RMS noise from the background signal

RMS noise from the blank signal

RMS noise from the dark current and amplifier-readout system

RMS noise in the analytical net-signal

Total root-mean-square (RMS) noise

Radiation damping constant, s-1

fraction of the plasma volume included in the detector field of
view

Frequency, Hz










Vo

Av,



hv



r(A)





Wpixel

WL

WG


XDPorSP plasn
SDPorSP




AZ

77det

Constants

C

e

6o

h

k or kB


Frequency of line center


Doppler broadening

Lifetime of a classical oscillator, s

Photon energy of the transition at frequency v, J

Free-bound continuum correction factor, dimensionless

Optical depth, dimensionless

Plasma velocity, 105 106 cm s-1

Electron-impact half-width, nm

Pixel size, Jpm

Lorentzian width, nm

Gaussian width, nm


Molar fraction of the analyte in the plasma for DP or SP


Ionization potential, eV

Lowering of the ionization potential, eV

Overall detection efficiency, count photon-' s


Speed of light in vacuum

Elementary charge

Permittivity of free space

Planck's constant

Boltzmann Constant


2.9979

1.6022

8.8542

6.6261

1.3807

9.1094


me Electron mass


x 108 ms-

x 10-19C

x 10-12 C2 v-1 m-2

x 10-34 Js

xl0-23 J K

x 10-31 kg









Avogadro's number

Gas constant


6.0221 x 1023 mof1

8.3145 J/mol K









Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

DIAGNOSTIC AND ANALYTICAL STUDIES OF LASER INDUCED PLASMAS

By

Heh Young Moon

August 2010

Chair: Nicolo6 Omenetto
Major: Chemistry

Since its early applications, Laser-Induced Breakdown Spectroscopy (LIBS) has

been recognized as a useful tool for solid state chemical analysis due to its numerous

attractive advantages as an analytical tool: e.g., simultaneous multi-element detection

capability, no sample preparation, rapid or real-time analysis, and allowing in situ

analysis requiring only optical access to the sample. However, the quantitative accuracy

of the technique depends on the complex fundamental processes involved in laser-

induced plasma formation, ablation, atomization, excitation and ion recombination. Thus,

problems arising from laser target coupling, matrix effects, line interference,

fractionation in target vaporization, the main assumptions of the methods, namely the

optically thin emission of spectral lines and the existence of local thermodynamic

equilibrium in the plasma should be properly addressed in order to obtain reliable

quantitative results [1, 2] .

The general scope of this research encompasses two aspects related to the LIBS

technique: one aspect is the fundamental study of the plasma characteristics and

another is an improved use of the technique in quantitative analysis. The main project is

to revisit and investigate some fundamental assumptions such as the existence of local









thermodynamic equilibrium (LTE) and optically thin plasma conditions (e.g., free of self-

absorption phenomenon) as mentioned above. Moreover, double-pulse LIBS, which is

one of the attractive spectroscopic methods for the diagnostics of the laser-induced

plasma due to lower detection limits and enhanced and longer sustained emission

signals for analysis, was also investigated herein in order to understand the relative

importance of the factors related to the intensity increases as well as the underlying

physical mechanisms. In general, LIBS signal enhancement is commonly attributed to

an increase of ablated mass from the target or to plasma reheating.

Furthermore, signals in LIBS measurement are influenced by the presence of

spurious signals or noises. Some types of noises are fundamental to a given experiment,

and although they may not be entirely eliminated, it is often possible to minimize them if

the limiting noise can be determined. The study of noise forms a part of the discussion

of errors in analytical measurement. The root mean square (RMS) value of a noise

source and the signal-to-noise (S/N) ratio are useful parameters to describe figures of

merit of the analytical procedure. In addition, the relative standard deviation (RSD) is

also related to the precision of the measurement. The generally useful S/N ratio

expression will be discussed with respect to analytical measurements in this study. The

noise expression occurring in LIBS measurement will be also explicitly discussed and

evaluated with some information about the type of noise present.









CHAPTER 1
INTENT AND SCOPE OF STUDY

Since the 1960s, soon after the first report of laser action in ruby [3], it was

realized that when the laser radiation was focused, the intense light beam was capable

of vaporizing and exciting solid material into a plasma, which is known as Laser-Induced

Breakdown Spectroscopy (LIBS) based on the optical emission spectroscopy of Laser-

Induced Plasmas (LIPs). It has been used as a powerful tool for fundamental studies

and numerous applications in analytical spectroscopy because it seems to be fairly

simple; the vaporization, atomization, and excitation processes are carried out in one

step by the laser pulse and setting up an apparatus with minimal/no sample preparation

to perform a LIBS measurement is quite simple. However, the basic physical and

chemical processes involved are not so simple. Thus, the importance of fundamental

study in LIBS has been increasingly recognized for better understanding in this field.

From the beginning, Chapter 2 provides a brief chronological overview of laser-

induced breakdown spectroscopy; it can be explained in terms of experimental aspects

based on the recent literature dealing with the fundamentals and its applications with

LIBS. Chapter 3 presents a basic physical study on the use of LIBS for quantitative

analysis. In addition, the chapter includes a discussion of the theoretical assumptions

on the state of plasma for achieving accurate quantitative analysis. Subsequently,

Chapter 4 and 5 focus on the experimental investigations of laser-induced plasmas. In

an attempt to simplify a very complex phenomenon of plasma, most of the methods

developed for LIBS diagnostic studies assume the following: the plasma volume under

observation is in Local Thermodynamic Equilibrium (LTE) and the spectral lines

measured are optically thin, i.e., free from self- absorption. These chapters (Chapters 4









and 5) describe the introduction of a novel approach (Line-to-continuum intensity ratio

method) for checking the validity of the LTE assumption and, for the first time, the

usefulness of a duplication mirror for evaluating self-absorption effects on the emission

line. Chapter 6 illustrates the use of double-pulse irradiation and its advantages. In this

chapter, the optimal conditions in our experimental system are described in terms of the

temporal and spatial evolution of plasma. The chapter discusses our efforts to explain

the coupling of the laser radiation with the plasma based on the use of spectroscopic

diagnostics of the plasma originated by a double-pulse laser. The possible dynamic and

physical mechanisms in the single- and double-pulse configuration responsible for the

enhancement of emission lines are investigated, and the optimal conditions found in

each case are also studied. Finally, Chapter 7 deals with considerations on the spectral

fluctuation approach in laser induced breakdown spectroscopy. For this approach,

within the simplifying assumptions made and the validity of these assumptions; i.e., all

noise sources present in a measurement are independent, it is argued that the behavior

observed by plotting the standard deviation and relative standard deviation of each

spectral element (pixel) versus wavelength can indeed be informative regarding the

characteristic aspects of the measurement. In addition, the chapter describes how the

approach can provide some information about the type of noise present in a LIBS

measurement and the limiting noise of the measurement.









CHAPTER 2
FUNDAMENTAL OF LIBS

Introduction

Laser-induced breakdown spectroscopy (LIBS) is one method of atomic emission

spectroscopy (AES) based on the fact that lasers tightly focused on solid, liquid or

gases (the target) create a plasma from which atoms and molecules emit. In principle,

the purpose of AES is to determine the elemental composition of a sample (a solid,

liquid, or a gas); examination of the emitted light provides the analysis because each

element has a unique emission spectrum useful to "fingerprint" the species. Thus, the

intensity of the emitted radiation and the frequencies at which the emission is observed

serve to identify and provide information on the number of atoms responsible for the

emission. The intensity of the radiation is proportional to the number of emitting atoms

as long as the atomic number density is low.

The chapter presents a brief overview of the history of LIBS, followed by a

description of its basic principle and the current experimental approaches, as well as a

summary of physics and physical chemistry regarding laser induced plasmas.

The Discovery of LIBS

Light emitting plasmas have been studied since the 1920s, and laser-induced

plasma since the 1960s [4]. The first published report as a potential spectroscopic

technique was a meeting abstract by Brech and Cross in 1962 [5], but initially the LIBS

plasma found greatest value as a micro-sampling source for an electrode-generated

spark. In 1963, with the development of the first pulsed Q-switched ruby laser [6], the

first analytical use for spectrochemical analysis of surfaces was reported by Debras-

Guedon and Liodec [7]. This was the birth of laser-induced breakdown spectroscopy. In









1964, Marker et al. reported the first observation of optically induced breakdown in a

gas [8] and Runge et al. discussed the use of the pulsed Q-switched ruby laser for

direct spark excitation on metals such as Ni and Cr in iron [9]. The first LIBS instrument

was introduced in 1967 followed by the development of several commercial LIBS

instruments by Jarrell-Ash Corp. (USA), VEB Carl Zeiss Jena Co. (Germany) and JEOL

Ltd (Japan). Although these instruments could be operated with the laser plasma

generating the spectral emissions, they could not typically compete in both precision

and accuracy with the development of high-performance elemental analysis technique

such as inductively-coupled plasma spectroscopy (ICP) and conventional spark

spectroscopy.

In the early 1970s, much of the research on the laser plasma and its uses

appeared in the Russian literature [10-13] and the classic book by Raizer, Laser-

induced Discharge Phenomena [14]. In the same time period, it was first recognized by

Cerrai and Trucco [15] and Marich et al. [16] that physical and chemical matrix effects in

laser-sampled spectrochemical analysis exist. It is now accepted that a variety of

physical and chemical effects play important roles in signal strength, and repeatability.

In the middle to late 1970s, aerosols became a subject of research. Lencioni discussed

the effects of dust and particles in the beam, which influenced breakdown [17]. Several

studies were performed for spectrochemical analysis of aerosols [18-20].

During the 1980s, as lasers and other LIBS components became smaller and the

drive for more portable and versatile instruments increased, LIBS experienced a rebirth.

The potential of LIBS as a more convenient atomic emission technique became

apparent to both industrial and academic laboratories. In 1981, two papers were









published for Los Alamos National Laboratory: the time-integrated [21] and time-

resolved [22] forms of the technique in gases. During that period, Los Alamos scientists

studied the detection of toxic materials on various chemical states (solid, liquid or gas)

with the use of this technique [23-29]. Some research also focused on diagnostics and

enhancements. Initial interest focused on the acoustic effect produced by plasma [30,

31]. In the late 1980s interest increased in making LIBS more quantitative. Niemax, et al.

contributed much work during this period [32-37]. Ko, et al. mentioned the usefulness of

internal standardization [38]. They concluded that internal standardization was not a

given in all cases, but the conditions for its use needed to be established for each

situation. In the mean time, the atomization and propagation properties of the plasma

plume were investigated by Leis, et al. [39].

Since the 1990s, applications and fundamental studies have developed rapidly. In

particular, during the past 20 years, the LIBS technique has made significant progress.

Many useful books and review articles have appeared [1, 2, 27, 40-46]. In particular, the

power of LIBS as a qualitative and quantitative elemental analysis technique is well

addressed from several groups in the US and the other countries such as Italy, Australia,

Canada and Spain. During this period, commercial instruments for coal analysis in the

Chadwick group [47] (Australia) and remote analysis by LIBS using a fiber optical cable

[48] at Los Alamos were demonstrated. In this time, quantitative LIBS studies also

continued. Palleschi's group in Pisa (Italy) discussed applications to pollutant detection

[49]. In particular, the development of the calibration-free LIBS (CF-LIBS) procedure in

1999 has made much a useful contribution for quantitative LIBS analysis [50]. In

addition, Mao, et al. in Russo's group at Lawrence Berkely Laboratory studied the









process of laser ablation [51]; otherwise, Winefordner's group began the discussion of

the variables influencing the precision of LIBS measurements by Castle, et al. in 1998

[52]. Gornushkin, et al. reported on a curve of growth methodology applied to laser-

induced plasma emission spectroscopy [53]. Moreover, the double-pulse approach first

suggested by Piepmeier, et al. [54] in 1969 and Scott, et al. [55] in 1970 resurfaced in

this period. In 1984, Cremers, et al. [56] performed a detailed study of the possible

applications of the laser double-pulse technique for analytical purposes. Research

regarding sources and applications of these enhancements has continued with many

advances in each area. As the field proceeded into the 1990s, applications to art and

biological analysis, in particular, received much attention [3, 57-60]. Detection of

elemental contaminants in soils also received considerable attention [40, 61-63].

Moreover, there has been a significant improvement of the instrumentation in LIBS,

which can be attributed to the availability of more robust, smaller, faster and less costly

laser sources, the development of sensitive gated imaging detectors (e.g. intensified

charge coupled devices, ICCD) and the advent of high-resolution spectrometers (e.g.

the compact echelle spectrometer) [64].

Since the late-1980s, the number of publications involving LIBS increased

exponentially each year [1] due to the unique advantages of LIBS: remote sensing

capabilities, in-situ analysis, little-to-no sample preparation, micro-destructive nature,

applicability to all media, simultaneous multi-element detection capability and relatively

simple instrumentation. Table 2-1 briefly describes some of the more important

milestones in LIBS development. Because LIBS is one of the most versatile analytical









methods, many applications studied in the early development of LIBS have resurfaced

due to increased needs or improved instrumental capabilities.

General Principle of LIBS [1]

In LIBS, the vaporizing and exciting plasma is produced by a high-power focused

laser pulse. As most commonly used and shown schematically in Fig. 2-1, a typical

LIBS system consists of a neodymium doped yttrium aluminum garnet (Nd:YAG) solid-

state laser and a spectrometer with a wide spectral range and a high sensitivity, fast

response rate and time gated detector. This is coupled to a computer which can rapidly

process and interpret the acquired data. Each firing of the laser generates a single LIBS

measurement. Typically, however, the signals from multiple laser shots are added or

averaged to increase repeatability and precision and to average out non-uniformity in

sample composition [1]. The LIBS instrument has many distinct advantages compared

with the conventional AES-based analytical method. An overview of the advantages and

disadvantages of LIBS is listed in Table 2-2. As such LIBS is one of the most

experimentally simple spectroscopic analytical techniques, making it one of the

cheapest to purchase and to operate.

One merely focuses a laser pulse in or on a sample, which can be gas, liquid,

aerosol or solid, to form micro-plasma. The spectra emitted are used to determine the

sample's elemental constituents. However, the basic physical and chemical processes

of plasma formation and evolution are not so simple. The reason for the complexity is

due to critical parameters that influence the ablation process: laser irradiance,

wavelength, pulse temporal duration and shape, physical / chemical properties of the

target material and composition/pressure of the surrounding environment. General

information on fundamental principles and instrumental aspects of laser-induced plasma









emission relevant to analysis, in particular, of solid samples will be covered in this

section.

LIBS Design (General)

A simplified experimental apparatus required for LIBS analysis is shown in Fig.2-

1 .The two basic components of the apparatus include the excitation source and

spectrometer with the detector. In general, a Nd:YAG laser, which generates energy in

the near infrared region of the electromagnetic spectrum, with a wavelength of 1064 nm,

is used as the excitation source. The pulse duration is ~ 10 ns generating an irradiance

which can exceed 1 GW-cm-2 at the focal point. The spectrometer consists of either a

monochromator (scanning) or a polychromator (non-scanning) and a photomultiplier

tube (PMT) or charge-coupled device (CCD) detector that converts the incident photon

flux into a measurable electrical signal. The most common monochromator is the

Czerny-Turner type while the most common polychromator is the Echelle type. Even so,

the Czerny-Turner configuration can be used to disperse the radiation onto a CCD,

effectively making it a polychromator. The polychromator spectrometer is the type most

commonly used in LIBS as it allows simultaneous acquisition of the entire wavelength

range of interest. Spectrometer response is typically from 1100nm (near infrared) to

170 nm (a deep ultraviolet), the approximate response range of a CCD detector. The

energy resolution of the spectrometer can also affect the quality of the LIBS

measurement. A high resolution system can separate spectral emission lines effectively

resulting in reducing line interference and increasing spectral selectivity.

Basics of Laser-Matter Interaction and Processes in Laser-Induced Plasma

Understanding the laser-matter interaction will allow ablation of stoichiometric

vapor and control of the laser-induced plasma properties for optimum LIBS performance.









When a short-pulse laser beam is focused onto the sample surface, the surface

temperature of the sample increases and then a small volume of the solid is ablated, a

process known as Laser Ablation (LA). This ablated mass further interacts with the laser

beam to form a highly energetic plasma that consists of free electrons, excited atoms

and ions. Laser ablation will be divided into three main processes for discussion in this

section: bond breaking and plasma ignition, plasma expansion and cooling, and particle

ejection and condensation. Figure 2-2 shows a summary of the three processes and

various mechanisms occurring during each process. During the plasma ignition process,

the mechanisms and plasma properties strongly depend on the laser irradiance and

pulse duration. However, the scope of this study was limited to a nanosecond laser

pulse; thus, the dominant mechanism in the plasma ignition is thermal vaporization: that

is, the temperature of the solid surface increases, and a well defined phase transition

occurs from solid to liquid, liquid to vapor, and vapor to plasma. As the next process,

plasma expansion begins after the plasma ignition process (see in the middle picture of

Fig. 2-2). The plasma expansion process will be governed by the initial plasma

properties (e.g. electron number density, temperature and expansion speed) which are

strongly dependent on the laser properties. In addition, it will be related to the initial

mass and energy in the vapor plume, and the surrounding gas where the free electrons

present in the plasma modify the propagation of laser light. The hot expanding plasma

interacts with the surrounding gas mainly by two mechanisms: (i) the expansion of the

high pressure plasma compresses the surrounding gas and drives a shock wave and (ii)

during this expansion, energy is transferred to ambient gas by the combination of

thermal conduction, radiative transfer and heating by the shockwave. Since vaporization









and ionization take place during the initial fraction of the laser pulse duration, the rest of

the laser pulse energy is absorbed in the vapor and in the expanding plasma plume.

This laser absorption in the expanding vapor/plume generates three different types of

waves, laser-supported combustion (LSC) waves, laser-supported detonation (LSD)

waves and laser-supported radiation (LSR) waves (for 'laser > G W/cm2) as a result of

the different mechanisms of propagation of the absorbing front into the cool transparent

gas atmosphere [65-67]. At the low irradiances used in LIBS experiments, the models

that most closely match experiment are LSC and LSD. The LSC wave occurs at low

irradiation (104 107 W/cm2), and the precursor shock is separated from the absorption

zone and plasma (see Fig. 2-3). Fresh shocked gas ingested by the LSC wave rapidly

heats. The LSC wave velocity is lower than that of the shock wave and the plasma

stays confined to the vapor and the surrounding ambient gas. Otherwise, LSD waves

occur at intermediate irradiation (107- 109W/cm2), the precursor shockwave is

sufficiently strong so that the shocked gas is hot enough to begin absorbing the laser

radiation without requiring additional heating by energy transport from the plasma. Thus,

the laser absorption zone follows directly behind the shockwave and moves at the same

velocity. As can be seen in Fig. 2-3, the LSD wave is typically observed to form ahead

of a target before it has even started to evaporate. Yalgin, et al. [68] also studied the

influence of ambient conditions on the laser air spark and found evidence in support of a

laser supported radiation wave (LSRW) model. According to this model, after the initial

breakdown, the plasma is heated to the point where it is opaque to the laser. A region

closer to the laser source is then heated by the UV emission from the hot plasma and

when sufficient electrons are generated, laser radiation is absorbed again via electron-









ion inverse Bremsstrahlung. As a result, a heating wave propagates into a cold gas in a

direction opposite to the laser direction, as shown schematically in Fig. 2-3. Finally,

during the plasma cooling process nano-sized particles will be formed from

condensation of the vapor. Actually, condensation starts when the vapor plume

temperature reaches the boiling temperature of the target material and stops at the

condensation temperature of the material.

As discussed above, laser ablation involves complex, non-linear physical and

chemical mechanisms that span several orders of magnitude in time with respect to the

different predominant emitting species under ambient conditions as well as the different

physical phenomena observed during the plasma expansion. Because the laser plasma

is a pulsed source, the resulting spectrum evolves rapidly in time. A schematic overview

of the temporal history of a LIBS plasma initiated by a single laser pulse is shown in Fig.

2-4 (a). Between its initiation and decay, the plasma evolves through several transient

phases [68, 69], as it grows and interacts with the surroundings. The initiation of plasma

formation over a target surface is dominated by strong continuum emission because

ionization is high. This light is caused by bremsstrahlung and recombination from the

plasma as free electrons, but when sufficient electrons are generated, the dominant

laser absorption mechanisms makes a transition to electron-ion inverse Bremsstrahlung.

Photo-ionization of excited states can also contribute in the case of interactions with

short wavelength radiations. The same absorption processes also are responsible for

the absorption by the ambient gas. When the laser pulse terminates, the plasma starts

to cool down. During the plasma cooling process, the electrons of the atoms and ions at

the excited electronic states decay into natural ground states, causing the plasma to









emit light with discrete spectral peaks. Throughout there is a background continuum that

decays with time more quickly than the spectral lines. For this reason, LIBS

measurements are usually carried out using time-resolved detection. In this way the

strong continuum emission at early times can be removed from the measurements by

turning the detector on after this continuum emission has significantly subsided in

intensity but atomic emissions are still present (see Fig. 2-4 (a)).

The majority of LIBS measurement is conducted by using a single pulse in which a

series of individual laser sparks are formed on the sample at the laser repetition rate. In

some cases, double pulse or multiple pulses for LIBS, in a various configurations, have

been used because it can result in large enhancements in signal intensities [27]. Figure

2-4 (b) illustrates the timing between two pulses, where At represents the temporal

difference between two laser pulses. Note that td is measured from the second laser

pulse in this case. More detail for double pulse LIBS will be described in Chapter 6.


























Lens


Array detector


Figure 2-1. Diagram of a typical laboratory LIBS apparatus.


Laser


Lens


2f '










Plasma ignition

* fs laser (1012- 1017W/cm2)
Electronic excitation and ionization
(10-15_ 10-17S)
Coulomb explosion (10-13 s)
Electron-lattice heating (10-12 s)

* ns laser (107- 1011 W/cm2)
Thermal vaporization (10-9 10 -8 s)
Non-thermal ablation (10-9 10 -8 s)
Plasma shielding (10-9 10 -8 s)



I


Plasma expansion
And cooling
Shockwave propagation
Plasma expansion (10-11 10-6 s)
Plasma radiation cooling (10-6- 10-4 s)


Particles ejection
and condensation
Nano particles formation (10-4- 10-3 s)
Ejection of liquid droplet (1086- 10-6 s)
Solid exfoliation (10-6- 105 s)


T ra
\a. 0^
0J C


Figure 2-2. A summary of laser ablation (LA) processes and various mechanisms
occurring during each process. Inserted figure shows the schematic diagram
of expanding laser produced plasma into ambient gas in detail. The plasma
plume is divided into several zones having high-density hot and low-density
cold plasma. The farthest zone from the target has minimum plasma density
and temperature. The laser is absorbed in low-density corona [70].


Bremsstrahlung
Continuum emission
la Shock wave in
ambient aas
-I

Cold plasma


rge

















* LSCwaeoic uis al low uradiabon
(10O- IC'Wcnm'j

* Th e precursor shock is separated from
the absorption zone andplasma

Amblent gas


* LSC wave occurs atintermediatirradiation
*.O'- OYWIcmn)

* The precursor shock is sufficiently strong so that
the shocked gas is hot enough to begin absocbing
the laser radiation with out requiring additional heating
by energy transport from the plasma
Ambient gas


Shock waves


IeIte d sample
esechon
SVayw plimereaches
C armileWi6WiiTU erdensity


Target


plasma


aA


Target


LSC wave


LSD wave


Figure 2-3. Timing of the physical phenomenon observed during the plasma expansion and two major types of laser
absorption wave schemes [68, 71].







44









Strong
Continuum
(a) emission


Ion


Laser H
pulse
o*Continuum

'~ t,


Neutrals


Molecules


10 100 1000 10000D 100000
Time elapsed after firing (nsI


10 100 1000 10000 100000
Time elapsed after firing first pulse (ns)


Figure 2-4. (a) Relevant time periods after plasma formation during which emission from
different species predominate. The box represents the time during which the
plasma light is monitored using a gatable detector. (Here, td is the delay time
and tw is the gate pulse width.) (b) Relevant timing periods for a double-pulse
configuration. (Here, At is interpulse delay time between two lasers.) [2]









Table 2-1. Significant milestones in the development of LIBS as an analytical technique
applicable to a variety of samples and circumstances [1]
Year Significant milestones
1960 Ted Maiman develops the first pulsed laser
1963 First analytical use of a laser-plasma on surfaces, hence the birth
of laser-induced breakdown spectroscopy
1963 First report of a laser plasma in a gas
1963 Laser micro-spectral analysis demonstrated, primarily with cross-
excitation
1963 Laser plasma in liquids were initially investigated
1964 Time-resolved laser plasma spectroscopy introduced
1966 Characteristics of laser-induced air sparks studied
1966 Molten metal directly analyzed with the laser spark
1970 Continuous optical discharge reported
1970 Q-switched laser use reported, results compared with normal
laser pulses
1971 Biological materials investigated with LIBS
1972 Steel analysis carried out with a Q-switched laser
1978 Laser spectrochemical analysis of aerosols reported
1980 LIBS used for corrosion diagnostics in nuclear reactors
1982 Initial use of the acoustic properties of the laser-induced spark
1984 Analysis of liquid samples and hazardous aerosols demonstrated
1988 Attempts made to enhance intensities through electric and
magnetic fields
1989 Metals detected in soils using laser plasma method
1992 Portable LIBS unit for monitoring surface contaminants developed
1992 Stand-off LI BS for space applications demonstrated
1993 Underwater solid analysis via dual-pulse LIBS demonstrated
1995 Demonstration of fiber optic delivery of laser pulses
1995 Multiple-pulse LIBS reported for use on steel samples
1997 LIBS use in applications in painted works of art and illuminated
manuscripts
1998 Subsurface soil analysis by LIBS-based cone penetrometers
shown
1998 Reports on the use of echelle spectrometers coupled with CCD
detectors
1999 Trace metal accumulation in teeth observed with LIBS
1999 Pulses from different lasers used to enhance LIBS performance
1999 Calibration-free LIBS introduced
2000 Report on commercial instrument for coal analysis
2000 Demonstration of LIBS on a NASA Mars rover
2000 First International Conference on LIBS Pisa, Italy
2002 Second International Conference on LIBS Orlando, FL
2004 Third International Conference on LIBS Malaga, Spain
2004 LIBS approved for 2009 Mars mission
2006 Forth International Conference on LIBS Montreal Canada
2008 Fifth International Conference on LIBS Berlin, Adlershof
Germany














Table 2-2. Advantages and disadvantages of laser-induced breakdown spectroscopy


Advantages
Simultaneous multi-element detection
capability
Minimal or no sample preparation


Simplicity
Rapid or real-time analysis


Capable of in-situ analysis requiring only
optical access to the sample


Only very small amount of material is
vaporized
Capability of some elements difficult to
monitor with conventional AES methods
Ability to all states of materials, e.g.,
gases, liquids and solids
Variety of measurement scenarios


Disadvantages
Difficulty in obtaining matrix-matched
standards
Variation in the mass ablated caused by
significantly inhomogeneous as a result of
either bulk or surface non-uniformity
Poor precision, typically 5 10 %
Relatively higher detection limits than
standard solution techniques (e.g., ICP-
OES)
Standard emission disadvantages: e.g.,
spectral interference depending upon the
instrumental resolution and the existence
of self-absorption of some lines.
Possibility of optical component damage
from high energy power of laser
Complexity of laser ablation under variety
experimental conditions









CHAPTER 3
FUNDAMENTAL INVESTIGATION OF LASER INDUCED PLASMA

Introduction

The aim of this chapter is to provide basic information on the use of the technique

of laser-induced breakdown spectroscopy (LIBS) for quantitative analysis. The

interaction of high-power laser light with a target material has been an active topic of

research not only in plasma physics but also in the field of material science, chemical

physics and particularly analytical chemistry [41]. When this high-power laser beam is

focused on a target (solid, liquid or gas), it produces a plasma, which is a local

assembly of atoms, ions and free electrons. Plasmas are characterized by a variety of

parameters, the most basic being the degree of ionization. A weakly ionized plasma is

one in which the ratio of electrons to other species is less than 10 %. At the other

extreme, highly ionized plasma may have atoms stripped of many of their electrons,

resulting in very high electron to atom/ion ratios. LIBS plasmas typically fall in the

category of weakly ionized plasmas [70].

In LIBS, the vaporizing and exciting plasma from a sample expands either in the

vacuum or in the ambient gas depending on the experimental conditions. As a result of

the laser-matter interaction, various processes may occur: e.g. ablation of material,

target acceleration, high energy particle emission, generation of various parametric

instabilities as well as emission of radiation ranging from the visible to hard X-rays

depending on the intensity of the laser. These processes have many applications, but

only the spectroscopic study of optical emission from the laser-induced plasma, known

as LIBS, on a solid target will be studied herein. The following sections will briefly

describe the plasma physics relevant to laser-induced breakdown spectroscopy that are









essential to understand this study and the applicability of LIBS. The chapter also

includes a discussion of the theoretical assumptions on the state of the plasma for

achieving precise quantitative analysis by LIBS.

Spectral Emission from Plasma

In a plasma, atoms and ions undergo transitions between their quantum state

through radiative and non-radiative processes. Non-radiative process involves collisions

and radiative processes involve emission, absorption, and fluorescence of radiation.

Figure 3-1 shows schematically transitions in an atoms or ions. These transitions are

[90]:

* u A(u, )[s'] >+hv (spontaneous radiative transition)

* +e c(i,u)[m3S-1] >u+e (excitation by electron impact)

* u+e F(u,)[3S-1 >/+e (de-excitation by electron impact)

* z+e p()[m3S-] >l+hv radiativee recombination)

* I+e s()[m3S-1] z+e+e (ionization by electron impact)

* z+e+e -a()[m6S-11 >/+e (three-body recombination)

In the above, levels land u are of the atoms or ions in the ionization stage (z-1) and z

is the ground state of the ions in the next ionization stage. The letter e in the initial state

(left-hand side) indicates the incident electron inducing the transition; otherwise, in the

final state (right-hand side) e represents the scattered electrons. The symbol "hv" is a

photon with frequency v emitted in the transition. The symbols shown above the arrows

represent the rate constants with the units for the transitions.

Among these processes, the most important are spontaneous radiative transitions

and collisional transitions induced by electron impact (collisions). In laser-induced









plasma, in particular, plasma emission is not a direct consequence of the photo-

excitation mechanism because the duration of the plume is relatively long in comparison

with both the radiative lifetimes of the emitting species and the laser pulse duration.

Rather, the impact excitation by thermal electrons can be adapted to explain the

phenomenon [72]. Laser-induced plasma emission consists of atomic and ionic spectral

lines and a broad-band continuum that is the result of electron-ion recombination

radiativee recombination) and free-free interaction (Bremsstrahlung). Identification of the

spectral lines and measurement of their intensities provide both qualitative and

quantitative information, but quantitative analysis is not simple due to the complexity of

the determination of quantitative line intensity [73].

The emission signal (counts photon) of a particular atomic or ionic line of an

element is given by the product of the excited state number density, n,(cm-3) the

spontaneous transition probability of the transition chosen, and the detection function,

fdet (cm3 counts photon 1. s) [2]

I = nAldet = nuA excfai7det (3-1)

where Vexc(cm 3) is the excitation volume seen by the detector, fal (no units) is the

calibration function, which describes the plasma characteristics in terms of optical depth

such as self-absorption/or self-reversal effects and 77det (counts photon 1 s) is the overall

detection efficiency. This equation can be expressed by three interrelated functions,

describing the initial interaction between the sample and the laser leading to ablation /

vaporization of solid material, fin, the excitation/ionization mechanisms leading to









atomic/ionic emission, f, and the characterization of the radiation environment, f,

(thin or thick plasma):

I = A 1ftffexcfdet (3-2)

These functions are related to the fundamental assumptions for simplifying a very

complex phenomenon in quantitative LIBS analysis as follows:

* the compositions of the plasma volume under observation is representative of the
sample composition (stoichiometric ablation)

* the plasma volume under observation is in Local Thermodynamic Equilibrium
(LTE), and

* the spectral lines measured are optically thin.

When the above conditions are satisfied, the reproducibility of the quantitative results is

assured in most cases.

Width and Shape of Spectral Lines [74]

The main diagnostic technique for plasma involves the relationship between

plasma properties and spectral line characteristics. In general, there are two major

reasons for determining the line shapes of spectral lines originating in plasma. The first

reason is the use of measured line shapes to determine physical properties of emitting

plasma such as the charged particle densities and temperature. The second reason is

to determine the absorption and induced emission coefficients which depend on the

oscillator strength and densities of emitting atoms in addition to the line shape. Figure

3-2 shows a hypothetical spectral line profile and identifies the different features. The

studies presented herein only deal with the physical properties from the line shapes of

spectral lines originating in plasma. In addition, line shapes and shifts can be a

diagnostic for the principle broadening mechanisms. In LIBS plasma, three different









processes may contribute to the finite width of a spectral line: natural broadening,

Doppler broadening, and interactions with neighboring particles (e.g. Stark broadening).

In the solid state the last interaction may take many different forms but if the discussion

is limited to free atoms and molecules, the interactions with other particles may be

treated under the heading of pressure broadening. Furthermore, in investigating line

broadening processes in emission it is essential to check for optically thinness in the

line and to make appropriate corrections for self-absorption if required because it affects

the line broadening.

Natural broadening. Spectral line profiles are determined by the dominant

broadening mechanisms. In the ideal case of a free atom the radiated intensity of a line

profile is spread over a frequency dependent Lorentzian profile having the form

I(v) = I (/4 4r)2 /[(v Vo)2 + (7 /4r)2] (3-3)

where Io is the intensity at the center of the line profile vo and y is the radiation

damping constant of

S= (2 2v2) /(3somc3) (3-4)

The lifetime of a classical oscillator is the inverse of damping constant

C = 1 / (3-5)

This spread of intensity over a range of frequencies is called natural broadening of the

spectral line and (y/27) is called full-width at half-maximum (FWHM).

Doppler broadening. However, except at very low atomic densities the ideal

condition is never realized in practice and natural broadening is always accompanied by

Doppler broadening which dominates the line shape near its center. Doppler broadening

resulting in 'Doppler effect' arises due to random thermal motions of the emitting atoms.









In general, a source moving towards an observer causes the wavelength to decrease

(blue shift) and a source moving away from an observer causes it to increase (red shift).

A large number of atoms having different velocities will emit a spread of wavelengths,

i.e., a broadened line. Thus, the resulting line profile by Doppler broadening is given by

a Gaussian profile:



12
I(v)= 2/(ln2/z) exp -41n2 V-_ (3-6a)
Av AvDJ

with FWHM AvD

AvD = (2vo /c)(2RTIn 2/M)1/2 = 7.16 x 10 7(T /M)1/2 (3-6b)

where vois the frequency of line center, M and R are the actual atomic or molecular

mass and the universal gas constant, respectively and T is the equilibrium temperature.

Often the two are of comparable magnitude. The resulting profile obtained by

convolution of the two is called the Voigt profile. Figure 3-3 compares the characteristics

of Gauss and Lorentz profiles of equal full-width at half-maximum (FWHM), and the

resulting Voigt profile. As shown in Fig. 3-3, the Gaussian will dominate close to the line

center; the Lorentz in the line wings. Thus, the combination of both types of profile

functions (Voigt profile) depends on the relative strength of the two effects.

Pressure broadening [74]. The presence of nearby particles will affect the

radiation emitted by an individual particle, causing a frequency disturbance and a phase

shift. There are two limiting cases by which this occurs:

* Impact pressure broadening: The collision of other particles with the emitting
particles interrupts the emission process. The duration of the collision is much
shorter than the lifetime of the emission. This effect depends on both the density









and temperature of the gas. The broadening effect is described by a Lorentzian
profile and there may be an associated shift.

* Quasistatic pressure broadening: The presence of other particles shifts the energy
levels in the emitting particle, thereby altering the frequencies of the emitted
radiation. The duration of the collision is much longer than the lifetime of the
emission process. This effect depends on the density of the gas, but is rather
insensitive to temperature. The form of line profile is determined by the functional
form of the perturbing force with respect to distance from the perturbing particle.
There may be a shift in the line center.

Pressure broadening may also be classified by the nature of the perturbing force

as follows: (i) Linear Stark broadening occurs via the linear Stark effect which results

from the interaction of an emitter with an electric field, which causes a shift in energy

which is linear in the field strength. (AV /r2); (ii) Resonance broadening occurs when

the perturbing particle is of the same type as the emitting particle, which introduces the

possibility of an energy exchange process (AV ~/r3)and the lines are symmetrically

broadened and unshifted. [75-77]; (iii) Quadratic Stark broadening occurs via the

quadratic Stark effect which results from the interaction of an emitter with an electric

field, which causes a shift in energy which is quadratic in the field strength. (AV ~/r4);

(iv) Van der Waals broadening occurs when the emitting particle is being perturbed by

van der Waals forces. Specifically, a fluctuating dipole in the radiating atom induces a

dipole to the neutral ground state atom and the corresponding interaction causes line

broadening. The energy shift as a function of distance is given in the wings by e.g., the

Lennard-Jones potential (AV ~ 1/r6) [78]. Actually, line shifts takes place only for

quadratic stark and Van der Waals interactions, n=4 or 6.

In general, Van der Waals and resonance broadening mechanisms are important

in weakly ionized plasma; Stark broadening otherwise is most important in highly-









ionized and high density plasmas where the strong electric field from the charged

species produces a broadening of the transitions between the split atomic levels. Thus,

among the pressure broadening mechanisms Stark broadening, which is the major

broadening effect in laser-induced plasmas, will be described herein in detail. When the

emitting species (atoms or ions) in a plasma are under the influence of an electric field

F = e/47ror2 by fast moving electrons and relatively low moving ions, both of the above

broadening mechanisms are completely negligible in comparison to the broadening

caused by the charged particles (Stark broadening). Thus, Stark line broadening from

collisions of charged species is the primary mechanism influencing the emission spectra

in conventional LIBS experiments. The interaction between the atom and this electric

field is described by the Stark effect which splits and shifts the energy levels of the atom.

However, only the hydrogen atom and H-like ions exhibit the linear Stark effect

proportional to F; whereas all other atoms exhibit the quadratic Stark effect

proportional to F2 and hence to 1/r4. Thus, it is obvious that the extent of Stark effect

will be negligibly small for a large distance r from an ion or electron.

In the Stark effect degenerated sublevels identified by the quantum number

mj representing the z component of the total angular momentum J are partially or

completely split, leading either to an unresolved, broadened, and shifted level, or a

resolved series of sublevels. Selection rules on the transitions between the sublevels

allow one to predict the intensity of the resulting line. The linear Stark effect splits the

energy levels symmetrically, resulting in a symmetric line pattern; the quadratic Stark

effect, otherwise, splits the energy levels asymmetrically with a shift, usually towards the

red, of the center of gravity of the line pattern.









Determining Electron Densities from Spectral Line Widths

The most powerful spectroscopic technique for determining the electron density n,

of a plasma comes from the measurement of the stark broadening of a spectral line. In

this method absolute intensities of spectral lines are not required, merely line shapes

and FWHM are sufficient. Both the linear and the quadratic Stark effect are encountered

in spectroscopy. However, only the hydrogen atom and H-like ions exhibit the linear

Stark effect, whereas all other atoms exhibit the quadratic Stark effect. This is the

reason that ideally information about electron density is extracted from the lines of H or

H-like ions, where the half width of the line profile can be calculated easily with a greater

accuracy. In the case of the linear Stark effect, the relation between electron density

and the line width is given by a simple relation [76]:

n,=C(ne,)AA3 (3-7)

where AA is the FWHM and the parameter C depends (only weakly) on n, and T,

which can normally be treated as being constant. The constant C for the H Balmer

lines is available in the literature [76]. The first choice for electron density determination

in LIBS plasma containing hydrogen is the Hp line (with an error of 5%) [76] because of

its large intensity and sufficiently large line broadening, which can be measured

precisely using a spectrometer of moderate resolution. The possibility of self-absorption

in this case is relatively small. The second best choice among the Balmer series is the

Hy line. The Ha line is suitable in the case where the electron density is not too high

(n ~ 1017cm 3), because at higher electron densities this strong line is quite susceptible

to self-absorption, which severely distorts the line profile. In the case of non-H-like









atoms, where the quadratic Stark effect is dominant, the relation between the electron

density and the line width [76] is

AAFwM 2[2+1.75x10-4n /4a (1-0.068n/6T -1/2)]x10 16 Wle (3-8)

The first term in the brackets gives the contribution from electron broadening, and the

second term stems from ion broadening. Here w is the electron impact parameter at

n ~ 1016cm 3, and a is the ion broadening parameter. The parameters w and a can be

found easily from the literature[76]. Since the second term in Eq. 3-8 is normally small,

the expression reduces to

AAFW &2x10-16wNe (3-9)

which is normally used for calculations in the case of plasmas generated from solid

targets.

In general, Stark width and shifts will be largest for the upper levels closer to the

ionization limit and for upper levels that originate in electron configurations that have

optical electrons with high angular momentum. Hence f levels are affected more than d

levels and so on. As one goes higher in atomic mass, the Doppler widths get smaller.

Hence, even for many strong lines that originate from upper levels that are still far from

the ionization limit, Stark broadening can dominate. Regarding shifts in wavelengths,

except for high f levels, these are typically less than 0.1 nm. Whether the Stark widths

and shifts of lines from LIBS plasma are observable depends on the optical and spectral

resolving powers of the spectrometer-detector system.

Plasma Opacity

Having introduced the concepts of line profile and line width, we can now discuss

the opacity of a plasma. Fundamentally, a plasma is optically thin when the emitted








radiation traverses and escapes from the plasma without significant absorption or

scattering. The (thermal) spectral radiance of a transition emitted from a plasma is given

by [79]:

I, (2) = ,h xp(2) ]} (3-10)
S4orA ) k (A)

where I(2A) is the spectral radiance (W cm-2 sr-1 nm-1) of the emission line, A,, is the

transition probability (s-1), h is the Planck constant (J s), n, is the population of the

excited level u (cm-1), c is the velocity of light (cm s-1), S,(2) is the spectral profile of

the line (cm-1), I is the emission (absorption) path length in the direction of the

observation (cm), and k (cm 1) is the net absorption coefficient, defined by the

difference in the population of the lower and upper levels of the transition. Note that Eq.

3-10 is the result of integration over the emission line-of-sight, assuming a spatially

homogeneous atomic distribution.

As clearly shown in Eq. 3-10, the formula contains the self-absorption term, given

by the last ratio in the right hand side of equation. If this term is multiplied and divided

by 1, one obtains by series expansion


'I(A) = A S()1 (3-11a)


where the parameter K. is defined as


K k(A)l (3-11 b)
{1-exp[-k2(A)/]}

In Eq. 3-11 b, the parameter K. is identical to that used by Konjevi6 [80]. (KZ) 1,

evaluated at the line center (A2), is also identical to the so-called self-absorption









coefficient (SA) derived by EI-Sherbini et al. [81]. Finally, if one uses the definition of the

optical depth (see, for example, [74], p. 294), r,

r,(A) k-(A)l (3-12)

The last term in Eq. 3-10 becomes

{1- exp[k(A)/]} _/{1-exp[-r,(A)]}


Thus, Eq. 3-11 a can be obtained by substituting Eq. 3-11 b into Eq. 3-10.

It is worth pointing out that this correction factor is the same as that reported in

astrophysics work [82, 83], and appropriate to the chosen physical emission/absorption

model [84-86].

Finally, when Eq. 3-11 a is integrated over wavelength, after making use of the

relations between the Einstein coefficients and the absorption oscillator strength of the

transition, and of the Boltzmann ratio for the atomic populations, valid under local

thermodynamic equilibrium conditions (LTE), one obtains the well-known expression for

the thermal emission as given by the radiation theory [74, 87-92], e.g.,

thermal = Banc -exp[-k(A)]} (3-14a)
line

thermal = e{1- exp [-k(A)]} (3-14b)
line

where BPlanck is the spectral radiance of the blackbody radiation given by the Planck or

by the Wien laws at T (W cm-2 sr-1 nm-1) and the integral terms are the expression of

the total absorption factors, k, is related to the emission coefficient (C.) by the

Kirchhoff's law, s, = kB,, valid for LTE. The ratio, s, /k,, is also called the "source

function" (see, for example, [90]). In the case of negligible self-absorption i.e., if the









optical thickness kl << 1 over the whole wavelength range of the line profile, then one

obtains

Thermal = B k,r (A)l (3-15a)
line

In the optically thin condition, therefore, Ithermal grows linearly with the wavelength-

integrated absorption coefficient, which in turn is directly related to the atom number

density. Otherwise, in the other extreme (optically thick) condition, e.g., kjl >>1, one

obtains

Ithermal =B (3-15b)

Under very strong self-absorption, the observed line intensity then reaches the

limit of black body radiation at the temperature T, and then the line loses its

characteristic shape, i.e., the observed line intensity no longer follows linearly the

absorption coefficient and the stronger lines effectively saturate. Moreover, the line

profile cannot be recovered. Figure 3-4 shows an example of emission lines with

varying optical thickness. For intermediate cases, i.e., if the optical depth (k2l) is not

too large, the line profile that would have been observed for the optically thin case may

be recovered by using K. as a correction factor, defined in Eq. 3-11 b. In quantitative

LIBS, the subtle onset of self-absorption poses a problem for converting line intensities

to concentrations. Self-absorption is also a major problem for calibration-free LIBS (CF-

LIBS). More detail will be described in Chapter 5. In this chapter, A method will be

presented to detect self-absorption easily in the laboratory by using a spherical mirror

behind the plasma and comparison of the intensity of a given line with and without the

mirror in place.









Thermodynamic Equilibrium and Temperature

Definition of thermodynamic equilibrium in laser-induced plasma [2, 74]. If

thermodynamic equilibrium exists, then plasma properties, such as the relative

populations of energy levels, and the distribution of the speed of the particles, can be

described through the concept of temperature. Complete thermodynamic equilibrium

would exist when all forms of energy distribution are described by the same temperature.

In fact, however, complete thermodynamic equilibrium is rarely achieved, so physicists

have settled for a useful approximation, Local Thermodynamic Equilibrium (LTE). In this

state, the collision rates must exceed the radiative ones by at least one order of

magnitude [76], so that the non-equilibrium of radiative energy can be neglected, while

for every point it is still possible to find a temperature parameter that satisfies the

Boltzmann, Saha and Maxwell distributions. Thus, the plasma electronic excitation

temperature T and electron density ne, which can be derived from the plasma emission

data, can be used to describe the plasma characteristics [74].

In laser-induced plasma the LTE assumption must be checked for LIBS analytical

applications aimed to quantitative analyses, since the current data processing

completely relies on their validity. Under LTE conditions, characteristic line emission

spectra are detected mostly from the atomic and first ionic excited species produced.

Thus, only neutral and singly ionized species will be considered in the following.

Provided that the radiative processes negligibly alter the balances of the collisional ones,

the populations' density and plasma ionization are ruled by Boltzmann and Saha

equilibrium relations [52]. This is the case of electron excitation kinetics driven plasma in

LTE, which is characterized by only one thermodynamic temperature, e.g. the electron









temperature Te. Under LTE conditions, the population of the excited levels for each

species follows a Boltzmann distribution:

NA g n A,plasmae -E, kT (3-16)
UA(T)

where NA and nAplasma indicate the population density of the excited level u of analyte

(or species) A and the total number density of the species A in the plasma respectively,

E and g are the excitation energy of the level and the statistical weight of the levels

(2J1, +1), respectively, J is the total angular quantum number of the term, k is

Boltzmann's constant (1.38 x 10-16 erg K), T is the absolute temperature, and UA is

the partition function of the species A at temperature T:

UA (T)= ge -EkT (3-17)


Similar considerations lead to Saha equation for atom/ion equilibrium as follows

n" (27nkT)3/2 2U-"(T) e (3-18)
n n1 h3 UU (T)


where n, is the plasma electron density, n' and n" are number densities of the neutral

atomic species and the single ionized species, respectively, E,L, is the ionization

potential of the neutral species in its ground state, me is the electron mass and h is

Planck's constant. In this equation, AEoJ, is a small correction of ionization energy due

to small scale polarization of the plasma, or the tendency of electrons and ions to be

surrounded by particles of the opposite charge [76].

For checking the validity of LTE, experimentally, the line-to-continuum intensity

ratio method will be described in chapter 4. One investigates whether the plasma









excitation temperature Texc obtained from a Boltzmann or Saha-Boltzmann plot is

different from the electron temperature Te resulting from the measurement of the

intensity of plasma continuum. By maintaining Texc Te in the theoretical expression for

the intensity ratio, any deviation from LTE condition can be assessed.

Measurement of plasma temperature. As described previously, under LTE

conditions, only one temperature describes the distribution of species in energy levels,

the population of ionization stages or the kinetic energy of electrons and heavier

particles. There are many methods for determining the plasma temperature based on

the absolute or relative line intensity (two-line method or Boltzmann plot/or Saha-

Boltzmann plot), the ratio of line-to-continuum intensity, etc. One of these methods may

be chosen under the appropriate experimental conditions. Under the assumption of

local thermodynamic equilibrium (LTE), the totally integrated intensity (W m-3 sr-1)

corresponding to the transition between the upper level u and the lower level / is given

by


l )h A4.- n4T -E)kT (3-19)
4z A,,U' (T)

where 2A, A,, and g, are the wavelength, the transition probability and the statistical

weight for the upper level, respectively; c is the speed of light, and the other symbols

have already been defined in the list of symbols.

Provided that the LTE hypothesis described above is fulfilled, the plasma

temperature can be calculated from the intensity ratio of a pair of spectral lines

originating in different upper levels of the same element and ionization state. For the

two-line method, Z, and j,, of the same species, characterized by different values of









the upper level energy (E, # Ej), the relative intensity ratio can be used to calculate the

plasma temperature as follows:


T = E J (3-20)
kIn
k In J, g, A,,

Assuming that the intensity values are the only factors affected by the

experimental error, the uncertainty in the temperature determination can be expressed

by

AT kT AR
T AE R

where AE is the difference in energy of the two states observed, R is the measured

ratio of emission intensities and AR is the uncertainty associated with the ratio. When

selecting a line pair, it is advisable to choose two lines as close as possible in

wavelength and as far apart as possible in excitation energy to reduce the effect of

varying spectral response of the instrument as well as the sensitivity to small

fluctuations in emission intensity. In Eq. 3-21, large values of AE will minimize the effect

of the uncertainty in R on the uncertainty in T [87].

However, relative intensities are not easy to measure precisely. A way to improve

temperature values is to use many emission lines corresponding to different energy

levels of a certain species in the plasma. Under the assumptions that the plasma is both

in LTE and optically thin, the population of the excited levels for each species follows a

Boltzmann distribution (see Eq. 3-16). We rearrange Eq. 3-19 into the form:

In =In or In gA- =In nAE) (3-22)
gAA, 4z UA (T) kT gA, UA1(T) kT








where all symbols have been already defined. This is the equation of a straight line with

slope of -1/kT. Hence, if one plots the quantity on the left against E, (of the upper

state for emission), and if there is a Boltzmann distribution, a straight line is obtained.

Therefore, the plasma temperature can be obtained via linear regression, without

knowing nAor UA(T). To improve this method, the use of many lines in some sense

"average out" the uncertainties from transition probability values, which reported in the

literature exhibit a significant degree of uncertainty (from 5 to 50 %).

Because emission lines from different ionization stages are usually present in

laser-Induced plasma, a combination of the Saha ionization and Boltzmann excitation

distributions can be used to measure the electron temperature under LTE assumption

[68]. The most common form of the coupled Saha-Boltzmann relation takes the form of

the ionic/atomic emission radiance ratio

I,, = i Aj,g J 2(2.mlekT) 2. e Eo, -E -E+Ee) (3-23)
,I- -. eh3 r (3-23)
I', A u, g,' X" nh )

The superscripts I and II denote atomic and ionic parameters, respectively. Here E,,, is

the first ionization potential and AE,,, is the lowering correction parameter. The coupled

form of the Saha-Boltzmann distribution can be modified as in the case of the

Boltzmann plot

IjAA,g[ 2(2zm kT)31 2 (E AE + EI E[)
In =rIn E (3-24)
JIAH I eh3 kT

Similar to the Boltzmann plot, this method allows for the determination of temperature

from the slope of the line (-1/kT) in Eq. 3-24. With the spread energy levels, the slope

from a linear regression calculation is less sensitive to measurement noise. Furthermore,









the electron density can now be obtained from the intercept. It should be noted that, in

contrast to the Boltzmann plot alone, the intercept of the coupled Saha-Boltzmann plot

does not require an absolute intensity calibration because the geometric factors cancel

out in the ratio [93]. In fact, an independent measurement of electron density can be

made via the Stark broadening technique, which does not require the plasma to be in

LTE.

For the diagnosis of early phase plasma, for instance, Liu et al. [94] used the line-

to-continuum intensity ratio, because line and continuum intensities are typically

comparable at the start of plasma evolution. Under the assumption of local thermal

equilibrium (LTE), the plasma temperature T can be determined by the line-to-

continuum intensity ratio I,, /ec, where sc is the continuum emission coefficient and

I, is the integrated emission intensity over the line spectral profile [95]:




U(T) -hv+ G exp(-hv)



C =[,. h24 3 2.005 x10 5[sK] (3-25b)
2563 6ek

where the G factor is the free-free Gaunt factor [96-98] and E factor is the free-bound

continuum correction factor which is analogous to the G factor, and all parameters are

identified in the list of symbols. When the continuum emission becomes weak, the

plasma temperature calculated from ratio of line to continuum is not accurate. The

plasma temperature, in this case, can be estimated by using a Boltzmann plot or Saha-

Boltzmann plot mentioned above based on measuring the relative intensities of lines









with known transition probabilities and degeneracies. Thus, all methods mentioned

above can be complementary to each other under the appropriate experimental

conditions.











Z (Ionization Continuum)


F(u, 1) A(u, 1)


m m -


a(I)(I)


(1)


c(,u)


S(1)


Figure 3-1. Energy level scheme and associated excitation/de-excitation processes. The
symbols shown above the arrows represent the rate constants for the
transition: i.e., C (/,p): excitation rate coefficient; F(p,/): de-excitation rate
coefficient; A(p,/): Einstein's A coefficient or transition probability for p-4/; S(/):
ionization rate coefficient; a(/): three-body recombination rate coefficient; P3(/):
radiative recombination rate coefficient; x(/): ionization potential of level /
(adapted from ref [90]).


............................................................................................... .............................................................................................................................................................................................................................................................................










I

( ......................................... ..


*
S* 0





*Line *rnel
*
1 *
















A1 0 A2

Figure 3-2. Spectral line profile. Here Ao is the central wavelength, Ai and A2are the
wavelength whose intensity is half of the maximum intensity I (Ao), and AA is
the full width at half maximum (FWHM) (adapted from [99]).






















69










0-% 0.12
S0.6 0-Gaussian Lorentzian
0.10
D 0.08
0
oM -4006

0 0.04
C L \
C 0.4 L 0.02
0.00
%- W -20 -10 0 10 20
SXV Copyright 20 B.M Tissue



-j

0.. O .



S0 1 2 3

relative frequency, v



Figure 3-3. Normalized spectral profiles versus relative frequency for pure Doppler (D),
pure Lorentzian (L) distributions of equal full-width at half-maximum (FWHM),
and the resulting Voigt (V) profile (adapted from ref [100]).











bb -----------
Ao



d











4-,
c


















01"


Figure 3-4. Spectral line profile as a function of gradually increasing atomic
concentration (a -4h). Note that the center of the line reaches the blackbody
radiation limit at high atom densities (adapted from ref [100]).









CHAPTER 4
LINE-TO-CONTINUUM INTENSITY RATIO IN LASER-INDUCED BREAKDOWN
SPECTROSCOPY AS AN EXPERIMENTAL CHECK TO LOCAL THERMODYNAMIC
EQUILIBRIUM

Introduction

The concept of local thermodynamic equilibrium (LTE) plays a vital role in plasma

physics and plasma spectroscopy. In the LTE model it is assumed that collision -

induced transitions and reactions are more frequent than radiative ones [76, 101, 102].

If space and time variations are sufficiently small so that at each point and instant a

local steady state population is established, the assumption of local thermodynamic

equilibrium will always be valid as long as radiative rate processes are small compared

with collisional processes. Thus, although the plasma temperature and density may vary

in space and time, the distribution of population densities at any instant and point in

space depends entirely on local values of temperature, density, and chemical

composition of the plasma. With this assumption of local thermodynamic equilibrium all

particle number densities neutral particles as well as ions- can be calculated from total

number densities and temperature, and they are allowed to be a function of time if the

relaxation time for the establishment of thermodynamic equilibrium is smaller than the

time variation of the densities and temperature. Therefore, it is very important to assess

the existence of local thermodynamic equilibrium as examining time-resolved plasma

phenomena. The uncertainties in predictions of spectral line intensities from a LTE

model plasma depend on the uncertainties in the values of these plasma parameters as

well as the atomic transitions probabilities.

The aim of this proposed research is to investigate several diagnostic methods in

order to examine time-resolved plasma phenomena, with emphasis on the evaluation of









the existence of equilibrium conditions at various stages of plasma evolution in LIBS.

For this purpose, the most interesting plasma diagnostic indicators are the electron

temperature Te and the electron number density ne, since one can predict from these

two parameters the extent of local thermodynamic equilibrium (LTE) which exists in the

plasma. Most studies in this field have been performed under the assumption of the

existence of such LTE conditions [68, 94, 103, 104]. The reason is that if the LTE

condition is verified it is possible to characterize the plasma by a unique temperature

which considerably simplifies the description of the plasma properties. Few studies,

however, have been devoted to the experimental evaluation of this assumption [101,

105-107]. One of the approaches that can be used for the evaluation of the LTE

condition is the Line-to-continuum intensity ratio method [94, 95, 107, 108]. This

approach has been described in the case of a high pressure, argon surface-microwave

plasma [94, 95, 107, 108] and, to the best of our knowledge, has not yet been applied to

laser-induced plasma. In this approach, the theoretical ratio between the intensity of

selected transitions, considered to be optically thin, and the underlying spectral

continuum is used. In these expressions, the excitation temperature and the electron

temperature are purposely kept different from each other. Experimentally, the plasma

excitation temperature, Texc, is obtained from a conventional Boltzmann/or Saha-

Boltzmann plot, and the ratio between the spectrally integrated line intensity and the

continuum intensity is measured. By inserting these two experimental values into the

theoretical expression, one can check whether the electron temperature derived in this

way is equal or different from the excitation temperature provided by the Boltzmann plot.

In this way, any deviation from LTE conditions can then be assessed [109].









Theory [107]

Under the assumption of local thermal equilibrium (LTE), the electron temperature

Te can be assumed equal to the excitation temperature Texc, namely Te = Texc= T.

However, putting Texc equal to Te in the expression for the ratio of the integrated

emission intensity to the continuum intensity does not provide an accurate

determination of Te when some deviation from LTE can be expected. Therefore, as

suggested by Sola et al. [107] in the case of an argon surfatron plasma, we propose to

maintain Texc Te in the line-to-continuum ratio expression (see below) in the laser-

induced plasma and to compare the value of Te obtained when the experimentally

determined Texc and line-to-continuum ratio are used in the theoretical expression.

Line-to-Continuum Intensity Ratio Method for Determining of Te

Under the assumption of local thermodynamic equilibrium (LTE), the totally

integrated radiant emissivity (W m-3 sr-1) can be expressed as a function of the

excitation temperature Texc and an experimentally measurable transition probability

A4,as given below:

I hc= h A1g. nA -EI/kT (4-1)
\a 42 AU4 (TUexc)

where all parameters have been already defined in Chapter 3.

A practical and useful form can be obtained by using Saha equation for atom/ion

equilibrium, i.e.,

Sn1 (2nekTo)32 2U-" (T) e
Sn1 h3 U (T) (4-2)


where all parameters are also identified in Chapter 3. By combining Eq. (4-1) and Eq.

(4-2) one obtains the integrated line radiation as the following expression:










I. = 1 A, nT exp n. E---n (4-3a)


1 h h3 2 1.09 x 106 (kg m5 s-2 K3/2) (4-3b)
8 1 (2mnk)kg

where all parameters are identified in the list of symbols. At this point, because Saha's

equation implies LTE, one assumes that Tion = Te= Texc. However, in the proposed

approach, the assumption that the ion temperature Tion is equal to the electron

temperature Te, was kept [110], but we keep the assumption of the electron temperature

Te different from the excitation temperature Texc. Equation (4-3a), thus, can be rewritten

by


Il =1.09 x10- 56 Azev u 3/2 exp n on _k (4-4)
UA(T) kTl kT^)

Continuum radiation from the LTE model plasma arises from the interaction of

initially free electrons with the positive ions or atoms that are present. The interactions

may be either free-free transitions (Bremsstrahlung) or free-bound transitions

recombinationn radiation) [76, 90, 102]. This calculation yields a semi-classical

expression for sc multiplied by correction factors such as the free-free Gaunt factor (G )

and free-bound continuum correction factor ( ) derived from quantum mechanical

considerations (see below), i.e.,

nn, hv hv
c (v) = C2 1 exp ) + G exp( )] (4-5a)


C2= 1676 x = 5.43 x 10-52 (kg m5 s-2 K1/2) (4-5b)
3c (6zmn3k)1/2 4co









Thus, taking the ratio of the frequency-integrated line intensity I,, to the non-

integrated continuum intensity sc one obtains


exp exp Eon E n
(v) = C A v kTex) V kT ) (4-6a)
(T) T(1-exp -)h + Gexp(-)


h433/2 3
C 6 -3e6k2.005 x10-5 (sK) (4-6b)
256;3e k

In addition, Eq. 4-6a can be further simplified by examining the term containing the

correction factors E and G. This G factor is the free-free Gaunt factor which is a weak

function of temperature and electron density, and improves the theoretical description of

the free-free continuum. Unfortunately, Accurate quantum-mechanical calculation of

Gaunt factors exist only for hydrogenic species [98]. Numerically, the value of G is

approximately unity [96, 97] so that the exponential term including G in Eq. 4-6a can be

negligible if Te and A are large. Such a condition indicates that free-bound transitions

dominate the continuum. The E factor is the free-bound continuum correction factor

which is analogous to the G factor. It corrects the semi classical expression for free-

bound continuum radiation. In the approach, the effect of E and G on the calculation of

the electron temperature in the theoretical expression (see Eq. 4-6a) will be discussed

below.

Moreover, the lowering of the ionization energy, AEo,, is required to get an

electron temperature in the expression of Eq. 4-6a. AEo is a small correction of

ionization energy due to small scale polarization of the plasma, or the tendency of

electrons and ions to be surrounded by particles of the opposite charge. Generally, this









factor has been calculated by several methods. One of the methods was suggested by

Unsold [111] who has derived a simple formula for estimation of AEo,

AE (6.96 x 10-7) x [-3] x 23 (eV) (4-7)

where ne is the electron density and Zeff is nuclear charge which acts on the optical

electron. (e.g. Zeff=1 for neutral hydrogen, Zeff =1 also for neutral helium, Zeff=2 for one-

fold ionized helium etc). The other method was suggested by Griem [76, 77, 102] with

the following formula for estimation of AE,o,

Z e2
AE = fe (4-8a)
4oPD

If one considers the shielding for heavy particles (ions or neutrals) by ions and electrons

in a thermal plasma, the Debye (or shielding) radius is in principle given by the formula:


PD 1/2 1/2 (4-8b)
e ) ne

According to above two Eq. 4-8a and 4-8b, we can simply get the formula in terms of

the temperature and electron density:

(Z ,T '1/2
AEon = 2.0866 x 10-8 e (eV) (4-9)
en

The theoretical expression of line-to-continuum intensity ratio method in Eq. 4-6a,

therefore, is only a function of temperature and known or calculable constants. The

experimental values of the ratio and of Texc can then be inserted into Eq. 4-6a to

calculate Te.

Experimentally, what is measured from the continuum intensity is the intensity over

a finite spectral band width (AA). For this reason, the experimental continuum intensity









should be expressed by csAv or cAA. This expression is agreement with units of both

sides in Eq. 4-6a. Thus, the final equation relating the ratio of experimentally observed

line-to-continuum intensity is:

-E EE Al
Iexp exp I "--
I(v)= 2.005 x10 A 1 kTexc kT A v (4-10 Oa)
e Uj,, Te F hv hv Av
S(1- exp ) )+G exp( )
I kT/ kT/

exp- E exp ( E,,o- AE, ,o
exp exp A--- *o A
or I (2)= 2.005 x10 sA4"g- 1 kTI)- kT )A (4-10 b)
S(1- exp ) + G exp(h)] A
kT, kT,

Experimental

A schematic of the apparatus for plasma emission measurements is shown in Fig.

4-1. A Nd-YAG laser (Brilliant, 360 mJ maximum pulse energy at 1064 nm and

maximum repetition frequency of 10 Hz) was focused on the sample surface with a

quartz lens (10 cm focal length). In this work, the laser was operated at 1 Hz and was

characterized by a pulse energy of 90 5 mJ of 6ns of duration. All measurements were

performed at atmospheric pressure. A positioning system consisting of a helium-neon

laser was used to optimize the sample-to-focusing lens distance. For all measurement,

the target was moved with a three-dimensional stage (x, y and z transition stage) and

translated horizontally every 10 laser shots. A controlled stream of air was used to carry

away the dust plume formed during the interaction.

A 5.0 cm diameter quartz lens, with a focal length of 7.5 cm, was used to collect

the plasma emission and to produce a one-to-one image of the plasma onto the

entrance slit of the monochromator. An adjustable iris was positioned close to the lens









in order to match the F-number of the spectrometer (F/6.5 system). A 35 um slit width

was used in all cases. The spectrometer (Acton triple grating, 0.5 m focal length) was

equipped with three gratings (1200, 2400 and 3600 grooves / mm), providing a

reciprocal linear dispersion of 1.57, 0.72 and 0.41 nm / mm, respectively. In the present

work, the 2400 grooves / mm grating was used. The spectrometer has a typical spectral

coverage of 10 nm and a spectral resolution of 0.03-0.05 nm. The detector is an

intensified CCD (ICCD 5764 / RB-E, Princeton instruments) with a photosensitive area

of 576 x 384 pixels, corresponding to (12.7 x 8.4) mm2. The spectral coverage by a

single pixel varies from 0.016 nm at 282 nm to 0.014 nm at 428 nm.

The ICCD is operated by its controller (ST-138, Princeton Instruments) and by a

pulse generator (PG-200, Princeton Instruments), allowing the choice of the gate width

and of the delay time for time-resolved acquisition. The gate width and the delay time

between the laser pulse and the beginning of the acquisition could then be adjusted in

order to maximize the signal-to-background and the signal-to-noise ratio. A delay time

of 1 ps was experimentally found to represent a good compromise between the

necessity of measuring accurately the continuum and of providing a satisfactory signal

to noise ratio for the transitions chosen. The data acquisition was controlled with the

Winspec32 software (Version 2.5.18.2, Princeton Instruments).

Results and Discussion

Electron Number Density (ne)

The emission spectra revealed noticeable line broadening, which is important for

the determination of the electron number density (see Fig. 4-2a). Major line broadening

mechanisms are Stark broadening (Lorentzian profile), Doppler broadening (Gaussian

profile), and pressure broadening as mentioned in the chapter 3. Stark line broadening









from collisions of charged species is the primary mechanism influencing the emission

spectra in these experiments. The determination of the electron density using Stark-

broadening has the advantage of not requiring the validity of LTE condition. The

electron number density related to the full width at half maximum (FWHM) of stark

broadening lines is given by the expression [68, 94, 103, 104, 112]


AA,,, r(nm)=2w +3.5a( [1-BN /3]w (4-11a)


where B is a coefficient equal to 1.2 and 0.75 for ionic and neutral lines, respectively

and ND is the number of particles in the Debye sphere and is estimated from


ND= 1.72 x109 ( ] 2 (4-11 b)
n[cm -3]) 1/2

The first term in Eq. 4-11 la refers to broadening due to the electron contribution whereas

the second term is attributed to the ion broadening. Since the contribution of the ionic

broadening is normally very small, it can be neglected and Eq. 4-11 la reduces to a much

simpler form as seen below:

A4t 2w (4-12)


In the above Ea. 4-11 a, w is the electron impact parameter and a is the ion

broadening parameter; w and a are function of temperature and are approximated by

second-order polynomials [113].

The chosen spectral line was fitted by a Voigt profile and the Lorentzian width (wL)

of the line was taken as AAFWImx (FWHMexp of the experimental spectral line), while the

Gaussian width (wG) is the instrumental line broadening that is predetermined using the









line width of a Hg hollow cathode lamp at Hg I 294.263 nm with 35 pm slit width, wG =


0.5 A. The line broadening wL was calculated by the equation as seen below,

AAFwrexp =[(w L +(wL/2)2)/2 +wL/2 (4-13)

In this way, it was possible to eliminate the instrumental broadening.

Over the time scale investigated, the measured electron densities were found to

have a trend, where ne decreases exponentially with the delay times, which vary from

the order of ~ 1019 cm-3 to ~ 1018 cm-3 in a delay range (100 ns to 3000 ns) as shown in

Fig. 4-2b. The corresponding lower limit of electron density is given by the McWhirter

criterion which has been used for assessing LTE conditions [114, 115].

ne > 1.6 x1012T17/2AE3 (4-14)

where T, is the electron temperature in Kelvin and AE is the largest energy transition in

eV. It is assumed that the distribution of population densities of the electrons is

determined by collisions with other particles rather than by radiative processes. In

general, it is only at later times that the electron density values converge toward this

lower limit.

In our study, the McWhirter criterion appeared to be fulfilled in the whole studied

delay time range due to the significant laser fluence (90 5 mJ laser pulse energy). The

measured electron densities, that is, are higher than the lower limit, which varies from ~

1019 cm-3 to 1017 cm-3for the range of obtained temperature (for T = 18,000- 7,500 K

and AE < 5.0 eV) as shown in Fig. 4-2. However, one should note that the McWhirter

criterion is necessary but not a sufficient condition for a plasma to be in LTE due to the

evolution of plasma in space and time. Thus, it is important to study the local









thermodynamic equilibrium (LTE) conditions in the plasma, and then assess any

derivation from LTE conditions in order to determine the best conditions at which they

are satisfied. This was done by comparing the excitation temperature (Texc) and electron

temperature (Te) in the line-to-continuum intensity ratio method as a function of the

delay time for an experimental assessment of LTE. In the study, the plasma seems to

reach the LTE state around 5.0 ps after its formation, as shown by the agreement

between Texc and Te in the theoretical expression of the line-to-continuum intensity ratio

method. Experimentally, in the beginning of the relaxation, in general, the electron

temperatures appear to be higher than the excitation temperatures due to its fast

evolution and the plasma being heated by inverse Bremsstrahlung. This means that

some time is required after the plasma formation in order to reach LTE. More studies

presented in the following sections.

Excitation Temperature (Texc)

The Boltzmann plot is a well-known method for determining the excitation

temperature (Texc) of the plasma using the Boltzmann equilibrium relationship without

knowledge of the concentration (or number densities) and the partition function in terms

of temperature. The Boltzmann plot method allows plasma temperature to be

determined through a simple linear regression with the slope by representing log (lui

X/guAul) against the upper energy level Eu in eV, provided that the transition probabilities

(Aui) from a given excitation state are known as shown in Eq. 3-22. However, for high

temperature, the energy spread in a single ionization state is not large enough to

provide accurate temperature values.









On the other hand, the Saha equation provides a relationship between transition

line intensities from different ionization stages. Using both equations together has some

advantages for determining temperatures in plasmas. First, it combines the improved

statistics of the Boltzmann plot due to the use of many emission lines with the greater

accuracy of the Saha analysis because of the larger energy spread available (see, for

example, [68, 116]). In other words, with a large range of energy values in the abscissa,

the presence of one or two outliers is not expected to significantly affect the slope of the

overall plot.

For the evaluation of the plasma temperature with this approach, the Boltzmann

plot and Saha-Boltzmann plot methods were used in the spectral profiles of the

transitions chosen. It is important to note that the measurements correspond to line-of-

sight averages and therefore one should be aware that spatial resolution is not taken

into account here. Figure 4-3 shows excitation temperatures obtained from both

Boltzmann and Saha-Boltzmann plots for several elements such as copper and barium

used in our work. Table 1 lists some spectral lines and their constants used in the study

(transition probabilities and statistical weights of these lines).

Electron Temperature (Te)

The electron temperature (Te) was calculated by taking the ratio of the frequency-

integrated line intensity I, to the experimental continuum intensity 6eAA multiplied by

spectral bandwidth (AA), namely the line-to-continuum intensity ratio method (see Eq.

4-10). As mentioned above, the electron temperature can be calculated by keeping Texc

; Te in the theoretical expression.









As pointed out in the theory section, provided that the free-free Gaunt factor and

free-bound continuum factor can be explained, Eq. 4-10 can be further simplified and

then the electron temperature Te can be calculated more precisely. For the study, the

Cu atomic line at 282.44 nm in pure copper metal was considered. As mentioned in the

theory section, since it is difficult for the correction factors G and E to be calculated

precisely, arbitrary values from 0.01 to 1 for both G and E were inserted into Eq. 4-10

in order to check how these values affect the calculation of Te as a function of delay time,

as can be shown in Fig 4-4. After 0.5 ps delay time, the calculated electron temperature

was identical for arbitrary values of G within an error range (about ~ 20 %), which can

be attributed to uncertainty in the Einstein transition probability A, (see in Fig. 4-4a and

b). Otherwise, for the free-bound continuum correction factor E, the calculated electron

temperatures showed a significant difference for different values of as a function of

delay time (see in Fig 4-4c and d). In the extreme case, e.g., at the shortest delay time

(td = 500 ns), the difference in electron temperatures was so pronounced that the

correction factor E increases from 0.01 to 5; i.e., it is out of the error range (> ~ 50 %),

which can be attributed to the Einstein transition probability A,. In our work, however,

G and E values of 1, respectively, in Eq. 4-10 were used for simplifying of the complex

calculation. It is worth nothing that this approach can assess the existence of local

thermodynamic equilibrium in examining time-resolved plasma phenomena, although

some error in calculation of electron temperature depending on correction factor E can

be expected.

The study was performed on three different samples such as a pure copper metal

(99.99 % Cu) and aluminum alloy sample (16.05% Cu) for copper and a BaCI2 pellet for









barium. Emission lines to be used for the line-to-continuum intensity ratio method were

selected according to the following criteria: (1) the line should be free of interference

with other lines, (2) it should be on a strong continuum radiation even at long delay

times and (3) it should be free from self-absorption.

Experimental results for Cu. In the case of copper metal, we used two different

gating and laser energy parameters (see Table 4-2) at short delay and long delay times,

respectively. If the experimental condition of the gating and energy parameters used at

long delay time is kept at short delay time, e.g. td < 300 ns, the ICCD camera is

saturated in the cases of ion species because the ionic emission is very strong at the

short delay time. For the purpose of spectrochemical analysis, especially the line-to-

continuum intensity ratio method, neutral atoms are more suitable, because they are

more sensitive and observable over a longer period of time. For this reason, the Cu

atomic line at 282.44 nm in pure copper metal (Fig. 4-5 and 4-6) and 296.12 nm in the

Al-alloy (Z8) sample (Fig. 4-7) were selected for analyzing signal-to-background ratio

because it is the highest signal-to-continuum intensity ratio as well as the best resolved

line even at long delay times.

As the delay time increased from 0.5 ps to 15 ps, the excitation temperature

decreased as seen in Fig. 4-6. However, for short delay times (td < 300 ns) after the

laser pulse, the excitation temperature could not be measured accurately because the

line emission can be imbedded in the continuum emission as seen in Fig. 4-5a. In

addition, during this period, 505 mJ laser-pulse energy was used due to saturation of

the ICCD camera. Galmed, et.al [117] showed that LTE conditions are fulfilled only in

the cases of 75-100mJ laser pulse energies. Thus, it is very hard to describe the trend









of the excitation temperature during this time period (td < 300 ns), as can be seen in Fig.

4-6a. The excitation temperature exhibited an initial fast decay from 22,328 K at 0.5 ps

after the laser shot to 13,783 K at 5.0 ps and a slower variation over the next 15 ps as

shown in Fig. 4-6c. Finally, the Cu lines disappear after this time (see Fig. 4-6d). While it

should be noted that the electron temperature also decreased exponentially as the

delay time increased until 5.0 ps delay time, but increased again after 5.0 ps delay time

due to the small signal-to-continuum intensity ratio. Moreover, at the short delay time (td

< 100 ns, see Fig. 4-6c), Stark shifts as well as Stark line broadening were observed.

Based on this result, plasmas seem to reach LTE around 5.0 ps after formation, as

shown by the agreement between the excitation and electron temperatures (see in Fig.

4-6c). A similar result of plasma temperature was also observed in the case of the

aluminum alloy sample (Z8) (see Fig. 4-7). For verification of this approach, it should

also be checked whether the electron temperatures measured at the Cu I 282.44 nm

line are coincident with that measured at different lines (e.g., Cu I 510.55 nm, Cu I

296.12 nm etc.) of the same element (e.g., Cu) in the copper metal. Figure 4-8 clearly

shows that this approach worked successfully; i.e., the electron temperatures calculated

at three different lines are very similar to each other.

Based on the result, it can be explained that in the beginning of the relaxation, the

electron temperature is much higher than the excitation temperature due to the plasma

being heated by inverse Bremsstrahlung, but after a certain delay time (in our work,

after 5.0 ps), plasmas reach local thermodynamic equilibrium. Thus, it is necessary to

study the local thermodynamic equilibrium (LTE) condition in the plasma and determine









the best conditions at which they are satisfied in order to analyze the emission spectrum

of the laser-induced plasma.

Experimental results for Ba II. The spectroscopic information of the barium ionic

lines which were used has been already represented in Table 4-1. Figure 4-9 shows the

time-resolved emission spectra from laser-induced plasma of Ba II lines at the several

delay times (0.1 ps < td < 3.0 ps). As observed before, the emission of ionic species

seems to decay much faster compared to that of atomic species. In the study, the Ba II

lines as well as the continuum radiation disappeared after a 3.0 ps delay time. This

means it is very difficult to get high signal-to-continuum intensity ratio after this delay

time. However, we have also observed a very similar trend in the case of Ba II lines

(compared to the result for Cu lines) within a certain range of delay times. For the study,

the Ba ionic line at 252.84 nm in BaCI2 pellet was selected. In Fig. 4-10, at short delay

times, the difference of the excitation and electron temperature was fairly considerable

due to the fast evolution of the plasma as well as inverse Bremsstrahlung during this

time period. However, this difference decreased gradually with increasing delay time, so

that the plasma seems to reach LTE around 0.8 ps after its formation (see Fig. 4-1 Oa). It

should be noted herein that the delay time period for achieving LTE was shortened in

the case of the ionic species compared with that of the atomic species. This result

makes us think that, in the case of the ionic species, the evolution of the plasma decays

rapidly and the plasma can reach the equilibrium state at a relatively short delay time. In

general, because the ionic species are in high-lying energy levels, the excitation

temperature can be comparable to the electron temperature at short delay times.









Conclusions

The concept of local thermodynamic equilibrium (LTE) has been widely used to

simplify the interpretation of spectral line intensities from laboratory and astrophysical

plasmas. If LTE is a good approximation of the plasma state, the plasma temperature

and electron density which can be easily derived from the emission spectra can be used

to describe the plasma characteristics and plasma analysis becomes possible. Thus,

there are many circumstances where it is important to have rather precise criteria to

identify the plasma conditions under which it is safe to assume LTE in order to carry out

a successful analysis.

The proposed method, namely line-to-continuum intensity ratio method, is very

useful to evaluate experimentally the existence of local thermodynamic equilibrium

conditions at various stages of plasma evolution with the overall goal of reaching a

better understanding of the chemistry and dynamics of the laser induced plasma. The

experimental results presented demonstrate well the usefulness of this approach by the

following results:

* The approach allows experimental checking of the existence of local
thermodynamic equilibrium conditions in time-resolved plasma.

* The McWhirter criterion appeared to be fulfilled in the whole studied delay time
range, but is not sufficient condition for LTE.

* In our result, the electron temperature was always higher than the excitation
temperature due to the plasma being heated by inverse Bremsstrahlung, but after
a certain delay time (in our work, between 3.0 and 5.0 ps ), plasmas reach the
local thermodynamic equilibrium state; i.e. the electron temperature is consistent
with the excitation temperature after that time.

* The delay time period for achieving the LTE condition was shortened in the case
of the ionic species compared with that of the atomic species due to the high-lying
energy levels of ionic species.









On the other hand, it should be also stressed that this method has some

limitations on the calculation of electron temperature due to the uncertainty from

Einstein transition probabilities A,, free-free Gaunt factors G and free-bound

continuum correction factors E. As mentioned above, although some error in calculation

of electron temperature, in particular, depending on correction factor E can occur, it can

be worthwhile to assess the existence of local thermodynamic equilibrium within time-

resolved plasma phenomena.

















Princeton Instruments, inc
Programmable Pulse Generator
Model PG-200


Quantel Brilliant Nd:YAG Laser
Pulse energy 90 + 5 mJ
Pulse duration 6 ns


12 nm
f=10 cm -1


He-Ne laser


2 fns = 15.24 cm 2 flns= 15.2,

Photodiode
3.04

Multi-meter


Figure 4-1. Experimental LIBS set-up












250000


200000-


o 150000-


"; 100000


' 50000-


0
24




o 3000-
0
2500

.- 2000

1500

1000
500
0
-ii
o 2
i 11


Wavelength (nm)


(b)


-0- Electron density in Ba II 252.84 nm
-+- Mininum electron density for LTE


0-*--o


0.5 1.0


2-.534-
2.5 3.0


Delay time (ps)

Figure 4-2. (a) Line broadening and (b) the electron number density calculated from
Stark-broadened line widths of the Ba II line at 252.84 nm at 90+5 mJ laser
pulse energy as a function of delay time.












Saha-Boltzmann plot
(a) Pure copper metal (99.99%)

1 0 h'




5c i o 5 P s
0 1 0 As



10 ps

15 Ais
-10 0
2 4 6 8 10 12 14 16 18
Energy (eV)

Saha-Boltzmann plot
lO (b) Al-alloy sample z8 (16.05% copper)

5_ 2 05 ILs


4 6 8 10 12 14
Energy (eV)


24000 (d)
22000
20000
18000
16000
a. 14000
E
* 12000
10000
10000-


16000

15000

14000

S 13000

a 12000
E
0)
I- 11000


16 18


I 2 4 6 8 10 12 14 16
Delay time (ps)


[e)


'a-


1 2 3 4 5
Delay time (is)


Boltzmann plot


15000



12000



* 9000


I-
6000


4 5 6
Energy (eV)


t


0.0 0.5 1.0 1.5 2.0 2.5 3.0
Delay time (ps)


Figure 4-3. (a and b) Saha-Boltzmann plots and (c) Boltzmann plot in different delay
times. (d f) Corresponding excitation temperatures versus delay times show
in the figure.




















-0- 50 ns
(a) -- 100- n
200ns
-y-300 ns
400 ns
m ____ -4- 500 ns




---- 00.
- V ----V---V-VYyTW
4 -- -4-4-4 44444


001


0 1
Free-free Gaunt factor (G)


80,000 -
(b
70,000-

60,000-

50,000-

40,000-

30,000- *
0-
20,000 -.
1=
10,000 ,
0 01


---500 ns
-0-1000 ns
1500 ns
--- 2000 ns
2500 ns
-4-3000 ns
5000 ns
-*-8000 ns
-*-10000 ns
-o-15000 ns


---------m-*-m-m- mmm

'V- VV--VTVT-W
4 4--4-4-4 44-4


0.1 1
Free-free Gaunt factor (G)


001 0.1 1 10

Fee-bound continuum correction factor ( )


-'-500 ns
-0-1000ns
1500ns
-V- 2000 ns
2500ns
-4-3000 ns
5000ns
---8000 ns
-*- 10000 ns
-g-15000 ns


Fee-bound continuum correction factor ( )


Figure 4-4. Electron temperature versus (a -b) free-free bound correction factor and (c-
d) free-bound continuum correction factor as a function of delay time.
























93


80,000-

70,000-

60,000-

50,000-

40,000-

30,000-

20,000-

10,000-












Short delay times


-50 ns
- -100 ns
200 ns
---300 ns
400 ns
- 5nn ns


*0 --I
a


- / *~
1 ,~


1.0 -


0.8-


0.6-


0.4-


0.2-


I- 0 0


a -

- ---- a a


282.0 282.3 282.6 282.9


Wavelength (nm)



Long delay times


-500 ns
- -1000 ns
1500 ns
- 2000 ns
2500 ns
--- 3000 ns
5000 ns
--- 8000 ns
- 10000 ns
- -15000 ns


282.0 282.2


282.4 282.6 282.8 283.0


Wavelength (nm)



Figure 4-5. Normalized line profiles of Cu atomic transition at 282.44 nm (a) at 50 ns < td
< 500 ns delays (laser pulse energy 50+5 mJ and gate width 50 ns) and (b) at
500 ns < td < 15000 ns delays (laser pulse energy 905 mJ and gate width
100 ns).


(a)


I %


0.0 -
281.7


1.2


0.9


0.6


0.3


0.0


%
















70000- (a) T(K) (c) o T (K)

60000- 0 T (K) 40000- 0 T (K)

50000 1 -
a 30000-
40000

0) 30000- a T
C L 20000-
F 20000- 1 Ii
Q --- ----- f
10000 103000- e
00 01 02 03 04 05 0 2 4 6 8 10 12 14 16
Delay time (ps) Delay time (ps)

Cu 1282.44 nm Cul 282.44 nm
250 b -0-ns 700--- -- -- -- -- -- 44.---|-u lu 0
20 (V g \ 50 --- H
2W- 0,01, I'"'"wVgtft, gd 600.... .
0 c s o --Vagtfiltting 0 500
o0 1504m0 + -.
VIgt ftting
2/- 503ns > 400 ...........................................- -- n- -
-^ "0 3_.0 -- ----,,-----,' -- Vg ti-
W 1a) f r0 C 300 8 D*ns

I I4 7- 1 ,, 2""- -


2EV 2821 2822 2823 2824 2825 2826 2827 2828 :'W 'V I 1S Ni
Waveleth, nm Wavelenth. nm

Figure 4-6. (a and c) Temporal evolution of the excitation and electron temperatures at
282.44 nm Cu I line from copper metal. (b and d) The line profile in the figures
corresponds to the Voigt profile fit of the emission lines at different delays
from plasma creation.











40000 -

35000-

30000-

. 25000-

a. 20000-

15000-


10000 -


(a)


0 T(K)
* T (K)


-.- -


Delay time (ps)
Cu 1296.12 nm


xlit


296 296.1
Wavelength, nm


Figure 4-7. (a) Temporal evolution of the excitation temperature and electron
temperature at 296.12 nm Cu I line of Al-alloy sample (Z8). (b) The line profile
in the figures corresponds to the Voigt profile fit of the emission lines at
different delays from plasma creation.
















-E-- T
ex c


/ TT (Cu I 282.44nm)
T (Cu I 296.12 nm)
S--V- T, (Cu I 510.55 nm)





____-------E----_


0.2


0.3


0.4


0.5


-LZ-T
exo
- 0- T (Cul 282.44 nm)
T (Cu I 296.12 nm)


---- T (Cu I 510.5'



T. .



L-S


5 nm)


0 2 4 6 8 10 12 14 16

Delay time (gs)


Figure 4-8. Temporal evolution of the excitation temperature and electron temperature
for Cu atomic lines at 282.44, 296.12 and 510.55 nm in a copper metal for (a)
short delay times (100 ns 5 td 5 500 ns) and (b) long delay time (500 ns 5 td <
15000 ns).




97


(a


a

(a

0

O

m
IL

E
. ,
I-


0-




a
E
aD
I-


(b)


\



















_2 .0 (a)

-5,0 0 2\ -
0-4 0=^ 3.A <-
008

05-.
0-2 4 --, -
- O'.---- --- 9--S"
228 230 232 234 236-
Wavelength (nm)


I Y -- 03


o05

0815
20

248 250 252 254 256 258
Wavelength (nm)


2N. 02

r 0 08 -.



258 260 262 264 266 268
Wavelength (nm)



01







(d) Wavelength (nm)
----W c------ 211 4)p
3.0

272 274 276 278 280 282
Wavelength (nm)


6- (e
n 5

0- 3-




384


0-1
02 4
03 '3
0.5 j
08 S

3.0 A
386 388 390 392 394

Wavelength (nm)


21/ 0-

I)0 a3.0It
- 410 412 414 416 418 420
Wavelength (nm)


_M 6
0
0 4

2


.2


3

2



CO
J>0


(g)


0o ---z------ v -3U 4
450 452 454 456 458 460
Wavelength (nm)


h)


0.3





490 492 494 496 498
Wavelength (nm)


Figure 4-9. Time-resolved emission spectra from laser-induced plasma of Ba II lines.

The spectra were recorded at 90 5 mJ pulse energy and the gate time of

the intensity was set by 0.1 ps.









98


CDP
1_5
o 1 2
09
$06.
S03
0D0
_ 0.0











(a)
22000 a)

20000-

18000- 4

16000-

14000-

12000 -

10000-

8000-

6000--_,
0.0


I I I I
0.5 1.0 1.5 2.0
Delay time (ps)


2.5 3.0


Ba II 252.84 nm


252_2 25Z4 25Z6 252_8 253 2532 2534 2536 2538 254
Wavelength, nm


Figure 4-10. (a) Temporal evolution of the excitation temperature and electron
temperature at 252.84 nm Ba II line of Al-alloy sample (Z8). (b) The line
profile in the figures corresponds to the Voigt profile fit of the emission lines at
different delays from plasma creation.


a)


0)
0-
E
a)
I-


O T (K)
* Te (K)









Table 4-1. Selected spectral lines and corresponding spectroscopic information of the
investigated elements(a)
Wavelength, Ao El Eu Au.
Species (nm) (eV) (eV) gu (108 s1)
Cu I 261.84 1.39 6.12 4 0.31
Cu 282.44 1.39 5.78 6 0.08
Cu I 296.12 1.39 5.58 8 0.04
Cu 324.75 0.00 3.82 4 1.37
Cu 327.40 0.00 3.79 2 1.36
Cu I 465.47 5.08 7.74 8 0.42
Cu I 510.55 1.39 3.82 4 0.02
Cu 515.32 3.79 6.19 4 0.60
Cu 521.82 3.82 6.19 6 0.75
Cu I 578.29 1.64 3.79 2 0.02
Cu ll 221.02 3.26 8.86 5 1.58
Cu II 221.81 2.83 8.42 3 3.41
Cu ll 222.88 2.98 8.54 1 4.11
Cu II 224.27 3.26 8.78 5 1.58
Cu II 224.70 2.72 8.23 5 3.70
Cu II 227.63 2.98 8.42 3 0.60
Cu II 229.43 2.83 8.23 5 0.25
Ba II 230.42 0.60 5.98 6 0.52
Ba II 233.53 0.70 6.01 8 0.81
Ba ll 234.76 0.70 5.98 6 0.11
Ba II 252.84 2.51 7.41 4 0.69
Ba ll 263.48 2.72 7.43 6 0.73
Ba ll 277.14 2.72 7.19 2 0.04
Ba ll 389.18 2.51 5.70 4 2.17
Ba ll 413.06 2.72 5.72 6 2.18
Ba II 416.60 2.72 5.70 4 0.35
Ba II 452.49 2.51 5.25 2 0.66
Ba ll 455.41 0.00 2.72 4 1.11
Ba ll 489.99 2.72 5.25 2 1.04
Ba II 493.41 0.00 2.51 2 0.95
(a) From NIST Atomic Spectra Database, http://physics.n5ist.gov/Phys.Ref
Data/AS D/htm I. ref. html


100









Table 4-2. Gating and laser energy parameters used for temporal characteristic and
line-to-continuum intensity ratio method of pure copper metal: (a) at the short
delay times with laser pulse energy 50 5 mJ and (b) at long delay times
with laser pulse energy 90 5 mJ


(a)
Delay time
(= td)
50 ns
100 ns
200 ns
300 ns
400 ns
500 ns


Gate width
(=tw)
50 ns
50 ns
50 ns
50 ns
50 ns
50 ns


(b)
Delay time
(= td)
500 ns
1000 ns
1500 ns
2000 ns
2500 ns
3000 ns
5000 ns
8000 ns
10000 ns
15000 ns


Gate width
(=tw)
100 ns
100 ns
100 ns
100 ns
100 ns
100 ns
100 ns
100 ns
100 ns
100 ns


101









CHAPTER 5
ON THE USEFULNESS OF A DUPLICATING MIRROR TO EVALUATE SELF-
ABSORPTION EFFECTS IN LASER-INDUCED BREAKDOWN SPECTROSCOPY

Introduction

This Chapter is mostly taken from our publication, which appeared in 2009 [166].

Tables and figures were reproduced with permission of Elsevier.

The concept of self-absorption, and its extreme case of self-reversal for

inhomogeneous temperature distributions, is intrinsically related to the measurement of

line intensities as mentioned in Chapter 3. When re-absorption of the emitted species by

the laser light becomes noticeable, the observed intensities will depart from the

expected values. In order words, starting with the most intense liens, it approaches a

flat-topped profile, evidence of self-absorption. Moreover, self-absorption has been

considered in the characterization of spectroscopic emission sources and used to

evaluate population densities in different sources [90].

Since the advent of LIBS as an analytical technique, in various works the effort for

correcting the self-absorption effect of spectral line has been reported in a number of

papers [29, 53, 81, 118-126]. Recently, several methods were proposed for evaluating

the reduced line intensities by self-absorption. Bulajic et al. applied on algorithm for self-

absorption correction to the procedure for calibration-free quantitative elemental

analysis, which have already been developed by [50]. The theory was based on the

Curve of Growth (COG) method, which was first proposed by Gornushkin et al. [53] in

laser-induced breakdown spectroscopy. In LIBS calibration plots, a simple method

which takes into account the effects responsible for non-linearity in the relationship

between line intensity and elemental concentrations was also presented [122]. For

qualifying the effect of self-absorption, El Shelbini et al. [81] proposed the evaluation of


102









self-absorption coefficients of aluminum emission lines in LIBS measurement. The

method was performed by comparing the measurement of the line width of the self-

absorbed lines with that of the corresponding non self-absorbed lines in order to

evaluate self-absorption coefficient. The electron density can be also evaluated by

relating the line width affected by self-absorption to the electron density. It was shown

that the use of the self-absorption correction method leads to more accurate

temperature values. Moreover, several authors established new methods for a

satisfactory fit between the theoretically and experimentally spectral lines strongly

deformed by self-absorption in Al resonant lines [121, 125-127]. However, the

mentioned methods require the necessity of changing the sample concentration or

calculation a curve of growth and some modeling or equilibrium hypothesis of plasma

parameters in LIBS.

Among the existing experimental approaches, one that seems to have been

ignored is the use of the "duplication factor" approach, also known as Gouy's method

[128], which has been amply described in flame work [87] and also for plasma work [80,

129-133]. Alternative methods have also been described [134-137] and claimed to have

the advantage that the knowledge of the mirror reflectivity is not required.

In this chapter, one illustrates the use of the duplicating mirror in LIBS, which have

been yet appeared in the field of LIBS, and proves its usefulness in characterizing the

effect of self-absorption and its temporal behavior during the evolution of plasma. It is

shown that this simple expedient provides a quick check for the existence of optically

thick plasma conditions, and one to follow the temporal evolution of the plasma optical

depth from the early decay of the continuum emission to the end of the plasma lifetime.


103









Moreover, the presence of the continuum emission is itself a way to measure mirror

losses, as pointed out by Konjevi6 [80]. The usefulness of this method will be checked

in the Saha-Boltzmann plot for the evaluation of the plasma temperature and correcting

the deviation from linearity at increasing concentrations in the calibration curve.

The Self-absorption Correction Factor KA

As mentioned in the previous section, K. can be evaluated by placing a mirror

behind the plasma [80, 129-133]. Alternative methods have also been described [134-

137]. In the case of a laser-induced plasma, this method appears more convenient than

that of placing an identical plasma directly behind the original plasma on the optical axis,

as done, for example, in flame work [87] or changing the length of the plasma discharge

axially viewed [134-136] or comparing transversal and longitudinal observations of the

plasma [137]. By using a spherical mirror located at twice the value of its focal length

from the plasma, two line profiles (with and without the mirror) can be obtained and

used for the determination of KA.

In order to evaluate correction for self-absorption, the pertinent equations

illustrating the parameters relevant to the experiment can be derived as shown by

Konjevi6 [80]. The expression for the intensity of radiation IA from the homogeneous

plasma layer (optical length, 1) in LTE can be represented:

I = B [l exp(-kj1)] (5-1 a)

IA,2 I,1 + GI,, exp(-k,2) = I,lj[1+ Gexp(-k,2)] (5-1 b)


R = 1_ 1 + G exp(-k,) (5-1 c)
I,'1


104









where B ,T is the spectral radiance (W cm-2 sr-1 nm-1) of the equilibrium radiation (or

blackbody radiation) at temperature, suffices 1 and 2 refer to measurements taken

without and with the mirror, respectively and k. is the absorption coefficient which is

related to Kirchhoff's law of radiation by B2 o, for LTE. In addition, the parameter G

includes reflection and absorption losses at the mirror, as well as imperfect matching of

solid angles, and can be evaluated by rationing the signal obtained for the intensity of

the plasma continuum, where k. is equal to zero, e.g.,

Ic
21
RC= _2,2 =1+G. (5-1d)


Usually, ratio Rc could also be determined at the line wings where absorption is

negligible; the continuum radiation, otherwise, should be chosen for more accurate

result.

In the expression of Eq. 5-1a, one can distinguish three cases depending upon the

value of k.1:

* If the line profile is in the condition of negligible self-absorption, e.g., optical
thickness k /<< 1 over the wavelength range of the line, then one obtains by
series expansion

IA = Bk,kl =f l. (5-2)

* In the other extreme condition, kl/ >>1 ,R Eq. 5-1 a may be written as I, = B T,,
e.g., observed line intensity reaches a black body radiation of temperature T, and
the line loses its characteristic shape, which means the observed line intensity no
longer follow the absorption coefficient. Moreover, the line profile cannot be
recovered.

* However, if optical depth, k.l <1, is not too large, the line profile for the optical thin
case may be recovered by using a correction factor of Eq. 3-11 b.


105








The expression of optical depth (see Eq. 3-12) can be also modified by the

pertinent equations illustrating the parameters relevant to the experiment: e.g.,

k,l = InR -1 (5-3)
RA -I I

Thus, the experimental correction factor, K,,,,,,, can be obtained by inserting Eq.

5-3 into Eq. 3-11 b for making to the useful equation in terms of the experimental ratios

Rc and R,:

K In [(R 1)/(R 1)] (5-4)
S(R 1)
(Rc -1)

The correction factor Kzcorcan be then multiplied on the line profile to retrieve the

optically thin line profile.

As pointed out [80], the method cannot be used for high values of the optical depth,

since the true line profile cannot be retrieved (see the extreme case, kj >>1). From an

experimental point of view, it is useful to consider the effect of variation in the plasma

optical depth on the correction factor. In the range of optical depths where the method

can be applied, it can be shown from Eq. 3-11 b and Eq. 3-12 that the relative error in

K, (see Eq. 3-11b) is a function of r e.g.,:





AK d F(r) (5-5a)
KA TA


106









From Eq. 5-5a, one obtains the correlation function F(r2) between the relative error of

correction factor K. and that of optical depth r~as below:

F(r,)l- (5-5b)
1-e '

The above equations indicate that the relative error affecting the correction factor, K2, is

smaller than that affecting the optical depth, rz, since F(r-) ->o >0 and

F(rc,) ->c > 1. It means the majority of the relative error affecting the correction factor

is from the optical depth. Experimentally the relative error, which is able to affect the

correction factor, is always less than 10%. For values of rz above ~3, for instance,

F(-r) ->o >1(within approximately 10%) and any variation in rzwill directly affect the

precision in determining of Kz,,..,.

Of even more practical significance is the behavior of the relative error in K ,r,,, as

a function of the experimental ratios RC and R,. As seen from Eq. 3-11 b, for r >>1, one

can be expressed as

K, k,l r, (5-6a)

From Eq. 5-3, one also can be expressed as


K, r,= In R- =ln Y (5-6b)


Rc -1
Y T -t (5-6c)
R, 1

Thus, the relative error can be expressed as


107









AKz co,, Aln(Y) 1 AY
KA CO~. ln(Y) ln(Y) Y

By comparing Eq. 5-7 with Eq. 5-5a, one can see that, since Y function (= e") grows

much faster than rAthe experimental error affecting Y will have an even less relevant

effect on K .,co.

From the experimental data, one can also calculate the "Duplication Factor",

D1(JA), expressed by the following relation [28, 87]:

D,(A) I(A,2fni1) I(A, fij) (5-8)
I, (A,ZJlj)

As seen in the expression, D(JA) represents the relative increase in line intensity,

or integral absorption, caused by doubling the product (fnal), and takes the asymptotic

values of 1 (at low optical depths) and 0.415 (at high optical depths) [87]. This quantity

was used in flame work [87] and was shown to provide complementary information to

that obtained by the curves of growth [87, 138].

The measured signal called "intensity" in most of the literatures has the form

multiplied by the optical conductance of the system (optics and monochromator) and the

instrumental function or slit function of the monochromator [100, 139]. For the

measurement of the integrated intensity, the instrumental function can be made larger

than the spectral profile of the line. However, when calculating the correction factor

wavelength by wavelength (or pixel by pixel), it must be much smaller that the line width.

Since the line profiles decreases as the delay time of observation increases, this last

condition is valid at early delays, but fails to hold at longer delays.


108









Experimental

The experimental LIBS set-up used in all measurements have already been

described in detail in Chapter 4. Only different thing is the spherical mirror which was

placed behind the plasma at a distance equals to its radius of curvature (see Fig. 5-1).

An optical shutter inserted between the sample stage and the spherical mirror allowed

spectra to be obtained with and without the mirror. In particular, the zero-order plasma

images obtained with and without the mirror were checked repeatedly, and merged

carefully together, before changing any of the experimental parameters, such as the

time delay and the spectral positioning of the grating. The result of such procedure is

shown in Fig. 5-1c.

Nine Al-alloy samples D28, V14, D33, B8, AA3, S4, R14, Z8, SM10 of known

composition (South Africa) were used. The compositions of the major components and

the spectral information pertinent to the transitions used in this work are reported in

Tables 5-1 and 5- 2 and in Fig. 5-2, respectively.

Results and Discussion

Evaluation of Rc

For an accurate evaluation of the parameter Rc, a relatively strong continuum

radiation at the far wings of the line (approximately five times the full width at half

maximum) was measured. Moreover, since the continuum emission dominates initially,

as can be seen in Fig. 5-3a, the ratio Rc can be determined at short delay times. Fig. 5-

3b illustrates a typical example of how this ratio was determined and calculated in the

case of the copper atomic line (510.55 nm). The calculated Rc at 1.0 ps delay time is

1.67, indicating that the reflection and absorption losses are about 30 % in our work


109









(see Fig. 5-4). Figure 5-5 also shows the calculated values of self-absorption correction

factor, Kcorr, for various values of RA and Rc For the value of Rc found

experimentally, it is clear that, as the ratio RA approaches 1, the line is strongly self-

absorbed, resulting in a relatively high correction factor, K,co.,. This condition is, of

course, expected from Eq. 5-1 c.

Evaluation of RA

Three elements, namely Cu, Fe and Mn, were considered and repeated

measurements performed with and without the mirror on selected spectral lines as a

function of the delay time after the laser pulse. In the previous section, Fig. 5-3 reported

a typical example of calculating RA from the ratio of peak intensities at a given

wavelength under line profile. The results obtained for Cu are collected in Fig. 5-6,

together with the wavelength behavior of the factors involved, e.g., RA in Fig. 5-6a and

Kcor,. in Fig. 5-6b. As expected, the center of the emission profile saturates at a much

faster rate than the line wings when the plasma length is doubled, as can be seen in Fig.

5-6a. The ratio RA was evaluated pixel by pixel (e.g., wavelength interval by wavelength

interval) in order to obtain an accurate value of the correction factor KZco, for each

spectral resolution element within the line profile, thus following the different effects of

the optical thickness on the different spectral intervals under the overall emission profile.

The calculated correction factor, KA,,,. obtained for each wavelength interval, was

then applied to the data obtained without the mirror in order to retrieve the corrected line

profile, as shown in Fig. 5-6c.


110









The profiles shown in this figure have not been corrected for the instrumental slit

function of the monochromator. As mentioned in the theoretical considerations, the

accuracy of the evaluation of K, ,., relies on the assumption that the spectral

bandwidth of the monochromator is much smaller than the line profile to be measured.

In our case, the full width at half maximum (FWHM) of the profile measured at 1 ps

delay time with and without the mirror varies from 143 pm to 122 pm, respectively. With

an experimentally measured bandwidth of 3 pm, assuming both Gaussian functions, the

error is therefore less than 5 %.

Temporal Behavior of KA,corr and DA(A)

The temporal evolution of the correction factor, K ,corr, is given in Fig. 5-7. Three

copper line (510.55 nm, 324.75 nm and 327.40 nm) were considered here, our choice

being motivated by their relatively significant correction factor resulting from the

comparison of the mirror / no mirror spectra. As shown in this figure, it is evident that all

three lines are affected by self-absorption and that the effect increases with the delay

time. This is in general expected for transitions involving the ground level (324.75 nm

and 327.40 nm) since the population of this level grows in the recombining stage of

plasma evolution. Also expected is the result shown that the transition at 510.55 nm,

whose lower level is 1.39 eV above the ground level (see Table 5-2), is the least

affected. The error bars affecting the measurements can be explained by the fact that at

early delays the continuum emission is strong and the line emission is weak (and the

line is embedded in the continuum see Fig. 5-3), thus affecting the evaluation of R,,

while at longer delays the continuum intensity decreases significantly, and therefore

affecting the measurement of Rc. Moreover, as pointed out before, since the profiles


111









are not corrected for the instrumental response, the accuracy in the calculation of KZ,,.,

the values was left uncorrected.

A similar behavior was observed for the three resonance transitions of Mn around

400 nm (see Table 5-2), as shown in Fig. 5-8. It is also worth noting that our results

agree qualitatively with those published by EI-Sherbini et al. [81].

As discussed in the previous section, an additional, related method of checking the

degree of self-absorption at the line center and in the wings involves the calculation of

the Duplication Factor, D,(A). This can be done again, as described before, using the

duplicating mirror and calculating D,(2) from Eq. 5-8. Figure 5-9 shows the data

obtained for the Cu line at 510.55 nm at different delay times. As shown, self-absorption

starts affecting the line profile at about 1 ps delay time and its effect increases as the

time delay progresses. As expected, the effect is stronger at the center of the profile. At

delay times shorter than 1 ps, D(2A) has an approximately uniform value (about 0.8),

as shown in Fig. 5-9a. These results are in agreement with those reported in Fig. 5-6 for

the same Cu transition. Similar considerations and cautioning remarks regarding the

variable accuracy of the data, due to the narrowing of the line profile at longer delays

also apply here.

In conclusion, within the accuracy limits of our calculations, the data shown justify

our statement about the usefulness of the mirror approach, and show that the temporal

evolution of self-absorption can be easily followed during the plasma expansion and

recombination.


112









Self-absorption Corrected Saha-Boltzmann Plots

A logical test to prove the usefulness of the mirror and the resulting correction

factor is its application to the study of the spectral profiles of the transitions chosen in

the Boltzmann and Saha-Boltzmann plots for the evaluation of the temperature of the

plasma. Self-absorbed lines will give intensity values lying below the line corresponding

to the best fit in these plots. The mirror approach will therefore quickly identify outliers,

allowing one to either exclude them from the fit or to apply appropriate corrections

factors. On the other hand, it is important to note that the measurements correspond to

line-of-sight averages and therefore one should be aware that spatial resolution is not

taken into account here.

It seems that, since most temperature evaluations are made with the Saha-

Boltzmann plot (see, for example, [68, 81, 116]), and therefore with a large range of

energy values in the abscissa, the presence of one or two outliers is not expected to

significantly affect the slope of the overall plot. In other words, it seems worthwhile to

note that the sensitivity of the temperature plot to self-absorption effects is not as

pronounced, provided that many lines of widely different upper state energy are used,

which should be the case of the Saha-Boltzmann approach [68]. In the case of a double

pulse experiment, and for temperature values in the range 11,000 K 12,000 K, El-

sherbini et al. [81] reported temperature differences of about 700 K when the data were

corrected for self-absorption, e.g., a difference of about 5 6 %.

Figure 5-10, 5-11 and 5-12 report our results, obtained on different elements,

different samples and at different delays. It should also be noted that the data were

obtained over a period of time of more than a year. The elements considered were Cu,

Al and Fe. This choice was mainly dictated by our previous experience with these


113









samples [116]. Strong lines for Al (308.22 nm, the unresolved doublet at 309.28 nm,

394.40 nm and 396.15 nm), Fe (371.99 nm) and Cu (324.75 nm and 327.40 nm) were

used to magnify the effect.

Figure 5-10 shows the data obtained at 1 ps delay for Al and Cu in two different

alloy samples. As seen from the comparison of Figs. 5-10 Oa and 5-10 Ob, when the

strongly self-absorbed Al lines are removed from the significantly larger than the

expected error in the measurements. On the other hand, when the same procedure is

applied to copper, as shown in Figs. 5-10 c and 5-10 d, the difference in temperature is

not so pronounced. Similar reason can be applied to the data obtained at different delay

times for Fe and Cu, shown in Figs. 5-11 and 5-12. The temperature decreases as the

delay time increases, as expected, and the corrected plots show a consistently lower

temperature when compared to the uncorrected one. From the trend observed in Figs.

5-11 and 5-12, one can conclude that self-absorption effects become more important at

longer delays: this can be seen from the difference between the corrected and non

corrected values for Fe at 1 ps and 3 ps, and in particular for Cu (Fig. 5-12), where the

longest delay time of 5 ps was used.

Self-absorption Corrected Calibration Curves

Another logical test for assessing the usefulness of the correction approach is to

apply it to the calibration curves obtained with standards whose concentration is high

enough to make the plasma optically thick. Indeed, in this case, the curves of growth

show the classical non-linear behavior where the spectrally integrated intensity versus

concentration starts bending towards the abscissa at a given critical concentration [53,

123].


114









In our work, experimental calibration curves were obtained for the Mg I line at

285.21 nm and the Mg II lines at 279.08, 279.55, 279.80 and 280.27 nm, in 8 Al alloy

samples with Mg concentrations ranging from 0.004 to 1.27 %. The spectroscopic

characteristic of the lines and the concentration of the magnesium in the Al alloy

samples were reported in Table 5-2 and shown in Fig. 5-2, respectively. The strong

resonance atomic and ionic lines at 285.21 nm and 280.27 nm were chosen "ad hoc" to

emphasize the effect. As expected, the calibration plots shown in Fig. 5-13 clearly

indicate the presence of strong self-absorption, the deviation from linearity starting with

sample alloy S4, containing 0.35 % of Mg. Figure 5-14 reports the calculated values of

the correction factor, K ,.,,, of both lines for the all the Al alloy samples investigated,

showing again that the correction factor is higher for the two most concentrated samples

(Z8 and R14). The lowest correction factor was obtained for sample D28 (0.07 % of Mg),

and in fact with this sample the line intensity practically doubled when the mirror was

used. As in the case of the temperature plots, K ,., was used for correcting the effect

of self-absorption of the line profiles. The corrected profiles were integrated and used in

calibration plot. The results of such procedure are also shown in Fig. 5-14. For both Mg

lines, linearity was restored.

Conclusions

The theoretical considerations given in this chapter and the experimental results

presented demonstrate that the use of a duplicating mirror in laser-induced plasma

experiments is characterized by the following features [166]:

* It allows a quick checking of self-absorption without the necessity of changing the
sample concentration or calculating a curve of growth.


115









* It gives the possibility of following the time evolution of the "optical depth" of the
plasma. This allows seeing when self-absorption sets-in during the plasma
evolution and how relevant its effect is on the transitions used for the construction
of the calibration curves.

* It allows the simultaneous observation of the effect of the duplication on a selected
transition and the associated continuum background. This allows correcting for the
mirror reflectivity losses and solid angle mismatch.

* It provides a way to correct for self-absorption (provided that the line is not strongly
self-absorbed). One can also use the wings of the transition if the continuum is
absent. A line profile is needed in this case.

* It allows identifying outliers in the Boltzmann plot used for temperature
measurements and improving the linearity of the analytical calibration curves.

* Finally, it may also alert the analyst of the potential existence of spectral
interference. The rationale behind this assertion is the following: Suppose that
one emission line in the spectrum of element A is self-absorbed and is also
simultaneously affected by a coincident spectral line emitted by element B.
Suppose that the line of element B is not self-absorbed. The duplication factor will
have a much higher value (closer to unity) than that expected from a self-absorbed
transition. In fact, the signal from element A will increase with the square root while
the signal from B will increase linearly.

It should also be stressed that one should not overemphasize the achievements

obtained by the use of the duplicating mirror. This statement is based upon the following

that were made in our work:

* The data provide only some kind of average line-of-sight information. This is
clearly relevant when one refers to parameters such as number density or optical
depth and temperature, since their physical significance can be no better than the
validity of the assumptions made in the derivation of the expressions. One of these
assumptions is that the plasma layer is homogeneous.

* The plasma is expanding, therefore setting a limit to the duplication of the same
original volume seen without the mirror. The limit will be imposed by the expansion
speed of the plasma and the plasma-mirror distance. For example, if the plasma
mirror distance is 30 cm and the expansion speed is 106 cm S-1, in the 2 ns
roundtrip of the radiation, the plasma has moved vertically by 20 pm. If 2 mm of
plasma height are imaged on the slit, about 1 % of the plasma re-sampled by the
mirror will be "new" plasma. This situation will hold for all the delay times
investigated. As a consequence, the minimum spatial resolution and the
continuum delay time (assuming experimental feasibility) will be 20 pm and 2 ns,
respectively.


116









* In its simplest arrangement, such as that used in the present work, the
measurements taken with and without the mirror will not interrogate the sample
plasma. In fact, the measurements are taken sequentially. The results will
therefore be conditioned by the reproducibility of the laser interaction with the
target as well as by the stability of the detection electronics.

* It is also important to realize that, due to the temperature inhomogeneity of the
laser-induced plasma, several strongly self-absorbed transitions can also show
self-reversal, e.g., a dip in the line center. Except in this extreme case, such dip
may pass unobserved when a low spectral resolution monochromator is used and
spatially and temporally integrated measurements are performed. If that is the
case, the use of mirror will not help distinguishing between self-absorbed and self-
reversal lines.

In spite of the last considerations, one has to realize that the measurements

reported in this paper reflect the majority of the analytical experiments reported in the

LIBS literature. It is felt that the simplicity of the experimental set-up will make the

duplicating mirror a useful addition to most LIBS experiments, allowing at least a quick

check for the existence of self-absorption. We therefore hope that it will find a more

widespread use among the LIBS community.


117
















Princeton Instruments, inc
Programmable Pulse Generator
_ Model PG-200


10 106 nm
1= 10 cm "-.


uantel Brilliant Nd:YAG Laser
Pulse energy 90 + 5 mJ
Pulse duration 6 ns


l~He-Ne laser
S OnOt.calr sruner _


r A&


Photodiode

Mulli-meler


slit




2 fiens 2 fns
plasma
mirror image


No iiiii-t-m-

0 0

0.5 Fes 1.0 FLS 2.0 fLs 3.0 FL% 5.0 1

With nlh-l-ol-

0 0 C111 0

0. _5 Fts 1.0 Fts 2.0 fis 3.0 IL% 5.0 ILS


Figure 5-1. (a) Scheme of the set-up used, with the addition of an external spherical
mirror; (b) Schematic representation of the plasma images on the slit with and
without the mirror, which is located at a distance from the plasma equal to its
radius of curvature; (c) zero order plasma images obtained with and without
the mirror. [From ref.166, reproduced with permission].


118


R = 2 f
Rrn irror = 2 fmiror













]

1.0 0.2 0.4 0.6 0.8 1.0 1.2
Composition of Mg (%)


Z8
R14
S4
AA3
B8
D33
V14
D28


18
.C16
S14
.C 12
%O 10
C 8
:^ 6
O
S.4
0 0


D28 V14 D33 B8 AA3 S4


I.-


IlL


R14 Z8


SM10


Al alloy samples

Figure 5-2. Magnesium, copper, and iron compositions in the 9- aluminum alloy
samples used. The insert represents the magnesium composition used to
obtain the calibration plots. [From ref.166, reproduced with permission].


119


D Mg
DCu
SFe










.ih


Kr'


1.


































(b)


0.5

1.0

,2.0
3.0 1
5.0


Wave 1 length (nm)


Cu I 510.55 nm
A with mirror/
v no mirror I


AA
AA


510.0 510.5 511.0
Wavelength (nm)



Figure 5-3. (a) Observed spectral profile of the copper atomic line at 510.55 nm for
different delay times from the onset of the plasma. (b) Experimental
evaluation of RA and Rc in the case of the copper atomic line at 510.55 nm.
The delay time is 1.0 ps and the gate width 0.1 ps. [From ref.166, reproduced
with permission].


120


j LU.;
4--)
S2.0

1.5

1.0

0.5

S0.0


0

r.j


I












1C U nomirror(/~)


/ .1 *no mirror (/c)

-D- with mirror (/c)
A 0C


U)

0
0
U,o
M
0
U-)




0
iu

C

E



0
0
0-


2.0


1.8


-1.6


Delay time (p[s)


Figure 5-4. Experimental ratio (Rc) of the continuum radiation with and without the
mirror observed at different delay times. The measurements refer to the
510.55 nm Cu line. The average value of Rc over the delay times is 1.60.
[From ref.166, reproduced with permission].


121


2.0-


1.5-


1.0


0.5


0.0-

0


Rd= Ic/
2


mx -A- ---



Overall average value of Rc =1.6

-%.
.------------\


5


-1.4


C)


-1.2


1.0


l I


--d.









3.0- "
.-- 1.1
2.5 1.3
A.. 1.5
2.0 .v-- 1.7
-*-- 1.9
1.5 2.0


0
Co


0


0


C)
S-'
05



0)


1.0


*XI
*m^Hm~




ii-


I I I
1.2 1.4 1.6
Rc


Figure 5-5. Calculated dependence of the correction factor KA,corr as a function of Rc for
different values of RA, e.g., for different degree of self-absorption. [From
ref.166, reproduced with permission].


122


1.0-

0.5-

0.0-


1.8 2.0
1.8 2.0










510.55 nm Cu I 510.55 nmCul
6 1.8


1.7 6-
^*(a) VithniTOr 1 (b) --.6-wtlimm .2
rU 4 :o17 r.e-Ud- A


5"
0 2,




AC A With mirror


S3001 vogiitting 1.:4









S100
510.3 510.6 510.9 510.4 510.6 510.8
Wavelength (nWavelength Wavelength (n(nm)

Figure 5-6. (a) Calculated values of R 510.55 nmCution of w at along the linens
obtained with and without the mirror and after correct ith error
All cases refer to the Cu I transition at 510.55 nm and -Voigto measuremetting, 1=60.48
4_j No mirror
r 300-
ref.166, re-Voigi fproduceditting --with permission]414
0 0 SA corrected
$200 ./


100


590.3 510.4 510.5 510.6 510.7 510.8 510,9
Wavelength (nm)

Figure 5-6. (a) Calculated values of RA as a function of wavelength along the line
profiles; (b) Correction factor KAcoras a function of wavelength and self-
absorption corrected line profiles (c) Voigt profile fit of the emission lines
obtained with and without the mirror and after correction for self-absorption.
All cases refer to the Cu I transition at 510.55 nm and to measurements taken
at 1.0 ps delay time. The average value of Rc (1.6) was used here. [From
ref. 166, reproduced with permission].


123














3.0-


2.5-



2.0-



1.5-


E 510.55 nm
o 324.75 nm
A 327.40 nm


1.0- 1



0.5 -.


Delay time (ps)


Figure 5-7. Temporal behavior of the correction factor KA,corr (evaluated at the line
center) for three Cu atomic lines at 510.55 nm, 324.75nm and 327.40 nm as a
function of different delay times after plasma formation. The error bars
reported were calculated assuming a maximum error of 10 % for each
correction factor (see text for discussion). [From ref.166, reproduced with
permission].


124















4-
C
0

0

"A


Mn (Al alloy S4)
--with mirror
1.0 js delay time -- no mirror
403.08 nm ..... dark current
403 31 nm
403 45 nm


-----^- ,.\-:\


402.5 403.0 403.5
Wavelength (nm)


1 2D
Delay


3time
time


4
(Gs)


1.7-
1.6
1.5-
1.4-
1.3-
1.2-
1.1
1.0
0.9--
0


Mn (Al alloy S4)
2.4 5.0 ps delay time with mirror
-no mirror
.... dark current
403 08 nm
A 403.31 nm

1 6 403.45 nm




0.8 "-
402.5 403.0 403.5
Wavelength (nm)


Figure 5-8. Temporal behavior of the correction factor, KA,corr (evaluated at the line
center) for three Mn lines at 403.08 nm, 403.31 nm and 403.45 nm as a
function of different delay times after plasma formation. [From ref.166,
reproduced with permission].


125


-I- 4
5
0

0


Q-
t-





























Wavelength (nm)


510.4 510.6 510.8
Wavelength (mrn)


1.5

1.2

-0.9

0.6

0.3

.0.0


Wavelength (nm)


0n
CD
tti












C3

0
U
0


.-^


Wavelength (nm)


510.4 510.6 510.8
Wavelength (nm)


Figure 5-9. Cu I emission profiles observed at 510.55 nm with and without the mirror,
together with corresponding calculated duplication factor DA at different delay
times. [From ref.166, reproduced with permission].


126


1.2

0.9 "

0.6

0.3
0























Al
Al alloy Z8
5 10 15
Energy (eV)


....... T = 12,400 K


I.'


a


-Cu
AI alloy D33
2 4 6


8 10 1'2
Energy (eV)


14 16 18


- Cu
Al alloy D33
2 4 6


0 excluded lines
--T = 12,300 K


8 10 1'2
Energy (eV)


14 16 18


Figure 5-10. Saha-Boltzmann plots constructed using atomic and ionic lines of Al and
Cu measured in the spectra of two different alloy samples. The data were
obtained at 1.0 ps delay time. Plots (a) and (c) show all the data while plots
(b) and (d) result after exclusion of the transitions affected by self-absorption.
[From ref.166, reproduced with permission].















127


- -... T = 12,000 K


20 25


10 15
Energy (eV)



















S
on


-2-

-4-

-6-


-8
2


4cC


0-
-2-
-4-

-6 -
-8-

-10 -


1 .0 js delay time
(a)



13,359 56 K

13,496 71 K .
LD Uncorrected
0 Corrected
Linear fitting R= 0-9977
- -Linear fitting R= 0 9987
gR ib 128


(b)


6 8 10 12
Energy (eV)


3.0 Ls delay time


14


11,995 40 K


0 Uncorrected
a Corrected
- Linear fitting R = 0.9987
- -Linear fitting R = 0.9989
4 8 12


Energy


(eV)


Figure 5-11. Saha-Boltzmann plot constructed using Fe atomic and ionic lines: (a) 1.0
ps delay time, and (b) 3.0 delay time. The two slopes result from the data
uncorrected (open squares) and corrected (open circles) for self-absorption.
The lines correspond to the best linear fitting of the data. [From ref.166,
reproduced with permission].


128


.









Cu I and II lines at 5.0 ps


5- Corrected
Linear fittir
-- Linear fittir


m -101(
n ._, nm .282.4 nm
S-5- 4- 324 7 n
'" ",_, ;11,097+ 63
2 465.1 nrmai ,,

-10 8
2 4 6 8 10 12 14
Energy (eV)


16 18


Figure 5-12. Saha-Boltzmann plot constructed using Cu atomic and ionic lines at 5.0 ps
delay time. The two slopes result from the data uncorrected (open squares)
and corrected (open circles) for self-absorption. The lines correspond to the
best linear fitting of the data. The transitions used (nm) are indicated. [From
ref.166, reproduced with permission].


129










280.27 nm Mg II


E Uncorrected
* Corrected
R = 0.996


Sim


Z8

R14



R14- Z8
E- ]


0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
Ma Concentration (%)


285.21


Wl Uncorrected
* Corrected
R = 0.997



S4 #


nm Mg I


R14


Z8


0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
Mg Concentration (%)

Figure 5-13. Experimental calibration plots of Mg using eight Al-alloy standard samples
with and without correction for self-absorption at (a) Ionic line 280.27 nm and
(b) atomic line 285.21 nm. Gate width: 0.1 ps; delay time: 2.0 ps; pulse
energy 905 mJ. The dotted lines connecting the uncorrected data are meant
as a visual aid while those drawn through the corrected data correspond to
the best linear fit. [From ref.166, reproduced with permission].


130


Cn

0
0
m
C-


1.0

0.8

0.6

0.4

0.2

0.0


C/)

0
C)
0O



o)
C-
C/
(2


0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0














0
0



0
-O

C

'-


0


3.5-

3.0-


2.5-


2.0-

1.5-


1.0-

0.5-


Eo Mg I 285.21 nm
SMg II 280.27 nm


za


R14
S S4
AA3
B8
D33
SV14


I
I


0.0 0.2 0.4 0.6 0.8 1.0 1.2
Composition of Mg (%)


Z8 R14 S4 AA3 B8 D33 V14 D28


Al alloy samples


Figure 5-14. Variation of the calculated correction factor KA,corr (evaluated at the line
center) for the Mg atomic (open squares) and ionic (open triangles) lines for
each Al alloy sample measured. The insert indicates the magnesium content
of each sample. The error bars reported were calculated assuming a
maximum error of 10 % for each correction factor (see text for discussion).
[From ref.166, reproduced with permission].


131


4 ,










Table 5-1. Elemental percentage composition of South African aluminum alloy
standards disks (APEX Smelter Co., South Africa). [From ref.166, reproduced
with permission].
D28 V14 D33 B8 AA3 S4 R14 Z8 SM10
Al 81.55 86.74 84.92 87.98 69.14 83.79 79.59 78.79 84.67
Si 9.66 6.2 8.54 2.33 17 1.03 14 0.84 2.92
Mg 0.004 0.025 0.038 0.076 0.2 0.35 0.87 1.27 1.08
Cu 1.76 4.05 2.89 6.95 8 2.64 2.05 16.05 2.8
Zn 3.6 0.42 0.59 0.52 3.2 10.9 0.48 0.79 5.45
Fe 0.98 0.9 1.15 0.8 1.77 0.119 0.63 1.09 1.96
Mn 0.59 0.58 0.4 0.4 0.21 0.38 0.92 0.26 0.295
Ni 0.43 0.33 0.5 0.5 0.106 0.18 0.97 0.53 0.065
Ti 0.033 0.17 0.055 0.16 0.078 0.12 0.16 0.17 0.055
Cr 0.21 0.18 0.047 0.17 0.1 0.13 0.11 0.15 0.2
Sn 0.3 0.28 0.048 0.155 0.12 0.15 0.12 0.26
Pb 0.34 0.14 0.165 0.08 0.13 0.1 0.245


132









Table 5-2. Selected spectral line and corresponding spectroscopic information of the
investigated elements(a). [From ref.166, reproduced with permission].
Wavelength, Ao0 El Eu Au.
Species (nm) (eV) (eV) gu (108 s1)
Cu I 282.44 1.39 5.78 6 0.08
Cu 296.12 1.39 5.58 8 0.04
Cu 324.75 0.00 3.82 4 1.37
Cu 327.40 0.00 3.79 2 1.36
Cu I 465.47 5.08 7.74 8 0.42
Cu I 510.55 1.39 3.82 4 0.02
Cu I 578.29 1.64 3.79 2 0.02
Cu II 221.02 3.26 8.86 5 1.58
Cu II 221.81 2.83 8.42 3 3.41
Cu ll 222.88 2.98 8.54 1 4.11
Cu II 224.27 3.26 8.78 5 1.58
Cu II 224.70 2.72 8.23 5 3.70
Cu II 227.63 2.98 8.42 3 0.60
Cu II 229.43 2.83 8.23 5 0.25
Fe 358.12 0.86 4.32 13 1.02
Fe 361.88 0.99 4.42 7 0.73
Fe 371.99 0.00 3.33 11 0.16
Fe 373.49 0.86 4.18 11 0.90
Fe 373.71 0.05 3.37 9 0.14
Fe 374.56 0.09 3.40 7 0.12
Fe 411.85 3.57 6.58 13 0.58
Fe II 258.59 0.00 4.79 8 0.81
Fell 259.94 0.00 4.77 10 2.20
Fell 261.18 0.05 4.79 8 1.10
Mg I 285.21 0.00 4.35 3 4.91
Mg II 279.08 4.42 8.86 4 4.01
Mg II 279.55 0.00 4.43 4 2.60
Mg II 279.80 4.43 8.86 6 4.79
Mg II 280.27 0.00 4.42 2 2.57
Mnl 403.08 0.00 3.08 8 0.17
Mn I 403.31 0.00 3.07 6 0.17
Mn 1 403.45 0.00 3.07 4 0.16
(a) From NIST Atomic Spectra Database,
http://physics.n5ist.gov/Phys.RefData/ASD/htm I. ref. html


133









CHAPTER 6
A COMPARISON OF SINGLE VERSUS DOUBLE PULSE LASER-INDUCED
BREAKDOWN SPECTROSCOPY

Introduction

Laser-induced breakdown spectroscopy (LIBS) is a useful tool for determining the

multi-elemental composition of a solid or liquid sample. Especially, the interaction of a

pulsed laser beam with solid materials is attractive to the scientific community for its

potential applications, including material treatment, physical and chemical analysis,

photo deposition, depth profiling and many other areas due to its advantages such as

fast response, high sensitivity and the wide range of materials that can be investigated

with simple sample preparation and experimental set-up. Despite the apparent simplicity

of the experimental apparatus used and of the work devoted to the spectroscopic study,

the processes involved in the interaction of laser with solid matter are rather complex,

up to now not completely understood and still under intensive investigation. Moreover,

one of the main limitations of LIBS concerns its lack of sensitivity [140, 141] when

compared to several competing atomic spectroscopic techniques such as inductively

coupled plasma atomic emission spectrometry (ICP-AES) or inductively coupled plasma

mass spectroscopy (ICP-MS). Double-pulse LIBS is one way to overcome this problem,

where the laser pulses are separated by a short delay time of the order of microseconds,

and has been introduced without any loss of reliability [142, 143]. In some cases, it is

expected that the use of the double-pulse method can lead to lower detection limits,

enhanced and longer sustained emission signals [144, 145] and internal standardization

[146].

The double pulse approach was first suggested by Piepmeier et al. [54] in 1969

and Scott et al. [55] in 1970. They suggested that, because a large portion of laser


134









energy is absorbed by the plasma plume, the second laser pulse could lead to further

excitation of species in the plasma. In 1984, Cremers et al. [56] performed a detailed

study of the possible applications of the laser double pulse technique for analytical

purposes. Since the initial study by Cremers et al. [56], many efforts have been devoted

to characterization of the mechanisms of the double pulse signal enhancement. Several

geometries of the laser beams have been considered. Most representative/ common

double pulse geometries have been based on collinear beams [56, 146-152] and on

orthogonal beams [141, 153-157] as shown in Figure 6-1. In the so-called collinear

geometry, the two laser pulses have the same axis of propagation. Otherwise, in the

orthogonal geometry, the two laser beams are directed by 90 degree with respect to

each other. It has been also differentiated by two configurations: the reheating scheme

and the pre-ablation air spark double-pulse scheme depending on which of the laser

pulses first reach the sample surface. In the reheating scheme, the second pulse

parallel to the target surface reheats the plasma induced by the first laser pulse [141,

153]. Otherwise, in the pre-ablation spark double-pulse scheme [154-157], the first laser

pulse is used to create an air spark above the sample surface resulting in a rarified

ambient environment in which the plasma generated by the second laser pulse can

expand to a larger size [140, 141, 153, 158]. These two configurations have been

successfully used to improve LIBS sensitivity for various matrices such as liquids [56,

148, 149] and a variety of solid samples [150] such as steel [146], aluminum [147],

brass [153] and glass [156]. The papers dealing with the collinear geometry

demonstrated an increase in intensity of emission lines, ranging from a factor of 2 [146]

up to 100 [147].


135









The enhancement in spectral line emission intensity of double-pulse LIBS depends

on several parameters: laser wavelength, interpulse delay time between the laser

pulses, ranging from a few tens of ns to several tens of ps, the distance between the

sample surface to the air spark, plasma density, etc. In particular, the time delay

between the two pulses is one of the most useful parameters to effectively tailor the

experimental conditions and to properly take advantage of different physical

characteristics of the expanding plume, as observing the long relaxation time of the

plasma, even in the milliseconds scale [159].

While readily implemented, the mechanisms and physics associated with double-

pulse LIBS that account for enhanced signal intensity are not yet clearly understood.

The aim of this work, based on the use of spectroscopic methods for the diagnostics of

the laser-induced plasma originated by a double-pulse laser beam, is to study the

coupling of laser light with plasma, to find the optimal conditions for the enhancement of

emission lines as a function of several parameters, and to study possible dynamical and

physical mechanisms in single- and double-pulse configuration. In particular, the

derivation for the expression of the emission intensity for a given line in a LIBS plasma

and the ratio of the double-pulse to the single-pulse intensity in terms of the

fundamental plasma parameters can be used to obtain useful physical information on

the change of plasma conditions between single- and double-pulse irradiation.

Experimental

Laser and Detector System

An experimental diagram for the double-pulse LIBS system used in all

measurements is shown in Fig. 6-2a. In order to analyze the processes of laser ablation

and plasma formation obtained in the orthogonal double-pulse LIBS configuration, two


136









different types Nd:YAG lasers were used. The laser used for sample ablation (Quantel

Brilliant Q-switched Nd:YAG laser, 360 mJ maximum pulse energy at 1064 nm,

maximum repetition frequency of 10 Hz, and pulse duration of 6 ns) with approximately

90 5 mJ/pulse was focused by a quartz lens (10 cm focal length). The laser used for

air spark beyond the sample surface (Laser photonics, YQL-102+ of pulsed Nd:YAG

laser, 200 mJ maximum pulse energy at 1064 nm and maximum repetition frequency of

20 Hz) with approximately 100 mJ/pulse in order to achieve the large signal

enhancements reported here was directed parallel to the sample and focused by a

quartz lens (5 cm focal length). Both lasers were operated at 1 Hz for the experiments

described here. All measurements were performed at ambient pressure. A controlled

stream of air was used to carry away the dust plume formed during the interaction.

The delay time between two laser pulses was changed by means of a delay

generator (SR250 Boxcar) and monitored using an oscilloscope (Tektronix, TDS

3012B). The delay generator enabled the two lasers to be fired simultaneously or have

a variable delay introduced between the two pulses. The measured temporal jitter of

each laser pulse with respect to the other was within 200 ns. The plasma generated by

the laser beam in air is referred to as the "pre-ablation air spark" since the plasma was

formed in the air above the sample and did not come in contact with the sample surface.

The laser beam for pre-ablation air spark was focused to a point above the sample

surface that coincided with the plasma that was generated by the ablation beam from a

sample. In the reheating scheme, the air spark was created after plasma formation. The

laser timing is often referred to as a negative time for the pre-ablation air spark pulses

prior to the arrival of the ablation pulse at the sample, but as a positive time for


137









reheating pulses after the ablation event. The distance from the sample surface to air

spark (hereafter named "d ") was varied in the range 0.1 4.5 mm by slightly shifting

the lateral position of the parallel beam lens for making the air spark at a fixed focal

length distance for plasma ablation.

A 5.0 cm diameter quartz lens, with a focal length of 7.5 cm, was used to collect

the plasma emission and to produce a one-to-one image of the plasma onto the

entrance slit of the monochromator. An adjustable iris was positioned close to the lens

in order to match the F-number of the spectrometer (F/6.5 system). A 35 pm slit width

was used in all cases. The spectrometer (Acton triple grating, 0.5 m focal length) was

equipped with three gratings (1200, 2400, and 3600 grooves/mm), providing a

reciprocal linear dispersion of 1.57, 0.72, and 0.41 nm/mm, respectively. In the present

work, the 2400 grooves/mm grating was used. The spectrometer has a typical spectral

coverage of ~ 10 nm and a spectral resolution of 0.03-0.05 nm. The detector is an

intensified CCD (ICCD 5764/RB-E, Princeton instruments) with a photosensitive area of

576x384 pixels, corresponding to (12.7x8.4) mm2. The ICCD is operated by its

controller (ST-138, Princeton Instruments) and by a pulse generator (PG-200, Princeton

Instruments), allowing the choice of the gate width and of the delay time for time-

resolved acquisition. The gate width and the delay time between the laser pulse and the

beginning of the acquisition could then be adjusted in order to maximize the signal-to-

background and the signal-to-noise ratio.

The data acquisition was controlled with the Winspec32 software (Version

2.5.18.2, Princeton Instruments).


138








Triggering System

In double-pulse work, the triggering system is more complicated than that used for

single-pulse experiment. The pre-ablation air spark and reheating double-pulse scheme

have different triggering systems. Figure 6-1 b shows the different triggering diagram for

each scheme. A more detailed explanation is given in the following section.

Results and Discussion

Optimization

Among configurations of multi-pulse LIBS, we describe here an orthogonal double

pulse LIBS technique: i.e., an orthogonal pre-ablation air spark and an orthogonal

reheating scheme. For selection of optimal plasma conditions in the double-pulse

arrangement detailed analysis of the complex spatial and temporal structure of the

laser-induced plasma is needed. In particular, the time-space plasma characterization is

important for clarifying the main mechanisms of the plasma occurring by these two

double-pulse configurations.

The samples used in this study were NIST 603 aluminum standard reference

materials (SRMs) and South African AA1 aluminum standards. For all measurements,

the Al II line at 281.62 nm (59,852 95,351 cm-1), Mg II line at 279.08 nm (35,669 -

71,491 cm-1), 279.55 nm (0 35,761 cm-1), 280.27 nm (0 35,669 cm-1) and 292.86 nm

(35,669 69,805 cm1 ) and Mg I line at 277.83 nm (21,850 57,833 cm-1) 277.98 nm

(21,870 57,833 cm-1), 278.30 nm (21,911- 43,371 cm-1) 285.21 nm (0- 35,051 cm-1),

Mn II lines at 257.61 nm (0 38,807 cm-1), 259.37 nm (0 38,543 cm-1), 260.57 nm (0 -

38,366 cm-1), 293.31 nm (9,473 43,577 cm-1), 293.93 nm (9,473 43,485 cm-1) and

294.92 nm (9,473 43,371 cm-1) and Mn I lines at 279.48 nm (0 35,770 cm-1), 279.83

nm (0 35,726 cm-1), 401.81 nm (17,052 41,932 cm-1), 403.08 nm (0 24,802 cm-1),


139









and 405.55 nm (17,282 41,933 cm-1) were chosen for the optimization study. The

compositions of the major components and spectral information pertinent to the

transitions used in this work are reported in Tables 6-1 and 6-2.

In our work, the laser pulse energy for ablation from the sample was set at 90 5

mJ; the laser pulse energy for the air spark above the sample surface was changed to

obtain the highest signal enhancement (100 5 mJ) and then all measurements were

performed with the two fixed laser pulse energies at atmospheric pressure. Therefore,

the major parameters for optimization were only for the distance (= d) from a sample

surface to air spark above a sample and interpulse delay time (= At) between the two

lasers.

Optimization for pre-ablation air spark double-pulse scheme. In the

orthogonal pre-ablation air spark double-pulse scheme the detector (ICCD 5764/RB-E,

Princeton instruments) was controlled by the Quantel Brillant Nd:YAG laser used for

plasma formation from a solid sample (see Fig. 6-2b). The time-resolved studies were

performed by controlling the small gate width tw (time during which the spectra were

integrated), the gate delay time td (time from which the spectra were acquired by the

detector) and the delay between two laser pulses At by delay generators (SR250

Boxcar) at the optimum distance d. In the study, the laser pulse for plasma formation (or

ablation pulse) was used as the time reference and hence pre-ablation air spark pulses

were described with a negative sign, while reheating pulses were positive relative to the

ablation pulses.

LIBS signal enhancement versus the interpulse delay time (At, up to 100 ps) for

the several different distances (d, 0.3 2.5 mm) is reported in Fig. 6-3 for the NIST Al


140









SRM 603 sample. The signal enhancement strongly depends on the distance (d) and

interpulse delay time (At) as shown in Fig. 6-3. These two experimental parameters

significantly affected the LIBS signal enhancement in our result. From the result, large

enhancements were observed around the interpulse delay time of 30 ps and distance

d of 0.5 mm from the sample surface for several spectral lines (see the region of the

highlighted gray color in Fig.6-3).

For checking the reproducibility of the signal enhancement, similar experiments

were also performed for the Al alloy AA1 sample. Figure 6-4 shows the LIBS signal

enhancements of several spectral lines at the optimized parameters in both NIST

aluminum SRM 603 and South African aluminum AA1 sample. The reproducibility of the

line intensity was 10 + 2 % depending on the distance (= d) and interpulse delay time

(At). When the pre-ablation air spark was brought in too early before the ablation pulse

(e.g., between -100 and 50 ps) or when the two pulses were too close together in time

(e.g., between 5 and -1 ps), smaller enhancements were observed, as shown in Fig.6-

4a and 6-4c. At short delay times in pre-ablation air spark double-pulse LIBS, the high

electron densities formed early by air plasma interrupt plasma formation from a sample

because they can absorb a large fraction of second laser pulse (or ablation pulse from a

sample) before it reaches the sample surface. Otherwise, at the optimum interpulse

delay time, where large enhancement are observed, the air spark formed by the first

pulse can have appropriate time to expand and cool before the ablative pulse is fired,

resulting in large LIBS signal enhancements. However, if the time interval between the

two laser pulses is too long, no enhancement will be observed since decreased plasma

shielding or the rarified air effect generated by the pre-ablation air spark no longer exists.


141









As mentioned above, in our experimental conditions, the largest enhancements were

observed at an interpulse delay time of ~ 30 ps in both samples. Optimized distance d

was in the range between 0.3 0.7 mm as can be seen from Fig. 6-4b and 6-4d. We

assume the lateral length of entire plasma is approximately 1.0 1.5 mm, which means

the pre-ablation air spark was focused to a point above the sample surface that coincide

with the center of the sample plasma that was generated by the ablation laser beam. In

addition, it is very interesting point that neutral lines with low excitation energy levels ,

e.g. Mg I lines at 285.21 nm (0- 35,051 cm-1), and Mn I line at 279.48 nm (0 35,770

cm1) have a relatively small enhancement compared to ionic lines with high excitation

energy levels for the same interpulse delay (Fig. 6-4).

Under the optimized conditions (e.g., d ~ 0.5 mm: At ~ 30 ps: laser pulse energy

for plasma formation from a sample ~ 90 5 mJ: laser pulse energy for air ablation ~

100 5 mJ), the use of orthogonal pre-ablation air spark double-pulse LIBS results in

larger signal-to-noise ratio, corresponding to larger sensitivity and lower detection limits,

as compared to conventional LIBS (single-pulse LIBS). The Al II line at 281.62 nm

(59,852 95,351 cm-1) and Mg I line at 285.21 nm (0- 35,051 cm-1) in an Al alloy

sample (NIST SRM 603) were chosen for assessing of the improvement of signal-to-

noise ratio (S/N) with the use of double-pulse LIBS. A significant LIBS signal

enhancement in the aluminum ionic line was recorded up to a 5.0 ps delay time, as

observed in Fig. 6-5. On the contrary, the resonance line, Mg I line at 285.21 nm (0-

35,051 cm-1), was found to have less enhancement. Based on the results, the signal-to-

noise (S/N) ratio was calculated for both atomic and ionic emission peaks at each delay

time (from 0.5 ps to10 ps). For calculation of S/N ratio, the analyte signals averaged by


142









50 laser shots were taken as net intensities at each emission peak, while the

background noises were taken from the root-mean-square (RMS) intensities of the

featureless continuum emission adjacent to each peak for 50 laser shots. For the Al II

line at 281.62 nm, the signal-to-noise (S/N) ratio was improved significantly by a factor

of 6 at 2.5 ps delay time; otherwise, for the atomic resonance line (Mg I line at

285.21nm), it led to a reduced S/N ratio and even worse with less or no LIBS signal

enhancement in Fig. 6-6. Thus, one can conclude that signal enhancement with

orthogonal pre-ablation air spark double-pulse LIBS results in the improvement of

signal-to-noise (S/N) ratio, corresponding to larger sensitivity and lower detection limits,

but only for particular spectral lines.

Optimization for reheating double-pulse scheme. For the reheating double-

pulse scheme, the detector (ICCD 5764/RB-E, Princeton instruments) was controlled by

Laser Photonics laser used for reheating of the plasma. The reason why we have used

the different triggering systems is that our interesting point is the time-resolved study of

plasma evolution in the reheating scheme as well as pre-ablation air spark scheme. If

the detector with some delay time, e.g. td = 2 ps, is controlled by the Quantel laser as

the pre-ablation air spark scheme, we should have only large averaged measuring or

integration time, e.g. tw = 30 ps, for the time-resolved study during the plasma decay

(see Fig.6-7). For example, figure 6-8 shows the enhanced signal intensities at the

different interpulse delays with the shorter integration time (tw= 0.1 ps) and longer

integration time (tw = 30 ps) in the reheating scheme with the triggering system

controlled by the Quantel laser. As shown in Fig. 6-8a, if the short integration time, e.g.

tw= 0.1 ps, was chosen in the triggering system controlled by the Quantel laser, there


143









are no enhancements after the interpulse delay time of 2.0 ps because time (td) from

which the spectra were acquired by the detector was set by 2 .0 ps, which means there

are no double-pulse effect after interpulse delay time (At) of 2.0 ps if the delay time (td)

is set to 2.0 ps (see Fig. 6-7a). If a large averaged integration time, e.g., tw = 30 ps, is

used, this problem can be solved. As shown in Fig. 6-8b, an enhancement was still

detected by a factor of 2 after an interpulse delay time of 2.0 ps. However, our study

focuses on time-resolved plasma spectroscopy. In order to overcome this problem in

our system, the Laser Photonics laser used for the reheating or re-exciting the plasma

was used to control the detector (ICCD 5764/RB-E, Princeton instruments), which

means that the emission signal could be obtained after this laser fired (see Fig. 6-2b).

One of the advantages in this triggering system is that we can easily check

experimentally whether sample ablation from the laser pulse for reheating occurs or not.

The image of the air spark created in air a few millimeters from the sample surface can

be observed with the ICCD camera even without plasma formation from the sample

because the detector was controlled by the laser pulse for the air-spark (see Fig. 6-9).

Figure 6-1 Oa shows a schematic of the time-resolved plasma study (tw = 0.1 ps) with the

triggering system controlled by the Laser photonics laser with the reheating double-

pulse scheme. As mentioned above, this triggering system is very useful for the time-

resolved plasma study because we can easily reheat or re-excite the plasma at specific

decay times during plasma evolution by changing the interpulse delay time between the

two pulses (see Fig. 6-10). In order words, one can adjust/or determine selectively the

reheated or re-excited position by changing the interpulse delay in our system. In our


144









study, the time-resolved plasma study was performed at a fixed ICCD delay time (td),

but at variable interpulse delay times (At) for the reheating scheme (see below).

For optimization of the reheating scheme, the LIBS analyses were also undertaken

with the NIST Al SRM 603 sample. As mentioned in Fig. 6-10 Ob, it is very clear that as

the interpulse delay between the two lasers increases, the plasma is gone between 20

and 30 ps. As described above, the time-resolved studies were performed using a fixed

gate width (tw= 0.1 ps) and gate delay time (td = 1.0 ps) for all measurements. The Q-

switch in the Laser Photonics laser is used to "dump" the beam out of the cavity after

some time delay. In our system for the reheating scheme, the laser output pulse

(reheating pulse) was generated at 800 ns after the regular Q-switching as shown in

Fig. 6-11. This is why the gate delay time in the reheating scheme was chosen to be

after 800 ns.

As mentioned above, the interpulse delay time At and the distance d from the

sample surface are important factors affecting the LIBS signal enhancement. Therefore,

the distance d was changed for several interpulse delay times for the optimization of the

reheating scheme as can be seen in Fig. 6-12. For all measurements, the reproducibility

of the line intensity was 5 0.5 % depending on the distance. The optimum distance (d)

from the sample surface to air spark was about 3.0 mm. In the reheating double-pulse

scheme, the LIBS signal enhancement was more affected by the distance d in

comparison with the pre-ablation air spark scheme. In addition, a significant

enhancement was observed with the increase of the interpulse delay time whatever the

distances (d) and transition lines are, as can be seen in Fig. 6-12. For checking the

reproducibility of the signal enhancement, a similar experiment was also performed for


145









Mn I and II lines in the Al alloy D28 sample. From Fig. 6-13, it is evident that the

interpulse delay time strongly affected the signal enhancement since a markedly high

DP/SP value was observed as the interpulse delay time increased. It can be explained

that the enhancement occurs at long delay times of plasma because most atoms can be

easily excited after plasma cools down. In addition, as observed in the pre-ablation air

spark scheme, neutral lines with low excitation energy levels, e.g., Mn I lines at 403.08

nm (3.075 eV), 401.81 nm (5.199 eV) and 405.55 nm (5.199 eV), have a relatively small

enhancement compared to ionic lines with high excitation energy levels for the same

interpulse delay in the reheating scheme in Fig.6-13. For the reheating scheme, the

greatly enhanced ionic emission intensities at the Al II 281.62 nm line at long delay

times (e.g., 9.0 ps) also result in improved signal-to-noise (S/N) ratios as can be seen in

Fig. 6-14.

Time-gated, Spectrally Resolved, One-direction Images in Single and Orthogonal
Double Pulse Pre-ablation Scheme

For this study, detailed information about density distributions of excited atoms

and ions in the expanding plasma of Al alloy sample was obtained by using the imaging

detection system in both the orthogonal pre-ablation air spark and reheating schemes.

Most of the emission lines detected were assigned to Mg, Al, Cr ions and atoms.

Spectrally resolved, time-resolved one-dimensional spatial (along the longitudinal

direction from the target surface) images of the expanding plasma from an Al alloy

sample are shown in Fig.6-15 (for pre-ablation air spark) and 6-16 (for reheating). The

left sides of Fig.6-15 and 6-16 show images for plasma produced by single-pulse

ablation regimes; while, images on the right side show the plasma ablated in the

orthogonal double-pulse pre-ablation air spark and reheating scheme. The vertical axis


146









corresponds to the plasma expansion which is generated from the sample surface (at z

= 1.0 mm in Fig.6-15 and 6-16); the horizontal axis represents the wavelength of the

emitted light. In the pre-ablation air spark scheme the gate width (tw) and interpulse

delay time (At) between the two laser beams were respectively 0.1 ps and 30 ps and

the distance (d) from the sample surface to the air spark was about 0.5 mm. In the

reheating scheme, the gate width (tw) and ICCD delay time (td) were 0.1 ps and 1.0 ps,

respectively, and d was about 3.0 mm based on the previous experiment for the

optimization. The magnification of all images, which was obtained by integrating the

sliced plasma plume (10 pixels) along the line of sight, was kept constant to assure

comparability of the recorded images.

In the orthogonal double-pulse pre-ablation air spark scheme the different stages

of the plasma expansion vertically from the sample surface (z = 1.0 mm) at the several

delays can be seen from the Fig. 6-17, which was obtained from the images in Fig. 6-15.

In the early stage of expansion (0.5 1.0 ps delay time) with the single-pulse regime the

plasma plume shows strong continuum emission and remains in contact with the

surface expanding above the sample surface as shown in Fig. 6-15. At the later stage of

the plasma evolution each individual emission lines can be easily identified, and the

plasma plume expands slightly. The maximum value in terms of the vertical direction of

the plasma plume was gradually increased by about 1.0 mm as the delay time

increased from 0.5 ps to 8.0 ps in Fig. 6-15. Otherwise, the presence of the pre-ablation

air spark laser pulse caused significant changes both in plume dynamics and emission

intensities of plasma. One of the interesting points is that in the double-pulse

configuration the plasma plume expands farther from the target surface at the early


147









stage of expansion and then comes back to the target surface after some delay time

(See in Fig.6-17) which is the opposite trend, in comparison with the single-pulse

configuration. This result can be explained with the fact that the plasma plume in the

case of double-pulse ablation is more separated from the sample surface in the

beginning of plasma formation compared to the case of the single-pulse ablation. From

the observed plume dynamics, the enhancement factor for line emission strongly

depends on the spatial distribution of the plasma plume. Therefore, some well defined

distances along the vertical plume should be used in order to quantify the enhancement

factor. For example, for the plasma zone (z = 2.5 mm region) located at a distance of

1.5 mm above the target surface (z = 1.0 mm) the enhancement factors depending on

the delay time after plasma formation were changed by a factor of 1 to 4 in Fig. 6-17.

That is, the enhancement factor had a tendency to decrease in the plasma zone near

the target surface and to increase at some distance from it at all delay times. In addition,

the recorded spectra in Fig. 6-17 show the spatial distributions of the excited atom and

ions in the vertical direction of the plume expansion. The plume originated from double-

pulse beam farther from the target along the z axis. The faster expansion in the double-

pulse configuration most probably results from the rarefied ambient atmosphere caused

by the first laser pulse for the pre-ablation air spark. Lower gas density in air allows a

larger plasma expansion and spatial dimension of the plasma plume within the same

time interval. This indicates that the second laser pulse initially interacts with the sample

surface under the good condition of rarefied ambient atmosphere, which is why the

plasma plume expands farther from the target surface at the early stage of expansion in

the orthogonal double-pulse pre-ablation air spark scheme. The plasma in air produced


148









by first laser beam decays within a few microseconds and its density will tend to be

much higher. Moreover, it is interesting to compare the expansion dynamics for different

plasma species present in the plume. The lines with relatively low excitation energy

levels, e.g. Mg I line at 285.21 nm (0 35,051 cm-1), have less enhancement compared

to the lines having higher excitation energy levels.

Similar experiments were performed in the orthogonal reheating scheme. As

mentioned above, Figure 6-16 shows time-gated spectrally resolved one-dimensional

images in the single and orthogonal reheating double-pulse schemes (tw = 0.1 ps: td =

1.0 ps: d = ~ 3.0 mm). A continuous spectrum for the reheating of the plasma plume

could be observed above the individual emission lines (see the right side images in Fig.

6-16(g) (I)) because the optimized distance d from the sample surface to the ablation

spark in air was about 3.0 mm. From Fig. 6-18, a little bump in the plasma zone (z = 4.0

- 5.0 mm region) located at a distance of 3.0 4.0 mm from the target surface (z = 1.0

mm) is evidence of ablation in air. Contrary to the pre-ablation air spark scheme, the

maximum value in terms of the vertical direction of the plasma plume was kept constant

(z = 2.0 -3.0 mm region) in all interpulse delays as shown in Fig. 6-18. In addition, the

images taken at all delays were more homogeneous and the plasma dimension

remained approximately constant, but the intensity of spectral lines gradually decreased

with increasing delay time. The enhancement of the emission lines did not occur until

2.5 ps. However, after 4.0 ps, a relatively strong increase in intensity could be observed.

That is, the enhancement factor had a tendency to decrease in the beginning of plasma

formation (short delay times) and then to increase after the plasma cools down in the

reheating scheme. The physical mechanisms involved in the reheating scheme and in


149









the pre-ablation air spark double-pulse scheme seems to be different. As the reheating

pulse directed in the plasma does not ablate further matter, the observed

enhancements may not be linked to an increase of ablated matter. Scanning electron

microscope (SEM) images in Fig. 6-19 were used to verify the physical mechanisms

between the reheating and pre-ablation air spark scheme. In the reheating scheme, the

observed enhancements are related to something else, not an increase of ablated

matter due to a rarefied air as in the pre-ablation air spark scheme. As mentioned in the

previous section, the reheating scheme induced improvements for lines coming from

high excitation energy levels, whereas neutral lines originating from low excitation

energy levels experienced decreases in intensity (see Fig. 6-13). Details of the study for

ablated mass will be discussed in the next section.

Spectroscopic Study of the Factors Concurring to the Intensity Enhancement in
Double-pulse LIBS

In this section, we focus on a spectroscopic study of the factors related to the

intensity increases in order to understand the physical mechanisms. The origin of the

LIBS signal enhancement is commonly attributed to an increase of ablated matter from

the target or to plasma reheating. It is worthwhile to derive both the expression of the

emission intensity for a given line in a LIBS plasma and the ratio of the double-pulse

intensity to the single-pulse intensity in terms of the fundamental plasma parameters.

The emission signal obtained with double- and single-pulse irradiation was here studied

in the approximation of a homogeneous spherical plasma in LTE.

Derivation of the analytical formula for the enhancement. The intensity of a

spectral line, integrated over the wavelength profile, can be written as follows:


150









-E,, kBT E,, kBT
= pneutra la. ."asma l Tu eurlAT plasma. plasma atom. neuo a l .eeutrE,A I T (6-1)


where the meaning of symbols is defined on the list of symbols. The efficiency response

of the instrument is neglected and the volume of plasma (T) is set as unity. Note that

Eq. 6-1 is the result of integration over the emission line-of-sight, assuming a spatially

homogeneous atomic distribution. The following quantities are supposed to vary from

single- to double-pulse case:

neutral" e- k IkB n, UE B tralA (T) (6-2)

Therefore, the ratio of the double-pulse to single-pulse intensity of a neural line obtained

from the same sample can be expressed as:

plasm ar plasm a A neutral,A Uneutral,A (T ) E 1 I
R DP __ DP DP A DP A DP SP kB [ TDP (6-3
neutral plasmar plasma neural neutral (T (6-3)
ISP n SP SP ASP s p DP )

By taking the logarithm in Eq. 6-3

Splasma. r plasma .. A neutral,A u neutral,A (TS 1 1 r
In Rt = In rI DP DP DP + In DP -DP
neutral plasm plasma A neutral,A Aneu"(tral,. k TDP (6-4)
"Sp SP S SSP SP F k DP B D sp
= aA +aneutral,A + bE


where aA is a constant term for any line of the analyte A, a n,,eura,,A is a constant term for

any line of the neutral species of A and b is a constant term for any line of any element

in the plasma.

Similarly, for an ionic line, the intensity enhancement can be also expressed as

follows:

plasmajr plasma A onicA U'oncA (TSP E 1 1
S DP I DP DP %DP DP ATu SekB TDP sp (6-5)
lonic S plasmarp lasma A ionic,A U icA e )
ISP nSP XSP asP SP


151










where all symbols are also defined on the list of symbols. By taking the logarithm in Eq.

6-5, the expression of the ratio can be modified by the equation having the useful terms:

plasmar plasma A. iomc,A U Tomc,n A (TP ) E(1 1
SF XSF %SP SS TT) _
lRI oc n DP DP DP +-ln
...rplasmaVP asma A io.ncA Aoic,.4 p ) p T SP\ (6-6)
= aA +aomc, A +bE,


Here, the constants aA and b are the same as in Eq. 6-4. The term acA is a constant

for any line of the ionic species of the analyte A. The ionized fraction of the analyte can

also be expressed in terms of the corresponding neutral fraction under the assumption

of plasma composed only by neutral and singly ionized atoms as follows:


a ionc, A = neutral,A A k ,a T) (6-7)



where k ah is the expression of the Saha equation:


kA (2nZmkBT)3 2 2U oncA (T) eEn/ kBT (6-8)
Saha h 3 uneutralA (T)


The expression of the enhancement of a neutral line in Eq. 6-5 can be also modified by

the useful expression with the constant terms, e.g. a a An and b which are the same

as defined in Eq. 6-4, by substituting Eq. 6-7 into Eq. 6-5 as follows:

S plasma plasma A neutral,A A e Tiomc,A \
Rin IcDP nDP P DP DPDP ksaha(TSP) SP (TSP) e kB TDP SP (6-9)
onic nplasmaVplasma A neutral,A kA (T e u ionmcA (T )
SP SP SP AXSP SP Saha DP ) DP DP

By inserting the expression of Saha equation k ha in Eq. 6-8 into Eq. 6-9:


plasmaVpr lasma A neutral,A e Tiomc,A 3/2 E ,+EJ 1 1
R IDP DP DP DP DP nSP u TSP) TDP TsDP (6-10)
oc plasma r plasma,, A neutral,A e v iomc,.A (T e (6-10)
I SP SP SP A SP SP n DP DP SP


152









By taking the logarithm in Eq. 6-10 the expression for the logarithm of the ionic line

enhancement can be comparable to that for the logarithm of the neutral line

enhancement (see Eq. 6-4) as follows:

plasma plasma A ionic,A UTonic,A T. A 1
In =n Dp DP XDP +ln CDP J (s -E 1
po cama V plasma A ....cA U .. cA T DP k T D
nSPp' SP sP asp u (TDP) k B TDP TSP

+ -In DP + ln (6-11)
L2 TSp) \nDP)
=aA +neutralA +b(E +E n) +c

In this expression, the constant terms aA ,aneutal,A and b are the same as defined in

Eq. 6-4. The constant c only depends on two plasma parameters such as the

temperature and electron number density in both single and double pulse cases.

Therefore, the derived expressions for the logarithm of the ionic and neutral line

enhancements can be easily used to obtain useful physical information on the change

of plasma conditions in between single and double pulse irradiation.

Plasma temperature and number density. As mentioned above, the expression

in Eq. 6-11 can be easily exploited to get useful information for plasma parameters such

as plasma temperature and electron number density in passing from single- to double-

pulse irradiation. For this study, some lines (which have different excitation energy

levels) from the same analyte can be selected for the enhancement plot based on the

logarithm of the experimental intensity ratio between single- and double-pulse irradiation.

As in the Saha-Boltzmann plot, the slope and intercept can be found by linear

regression of the experimental points. First of all, the slope in plot has some information

about plasma temperature similar to the Boltzmann or Saha-Boltzmann plot. However,

the slope in this enhancement plot represents the difference of temperature between


153









two plasmas occurring by single- and double-pulse irradiation. Therefore, a positive

slope means that the plasma temperature in the double-pulse spectrum is higher than

that in the single-pulse spectrum as shown in Eq. 6-11. In addition, the constant c term

can be neglected in the hypothesis that both plasma temperature and electron number

density do not change dramatically from SP to DP: that is, all constant terms (e.g.

aA' anetrlA and b ) in Eq. 6-11 will be the same as defined in the expression for the

logarithm of the neutral line enhancement (see Eq. 6-4). In this case, the intensity ratio

of neutral and ionic lines of the same element can be plotted on the same graph,

provided E. + EA,,, is used as the abscissa instead of E, in Eq. 6-6.

Moreover, the y-intercept of the linear regression of points in the enhancement plot

(Eq. 6-11) is related to the degree of enhancement of the total number of analyte neutral

atoms in the plasma, which may arise both from the variation of ionization equilibrium

and from a variation in the ablated/atomized mass. In Eq. 6-11, the first constant term

aA depends on the ratio of the number of analyte atoms in the DP and SP plasmas. If

the ablation can be considered stoichiometric, one would expect that the analyte molar

faction doesn't change from the SP to the DP spectrum. The second term aneutral A

depends on the ionization equilibrium and partition function. It can be easily calculated,

provided the plasma temperature (T) and electron number density (n,) are known. If

this second term aneutralA is calculated, the first term can be also calculated by difference

from the slope obtained experimentally (e.g. a slope is equal to aA +a neutlA). Some

examples from the study will be given below.


154









Example: Results for NIST Al SRM 603 sample. Several mechanisms may be

responsible for the observed enhancement of emission plasma characteristics as a

result of a double pulse laser effect. A number of suggestions in the literature

addressing the mechanisms of enhancement of the double-pulse LIBS signal have been

proposed. However, further study is needed to understand the mechanisms of double-

pulse enhancement. These examples are helpful for studying how the physical

conditions in the plasma are expected to vary as the plasma generate in time in both

single- and double-pulse configurations. The approach described in this section gives

information at a glance on the change of plasma temperature in passing from SP to DP

irradiation in the same sample.

The analytical lines used in the present work were centered at 282 nm both for

Mg I 277.83 nm, 277.98 nm, 278.30 nm and 285.21 nm and for Mg II 279.08 nm, 279.55

nm, 280.27 nm, and centered at 292 nm for Mg II 292.86 nm in NIST Al SRM 603

sample, as listed in Table 6-2. Figure 6-20 shows the enhanced signal intensities at

delay times from 0.5 ps to 10 ps, where the double-pulse intensity enhancement of both

neutral and ionic Mg lines is apparent in (a) the pre-ablation air spark scheme and (b)

reheating scheme. In the pre-ablation air spark all measurements have been performed

at the optimum conditions as described in the previous section for optimization in Fig. 6-

4 (d = 0.5 mm; At = 30 ps). The ratio of DP/SP integral intensity reaches a factor of 8,

depending on the distance from the sample surface and delay time as well as different

excitation lines in Fig. 6-3. In addition, it should be noted that the degree of the

enhancement should be different, depending on the choice of the collection region of

the plasma as mentioned in the previous study. In our study, the LIBS signal


155









enhancement was obtained by spatial integration (the same pixels in single and double

pulse) over the whole plume. Both neutral and ionic lines were used to build the

logarithm enhancement plot, following the representation of Eq. 6-11, but neglecting the

constant term c as mentioned above. The logarithmic plots of neutral and ionic line

enhancements in the pre-ablation air spark scheme are shown in Fig. 6-21. A slope

(=AT) and y-intercept (=q) are presented in each plot. The corresponding spectra for

building the logarithm plots are shown in Fig. 6-22(a, Acenter = 281.5 nm) and (b, Acenter=

292 nm). The temperature difference (AT) and y-intercept (q) between single- and

double-pulse in terms of the delay time are also presented in Fig. 6-23b. For the pre-

ablation air spark configuration it should be noted that a relatively high temperature

difference between the single- and double-pulse was detected at short delay times. This

result corresponds to the enhancement plot in Fig. 6-20a. Otherwise, the slope of the

linear regression is negative at 10 ps delay time (see Fig. 6-21 i and Fig. 6-23b), which

means the increase of intensities observed in the double pulse case cannot be

explained only by a change in the plasma temperature. It is of interest to note that the

strong enhancement at short delay times for the orthogonal pre-ablation air spark

configuration is related to an increase in the temperature, but not at long delay times.

Furthermore, the experimental y-intercept values can be used to get information

on the change of atomized mass. As mentioned in the previous section, both constant

terms aA and aneuwalA in Eq. 6-11 can be calculated from the y-intercept of plot, provided

the plasma temperature (T) and electron number density (ne) are known. Plasma

temperature and electron number density were estimated by means of spectroscopic

measurements. If the plasma is in LTE in each temporal window considered, then the


156









population density of atomic and ionic electronic states is described by a Boltzmann

distribution. By measuring the relative line intensity it is then possible to estimate the

temperature, through the slope of a straight line in the Boltzmann plot. In our study, a

Saha-Boltzmann plot was used for deriving plasma temperature due to the advantage of

using many lines of widely different upper-state energy, as shown in Fig. 6-24.

As mentioned in Chapter 4, the method for the electron number density

measurement using Stark-broadening of selected line was used. The electron number

density relationship to the full width at half maximum (FWHM) of Stark broadening lines

has been given in Eq. 4-12. In this chapter, electron number density has been estimated

for the Al II line at 281.62 nm in single- and double-pulse configuration (see Fig. 6-23c).

The starting value of n, for plasma generated by the double pulse excitation is relatively

lower than in the case of single excitation, but it also changes slowly with time. Overall,

the electron number densities in the double-pulse irradiation are a little bit higher over

the delay time than that in the case of single-pulse irradiation, but not very significantly

so. Therefore, all constants (e.g. aA aneutral,A and c) in Eq. 6-11 could be calculated by

inserting plasma temperature (T) and electron number density (n,) estimated by means

of spectroscopic measurements into Eq. 6-11, but neglecting the constant term c.

Summarized values for them are given in Table 6-3 and 6-4 as well as Figure 6-23. As

shown in Fig. 6-23d, it is very clear that as the delay time increases, the enhancement

of total number density of atoms and ions in the plasma was exponentially increased

until 3.0 ps, which is the time scale of limitation for an enhancement, and then gradually

decreased after 3.0 ps. Thus, the observed enhancements in emission of Mg atomic

and ionic lines for the orthogonal pre-ablation air spark configuration may be the result


157









of increased temperature and total atomic and ionic number density as shown in Figure

6-23 and Table 6-3. It is evident that the pre-ablation spark causes rarefaction in the air

which leads to the increased plasma volume and enhanced ablation observed by the

imaging of the produced plasma (see Fig. 6-25c and 6-25d) and craters (see Fig. 6-

251a and 6-25b) in the single- and double-pulse configuration.

A similar experiment was also performed in the reheating configuration. Figure 6-

12 shows the optimum condition for the reheating double-pulse configuration. The

optimum distance (=d, mm) from the sample surface to the air-spark was set between

1.0 and 3.0 mm, which depends on the interpulse delay time. As the interpulse delay

time decreases, the optimum distance is closer to 1.0 mm as shown in Fig. 6-12.

However, a significant signal enhancement for two lines (see Fig. 6-12a and 6-12b))

was observed for distances d around 3.0 mm reaching a maximum enhancement of ~

40 (@ A II 281.62 nm) and ~ 16 (@ Mg II 270.08 nm) for the longer delay time. It is

manifest that the distance d strongly affects the signal enhancement depending on the

interpulse delay time. This behavior was also observed for several spectral lines by

plotting the LIBS signal enhancement vs. interpulse delay time as shown in Fig. 6-12c.

All measurements were performed under the optimum conditions (d = ~ 3.0 mm; td = 1.0

ps; tw = 0.1 ps). The logarithmic plots of neutral and ionic line enhancements and their

corresponding spectra are shown in Fig. 6-26 and 6-27, respectively. The slope of the

linear regression (= At) was negative until 1.5 ps and then changed to positive as seen

from Fig. 6-26 and 6-28b. It can be explained that the enhancement occurs at the longer

delay time because most atoms can be easily excited after the plasma cools down. The

temperature difference and y-intercept between single- and double-pulse in terms of the


158









delay time are also presented in Fig. 6-28b. Contrary to the pre-ablation air spark

configuration, as the delay time increase, the temperature difference between SP and

DP also increases, which means much stronger enhancement occurs at the longer

delay time. As described above, plasma temperature and electron number density were

estimated by means of spectroscopic measurement (see Figure 6-24 and Table 6-6).

Correlations between LIBS signal enhancement and plasma temperature were found.

In other words, the increase of plasma temperature is possibly the main factor in the

correlation between the excitation energy levels and the increase in emission intensity

enhancement from Mg atoms. Based on known plasma temperature and electron

number density, the change of atomized mass was also calculated for checking another

cause of the enhancement factors as shown from Figure 6-28d and Table 6-5. The

interesting feature observable from Fig. 6-28d is that no significant enhancement of the

number density of atoms and ions in the plasma was detected. Thus, the observed

enhancements in emission of Mg atomic and ionic lines for the orthogonal reheating

configuration are most likely the result of increased temperature.

Conclusions

The aim of this study was to find the optimum experimental condition for the large

enhancement of emission lines as a function of several parameters and to study

possible dynamical and physical mechanisms based on the use of spectroscopic

methods for the diagnostics of the laser-induced plasma originated by a double-pulse

laser beam. The theoretical derivation of the emission lines in a LIBS plasma and the

ratio of the double- and single-pulse intensity in terms of the fundamental plasma

parameters were used to get useful physical information on the change of plasma


159









condition as well as understand the LIBS enhancement. The experimental results are

following:

* In our study, two different schemes in orthogonal double-pulse configuration, i.e.,
pre-ablation air spark and reheating double-pulse schemes, were used. In both
schemes, the optimum conditions for getting large enhancement were different
and the interpulse delay time At and the distance from the sample surface to air
spark d are the most important parameters affecting a LIBS signal enhancement.

* From the study of plume dynamics in laser induced plasma, an enhancement
factor for line emission strongly depends on the spatial distribution of plasma
plume. Thus, some well defined distance along the vertical plume should be used
in order to quantify the enhancement factor.

* The observed enhancements of emission lines for the double-pulse pre-ablation
air spark scheme may be result of increased temperature and total atomic and
ionic number density; otherwise, the LIBS signal enhancements for the double-
pulse reheating scheme result only in increased temperature.


160








Orthogonal configuration


Pre-ablation air spark scheme



<>


Reheating scheme



4=>


(c)


Figure 6-1. Common pulse configurations. (a) Collinear configuration, in which the first
and second laser pulses are both focused on/or into a sample. In orthogonal
configuration, a single ablative pulse is coupled with either (b) a pre-ablation
air spark that is parallel to and up to several millimeters above the sample
surface or (c) a reheating pulse [70].


161


43,


(a)


Collinear configuration






































Figure 6-2(a). Scheme of the set-up showing LIBS system for both single- and double-
pulse operation.


Delay generated here


Trigger IN, +o Taj+ t


.iggne I".Ii BUSY 500
-s4 4 ..OUT


Signal
Lamp IN


Plasma timing of pre-ablation air spark
Sto+ tHP FL-QS -QS-ighL
Plasma timing of ablation
So+tBox1 +tBox2+ At.set QS AS-Lght


Trigger IN, to


ut.1c,to tHP ha a
to+ti, +A1,I

h OUT


Q-Swicch OUT
For pre-ablation air spark
IOT -OU Forreheating

....... ........................
,,, .Mal Sync


Figure 6-2(b). Timing and triggering system used for both pre-ablation air spark and
reheating double-pulse schemes.


162


BUSY 500
ouT
+ t 1Swich + 2 + At"t
= -Swich OUT


Flash lar


Q-Sw


I|


Loe htnc


U'A^^^^^M ~ L- M y^-^^^^^^^






















*~



V
7 V
4 It
'4 ''*1
- 4 47


- 3.0-
a)
E 25-
a)
C.
S2.0-

S1 5-
-i

r 1.0-
CO

S0 5-

0.0-
-


-100 -80 -60 -40 -20 0

Interpulse delay time (ps)


Mgll 280 27 nm


-*-d=0.3 mm
-*-d=0 5 mm
d=1 0 mm
-v d=1.5 mm
d=2 0 mm
-- d= 2.5mm

4^


// i/
-\/' /.*- 3"


/ 1


mm


(b)
- d=O 3 mm
-*-d= 5 mm
d=1 0 mm
-T- d=1.5 mm
d=2 0 mm
d=2.5mm

v< ^ ^
m'^ ~~~~


*I'* 4 4.
4 4


- (a)
. -_-d=0.3mm
6- -*- d= 0.5 mm
d=1.0 mm
5- -- d=1 5 mm
d=2.0mm
4- -4-d=25mm

3-

2- v-T


11 281.62 nm


Al
(d)

--d=0 3 mm
-*- d=0.5 mm
d=1 0 mm
-- d=1 5mm
d=2.0 mm
-4-d=2 5 mm


I/


4


N-




* i


/ \ ;'


-100 -80 -60 -40 -20
Interpulse delay time (gs)


3 56 nm 3.0-
C

E 2.5-
I a -. -

-* 2.0-

a) 1.5-
1 -
4. -4 ) -

-M_ D 0.5-
_:


Mg I 285 21 nm


(f)
-*-d=0.3 mm
---d=0.5 mm
d=1.0 mm
-v -d=1.5 mm
d=2.0 mm
-4 -d=2.5 mm
*4.


/ /I

--A^


r ,



4 4 y*i~




44


-100 -80 -60 -40 -20
Interpulse delay time (gs)


Figure 6-3. LIBS signal enhancement at the several different transition lines for the

several elements (Al II, Mg I and II and Cr II) versus the interpulse delay time

(At, up to 100 ps) at several different distances (d, 0.3 2.5 mm) in SRM

603 sample.







163


Mg II 279.55 nm


./ 1


-100 -80 60 -40 -0 0
Interpulse delay time (g s)


-100 -80 -60 -40 -20

Interpulse delay time (ps)


--d=0.3 mm
*- d=0 5mm
d=1 0 mm
Sd=1 5mm
d=2 0 mm
4i-d=2.5mm

V


-100 -80 -60 -40 -20

Interpulse delay time (gs)


I Mg II 279.08 nm


SCr II 28














(a) d = 0.5 mm
Al SRM 603
-D- Mg II 279.08 nm
-O-Mg II 279.55 nm
Mg II 280.27 nm
---Al II 281.62 nm
Cr II 283.56 nm
-]-Mg 1285.21 nm


-100 -80 -60


I7


8 -
E 7-
6





' C 2-
4-
1-



1 4


-40 -20 0


At = 30 ps
Al SRM 603


.1


L Mg lI 279.08 nm
0 Mg II 279.55 nm
Mg II 280.27 nm
V A] II 281.62 nm
Cr II 283.56 nm
<] Mg 1 285.21 nm


VT

C


D 0.5


Interpulse delay time (us)


1.0 1.5 2.0 2.5
d (mm)


(C) d=0.5 mm
Al alloy AA1
-n-Al II 281.62 nm
-0-Mg II 280.27 nm
Mg I 285.21 nm
-7--Mn I 279.48 nm


-30 -20 -10 0
delay time, At (4s )


(d) At = 30 us
Al alloy AA1


0.0 0.5 1.0 1.5
d (mm)


Figure 6-4. Pre-ablation air spark double-pulse configuration signal enhancement
versus the interpulse delay time (=At) in (a) NIST Al SRM 603 and (c) South
African Al AA1 sample and signal enhancement versus the distance (=d,
mm) from the sample surface to air spark above the sample in (b) NIST Al
SRM 603 and (d) South African Al AA1 sample.

















164


A II1281.62 nm
Mg II 280 27 nm
Mg 1 28521 nm
Mn I 279 48 nm
Mn I 279 83 nm


-50 -40
Interpulse


Al alloy AA1 sample
r0- -


2.0 2.5



















--




281 282 283 284 285 286
Wavelength (nm)






-


9x107
x- x107
-7x107
- 6x107
- 5xlo &
- 4x107
3x107
- 2x107
- 1x10
-0


0 1 2 3 4 5 6 7 8 9 10
Delay time(p.s)


281 282 283 284 285 286
Wavelength (nm)



Figure 6-5. Spectra showing Al II 281.62 nm and Mg I 285.21 nm emission lines of
interest in terms of delay time in Al alloy sample (SRM 603) in both (a) single-
pulse and (b) orthogonal pre-ablation air spark double-pulse configuration. (c)
For each emission line, graphs of LIBS signal enhancement with use of the
double-pulse irradiation versus several delay times from 0.5 ps to 10 ps.


165

















(a) -- enhancement
-E- S/N improvement

\ Al II 281.62 nm










2 4 6 8 10
Delay time (ps)


6 n



0
CD

3D


2.5
(U
E 2.0
C
ro
LC 1.5


(b) -0- enhancement
-D- S/N improvement
Mg I 285.21 nm










2 4 6 8 10

Delay time (ps)


Figure 6-6. Signal-to-noise (S/N) ratio as a function of delay times for each Al II and Mg
I emission line.


166


-o
0
2














S/ t, =gate width
td =delay time
At= interpulse delay time
=0.1 ***...... laser pulse (laser photonik
for the reheating of plasma

= 2.0 ps
1t=1.0 Ps
0 plasma decay time 50 ps


At=1.0 ps
Laser Photonics pulse Output


Quantel
Laser pulse Output


0 plasma decay time 50 ps


At=1.0 ps
Laser Photonics pulse Output


Quantel
Laser pulse Output


Figure 6-7. Triggering scheme for the time-resolved study of plasma evolution in the
reheating double-pulse scheme (a) with short gate width of 0.1 ps and (b)
long gate width of 30 ps (averaged measuring) of plasma in the triggering
system initiated by the Quantel Brillant laser.


167











Al II 281.62 nm


0 2000 4000 6000 8000 10000


E

S2
S0
C
.c



"4
CO
m3.
Z ,


0 300 600 900 1200 1500 1800 2100
interpulse delay (ns)


0 2000 4000 6000 8000 10000


S i I I I I i
0 300 600 900 1200 1500 1800 2100
interpulse delay (ns)


Figure 6-8. LIBS signal enhancement versus interpulse delay in the reheating double-
pulse scheme (a) with short gate width of 0.1 ps and (b) long gate width of
30 ps (averaged measuring) of plasma in the triggering system initiated by the
Quantel Brillant laser.


168


--------------
.i. O_ _-9


.4.
0


AI II 281.62 rnm





















(b) Single pulse


(c) Only air spark without sample plasma


I In reheating scheme I


6 (d)


--Single pulse
--Double pulse
--- aair spark


255 258 261


264


Wavelength (nm)


Figure 6-9. Plasma images in (a) double-pulse, (b) single-pulse and (c) only air spark
(without sample plasma) at the center wavelength of 259.09 nm in aluminum
alloy AA1 sample. (d) Intensity enhancement compared to only air spark
(without ablation) laser pulse as well as the LIBS signal from the ablation
laser pulse only.


169


CO
0
0
to
C0

*-'
U)
C
0)


(a ouble pulse












(a) t, =gate width
td =delay time
At= interpulse delay time
... = position of laser pulse
0 0 s (Laser Photonics) for the
Sreheating of plasma
t=0.1

*td= 1.0 ps
2.0 s (variable delaysII
t 2.0 ps (variable delays


0 plasma decay time (ps)


A =.O0 ps
S Laser Photonics pulse Output

Quantel
Laser pulse Output


50


-v 10000-

8000-

" 6000-
0C
4000-

0C 2000-

0-


. .A ^ (b)


0 5000 10000 15000 20000 25000
Interpulse delay (ns)


Figure 6-10. (a) Time sequence for the time-resolved study of plasma evolution in the
reheating double-pulse scheme. The acquisition time after the ablating laser
pulse is about 3.0 ps (tw:0.1 ps; td: 1.0 ps; At: 2.0 ps). (b) Peak intensity as a
function of decay time of plasma for selected neutral and ionic lines (tw:0.1 ps;
td: 1.0 ps; d:3.0 mm) and inserted figure shows a log-log scale plot of the
same data.


170


1000 .
.,




100 -A- AIII281.B2nm \
-*-Mg I 26027 nm
Mg II 279.11 nm \ T
-T- Mg 1285.21 nm .
100 10D0 10DOO
S Interpulsedelay(ns)
-l1-"t-.=t.-t-,- ..Y .--






















Laser photonics Q-switch Out


(b) Timing between laser output pulse and (C)
HV gate pulse (td)
o 10-
E
2500 a)
y =1002.2x- 827-73 U
2000 R=0.9998 ...
1500-
S 1000-
01 500 ----- --- -
E 0o-
i -50 1 2 3 0i .
1 Delay time @ HV gate pulse (ps)
-1000
-i500


Al II 281.62 nm


Al alloy D28 sample


S





* I



I


0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Delay time, td (1is)


Figure 6-11. (a) Time sequence of the experimental set-up in the case of the reheating
double-pulse scheme. (b) Timing between laser output pulse and HV gate
pulse (PG-200 Delay Trigger out) at the different delay time td. (c) LIBS signal
enhancement (log-scale) of Al II 281.62 nm as a function of the delay time td.


171


Laser pulse
output


HV Gate pulse
(PG-200 Delay Trigger Out)

Timing = -0.8 ps
at ta= 0.028 ps


... I -Gath width = 0.1 us


Timing =+ 2.16 ps
.... at td = 3 ps












Mg II 270.08nm n


--- d= 0.3 mm
-0--d =0.5 mm
d=1.0 mm
--d =2.0 mm
d =2.5 mm
-K--d=3.0 mm
d=3.5 mm
--- d=4.0 mm


2 4 6 8
Interpulse delay time (4s)


2 4 6 8 10
Interpulse delay time (4s)


(c)
---Mg II 279.08 nm
----Mg II 279.55 nm
Mg II 280.27 nm
--Al II 281.62 nm
Cr II 283.56 nm
--Mg I 285.21 nm


d = -3.0 mm


0 2 4 6 8 10

Interpulse delay time (4as)



Figure 6-12. LIBS signal enhancement versus the interpulse delay time (=At) at the
several distances (=d, mm) from the air-spark to sample surface in a
selected line (a) Mg II 279.08 nm and (b) Al II 281.62 nm and (c) at the
maximum distance (d = ~ 3.0 mm) for several transition lines in the reheating
double-pulse configuration.


172


SAI II 281.62 nm I














C)
E
C)
w
0
CU
-3

C)


0)
C:
Cn
CO


-L-Mn II 259.37 nm (Ek = 12.21 eV)
-0- Mn II 260.57 nm (Ek = 12.29 eV)
Mn II 293.31 nm (Ek = 12.83 eV)
-V- Mn II 293.93 nm (Ek = 12.82 eV)
Mn II 294.92 nm (Ek = 12.81 eV)
-<- Mn I 401.81 nm (Ek = 5.199 eV)
-[->-- Mn I 403.08 nm (Ek = 3.075 eV)
-0-- Mn I 405.55 nm (Ek = 5.199 eV)


Al alloy D28


,/ /


7
- sN.~I~


0 2 4 6 8
Interpulse delay (gs)


Figure 6-13. LIBS signal enhancement versus the delay between the two laser pulses
At in the reheating double-pulse scheme for selected neutral and ionic lines
(gate width: 0.1 ps; delay time: 1.0 ps; d: 3.0 mm).


173















12- 12
(a) -U- Enhancement
10- -(- SIN improvement 10

8- -8

6- -6

4- -4
El


.-----------------------
0 2 4 6 8 10
Interpulse delay time (ps)


0 2 4 6 8
Interpulse delay time (ps)


Figure 6-14. Signal-to-noise (S/N) ratio as a function of delay times for each Al II and
Mg I emission line.









































174


(d) ---Enhancement
--- S/N improvement
/ Mg I 285.21 nm


S-----------


1.5 (C
:Z


1.0


I r






































Figure 6-15. Time-gated, spectrally resolved, one-directional images of the laser-
induced plasma of a Al alloy sample (603), obtained in the single (left
images) and in the orthogonal pre-ablation air spark double-pulse mode (right
images). The gate width and interpulse delays between two laser pulses were
kept by constants (0.1 ps and 30 ps respectively), and the ICCD gate delays
were 0.5 (a,g), 1.0 (b,h), 2.0 (c,i), 3.0 (d,j), 5.0 (e,k) and 8.0 (f,l).


175







































Figure 6-16. Time-gated, spectrally resolved, one-directional images of the laser-
induced plasma of a Al alloy sample (603), obtained in the single (left images)
and in the orthogonal reheating double-pulse mode (right images). The gate
width and ICCD gate delays were kept by constants (0.1 ps and 1.0 ps
respectively), and interpulse delay times (At) between two laser pulses were
0.5 (a,g), 1.0 (b,h), 1.5 (c,i), 2.5 (d,j), 4.0 (e,k) and 6.0 (f,l).


176

















a) td 0.5 1is
-*-A II 281 62 nm (SP)
-1-AI II 281 62 nm (DP)
SA- Mg I 285 21nm (SP)
--Mg I 285 21 nm (DP)
- Cr II 283 56 nm (SP)
-.-*Cr II 283 56 nm (DP)
* *--.-Mg II 280 27 nm (SP)
-a- Mg 11280 27 nm (DP) ,00 -*


100




8 60

0

40


5 20
-E


3
Z,m mm


80 80-

D 70-
O
0 60o-
o 50-
5 40-
I 30-
c 20-
- 10-

0-
0




80-

70

C 60
50

0 40-

30

C 20

10.

0








16

14
0I
c12

--,0
010


6

c 4
c 2


0


(e) t, 5.0 gs
- -Al II 281 62 nm (SP)
- --A II 281 62 nm (DP)
- A- Mg 1285 21 nm (SP)
S-A-Mg I 285 21 nm (DP)
- Cr II28356 nm(SP)
---Cr- I 283 56 nm (DP)
*******Mg II 280 27 nm (SP)
--*- Mg II 280 27 nm (DP)

-1a




@.. t ~.


0 1


2 3
Z, mm


4 5 6


Z, mm


-





-

-
-
-

-

-

-

-

-


(


Figure 6-17. Spatial intensity profiles of atomic and ionic emission lines of Al, Mg, Cr at

different delay times from 0.5 ps to 8.0 ps in the pre-ablation air spark

scheme. The acquisition time (= tw) and interpulse delay time (At) between

two laser pulse was fixed at 0.1 ps and 30ps.








177


(


3
Z, mm


(d) td 3.0 is
0 ---Al II 281 62 nm (SP)
55 --*-AI II 281 62 nm (DP)
Mg I 285 21 nm (SP)
50 --Mg I 285 21 nm (DP)
5 -CrI 283 5 nm (SP)
--I-* Cr II 283 56 nm (DP)
0 ......Mg II 28027 nm (SP)
35 Mg I 280 27 nm (DP)

30-
25
?0 .l I

15 at *- a a .


5-A

0 1 2 3 4 5 6
Z, m m


(f) t 8.0 s (f
4 ----Al 211 62 nm (SP) *
.-Al I 281 62nm (D)P) 0
I a- Mg 1 25 1 nm (SP) "
-A-Mg I 285 21 nm (DP) .
3- I- -Crll 28356 nm (SP) .
-.--Cr | 283 56 nm (DP)
*.** IMg I 280 27 nm (SP) oo tt
-*- Mg II 280 27 nm (DP)
A. 1 2
2- 21


/A A'





0 1 2 3 4 5 6
Z, m m



































Z, mm


,(c) At = 1.5 gS


--AlII 281.8
-m- Al II 2?1


0\ A- Mg 285.
j0 -A-Mg 1285.:
-- Cr II 283.
S --Cr II 283.!
S .*..*. Mg II 280
-.- Mg ll280

0.m


./;IL$^&^^


2 nm (SP)
2 nm (DP)
21 nm (SP)
21 nm (DP)
56 nm (SP)
56 nm (DP)
27 nm (SP)
.27 nm (DP)


25-


j 20
O
0
0 15-


10-

C
0) 5-
CS


U -m minm- ily a a m
0 1 2 3 4 5 6
Z, mm


(e) At = 4.0 gs


--Al II 281.62 n
-=-Al II 281 62 n


1/ A- Mg I 1285.21 n
'. -A-Mg I 285.21 n
0 -*- Cr II 283.56 n
; --4--Cr II283.56 n
Mg II 280.27
-.-Mg II 280.27



SA


!ii..".eiA


0 1 2 3
Z, m m


m (SP)
m (DP)
im (SP)
m (DP)
m (SP)
m (DP)
nm (SP)
nm (DP)


(d) A t


3
Z, mm


2.5 gLs


-=-AI II 281.6;
--- Al II 281.6;


*'* A- Mg I 285.2
I .4 -A-Mg 1285.2
'* --- Cr II283.51
--4--Cr II 283 51
S ****-Mg II 280.2
S -.a-.Mg II 280.2
A M
,, ,-,
il %

l./14 eBI =,;''


Snm (SP)
Snm (DP)
1 nm (SP)
1 nm (DP)
8 nm (SP)
6 nm (DP)
7 nm (SP)
7 nm (DP)


1 2 3 4 5 6
Z, mm


6 (f)At = 6.0 s


C= 4-
0
0
- 3-

S2-

CA 1
C*-


4 5


-=-Al II 281.62 r
-- Al II 81 01 m",


A- Mg I 285.21
-A-Mg I 285.21
S -4- Cr II 283.56
--*--Cr 11 283.56
? ...* -.- M g II 280.27
:, \ -.*-.Mg II 280.27


.A' k \ .

n' mmt "
: :.. .


nm (SP)
nm (DP)
nm (SP)
nm (DP)
nm (SP)
nm (DP)
nm (SP)
nm (DP)


0 1 2 3 4 5
Z, mm


Figure 6-18. Spatial intensity profiles of atomic and ionic emission lines of Al, Mg, Cr at
different delay times from 0.5 ps to 6.0 ps in the reheating scheme. The gate
width and ICCD gate delays were kept by constants (tw: 0.1 ps and td: 1.0 ps
respectively).





178


15

U)
- 12

0
o 9.
0

S6


=









































Figure 6-19. SEM images of craters produced 50 consecutive samplings of Al alloy
sample (a) in the single-pulse and (b) in the double-pulse (At = 20 ps) using
the orthogonal pre-ablation air spark mode, and (c) in the single-pulse and (d)
in the double-pulse (At = 5.0 ps) using the orthogonal reheating mode.












179















(a) Pre-ablation air spark
-0- Mg I 277.83 nm
-0- Mg I 277.98 nm
Mg I 278.3 nmrn
S-- Mg II 279.08 nm
Mg II 279.55 nm
S- --Mg II280.27 nm
"- Mg I 285.21 nm
-0-Mg II 292.86 nm




0 2 4 6 8 10

Delay time (ps)


(b) Reheating
--- Mg I 277.83 nm
-*- Mg I 277 98 nm
Mg I 278.30 nm
- Mg I 285.21 nm
V Mg II 279.08 nm
-- --Mg II 279.55 nm
<1 Mg II 280.27 nm
- 0- Mg II 292.8 m ...-o

i 7 ij i



1 2 4 6 8 1
Delay time (gs)


Figure 6-20. Signal enhancement versus delay times at the different Mg atomic (solid
dots) and ionic (open dots) lines (a) In orthogonal pre-ablation air spark and
(b) in reheating scheme LIBS.


180


















1 5
10

056
S00

S-10

-15

-20
-25


* 0,5 s delay time
- near fit (R = 0.816)
MI 279 Mgln 279 T nm
MMglB5?2 n vg1292 8



S Mg 2779nri
9 Mg!277 83nm

',T = 0.1462 0.0423
q=- 1.757 0.473

2 4 6 8 10 12 14 16 18 20
E +E, (eV)


20 (d) Mgli292Sa r

2 Os delay Ime ugl 27?9.J0
-- Linear fit (R-0. 972)
II 279,55 nm
1.0 hMgIIO11027 nm
27738 rm
0.5 Tg 27e2nn
M2115.21 & g277.Oan i

0.0 -

-0.5 AT=01249+00123
q-10 =-03030.138

S2 4 6 86 10 12 14 16 18
E + Eo (eV)


201 ()


* 5.O gs delay time
- Linearfit (R=0 934)

2Mlg l s7i, n
S277 8279.55 mri
79 e71.2 .9 M 2.

1112 Cl *11277.13 "m


AT =0.065 10.0111
q= 0.0941 0.114

0 2 4 6 8 10 12 14 16 18
E + E-n (eV)


2.0 (b) 0l 22.8ri/
S1.0 as delay time .
1.5 Linear fit (R= 0.940) Ugl O .a nm

10Mg!l 27955 rim
Mll 29 2 .27mri
MgI 285 21 277.9anm
0.0- / Mg12718 nm

- -0.5 /

-.10 AT = 0.1661 0.0245
q=- 0987 0.274
0 2 4 6 8 10 12 14 16 18
E + E, (eV)


20.( )
2.5psdeay ime MI2795.8nm
-- Linear it (R= 0.905)

MgI 28'0.27nrm1 12a9f1 n2 m
10 MgI 279.5
5.98nm
0.5 ug28as.21 277 nm

010-
.T= 0,1061oo214 |
05 =-01114t-l8

0 2 4 6 8 10 12 14 16 18
E + E (eV)


0. 9 (h)
e 8.0 ps delay tbme
Linear fit (R=0 259)
0G6 Mg12779anm Mgl12790Brm
ugl2713n *
03 278 U nm
iM.279 55nm
0.3 MgM l289.21nm u Mmg280.27 nm


0.0
T= 0.00804+ 0.0150
q=0.3254 0.160
-0.3 .
0 2 4 6 8 10 12 14 16 18
E, + ES- (eV)


1.5 delay tme U911 29218
1.5-- Linear fit (R=0.957) /
Ugll 279.55 m .
10 MgI 28027 l mli

0.5 277.9Bnm
o MgI 285721 nt C MCI 277.83 nm
0.0 a MCI 275.32 r11

-05 AT= 0. 1464 0.0181
q- 0.645 0.203 I
-1.0
0 2 4 6 8 10 12 14 16 18
E + El, (eV)



1 J i1 27ga go

1.2 MglI 280.27 rim
1.0 Mul 27.55 nm
W M MgJll 292266 im
Sg1i 277.98 m
*Mgl277.83nm
r 0<. ,,,,4
0 21 .
I2 T= 0069321 0.0180
00 q=0.206 001
0 2 4 6 8 10 12 14 16 18
E + E (eV)


1.4 (I)

1.2 100 As delay bime
--Linear fit (R=0.932)
1.0

08
(0 *Mg277 Inmri
0.6 *MgI27013nm
S MgI 25.21 rm
r 04
S04II 279 55 nm
0 2 88.27 nm
T = -0 06009 0.0117
00 q=1 019 0.124 Mg


Figure 6-21. Logarithmic plots of neutral and ionic line enhancements at the different

delay times from (a) 0.5 ps to (i) 10 ps (in the pre-ablation air spark scheme).



























181


0 2 4 6 8 10 12
Ei + E (eV)


1.5



105



0 0

-05


14 16 18


I


















(a)
80 t- 0 5 s 1q

A60-
50 Mn

24 0 -



10 Mg I lines Cr I

276 278 280 282 284 286
Wavelength (nm)


70


76 278 280 282 284 286
Wavelength (nm)


6 278 280 282 284 286
Wavelength (nm)



t =25 s


276 278 280 282 284 286
Wavelenath (nm)n


t=8 0 s


276 278 280 282 284 286
Wavelength (nm)


280 282 284
Wavelength (nm)


=30-s


6 278 280 282 284 286
Wavelength (nm)


6 278 280 282 284 286
Wavelength (nm)


Figure 6-22 (a) LIBS spectra in both single (black color) and double pulse (gray color) at
the different delay times for the pre-ablation air spark scheme (Acenter = 281.5

nm, At = 30 ps and tw = 0.1 ps).























182























S=0.5 Fe I and Mg DP


M II









6 288 290 292 294 296 29E
Wavelength (nm)


(b)


(3
0
'A,
C

















43
0
C

'A,
C
a


---P
---S


, JLJuL

286 288 29 2 294 296 29E
Wavelength (nm)


t = 1.0I s


12-

10-

8-

6-
4-

2-

0-
21


286 288 290 292 294
Wavelength (nm)



0.25 i =8.0 S

C 0.20



0.05

0.0015



286 288 290 292 294
Wavelength (nm)


t 1 51s


286 288 290 292 294 296 298
Wavelength (nm)


20 t 3 0


-DP
-SpI


15
a
1 0


o 0

S00-

286 288 290 292 294 296 290
Wavelength (nm)


^ 024- t24-10 _]
P 0 18-
0
O 0 15
0O 0 12
0 09
C 0 0-
C 03 -92


296 298 286 288 290 292 294 296 298
Wavelength (nm)


Figure 6-22 (b). LIBS spectra in both single (black color) and double pulse (gray color)

at the different delay times for the pre-ablation air spark scheme (Acenter = 292

nm, At = 30 ps and tw = 0.1 ps).




















183


16 288 290 292 294 296 2!
Wavelength (rim)



t 2 5 -D




d s


6 t =-20s -1
5 -

4








286 288 290 292 294 296 2
Wavelenath (nm I


296 2
















18,000
17,000
16,000
15,000
14,000
13,000
12,000
11,000
10,000
9,000


2 4 6
Delay time (gs)


8 10


02- ( .b)
-2


0 0 0
.o
0_- 1



_-02- --2
< -0 2 -*- AT (slope) -2
--- q (intercept)
-0.3 ... .. -3
0 2 4 6 8 10


Sn


2.0-

- 1 5 -

1 0-

0.5-
t-


(d)
The enhancement of total number density
of atoms and ions in the plasma

0

*
/





I 2 4 6 8 10
Dealy time (uLs)


Figure 6-23. (a) Plasma temperature obtained from Saha-Boltzmann plot, (b)
temperature difference (AT = slope) and intercept (= q) from the logarithm
plots of neutral and ionic line enhancements, (c) electron number density
using Stark-broadening (Al II 281.62 nm) and (d) The enhancement of total
number density of atoms and ions in plasma from Eq. 6-11 at the different
delay times.


184


2 4 6 8 10
Delay time (pis)


-*- Single pulse
-*-- Double pulse


9 (c)
8-
7-
6-


4-
3-
2-
Single pulse
S Double pulse
0




























4 6 8 10 12 14 16 18
E +E. (eV)
upper ion


4 6 8 10 12 14 16 18
E +E. (eV)
upper ion


4 6 8 10 12 14 16 18
E +E. (eV)
upper ion


* 0.5 is .
* 1.0 ns
1.5 .is ,
v 3.0 sis
4.0 (is
< 9.0 (Is

4 6 8 10 12 1
E +E. (eV)
upper ion


16 18


Figure 6-24. Saha-Boltzmann plot in both (a) single and (b) orthogonal pre-ablation air
spark double-pulse configuration and (c) single and (d) orthogonal reheating
double-pulse configuration.











185


0

< -4

- -8

-12

-16


4 (d) Double Pulse





































Figure 6-25. SEM images of craters produced 50 consecutive samplings of Al alloy
sample (a) in the single-pulse and (b) in the double-pulse (At = 20 ps) using a
pre-ablation air spark. Spectrally resolved one-directional images of the laser-
induced plasma of a Al alloy sample, obtained (c) in the single and (d) in the
double-pulse ablation mode (td = 2.0 ps; tw = 0.1 ps; At = 30 ps).


186


4.3mm Single pulse (C)

3.Omm

1.5 mm


Double pulse (d)
At= 30 ps















(a)
0.5,sdaybtmn
-- Unearfit




12771 27 9 n r

fi IEE27rrn

AT =-00299 001445
q= 03972+0.1614

0 5 10 15
E+ E (eV)


(d)
* 30psddeaytir
-Ureaft


.^'*^ 127f" Zr nli
0-


AT =0.05485 0.01615
q=-04518+01805

0 2 4 6 8 10 12 14 16 18
E+ E (ev)


(b)
* 1.0pdelaytirn
- Linerfit


t 1278E 36mi
*--- 4U 12,77 3 oil I279l fm



AT=-00344 04+ 0.C41
q= 0.5397+02281

0 2 4 6 8 10 12 14 16 18
E + E (eV)\
J I n mi


UJ
C
-


* 40psde*lin
-- Linr fit


1 2 279501 r2
WI 292 9Bi,




-1
AT = 0.07331 0.0180B
q =-0.4172+0.221
0 2 4 6 8 10 12 14 16 18
E + E (eV)
I w


(c)
1.5psdlaytinr
2--LUnerfit

1

--- 8l 3 4lj in ii 2 -^7H1 1232-B1r'
0 l I I2? r;nr1 2


-1

| : : f : i:, ," :,':0 -

0 2 4 6 8 10 12 14 16 18
E + E (V)
j cn


D 2 4 6 8 10 12 14 16 18
E + E (dv)
J wH


Figure 6-26. Logarithmic plots of neutral and ionic line enhancements at the different
delay times from (a) 0.5 ps to (f) 9.0 ps (in the reheating scheme).


187


CT















(a)
2 rl A t = 0 5 s


I--DP


250


C l 200
200 200
o 100 1
o 0
o0

S50 150-



I---------------- 0.
278 280 282 284
Wavelength (nm)


140
120-
100-
0
0 80-
G0-
' 40
20-
0


At =1.04s








AL


- 180
S 160
S140
S120
o0 100
80
60
40
20


278 280 282 2E
Wavelength (nm)


24


"- 24
At=30s DP 100 At=40s D P
-SP -SP

0 I16

40
20-


278 280 282 284 278 280 282 284
Wavelength (nm) Wavelength (nm)


At =1.5 DR









278 280 282 284
Wavelength (nm)


Ait =9. s DP
SP


278 280 282 284 286
Wavelength (nm)


Figure 6-27 (a). LIBS spectra in both single (black color) and double pulse (gray color)
at the different delay times for the reheating scheme (Acenter = 281.5 nm, td =
1.0 ps and tw = 0.1 ps).


At = 0.5 4s


DRP


16
14
12
10-
8j
6
4-
2
288 290 292 294 296
Wavelength (nm)


12 t=1.0 DP 12 At =1.5 D sD


0 0

6 6


2 -2

288 290 292 294 296 288 290 292 294 296
Wavelength (nm) Wavelength (nm)


8-
7 At= 3.0 s
6-
5 |


2
41





288 290 292 294 296
Wavelength (nm)


06

4

12

a


At=40[s D
---SP








288 290 292 294 296
Wavelength (nm)


288 290 292 294
Wavelength (nm)


Figure 6-27 (b) LIBS spectra in both single (black color) and double pulse (gray color) at
the different delay times for the reheating scheme (Acenter = 292 nm, td = 1.0 ps
and tw = 0.1 ps).






188


296


L


**" **'1













14,000
13,500
- 13,000
12,500
12,000
11,500
E 11,ooo
- 10,500
10,000


-*-Single pulse
-*-Double pulse

2 4 delay time (
Interpulse delay time ([is)


0.18-
0.15-
0.12-
0.09-
0.06-
0.03-
0.00-
-0.03-
-0.06-
-0.09-
0


2.5

2.0-

1.5-

1.0-


0.5-

00


(c)
5-

4-

3-

2


--*-Single pulse
0-*- Double pulse
0 2 4 6 8 10
Delay time (ts)


-*-AT (slope)
-*- q (intercept)
2 4 6 8 11
Delay time ([is)



(d)
The enhancement of total number density
of atoms and ions in the plasma


S0* \--- *


-1

-0

-1

--2


0 2 4 6 8 10
Delay time ([s)


Figure 6-28. (a) Plasma temperature obtained from Saha-Boltzmann plot, (b)
temperature difference (AT = slope) and intercept (= q) from the logarithm
plots of neutral and ionic line enhancements, (c) electron number density
using Stark-broadening (Al II 281.62 nm) and (d) The enhancement of total
number density of atoms and ions in plasma from Eq. 6-11 at the different
delay times.


189


. ..I- I -- -- I I -- -- I I -- -









Table 6-1. Concentration of several elements in NIST Al SRM 603 and South African Al
alloy standards AA1 and D28 (APEX Smelter Co., South African)
Element SRM South African South African
603 AA1 D28

Al 97.69 69.57 81.55

Si 0.520 14.6 9.66


Mg 1.01 0.170 0.004


Cu 0.290 5.70 1.76


Zn 5.90 3.6


Fe 0.210 1.73 0.98


Mn 0.540 0.59


190










Table 6-2. Selected spectral lines and corresponding
investigated elements(a)


Species Wavelength A


Al II

Mn II

Mn II

Mn II

Mn II

Mn II

Mn II
MnI

MnI

MnI

Mn I
Mg II

Mg II

Mg II

Mg II

Mg I

Mg I

Mg I


Mg I


(nm)
281.61

257.61

259.37

260.57

293.31

293.93

294.92

279.48

401.81

403.08

405.55

279.08

279.55

280.27

292.86

277.83

277.98

278.30

285.21


(10 1/s)
3.83

3.025

2.636

2.711

1.959

1.855

1.859

3.70

0.254


0.170

0.431

4.01

2.60

2.57

1.15

1.82

1.36

2.14


4.91


Lower
(cm-1)
59,852

0

0

0

9,473

9,473

9,473

0

17,052

0

17,282
35,669

0

0

35,669

21,850

21,870

21,911


spectroscopic information of the


Lower
(eV) glower
7.42 3

0 7

0 7

0 7

1.18 5

1.18 5

1.18 5

0 6

2.11 10


0

2.14

4.42

0

0

4.42

2.71

2.71

2.72


0 0 1 35,051 4.35


(a) From NIST atomic spectra Database,
http://physics.nist.gov/PhysRefData/ASD/lines_form.html


191


upper


Eupper Eupper


Upper
(cm-1)
95,351

38,807

38,543

38,366

43,557

43,485

43,371

35,770

41,932

24,802

41,933

71,491

35,761

35,669

69,805

57,833

57,833

43,371


Upper
(eV)
11.8

4.812

4.779

4.757

5.401

5.392

5.378

4.43

5.20

3.08

5.20

8.86

4.43

4.42

8.65

7.17

7.17

7.17









Table 6-3. All parameter values mentioned
ablation air spark scheme)


in Eq. 6-11 at different delay times (pre-


PlasmaT rPlasma
Delay time Y-intercept a a n D D
(s) ( q) neutral, Mg Mg Plasma Plasma


0.5

1.0

1.5

2.0

3.0

5.0

8.0

10


-1.757

-0.987

-0.645

-0.303

0.206

0.0944

0.325

1.019


-1.143

-1.191

-0.9668

-0.8345

-0.4382

-0.4891

0.005991

0.6686


0.6139

0.2041

0.3218

0.5315

0.6442

0.5835

0.3190

0.3504


0.4410

0.1726

0.1912

0.02944

0.03751

0.05959

0.06621

-0.1977


0.5413

1.226

1.380

1.701

1.904

1.792

1.376

1.420


192









Table 6-4. Plasma temperature and electron number density in both single and
orthogonal pre-ablation air spark double-pulse configuration at different delay
times.


Plasma temperature
(K)


Electron number density
(1017 cm-3)


SP

14017 +245

13316 +168

13052 +155

12630 +155

12408 +141

11582 +158

10715 +148

10259 + 137


DP

15679 +227

15632 +237

14657 + 201

14194 + 180

13084 + 148

12217 + 189

10752 + 169

9696 + 127


193


SP

5.13

4.57

4.02

3.69

3.4

2.96

2.9

2.9


DP

5.11

4.54

3.99

4.07

3.49

3.04

2.90

3.01









Table 6-5. All parameter values mentioned in Eq. 6-11 at different delay times
(reheating scheme)
Delay time Y-intercept naa naDp Dp
(ps) (= q) eutral,Mg Mg C PlasmaPasma

0.5 0.3972 0.1265 0.2707 0.05759 1.311

1 0.5397 0.2455 0.2943 -0.04247 1.342

1.5 0.3960 0.09525 0.3008 -0.07828 1.351

2.5 -0.1873 -0.2420 0.05469 -0.12697 1.056

3 -0.4518 -0.3657 -0.08612 -0.2457 0.9175

4 -0.4172 -0.6381 0.2209 -0.1051 1.247

9 -0.6664 -0.9457 0.2793 0.003432 1.322









Table 6-6. Plasma temperature and electron number density in both single and
orthogonal reheating double-pulse configuration at different delay times.

Delay time Plasma temperature Electron number density
(ps) (K) (1017 cm-3)


SP

13077 + 151

12883 + 171

12754 +158

11748 +137

11607+ 171

10041 +148


DP

12741 +

12523 +

12732 +

12792 +

12867 +

11247 +


188

165

167

146

134

165


SP

3.80

3.32

3.05

2.65

2.53

2.15


DP

3.45

3.32

3.29

3.85

3.28

2.54


194









CHAPTER 7
CONSIDERATION ON THE SPECTRAL FLUCTUATION APPROACH IN LASER
INDUCED BREAKDOWN SPECTROSCOPY

The acceptability of laser-induced breakdown spectroscopy (LIBS) is still related to

the problem of quantization involving accuracy, i.e. repeatability and trueness. In a LIBS

analysis, there are many parameters that affect the precision and accuracy of a

measurement. Some of them can be controlled, such as the stability of the laser pulse

energy, and others are dependent on the sample. A list of important parameters that

affect a LIBS analysis is presented in Table 7-1. The fluctuations of emission signal can

be influenced by these parameters. Thus, the study of the fundamental noise

characteristics in LIBS spectra is important for optimizing the analytical utility of the

technique.

Several papers have been published in several fields regarding spectroscopic

noise [160-164]. Alvarez-Trujillo et al. compared a new spectral data processing

scheme (i.e., the standard deviation of collected spectra) with the traditional ensemble-

averaging of LIBS for non-homogeneous analyte system (e.g., aerosol system) [160,

161]. For comparison between two methods, signal-to-noise (S/N) ratio and relative

standard deviation (RSD) were calculated and the limiting noise of the measurement

was also studied as detailed by Ingle and Crouch [100]. Poussel and Mermet [163]

reported some correlation between background signals in inductively coupled plasma

atomic emission spectrometry (= ICP-AES) to study effects on precision, limit of

detection and limit of quantitation. The shape of the RSD curve of the net signal as a

function of the concentration was also studied from both a theoretical and practical

aspect. It was argued that this analysis seems to show the relevance of the various

noise types as well as the limiting noise of the measurements [162].
195









As shown in several studies, the standard deviation (i.e., the root mean square

noise) of the background may be the result of several fluctuating factors such as plasma

temperature, electron number density, laser energy fluctuations and mass ablated by

laser pulse (since it may be contributed to the electron number density and plasma

temperature). Thus, the behavior observed by plotting the standard deviation (SD) and

relative standard deviation (RSD) of each spectral element (pixel) versus wavelength

can indeed be informative. First of all, all possible limiting noises present in a LIBS

measurement will be simulated by making the plot mentioned above and then compared

with the results obtained in our work for studying the relevance of the various noise

types as well as the limiting noise of the measurements. A possible correlation between

the background fluctuation and the analyte signal will be also studied. In addition, as a

complementary approach, the plot of signal to noise (S/N) ratio versus signal (or

concentration) will be shown and discussed in this chapter since the S/N ratio is the

reciprocal of the RSD.

Theory

The lowest signal intensity that can be detected is determined by the fluctuations

of the background signal, denoted as noise. The study of noise forms a part of the

discussion of errors in analytical measurement. Usually, noise includes fluctuations

which do not obey a regular distribution law, such as those produced by spikes on the

line voltage or other disturbances from electrical equipment in the vicinity. The causes

of these noise sources may be found in the light sources, the absorbing medium, the

detectors and the electronic measurement systems used in optical spectrometry. The

noise intensity can be expressed as the standard deviation of the background signal


196









measurements, denoted as the root-mean-square (RMS) noise, or the peak-to-peak

value which is the difference between the minimum and maximum background signal.

In a typical LIBS experiment, the noise in a signal includes both the noise in the

background and the noise in the signal. A priori, one does not know whether two noises

are correlated or uncorrelated. On logical grounds, one could suppose that, at least at

the beginning of the plasma formation or at early evolution times, the background

continuum and the signal would show some correlation in view of the fact that the origin

of the fluctuation (temperature, electron number density and ablated mass) are similar

for both. Otherwise, at long delays, the continuum background decays and the signal

fluctuation due to the sampling process will then become the dominating cause of noise,

at least for signal levels not too close to the detection limit.

When making measurements in LIBS, more than one noise source occurs, and so

must be considered whatever measurement system is being utilized for the signal

measurement. To calculate the variance in q as a function of the variances in x and y

we use the following (general derivation of the propagation of errors) [165]:


2 += -- 2 2 +272+ 2xy (7-1a)


In the above equation, o-x is the covariance of xy. Using the definition of the correlation

coefficient,

0 =-- (7-1 b)
x y

We obtain the working expression:

q2 a 2 2 + 2+ 2 Lq' q xuy (7-1 c)


197









where 0 is the correlation factor, which takes into the account the possibility that the

two variables are correlated or uncorrelated. That is, if the correlation factor is zero

(6 = 0), it can be explained by totally uncorrelated noise sources in which the last term

in Eq 7-1c is zero. Otherwise, the correlation factor can also vary between +1 (totally

correlated noise sources) and -1 (anti-correlated noise sources) [100].

In luminescence and emission measurements, the experimental spectral peak

intensity (S, o ) consists of the sum of the analytical net-signal (S,,, o ) plus the blank

signal (Bt, ) including contributions from the background signal (or plasma continuum,

B ) and the dark signal (D ). Then, the net signal (Sne, ) is obtained by subtracting

the value of the blank signal (B, ). An example of the description of net signal is shown

in Fig. 7-1. That is, the simplest net signal measurement consists of the peak intensity

at the central wavelength Ao of the analyte line Snet2 and an off-peak measurement of


the background at a single position B if the dark signal can be negligible. It sho

be noted that the background is measured at some distance from the line center and

assumed to be representative of the "true" background value present under the line

peak, excluding any contribution from the line wings. In the Appendix, we list all

parameters measured experimentally and their meaning. Using the above definitions,

the noise in the plasma background associated with analyte line and the noise

measured at the line center, due to the contributions of both analyte line and plasma

background, would be given by the following expression:

o-(Bp,Zoffpeak) (7-


uld


1d)


198









and the root mean square noise o-, in the total emission signal can be shown as

follows:

( 12 12 1/2
o-, = o-( ,ffpeak + O-(ne,)] +20[o-(B ,offpeak)O-(Sne, )] (7-1 e)

If the net signal due to the analyte line is obtained by subtracting the background signal

Bp,, from the total signal S, Ao, the propagation of error caused by the background

correction can be made as follows:

dff- = { (BP, off-peak ] 2 2 20- (BP, offpeak ) }1/2 (7-1f)

In order to simplify the writing, from now on we will indicate the net average signal to the

analyte with S, the average plasma background with B, the noise in the background

with aB, the noise in the signal with as, the total noise with a, (- as + au) and the

noise of the difference with udff (- u u-B).

Standard Deviation Limiting Cases

Case a-1: a-B >> as. In this case, it is assumed that the noise in the signal is much

less than the noise in the background. In other words, the measurement is background-

noise limited. Note that this is not likely to be the case in reality, although it may hold

when the signal level is very low and the background is still high (e.g., close to the limit

of detection and at short delay times). Whatever the reason might be, if 0-B >> s, Eq.

7-1e simplifies to:

a, = [2 + 20sB 12- B (7-2)

The last approximation holds whenever as << 1/20. Should this be the case, the plot

of the standard deviation versus wavelength, simulated in Fig. 7-2a, should remain at


199








the same level as that corresponding to 0-B. This will hold irrespective of whether the

two noises are correlated or not.

Case a-2: -B =o-s. The noise in the background and the noise in the signal are of

comparable magnitude, i.e., it is assumed that aB =O-s. Note that one does not

measure o-s directly, since o-B = s. In this case, Eq. 7-1 e becomes

0t = [0 +0 2 + 200 1/2= [2 2(1 +0) 1/2 (7-3a)

i) 0=0

If us and c-B noises are completely uncorrelated, i.e., if 0 = 0, the total

noise will be given by

0- = V2o-s = V20-B (7-3b)

As a consequence, when the standard deviation is plotted as a function of

wavelength, one should observe an increase of a factor 1.414 at the

location of the spectral lines (see in Fig. 7-2b).

ii) 0 =1

In this case, Eq. 7-1e can be simplified as follow:

0-, = [0-2 + 2- + 200- 1/2= (40-2)1/2 = 20- (7-3c)

iii) = -1

In anti-correlated case,

o, = 0 (7-3d)

Figure 7-2c and 7-2d show the simulated plots when 0 = 1, respectively.


200









Case a-3: -B << o-s. This is the case in which the noise in the signal dominates

over that of the background, i.e., -B << -s. When this is true, the resulting total noise

expression will be given by

[, = C52 + 20tsaB ] 1/21 2 S (7-4)

The last approximation holds whenever << -s/20. Note that, in analytical practice,

the signal is measured at moderately long delay times, when the plasma continuum has

decayed to a negligible (or low) level. The fluctuations in the signal (due to the sampling

process and the inherent signal noise) are then expected to dominate those of the

background. The simulated plot of the standard deviation versus wavelength shown in

Fig. 7-2e should then be characterized by an increase observed at the locations of the

analyte peaks: e.g., such increases should correspond to the ratio (o-s /oe). For

example, if o-s = 10-, the increase will be a factor of 10. Note that us changes with

S ( it increases with S), although the exact nature of the change is not known, since the

type of noise is unknown. As shown in the previous background-noise limited case, the

above outcome holds irrespective of the value of the correlation coefficient.

Case a-4: This is the most general cases, in which 0UB and us can assume any

value. The total standard deviation then becomes:

[ 2+ + 2 ]1/2 (7-5a)

As pointed out before, us is not measurable directly. In the case in which the noises are

totally uncorrelated (0= 0), one can write:

(t )exp ( 2alc B (7-5b)p
(S )2l = ( )e2xp (B )Exp

201








as can be calculated by the difference between two experimentally measured values.

However, when the noises are correlated, as cannot be calculated without 0, which is

unknown. In fact, the resulting quadratic equation below cannot be solved.

(e,)2 (oS )2alc + (B )2 + 20 s (GB -)xp
ex a E e (7-5c)
(O.s )2 [20(0.B )exp S + [(B )2xp (otxp 0

In order to be able to calculate 0, one can adopt the following procedure. The

standard deviation of the difference between (S + B) and B, i.e., Cdf, can be

experimentally evaluated from the measurement. For each spectrum i (laser pulse), the

total counts due to (S+B), are measured simultaneously with B,. B, is then subtracted

from (S+B), and the resulting S, is obtained for each spectrum. Repeating this

operation for all N spectra, one can calculated the standard deviation of S,, i.e.,

adff ( ). In practice, what is done is the following:

[(S+B)a+B]- [Bo=-B S +da (7-6a)

with the result that

(d )clc = [(t p (B xp 20(t )exp (B exp 1/2 (7-6b)

In Eq. 7-6b, the only unknown is 0, which can then be calculated by the following

relation:

(O ) 2 + B ( 2 ) (udi. )2
0 = exp exp d- alc (7-7)
2(.t )exp (BR )exp

It can be seen that similar arguments as those already discussed before apply here. In

fact: if a, = a,. we have


202









(-d) [p t x B xp]12 [ k +(20-B 12 (7-8)

It can be calculated experimentally, since the background in this case has been

measured twice. From Eq. 7-6b, it should be noted that if all noise sources are totally

uncorrelated, the noise of the net signal (oad) ,l can be simply calculated from Eq. 7-8

because (o-,)exp and (o-B)exp are known values experimentally and then compared with

the experimentally measured noise of the net signal (cadf)exp in Eq. 7-6a. The high

difference between the calculated and measured noise (= Aodff) implies a high

correlation between noise sources because the assumption about the correlation

between noise sources from Eq. 7-7c is not valid, which means that 0 ; 0. Thus, it will

be worthwhile to compare the difference between the calculated and measured SDs of

net signal with the correlation factor e in order to understand the multiplicative nature of

noises.

Relative Standard Deviation Limiting Cases

It is relatively straightforward to extend the previous considerations and discuss

the spectral behavior of the relative standard deviation (RSD) of the various signals

defined before. By definition, RSD can be defined as:

(RSD)B = B (7-9a)
B

(RSD) o- [o-2 + -+20o-Bc-s ]1/2 (7-9b)
(RSD)( = '- ( B) (7-9b)
(S+B) (S+B)



Case b-1: o-B >>o- s;0=, +land-1. Here, the following relations apply:


203









(RSD)B (7-10 a)
B

(RSD), = B (7-1 Ob)
S+B

(RSD), B (7-1 Oc)
(RSD)B S + B

In this case, in the plot of the relative standard deviation versus wavelength, the total

analyte peak intensity at Ao should decrease with respect to the relative standard

deviation of the background, since (S+B) > B. This is shown in the simulated Fig. 7-3a.

Case b-2: o0- = -. The pertinent equations in this case are:

(RSD)B B (7-11 a)
B

(RSD)t -[2o-2 (1 + 0)]1/2
(RSD), (7-11b)
S+B

i) 0=0

The pertinent equations in this case are:

(RSD)B = (7-12a)
S+B

(RSD) = B = B (7-12b)
(RSD)B S +B )JB S++B

The total RSD will decrease compared to the(RSD)B, but not as much as in

Case 1 (a factor of 1.414 less, see simulated Fig. 7-3b).

ii) 0=1

(RSD), 2o-B )B )=2( B (7-13)
(RSD)B B2 (7-13)B
(RSD), S + B ja S+ B


204








In this case, if the signal and background have the same magnitude, the

RSD plot will show no features at each peak (see simulated Fig. 7-3c).

iii) 0 -1

In this case, the (RSD), will be zero, since o- = 0 (see simulated Fig. 7-2d).

Case b-3: B <

(RSD)0 = -2+20-S 0 7/2 -S (7-14)
S+B S+B
(RSD) s S B -s
SB = ) = B )E(7-14b)
(RSD)B S + B B S +BB o-B

It can therefore be seen that the plot of the RSD versus wavelength will either

present no features, decreases or increases depending upon the values of the ratios in

Eq. 7-14. In the peculiar case in which the noise ratio (o-s /0-B) is equal to the ratio

[(S+B)/B], the RSD will be a flat featureless line when plotted versus wavelength. One

can argue that, at reasonable plasma decays (several microseconds), the first ratio will

have a predominant effect, since B << (S+B), while at early plasma decays B ~ (S+B)

and therefore the RSD plot should show an increase at the location of the spectral lines.

It should be noted that in this limiting case, it is irrelevant whether 0 = 0, +1 or -1. In

other words, correlation between the various noises should play no role.

Case b-4: General Case.


(RSD)t = (0- + +2OBS/O2 (7-15)
S+B

i) 0=0

2 + /2
(RSD), = (-s (7-16a)
S+B
205









(RSD) ( B (7-16b)
(RSD)B S+B oB

Here, one should take advantage of the procedure outlined in the previous

section to calculate o-s (after evaluating 0). It should be also noted that Eq.

7-16 reverts Eq. 7-14 and Eq. 7-10 in the cases where o-s is much greater

or much smaller than o-B, respectively.

ii) 0= 1

() 2 + +0" + /2
(RSD) = SB (7-17a)
S+B

(RSD)t ( B ) [(2+ o"2+2"so"B /2
(RSD) [ B (7-17b)
(RSD), S+B B aB

iii) = -1

)( +o -- 20O-SBY/2
(RSD)- = +BU (7-18a)
S+B

(RSD) B [(O2+O -2 sB (7-18b)
(RSD)B S+B) B

Experimental

The LIBS experimental system has already been described in detail in Chapter 4.

The schematic of the set-up is illustrated in Fig. 4-1. In our study, simultaneous

measurements have been performed using the spectrometer (Acton triple grating, 0.5 m

focal length) equipped with the intensified CCD detector (ICCD 5764/RB-E, Princeton

instruments). All measurements in this study were carried in atmospheric pressure and


206









performed with a fixed laser pulse energy of 90 5 mJ. The experimental conditions

and samples used for each study will be described in detail in the next section.

Results and Discussion

As mentioned above, all measurements were acquired with a grating

monochromator equipped with and intensified CCD and the following considerations

should be also mentioned before we make a discussion for consideration on the

spectral fluctuation study in LIBS:

* The different spectral windows are considered to consist of a few isolated spectral
lines, superimposed on a flat background continuum, reflecting the elemental
composition of the sample.

* The spectra can be obtained at different delay times from the onset of the plasma
at a fixed integration time.

* Each spectrum is the result of a single laser shot fired on the same location of the
sample.

* The data are not spatially resolved and the entire plasma height is binned (pixel
column).

* For each spectral window considered, a certain number of single-pulse spectra are
obtained. For each pixel (or equivalently for each spectral resolution element) the
average signal levels for the background, single plus background, net signal are
computed, together with their corresponding standard deviation and relative
standard deviation values (see Fig. 7-4).

* The background and the signal plus background are acquired simultaneously, and
may therefore show some correlation.

* The only noises considered are background noise and signal noise: therefore, the
dark current noise is neglected, together with excess detector noise and readout
noise in the study.

Several experiments were performed under various experimental conditions in

different samples to understand the limiting type of noise present in a measurement.

Figure 7-5 shows Zn and Cu atomic emission lines for both 55 single-shot ensemble-

averaged spectra and their standard deviation curves at the same spectral window in

207









both Al alloy sample (D28) and NIST brass standard (1113). The standard deviations of

the spectra collected represent the variability in the analyte signals on a pixel column by

pixel column basis across the CCD array. Based on the simulated shape of the plot of

SD versus wavelength illustrated in the previous section, they are close to the case in

which the noise in the signal dominates over that of the background because Us

changes proportionally with a signal, i.e., case a-3; -s >> o-B (see Eq. 7-4). Figure 7-6

shows 55 single-shot LIBS spectra at the peak of Zn I 330.3 nm in both Al alloy sample

(D28) and NIST brass standard (1113) and each correlation factor 0 value between two

major noise sources was represented on the figures. The gate width and delay time

were 0.1 ps and 2.0 ps, respectively with the laser pulse energy of 90 5 mJ. For 55

single-shot spectra, the total noise (cr)exp was obtained by the experimental standard

deviation at the line center of Zn I 330.3 nm and the background noise (CoB)exp was

obtained by RMS noise at some distance on either side of the Zn I emission line, and

then the experimental standard deviation of net signal (d)ff exp was obtained by

correction of the background contribution under the Zn atomic line (see Eq. 7-6a). Each

0 value calculated is 0.527 and 0.871, respectively in both Al-alloy D28 sample (3.60 %

of Zn) and NIST brass 1113 standard (4.808 % of Zn). At a relatively high concentration

(e.g., 4.808 % of Zn in NIST brass standard), a high degree of correlation was observed.

This result may suggest that the correlation between noise sources depends on analyte

concentrations. For further study, correlation factor 0 values were also calculated as a

function of increasing Mg concentration in South African Al-alloy samples as shown in

Fig. 7-7. When the composition of Mg in Al-alloy samples increased, a high correlation

factor 0 was obtained. In particular, at the minimum concentration of Mg (0.004 % of

208









Mg), a correlation factor 0 is close to zero (0-~ 0.014, see Fig. 7-7c), which means no

correlation between noise sources at a low concentration. It would be explained that at

a low concentration, the continuum background decays significantly and signal

fluctuation due to the sampling process may be a major cause of the total noise. On the

other hand, the high degree of correlation between the noise in the background and the

noise in the signal, at a high concentration of the analyte, would be due to the origin of

the fluctuations, e.g., plasma temperature, electron number density and ablated mass.

For further study, the RSD approach was used for the examination of the spectral

behavior of the relative standard deviation of the various signals. It is very useful, even if

only approximately, to the identification of the limiting noise and to the different roles

played by the limiting noises during the lifetime of the plasma. Several limiting cases

simulated in the theory section were studied by plotting of the relative standard

deviation (RSD) versus wavelength in several samples under different experimental

conditions. One of the interesting points is that as the concentration of analyte in the

sample increases, the RSD value starts to decrease around the peak of the analyte. For

instance, Figure 7-8 and 7-9 clearly shows some changes of the RSD curves with

increasing of Mg and Cu compositions in South African Al-alloy samples and NIST

brass standards, respectively, at fixed delay time and gate width; i.e., 2.0 ps delay time

and 0.1 ps gate width. They would be applied to case b-3 because in the plot of

standard deviation versus wavelength in both figures, the SD curves were characterized

by an increase at the line center in comparison with the background intensities in all

samples (see Fig. 7-8b and 7-9b); in other words, s >> o-B. In this case, the plot of the

RSD versus wavelength depends upon the ratios of the right-hand side in Eq. 7-14b as


209









mentioned before (see Fig 7-3d). As examples, Figure 7-8d and 7-9d show clearly the

dependence of the ratios in Eq. 7-14b. At high concentrations of Mg and Cu, the RSD

values around the peaks shows a decreasing trend compared to the plasma

background intensity because S+B>> B (see the values of the ratios in Eq. 7-14b). In

contrast, as the concentration of the analyte decreases, the RSD value of the

background emission is relatively smaller than that of the line emission.

Temporal evolution of limiting noises. As an illustration of the above discussion,

limiting noises also depend strongly upon the temporal evolution of the plasma as well

as the analyte composition in a sample. A logical test for checking the temporal

dependence of limiting noises was performed at the Mn II 259.37 nm line for several

delay times in an Al-alloy sample (AA1) as shown in Fig. 7-10. Each spectrum,

measured for several delay times from 0.5 ps to 8.0 ps at a fixed gate width of 0.1 ps,

was averaged from 50 laser shots. The standard deviation curves at each delay time

were also plotted as a function of wavelength in Fig. 7-1 Ob. The result corresponds to

the shape simulated in Fig. 7-2e of the case a-3, i.e., a- << s. Let's consider a more

general case by using case a-4. As mentioned above, the correlation factor 0 values

between two major noise sources can be calculated by using Eq. 7-7 for each delay

time. In Fig. 7-1 Oc, as the delay time increases, a low correlation was found. That is, at

short delay time, a high correlation was observed due to the reduction of the

contribution of the shot noise to the total noise compared to the background noise, since

it is well known that shot noises are uncorrelated; at long delay time. On the other hand,

a low correlation was observed due to a significant decrease of the background

intensity.


210









Further study, as mentioned above, was also performed by plotting the relative

standard deviation (RSD) as well as the standard deviation (SD) as a function of

wavelength (a pixel column by pixel column basis across the CCD array) because the

RSD approach is very useful especially to the different roles played by the limiting

noises during the lifetime of the plasma. Figure 7-11 shows the RSD curves, which

correspond to Fig. 7-10, at the Mn II 259.37 nm line in the Al-alloy sample (AA1) for

different delay times. As the delay time increases, the RSD curves, which show no

enhancing features at the spectral positions of the analyte lines, are characterized by an

increase observed at the location of the analyte peak (e.g., at Mn II 259.37 nm). For

other instances, Figure 7-12 and 7-13 show the data sets obtained at extreme delay

times such as short delay and long delay times for the Ba II line in a BaCI2 pellet and for

several analyte peaks in the Al alloy sample (S5), respectively. At long delay times in

both samples, the relative standard deviation at the analyte peak (e.g., see the Ba II line

at 3.0 ps delay time) was characterized by an increase compared to the RSD in the

plasma background; while at short delay times, it show no features in the entire spectral

region. At the short delay time in which the strong plasma continuum emission appears

due to Bremsstrahlung and recombination radiation, the RSD value does not reveal any

significant difference between line emission and plasma continuum emission, which

would suggests some similar correlation in the degree of shot-to-shot variability over the

entire spectral range including the Ba ionic line and plasma continuum radiation as

shown in Fig. 7-12a. A similar result was observed in the data obtained from the Al-alloy

(S5) sample, as shown in Fig. 7-13. Thus, at the beginning of the plasma the limiting

noise in a measurement may be characterized by case b-2 (0 = 1) simulated in the


211









theory section because o-B o-s as shown in Fig. 7-13b. Case b-2 is valid only when the

signal and background intensities are same magnitude in order to get flat featureless

lines in the entire spectral region. However, there was very little difference between the

signal and background intensities at short delay time, but not a noticeable difference

when compared to that at long delay time of plasma. At the beginning of the plasma,

therefore, continuum emission is very dominant, and it can be comparable with line

emission. In other words, at early evolution times, one could suppose that the

continuum emission and line emission are correlated with each other (case b-2; i.e.,

-B & -s : 0= 1). In contrast, at long delay times, the continuum emission decays to a

negligible level and the fluctuations in the signal due to the sampling process and the

inherent signal noise would be the dominating sources of noise. This would suggest that

the signal fluctuation at the analyte peak dominates in comparison with that at the

continuum emission; hence, this case can be characterized by case 3 (-B <
standard deviation curves in Fig. 7-12d and 7-13d support the above discussion at long

delay times. Of course, in this case, the RSD curves depend upon the values of the

ratios as /o-B and B/B+S in Eq. 7-14b. As discussed in the theory section, it should be

noted that in these limiting cases, it is irrelevant whether 0 is equal to 0, +1 or -1. In

other words, correlation between the various noises should play no role at long delay

times.

As discussed above, the background correction for getting the net signal is not

ideal because in the study, it was assumed that an off-peak measurement of the plasma

background Bp, _e, is equal to the background intensity at the analyte peak Bp, 4 (see

Fig. 7-1). Thus, the main limitation of the procedure is related to the accuracy of the

212









background correction. We performed logical tests in order to know how different pixel

sizes and positions for a background selection can affect the calculation of a correlation

factor 0 because 0 depends on the shape of the background (whether it is flat or not)

and the selection of the background location. First of all, the correlation factor 0 was

plotted as a function of standard deviation as well as concentration for different pixel

sizes, such as a single wavelength (or 1-pixel) at 284.748 nm as well as the one

averaged by 20 pixels as shown in Fig. 7-7. The result for both pixel sizes showed

significantly similar values except for 0.004% Mg (see Fig. 7-7d). Moreover, several

regions (e.g., A, B, C and D) of the background intensity near the peak of Mn II 259.37

nm were selected and compared with a single pixel of the background region A ~ C in

order to study the dependence of the background selection on the calculation of a

correlation factor 0 in Fig. 7-14. Each 0 value calculated shows a slight discrepancy

with the overall average value of ~ 0.4, but it is not significant whatever the background

regions are or the pixel sizes are in our experiment. However, the line intensity may

have been influenced by the contribution from the true continuum, such as that which

originates from the plasma electrons, to the whole spectra. Thus, it is important to select

appropriate shape and location of the true background. However, even though the

accuracy of a correlation factor 0 depends on several factors, this study is valuable in

order to show the relative degree of correlation at the different experimental conditions

(e.g., different delay times, laser pulse energies, different concentrations and so on). In

addition, Figure 7-15 shows the experimental percentage RSD of the net line intensity

(% RSDnet ) as a function of the analyte concentration. For the study, the Mg I 285.21

nm line in 7 Al-alloy samples and the Zn I 330.26 nm line in 6 NIST brass standards


213









were used. At low concentrations, the values of % RSDnet were relatively high compared

to the high concentrations of the analytes. Thus, the background intensity used for

correction can has a significant role in the accuracy of the approach at a low

concentration. For instance, at low concentration, a correlation factor 0 obtained by a

single-pixel measurement in the background region had a value of 0.46; for the

measurement averaged by 20 pixels. On the other hand, it had a value of 0.014 as

shown in Fig. 7-7d. That is, the discrepancy of the correlation factor 0 for the use of the

different backgrounds (e.g., different pixel-size or location of background) was about

44.6 %. In contrast, the discrepancies at higher concentrations were within 10%. This

discrepancy resulted in a high % RSDnet at the low concentration. Therefore, any minor

change in the shape of the background in the selected window and the matrix effect in a

various samples will result in an inadequate background correction and a wrong RSD of

the net signal, which may be the limitation in the determination of % RSDnet at low

concentrations.

Characterization of the type of limiting noises. To provide some additional

insight into the nature of spectral noise, a complementary approach aimed at identifying

the type of noise affecting the measurement was used, i.e., it consists in repeating the

above described procedures with a plot of the log of Sner,, /o-t as a function of the log of

the analyte net signal Snet,4, since the S/N ratio is the reciprocal of the RSD. This is

equivalent to a plot of the relative standard deviation versus signal. From the results

obtained on each sample, the plot of the signal to noise versus signal (e.g,

concentration of the analyte) will provide the information sought.


214









To study the dependence of the S/N on the analyte signal, log Snet,4 was obtained

with the Mg I line at 285.21 nm in the South African Al-alloys containing increasing Mg

concentration (Fig. 7-16a). The delay time and gate width were fixed at 2.0 ps and 0.1

ps, respectively. The curves show a linear response with a slope near 0.5 (slope ~

0.460). If signal shot noise becomes dominant, a log-log slope is 0.5 because of the

square root dependence of signal shot noise on signal, as detailed by Ingle and Crouch

[100]. Otherwise, if background and/or signal flicker noise is significant or dominant

compared to signal shot noise at certain signal levels, a log-log slope no longer follows

the square root dependence of signal shot noise on signal. In other words, the presence

of signal flicker noise or background noise reduces the S/N to a value below that

achievable if only signal shot noise is present. Analysis of the S/N study revealed an

agreement with the results obtained for the RSD study. From the result obtained for Al-

alloy samples at 2.0 ps delay time, the limiting noise of the measurement can be

characterized by signal shot noise (due to the sampling process and the inherent signal

shot noise). Otherwise, Figure 7-16b shows the case in which the log-log slope in the

plot is close to unity. NIST brass standards were used for these experiments (at the Zn I

330.3 nm emission line), and the delay time and gate width used was the same as

above. As an illustration of the above, where background noise is dominant, the log-log

slope is unity [100]. Thus, the assumption that all noise sources, in most cases, are

totally uncorrelated, is not valid from our results.

From the experimental considerations mentioned in the previous discussion, it is

hypothesized that the only noises considered are background noise and signal noise.

That is, the dark current noise can be neglected, together with excess detector noise


215








and readout noise. For checking the hypothesis, we can also use the propagation of

errors for two quantities by the method described above, such as background noise and

dark current noise:

b "ank = + + 20_JD]112 (7-19a)


(0blank)exp [ xp +( exp]12 ,if 0=0 (7-19b)

where 0 is the correlation factor between plasma background noise and dark current

noise. Thus, if the correlation factor is zero, it can be assumed that the assumption in

our approach is valid, i.e., the dark current can be negligible. In Eq. 7-19b, we assumed

that the two noise sources are totally uncorrelated (i.e., 0 =0), and then compared the

values obtained from (oB)exp and (o-D)expwith (lank)exp because these values could be

obtained experimentally from the data sets. If two noise sources are uncorrelated,

(o-lank)exp should be equal to (o-B xp plus (oD)exp.

Since the correlation between the analyte signal and the background depends

strongly upon the delay time chosen for the measurement, two extreme delay times,

e.g., short delay time and long delay time, were chosen for the study as shown in Fig. 7-

17. At the short delay time, the two noise sources are totally uncorrelated; i.e., the

values in both sides of Eq. 7-19b are of very similar magnitude (i.e., (2ank)exp= 1.105 x

108 and (oB)exp exp = 1.106 x 10 ) and aB is 44 times larger than o-D; while, at the

long delay time, there is some discrepancy between (oank)exp and (o-')exp +(O'2)exp

compared to that at the short delay time, but it is barely significant (i.e., ( lank)exp= 3.058

x 108 and (QO)exp + ()exp= 2.624 x 108), and -rB >o c by 6.7 times. Thus, some


216









correlation between the background and dark current can exist at long delay time

because the background decays significantly. However, in this study, we conclude that

the contribution of dark current can be considered negligible for a reasonable delay time,

but it should be checked due to the decrease of the plasma background during the

lifetime of the plasma.

Finally, this approach may also alert one to the existence of self-absorption at

analyte peaks from the standard deviation curve. Fig. 7-5 shows that the standard

deviation curve appears to scale with the ensemble-averaged line profile across the

entire spectral window in the Al-ally sample (D28); otherwise, in the NIST brass sample

(1113), it is not the same scale with the line profile. For further study, a full width at half

maximum (FWHM) was determined by fitting a Voigt profile for the Cu I resonance line

at 324.7nm for a comparison of the line width between the SD curve and the line profile

in each Al-alloy and NIST brass sample as shown in Fig. 7-5. At a high concentration of

Cu (95.19 % of Cu in NIST brass 1113), the FWHM values of line profile and SD curve

showed a significant difference by ~ 0.07 nm (see Fig. 7-5c and d). In other words, the

peak in the SD curve was broadened compared to that in the line profile. In contrast, at

a low concentration of Cu (1.76 % of Cu in Al-alloy D28), the FWHM values in both line

profile and SD curve showed the same values (about 0.12 nm); hence, the SD curve

appears to scale with the line profile. From these results, we found a very interesting

point that it is possible to check for the existence of self-absorption using only the SD

curve. In our study, this trend was also proved several times. For instance, the samples,

e.g., Al-alloy D28 (0.004 % of Mg) and S11 (1.11 % of Mg), containing two extreme

concentrations were chosen based on our previous work (see Fig. 7-18); i.e., the mirror


217









experiment for checking of self-absorption [166]. All results corresponded to those in the

case of the Cu I resonance line. That is, the FWHM values in both the SD curve and line

profile were different at a high concentration (1.11 % of Mg), but not at a low

concentration (0.004 % of Mg). Thus, this approach is very informative for checking for

self-absorption as well as for examining the limiting noise of measurement.

Conclusions

All considerations made in the study relate to the signals and associated standard

deviations and to the precision of the measurement; i.e., to the relative standard

deviation. Within the simplifying assumptions made and the validity of these

assumptions, it is argued that the behavior observed by plotting the standard deviation

of each spectral element (pixel) versus wavelength, as it results from a series of a

number of single-shot spectra, taken with a series of samples containing increasing

concentration or a single sample in the same spectral window for different delay times,

can indeed be informative with respect to the following characteristic aspects in a

measurement:

* It indicates the precision in a LIBS measurement and temporal evolution of plasma.

* It assesses the degree of correlation between the plasma background and the
analytical signal.

* It suggests, even if only approximately, the identification of the limiting noise and
to the different roles played by the limiting noises for temporal evolution of plasma
as well as different concentrations.

On the other hand, while being informative for the limiting noise in a measurement,

the above considerations can also provide some information about the type of noise

present in a measurement. One can concluded that the measurement is affected by

shot noise, since it is well known that shot noises are uncorrelated. In addition, a


218









complementary approach aimed at identifying the type of noise affecting the

measurement was also used. The above described procedure using several samples

containing increasing concentration of an analyte are very similar. From the results

obtained on each sample, the plot of the S/N versus signal (or concentration) provides

the information sought. Needless to say, this is equivalent to a plot of the RSD versus

signal (concentration), since the S/N ratio is the reciprocal of the RSD.

The experimental results in our study are characterized by the following features:

* The correlation between the peak signal and the background depends strongly
upon the delay time chosen for the measurement. In the SD and RSD curve
approach, for instance, it was observed that there is no correlation between noise
sources at long delay time; otherwise, there is some similar correlation between
atomic emission and plasma background at short delay time.

* The correlation also depends upon the concentration of an analyte. At high
concentrations, noise sources contributed around the emission line are strongly
correlated with each other.

* The degree of correlation between major noise sources in LIBS measurement was
calculated, as the correlation factor 0. It allows quantitative analysis for the degree
of correlation under different experimental conditions (e.g., different delay times,
laser pulse energies, different concentrations and so on). The accuracy of this
approach can be limited in the background correction for getting the net signal
because in the study, it was assumed that an off-peak measurements of the
background (B, off-peak ) is equal to the background measurement under the peak of
the emission line (Bp, ). Thus, it is important to select appropriate shape and
location of the true background, in particular, in the case of weak backgrounds.

* From the result of the correlation factor 0 obtained, the high degree of correlation
between noise sources is related to the reduction of the contribution of the shot
noise to the total noise compared to background noise. Thus, it can be explained
that at short delay time or high concentration, a high correlation was observed due
to the reduction of the contribution of the shot noise by high background intensity.

* From above results, the assumption that all noise sources, in most cases, are
totally uncorrelated, is not valid. In addition, from the plot of log (S/N) versus log
(s), both signal shot noise and signal flicker noise/ or background noise may be
influencing each other on the measurement.


219









* This approach hints the existence of self-absorption by comparison of a full width
at half maximum (FWHM) of the line profile with the associated SD curve.


220













Al II281.62 nm

S --








I--i
-- B ^





281.0 281.5 282.0 282.5 283.0

Wavelength (nm)


Figure 7-1. An example of the description of net signal: i.e., the simplest signal
measurement consists of the peak intensity (Snet,,A) at the central wavelength
of the analyte line and an off-peak measurement of the background at a
single position (BA0,off-peak )


221














-(a)



B^ B+SZ----- ------------------1 S
>
Ca

3 3 Ca

Ln
8C
o a _,


0-0, 1
a [a,- + 20->02] --2-a
/ \
I I

X (Pixels)


(b)/






(iec


X, (Pixels)


0= 0


U 0I5
^-^ ^-v-- ^ \>^%=c



04--- 't


0=1


-32o =2


k (Pixels)


0


a
_0


"0
C
Co


-s = -rB
0=-1


4


2. (Pixels)


as a5
9=0, 1

---:-- -- "-- : /

. ... (on I ,*- __ -
'5

-- -- -- -


a (Pixels)


Figure 7-2. In standard deviation (SD) limiting cases, simulated shapes of the plot SD

versus wavelength.


222


B


(e)
B,+S ------


BS,--------------------------




B


CfB) 2











TS <<
0=0, l1


(R~
Q~5L~ SZB2BJ c~)


---Pixels (-) ,2

PiRxels () '2


0=0


(I~JB&~(S Q


01 Pixels () 0,2


US = 9"B


(c) 0 +1
S(SD= (RS D), 2







P (
,1 Pixels (.)0o,2


2B "
CS+B)
S>B


S=B


S

(d) S
8 0=0, 1
(RSD) (RSD),B

B



It depends upon thevalue
of the ratios (ola ) and
S Pixels (B( S)

Pixels (X) 0,2


Figure 7-3. In relative standard deviation (RSD) limiting cases, simulated shapes of
the plot RSD versus wavelength.


223














3.Oxl 0
2.5x105
2.0xl 05
1.5x105
1.0x105
5.0x1 0
0.0


324 326 328 330 332
Wavelength (nm)


250000-


200000-


150000-


100000-


50000-


0


324.771 -- 55-shot ensernble-averaged
(b) Standard deviation
Relative standard deviation
AI alloy D28
327.428



330.259

328.243




324 326 328 330 332


-24

-20

-16

-12

-8

-4

-0


Wavelength (nm)



Figure 7-4. (a) 3D LIBS spectra for 55 laser shots in an Al-alloy (D28) sample and (b) a
55-shot ensemble-averaged LIBS spectrum (black line) with both associated
standard deviation (red line) and relative standard deviation (blue line). Used
gate delay time and gate width are 2.0 ps and 0.1 ps, respectively.


224












Cu I Cul I
(a) 24771 AI-alloy D28 2.5x10' (b) 324.771 Standard deviation
1 76 % of Cu
3.60 % of Zn 2.0x10 -
1.5x105- Cu I Cu I
S327.428 327.428
S1.5x10 -
5 U)
S1Ox 0x10 -- -
S"FWHM Zn I 1.0x104- FWHM
~0 12 nm 330.259 0 12 nm Zn I
330244
5 x04 Zn I 5.0x10 Zn


0.0 .. 0.0 '- '
324 326 328 330 332 324 326 328 330 332
Wavelength (nm) Wavelength (nm)


Cul __S n rD io
1 4x106 (C) 324.771 NIST 1113 1 x10-(d) 324771 Standard Deviation
1.2x106 I Cul 95.19% of Cu 327.412
327.428 4.808 % of zn 8 O0x10
1 Ox- 10M
60x10'-
8.0x10
S6 Ox105 FWHM 4 Ox4 FWHM 330.774
-0 19 nm Cu I 26 n
4 Ox105- Cul 330.79 329 041
Zn 1329.041 2 Ox1Q 0 328.25
2 Ox100 32825 Zn 1 331 709
0.0 .. 00
324 326 328 330 332 324 326 328 330 332
Wavelength (nm) Wavelength (nm)



Figure 7-5. Zn and Cu atomic emission lines for both (a and c) 55 single-shot ensemble-
averaged spectra and (b and d) associated standard deviation curves at the
same spectral range in Al alloy sample (D28) and NIST brass standard (1113),
respectively. In both samples, the settings on the detection system were 2.0
us and 0.1 ps for the gate delay time and gate width, respectively. Each full
width at half maximum value of Cu I resonance line at 324.7 nm was obtained
by fitting a Voigt profile (see the blue arrows).


225












(a) 0 -0.527
(o-u). 5S7S9


Zn I 330.3 nm


7000 (I d f)l!')e p 5565
70000-
60000

40000- -
50000 .. .

20000 -.
10000- -. .
--- --------------- -- B
329.0 329.5 330.0 330.5 331.0 331.5
Wavelength (nm)



(b) 6- 0.871 cu I


400000


300000

S200000
.i
( 100000
4-I
_0
c


Zn I 330.3 nm ,
(x)321()1
6X ,)o io .tf ...
,,3 .'/ l


I-




.. -_- .-B-.-
3 5- 0- 3 5 8217
329.5 330.0 330.5 331.0 331.5


i-f. k


Wavelength (nm)



Figure 7-6. (a and b) 55 single-shot LIBS spectra at the peak of Zn I 330.3 nm in both
Al-alloy sample (D28) and NIST brass standard (1113), respectively. (The
used gate delay time and gate width were 2.0 ps and 0.1 ps, respectively.)
Each correlation factor 0 between two major noise sources was calculated at
the peak of Zn I 330.3 nm by using Eq. 7-7. In Al-alloy sample (D28), 0 is
0.527, while in NIST brass standard (1113), 0 is 0.871.


226


(070) =




















-1.11 %ofMg
B000000 1.08 %ofMg > 1000000
B70%of Mg *"g .
a -0 150% of Mg C-
E 0210 %of Mg 500000-
'0.07 %ofMg C
00'004 ofMg
281 282 283 284 285 286 287 0
Wavelength (nm) 284.0 284.5 285.0 285.5 286.0 286.5
Wavelength (nm)


Mg I 285.21 nm
1.8 () Mg I 285.21 nm 1.2 (d)

0o .,0 0.8- .-

0 0.9- Q -
0 .6 04
|06 I 02.
o 0.3 0 0.0 2
0.3-. *0 averaged by 20 pixels
0.0. [ averaged by 20 pixels -0.2- single pixel at 284.75 nm
00 0.2 0.4 06 0.8 1 0 1.2 0 2000 4000 6000 8000 10000 12000
Mg concentration (%) Standard deviation



Figure 7-7. (a and b) LIBS spectra for the several Mg compositions in Al-alloy samples
(Square box indicates the region for zoom-in) and (c and d) experimentally
calculated correlation factor as a function of both concentration and standard
deviation of the background measured near Mg I 285.21 nm, respectively.
Either a single pixel or 20 pixels measurement was used for the determination
of the standard deviation of the background measured.


227













Al- alloy samples


Standard deviation


0
SM10 (D


AA3



D28
---"-- AA 'A---'"-A- A 3
278 280 282 284 286
Wavelength (nm)


Zoom in


Wavelength (nm)


280 282 284
Wavelength (nm)



Mg I 285 21 nm


284.5 285.0 285.5
Wavelength (nm)


Figure 7-8. (a) LIBS spectra (ensemble-averaged) showing the Mg I and II lines and Al
II line and (b) standard deviation curves for 50 laser shots in 6 Al-alloys
samples. (c) Relative standard deviation (RSD) curves as calculated from the
quotient of the standard deviation (square box indicates the region for zoom-
in). (d) RSD curves showing the increase of Mg composition.


228


1.8x101
1.5x10
1.2x10'


g.Oxl10
9.0x10-

3o.0x10
0.0


\ 1 08 %of Mg

NA 0.870 %of Mg

0.200 %of Mg


k,- 0.038 %of Mg

0.004 %of Mg

286.0













| Standard Deviation


NIST brass standard
(a) Cul Zn I


2 0.
1 6.
S12x
8 x0
4 Ox


324 326 328 330 332
Wavelength (nm)


20 1(c)


S12
Zoom15
1110
1 o8 Zoom in


324 326 328 330 332
Wavelength (nm)


1107



1115
1112
1113
324 326 328 330 332
Wavelength (nm)


Cu I 324.7 nm
(d) 62.111% of Cu


S65.362% of Cu


S 87.184 % of Cu

88.234% of Cu



95.192 %ofCu


Figure 7-9. (a) LIBS spectra (ensemble-averaged) showing the Cu I and Zn I lines and
(b) standard deviation curves for 50 laser shots in 7 NIST brass standards. (c)
Relative standard deviation (RSD) curves as calculated from the quotient of
the standard deviation (square box indicates the region for zoom-in). (d) RSD
curves showing the increase of Cu composition.


229













Mn II 259.37nm


30x10 -

2








2.5x10 n(b)
2.0x104
1 .5x104

1.0x104

5.0x103
0.0


0 0 -


/ 0.5 js


1.0 Vs
.5 p.s


Wavelength (nm)

Standard Deviation


258.8 259.0 259.2 259.4 259 6 259.8
Wavelength (nm)




(c)








ely-time ( s) ---_-

0 1 2 3 4 5 6 7 8
Delay time (.s)


Figure 7-10. (a and b) LIBS spectra and standard deviation curves as a function of
wavelength for different delay times at Mn II 259.37 nm in Al-alloy (AA1)
sample. (c) The plot of correlation factor 0 versus delay time.


230










Mn II 259.37 nm


-- -- 0.5 is
1.0 [[s
1.54 s


O 4.0 4s

8.0 ps
258.8 259.0 259.2 259.4 259.6 259.8
Wavelength (nm)


Figure 7-11. The plot of a relative standard deviation versus wavelength for different
delay times at Mn II 259.37 nm in Al-alloy (603) sample.


231


















n
10 O
L


U) 4000


Wavelength (nm)


Wavelength (nm)


A


(d) 3.0 ps delay time Standard Deviation f


0
-10 Q,


(c) 3.0 ps delay time -- Intensity
Ba II % RSD









RSD curve
-----.u-- I ---


XUx i ; ----------'------'--r
248 250 252 254 256 258
Wavelength (nm)


2000


U I .. .
248 250 252 254 256 258
Wavelength (nm)


Figure 7-12. (a and b) The ensemble-averaged spectra for Ba II in BaCI2 pallet at 0.5 us
and 3.0 us delay times, respectively with each RSD curve and (c and d)
associated SD curves.


232


5x 10o


4x10'


3x10'


"F 2x10'

- 1x105


lx10i-

lx10i-

9x104-

8x10' -

7x104

6x104-












1 .0 x 1 0 5 -d r----
(b) 0.5 ps delay time Standard Deviation
a oxi '4


IO
10


Wavelength (nm)


Wavelength (nm)


Wavelength (nm)


Wavelength (nm)


Figure 7-13. The ensemble-averaged spectra for several elements in Al-alloy (S5)
sample at (a) 0.5 us and (c) 5.0 us delay times, respectively with each RSD
curve (blue line) and (c and d) associated SD curves.


233


5x106

4x106

.-, 3x106
c
| 2x106

IxIo0


(a) 0.5 ps delay time -- Intensity
--% RSD





FeI+NiI Fel












. (a)


0UUUUUU0

800000

600000

400000

200000-


600000-

500000

400000-

300000-

200000-

100000-
Ut


Al alloy AA1


at 2 0 us delay time


254 256 258 260 262 264
Wavelength (nm)


(C) Mn II 259.37 nm
at 2.0 ps delay time a


(averaged by 10 pixels) o o

l D .
4T C a Ic ".


25000-

20000-

15000-
(0
10000-

5000-

0-
25


1 5

1 0.

05

S0.0

-05


258.6 2589 259.2 259.5 2598
Wavelength (nm)


Mn II 259.37 nm


B.8 258.9 256.2 25B.5 252.8
Wavelength (nm)


A *w B
A D a


1 I .


2600


N* *
C


* single pixel in the region A-C
* averaged by 20 pixels


2800 3000 3200 3400 3600 3800
Standard Deviation


Figure 7-14. (a) LIBS spectrum at 2.0 us delay time in Al-alloy (AA1) sample including
0.540 % of Mn and (b) the standard deviation curve only near Mn II 259.37
nm line. (c) LIBS spectrum showing Mn ionic emission line at 259.37 nm. The
region A, B, C and D indicate the region selected for RMS noise calculation.
(d) Experimental values of the correlation factor 0 as a function of standard
deviation of the background measured by 10 pixels (the region A,B ,C and D:
black squares) and single pixel (the region A~C, blue dots).


234


i


























Mg I 285.21 nm
0.0 02 04 06 08 1.0 1.2
Mg Concentration (%)


0 ,


r 12
0)

a) 9
-c
Z 6
4--
0

u) 3
r _


2 4 6 8 10 12 14 16
Zn Concentration (%)


Figure 7-15. Experimental percent RSD of the net signal (% RSDnet) as a function of the
analyte concentration (a) at Mg I 285.21 nm line in 7 Al-alloy samples an (b)
at Zn I 330.26 nm line in 6 NIST brass standards.


235


Zn I 330 26 nm











(a)

4 Mg I 285.21 nm


3- 3


^ 2 -- ..- '-
0 log-log slope = 0.460

1-

Al-alloy samples
5.4 5.6 5.8 6.0 6.2 6.4 6.6 6.8 7.0
Log (S)


3-
(b)

Zn 1 330.26 nm



I ---'-'-
0) log-log slope ~ 1.16
0 1-



0 ,NIST brass standards
5.4 5.5 5.6 5.7 5.8 5.9 6.0 6.1
Log (S)


Figure 7-16. The log of the signal-to-noise (S/N) ratio as a function of the log of net-
signal for (a) Mg I 285.21 nm in 5 Al-alloy samples and (b) Zn I 330.26 nm in
7 NIST brass standards.


236












20x10'


1.5x10


- 1.Ox10


5 Ox10


(a) 0.5 ps delay time S

Fe I
FeFe







Al alloy sample (SM10)


363 364
Wavelength (nm)


365 362.0 362.5 363.0 363.5 364.0 364.5

Wavelength (nm)


363 364 365 362.0 362.5 363.0 363.5 364.0 364.5
Wavelength (nm) Wavelength (nm)


Figure 7-17. (a and c) LIBS spectra and (c and d) associated SD curves at both 0.5 us
and 3.0 ps delay times, respectively in Al-alloy (SM10) sample.


237










5x104

4x104

3x104

2x104 U

1x104

0


284.6 284.8 285.0 285.2 285.4


Wavelength (nm)


2.0x1 07--
(b)

1.5x1 07


1.0x107


5.0x1 06


0.0 ,
284.6 284.8


S1 1.0x106
Intensity .
-SD
8.0x105

Al-alloy D28 (1.11 % of Mg)
-6.0x105
M l

M FWHM -4.0x105
~ 0.17 nm
S2.0x105
285F0 2852 285WH 4 285
0.13 n 0 .0
285.0 285.2 285.4 285.6


Wavelength (nm)


Figure 7-18. (a and b) LIBS spectra and associated SD curves at Mg I 285.21 nm in the
samples containing two extreme concentrations such as Al-alloy D28
(0.004 % of Mg) and S11 (1.11 % of Mg).


238









Table 7-1. Factors affecting quantitative analysis


Source Factor Comments


Laser


Detector


Sampling parameters


Sample


Laser pulse energy,
laser pulse power,
repetition rate

Detector gain


Linearity of response


Lens-to-sample distance


Changes in optical path
transmission to/from
sample

Change of atmosphere
above sample

Uniformity of
composition

Uniformity of surface


Chemical matrix effects


Physical matrix effects


Typically stable to within a few percent
for constant temperature operation


Keep constant or calibrate response if
gain in changed

Operate in region of linear response or
change gain to maintain linearity

May be maintained through an
automated focusing system; less a
problem for longer focal lengths; use of
a collimated beam to form the plasma
can minimize effects

Absorption/scattering of laser pulse
over optical path to sample by gases
and aerosols

Gas pressure and composition affect
ablation and plasma properties

Sufficient averaging to obtain
representative sample

Sufficient averaging to obtain
representative sample

Under certain experimental conditions,
effect may be reduced

Under certain experimental conditions,
effect may be reduced


239


using LIBS.









Table 7-2. Elemental percentage composition of South African aluminum alloy
standards disks (APEX Smelter Co., South Africa).


Element
Al
Si
Mg
Cu
Zn
Fe
Mn
Ni
Ti
Cr
Sn
Pb


Element
Al
Si
Mg
Cu
Zn
Fe
Mn
Ni
Ti
Cr
Sn
Pb


D28
81.55
9.66
0.004
1.76
3.6
0.98
0.59
0.43
0.033
0.21
0.3
0.34


AA1
69.58
14.60
0.170
5.70
5.90
1.73
0.540
0.600

0.280
0.500
0.380


V14
86.74
6.2
0.025
4.05
0.42
0.9
0.58
0.33
0.17
0.18
0.28


S5
74.95
2.240
0.090
5.750
14.94
0.760
0.550
0.210
0.110
0.110
0.110
0.120


D33
84.92
8.54
0.038
2.89
0.59
1.15
0.4
0.5
0.055
0.047
0.048
0.14


S11
89.20
0.450
1.110
0.980
6.850
0.570
0.500
0.100
0.065
0.115


B8
87.98
2.33
0.076
6.95
0.52
0.8
0.4
0.5
0.16
0.17
0.155
0.165


SM1
96.46
0.390
1.000
0.970
0.500
0.410
0.110
0.050


AA3
69.14
17
0.2
8
3.2
1.77
0.21
0.106
0.078
0.1
0.12
0.08


S4
83.79
1.03
0.35
2.64
10.9
0.119
0.38
0.18
0.12
0.13
0.15
0.13


R14
79.59
14
0.87
2.05
0.48
0.63
0.92
0.97
0.16
0.11
0.12
0.1


Z8
78.79
0.84
1.27
16.05
0.79
1.09
0.26
0.53
0.17
0.15


SM10
84.67
2.92
1.08
2.8
5.45
1.96
0.295
0.065
0.055
0.2
0.26
0.245


SM9
85.34
1.690
0.430
3.000
3.700
3.700
0.760
0.200
0.070
0.380
0.310
0.320


Table 7-3. Elemental percentage composition of NIST brass standards.
Element 1107 1108 1110 1111 1112 1113 1114 1115 1116
Cu 61.210 64.950 84.590 87.140 93.380 95.030 95.450 87.960 90.370
Zn 37.340 34.420 15.200 12.810 6.300 4.800 3.470 11.730 9.440
Fe 0.037 0.050 0.033 0.010 0.070 0.043 0.017 0.130 0.046
Mn 0.025
Ni 0.098 0.033 0.053 0.022 0.100 0.057 0.021 0.074 0.048
P 0.009 0.008 0.009 0.005 0.008
Pb 0.180 0.063 0.033 0.013 0.057 0.026 0.012 0.013 0.042
Sn 1.040 0.390 0.051 0.019 0.120 0.064 0.027 0.100 0.044
Note: Certified values are obtained from the NIST standard reference materials
database,http://ts.nist.gov/measurementservices/referencematerials/index.cfm


240









Appendix


Glossary


S,4 = (D +Bp,4 +S)



S, = (DAA, + Bp, AA2, + SA)

Sn,,, = (S, 4-D4 -Bp, 4)


Snet, A2 = (St DA, Bp, AA, )


B, = (D +Bp, 4)


Bt A = (DA + B p, AA,)


B, --(Bt


-D 4)


Bp,A =(B, -DA2,)


D4

DAA


B,






B Aff-pdk


B p, Aff-peak



Bp, A of-peak


Average total counts due to dark signal, plasma
background and signal, measured at the center of the
line 2o (line peak).
Average total counts due to dark signal, background
and signal, spectrally integrated over the line width.
Average net counts due to signal, measured at the
center of the line (line peak).
Average net counts due to signal, spectrally integrated
over the line width.
Average total counts due to plasma continuum with
dark signal measured at the center of line (line peak)
Average total counts due to plasma continuum with
dark signal, spectrally integrated over the line width.
Average counts due to plasma continuum measured at
the center of the line (line peak).
Average counts due to plasma continuum, spectrally
integrated over the line width.
Average counts due to dark signal measured at the
center of line (line peak).
Average counts due to dark current, spectrally
integrated over the line width.
Average total counts due to plasma continuum with
dark signal measured at a wavelength in the vicinity of
the line (off-peak), but not in the line wings.
Average total counts due to plasma continuum with
dark current, spectrally integrated over the same
number of pixels used for AA,, but measured in the
vicinity of the line (off-peak), and not including the line
wings.
Average counts due to plasma continuum measured at
a wavelength in the vicinity of the line (off-peak), but
not in the line wings.
Average counts due to plasma continuum, spectrally
integrated over the same number of pixels used for AA,,


241









but measured in the vicinity of the line (off-peak), but
not including the line wings.
Average counts due to dark current measured at a
wavelength in the vicinity of the line (off-peak), but
not in the line wings.
Average counts due to dark current, spectrally
integrated over the same number of pixels used for AA,,
but measured in the vicinity of the line (off-peak), and
not including the line wings.


242









CHAPTER 8
CONCLUSION AND FUTURE WORK

Summary

The general scope of my research involved largely two aspects related to the

fundamental study and the analytical characterization of the technique Laser Induced

Breakdown Spectroscopy (LIBS). This project revisited and investigated in more details

some of the conditions and/or assumptions commonly made in LIBS, such as the

existence of local thermodynamic equilibrium (LTE) and of optically thin plasma

conditions, i.e., the absence of the phenomenon of self-absorption. Moreover, double-

pulse LIBS was also studied with the aim of understanding the relative importance of

the factors concurring to the enhancement of the emission line intensity as well as the

underlying physical mechanism. Finally, the spectral fluctuation approach, a novel way

of data analysis in LIBS, was also investigated and proven to be very informative to

determine the type of noise present in a measurement as well as the limiting noise of

the measurement.

Line-to-continuum intensity ratio method. Most studies in LIBS measurements

have been performed under the assumption of the existence of LTE conditions. The

LTE state is a good approximation in describing the plasma conditions, but the reliability

of the hypothesis is heavily dependent on various experimental factors such as the

temporal evolution of the plasma, and the spatial inhomogeneities associated with its

transient behavior. Thus, it is essential to investigate the plasma parameters as

thoroughly as possible in order to determine the existence of LTE conditions or the

extent of departure from it. To this purpose, a line-to-continuum intensity ratio method,

discussed in Chapter 4, was used for the evaluation of LTE. In this approach, the


243









theoretical ratio between the intensity of selected transitions, considered being optically

thin, and the underlying spectral continuum were used (see Eq. 4-6). In these

expressions, the excitation temperature and the electron temperature were purposely

kept different from each other. Experimentally, the plasma excitation temperature, Texc,

was obtained from a conventional Boltzmann plot/or Saha-Boltzmann plot, and the ratio

between the spectrally integrated line intensity and the continuum intensity was

measured. By inserting these two experimental values into the theoretical expression in

Eq. 4-6, one could check whether the electron temperature derived in this way was

equal or different from the excitation temperature provided by the Boltzmann plot,

therefore assessing any deviation from LTE conditions. It was evident from the results

that LTE is a good approximation in describing the plasma conditions usually after a

delay time from the onset of the plasma of 2.0 ps. In addition, it was found that the delay

time necessary for achieving LTE was reduced in the case of the ionic species

compared to that of the atomic species, due to the high-lying energy level of ionic

species.

Self-absorption. In LIBS, emission measurements are often affected by the

phenomenon of self-absorption, i.e., the plasma conditions are optically thick. Various

ways of accomplishing this task are described in the plasma literature [29, 53, 81, 118-

126]. My research proposes the application of an old method [128] for quantifying the

effect of self-absorption on atomic and ionic emission lines. Chapter 5 illustrates this

method, which is simple and quick to implement, does not need either changing the

sample concentration or calculating a curve of growth [53], and uses an external mirror

to double the optical path length of the plasma emission in direction of the


244









monochromator. The calculation of the so-called duplication factor as well as the

comparison of the line profiles obtained with and without the mirror allowed not only to

prove the existence of the self-absorption effect but also to apply a correction factor and

to retrieve the original profile.

Spectroscopic study of the factors concurring to the intensity enhancement

in double-pulse LIBS. One of the most attractive approaches to improve the LIBS

sensitivity and reproducibility without losing its non-selective behavior is to use the

double-pulse excitation scheme. For example, the matrix-matched requirement, which is

a well-known limitation of nanosecond laser ablation, can be partially reduced by using

double-pulse scheme. In Chapter 6, in agreement with the results of the literature, we

observed a significant improvement of the signal-to-noise (S/N) ratio in the orthogonal

double-pulse (DP) scheme compared to the LIBS single-pulse (SP) scheme. Several

mechanisms may be responsible for the observed enhancement, and a number of

suggestions addressing the mechanisms of enhancement of the double-pulse LIBS

signal have been proposed. However, the mechanisms of the double-pulse

enhancement are not completely understood and the topic is still the subject of

investigation.

In our study, two different schemes in orthogonal double-pulse configuration (i.e.,

pre-ablation air spark and reheating double-pulse scheme) were optimized with the aim

of achieving the largest enhancements. A novel spectroscopic approach to characterize

the factors concurring to the enhancement was also performed in order to understand

its physical mechanisms. The approach is based on the theoretical relation between the

logarithm of the ionic and neutral line enhancements as a function of the excitation


245









energy of the lines investigated (as shown in Eq. 6-11). Such approach gives

information at first glance on the change of plasma temperature, number density and

neutral/or singly ionized fraction of the atoms of the analyte in the plasma, when the

sample irradiation conditions on the sample change from SP to DP.

Noise analysis in LIBS. In all analytical methods, and therefore in LIBS as well,

the precision of a measurement is limited by noise/or fluctuation in the measured

signals. Thus, the study of the noise in LIBS spectra is essential for understanding

these fluctuations and their effect on the results. In Chapter 7, we have simulated many

possible limiting noise situations present in a LIBS measurement by observing the

behavior of the plots of the standard deviation and relative standard deviation resulting

from many single-shot spectra on a pixel-by-pixel (wavelength) basis. Moreover, a

possible correlation between the noise in the background and the noise in the signal

has been also studied. The degree of correlation between these noise sources in LIBS

measurement was calculated experimentally, and then the relevance of the noises was

evaluated by the correlation factor 0. Finally, a complementary approach for identifying

the type of noise affecting the measurement was also used, as detailed by Ingle and

Crouch [100]. This approach relies on the slope of the plots of the S/N as a function of

the log of the signal (concentration). This procedure is equivalent to a plot of the relative

standard deviation versus signal, since the S/N ratio is the reciprocal of the RSD. By

carefully analyzing the results, it was clearly shown that the noise type as well as the

limiting noise source strongly depends on the delay time and on the measuring gate

width, i.e., on the temporal evolution of plasma. Moreover, our results also indicated a


246









temporal dependence of the degree of correlation between the line emission and the

underlying background continuum.

Future Work

The verification of the existence of local thermodynamic equilibrium by the line-to-

continuum intensity ratio method should be continued and applied to different LIBS set-

ups and irradiation geometries. In fact, the reliability of the LTE assumption is heavily

dependent not only on the temporal evolution of plasma, but also to various

experimental factors in LIBS measurement, including the laser pulse energies and the

environment.

Similarly, the application of the mirror approach described in Chapter 5 for

studying self-absorption effects can be extended to double-pulse LIBS as well. To the

author's knowledge, no studies have yet appeared discussing specifically the effect of

self-absorption in double-pulse LIBS. In our preliminary double-pulse work, such effect

was indeed observed for several lines, which were optically thin in the corresponding

single-pulse experiment. By applying the same correction procedure outlined in Chapter

5, the non linearity in the calibration curves (due to the effect of self-absorption) can be

accounted for, thus extending the linear dynamic range of the technique.

Finally, the spectral fluctuation approach should be applied to a large variety of

sample targets, illumination conditions and acquisition settings (delay time and

measuring gate width), as well as to different environments (air, other gases, reduced

pressures, etc.).

As a general conclusion, it appears that there is still ample room for improvement

not only in the theoretical modeling of the LIBS plasmas, but also in devising more

refined experimental set-ups and novel approaches to data analysis.

247









LIST OF REFERENCES

[1] Cremers, D. A.; Radziemski, L. J. Handbook of laser-induced breakdown
spectroscopy, John Wiley & Sons, Ltd 2006.


[2] Miziolek, A. W. P., V.; Schechter, I. Laser Induced Breakdown
spectroscopy:Fundamentals and Applications, Cambridge, UK; Cambridge
University Press 2006.


[3] Maiman, T. H. Nature, 1960, 187, 493-494.


[4] Radziemski, L. J. Spectrochimica Acta, Part B: Atomic Spectroscopy, 2002, 57B,
1109-1113.


[5] Brech, F.; Cross, L. Applied Spectroscopy, 1962, 16, 59-62.


[6] Maiman, T. H. British Communications and Electronics, 1960, 7, 674-5.


[7] Debras-Guedon, J.; Liodec, N. Bulletin de la Societe Francaise de Ceramique,
1963, No. 61, 61-8.


[8] Maker, P. D.; Terhune, R. W.; Savage, C. M. Proceedings of the 3rd International
Conference on Quantum Electronics, Paris, 1964, 2, 1559.


[9] Runge, E. F.; Minck, R. W.; Bryan, F. R. Spectrochimica Acta, 1964, 20, 733-6.


[10] Raizer, Y. P. Breakdown and heating of gases under the influence of a laser
beam 1966.


[11] Afanas'ev, Y. V.; Krokhin, 0. N. Soviet Physics JETP, 1967, 25, 639-645.


[12] Biberman, L. M.; Norman, G. E. Uspekhi Fizicheskikh Nauk, 1967, 91, 193-246.


[13] Buravlev, Y. M.; Nadezhda, B. P. Atom. spektroskopiya i spektr. analiz., 1974,
292-5.


248









[14] Raizer, Y. P. Laser-induced Discharge Phenomena, Consultants Bureau: New
York 1977.


[15] Cerrai, E.; Trucco, R. Energia Nucleare (Milan), 1968, 15, 581-7.


[16] Marich, K. W.; Carr, P. W.; Treytl, W. J.; Glick, D. Analytical Chemistry, 1970, 42,
1775-9.


[17] Lencioni, D. E. Applied Physics Letters, 1973, 23, 12-14.


[18] Belyaev, E. B.; Godlevskii, A. P.; Kopytin, Y. D. Kvantovaya Elektronika
(Moscow), 1978, 5, 2594-601.


[19] Edwards, A. L.; Fleck Jr, J. A. Journal of Applied Physics, 1979, 50, 4307-4313.


[20] Ivanov, A. K.; Kopytin, Y. D. Soviet Journal of Quantum Electronics, 1982, 12,
355-357.


[21] Loree, T. R.; Radziemski, L. J. Plasma Chemistry and Plasma Processing, 1981,
1, 271-9.


[22] Radziemski, L. J.; Loree, T. R. Plasma Chemistry and Plasma Processing, 1981,
1, 281-93.


[23] Cremers, D. A. Applied Spectroscopy, 1987, 41, 572-9.


[24] Cremers, D. A.; Archuleta, F. L.; Martinez, R. J. Spectrochimica Acta, Part B:
Atomic Spectroscopy, 1985, 40B, 665-79.


[25] Cremers, D. A.; Radziemski, L. J. Analytical Chemistry, 1983, 55, 1252-6.


[26] Cremers, D. A.; Radziemski, L. J. Applied Spectroscopy, 1985, 39, 57-63.


[27] Cremers, D. A.; Radziemski, L. J.; Loree, T. R. Applied Spectroscopy, 1984, 38,
721-9.


249









[28] Radziemski, L. J.; Cremers, D. A.; Loree, T. R. Spectrochimica Acta, Part B:
Atomic Spectroscopy, 1983, 38B, 349-55.


[29] Radziemski, L. J.; Loree, T. R.; Cremers, D. A.; Hoffman, N. M. Analytical
Chemistry, 1983, 55, 1246-52.


[30] Belyaev, E. B.; Godlevskii, A. P.; Kopytin, Y. D.; Krasnenko, N. P.; Muravskii, V.
P.; Shamanaeva, L. G. Pis'ma v Zhurnal Tekhnicheskoi Fiziki, 1982, 8, 333-7.


[31] Kitamori, T.; Yokose, K.; Suzuki, K.; Sawada, T.; Gohshi, Y. Japanese Journal of
Applied Physics, Part 2: Letters, 1988, 27, L983-L985.


[32] Ko, J. B.; Sdorra, W.; Niemax, K. Fresenius Zeitschrift Fur Analytische Chemie,
1989, 335, 648-651.


[33] Lawrenz, J.; Niemax, K. Spectrochimica Acta Part B-Atomic Spectroscopy, 1989,
44, 155-164.


[34] Leis, F.; Sdorra, W.; Ko, J. B.; Niemax, K. Mikrochimica Acta, 1989, 2, 185-199.


[35] Leis, F.; Ko, J. B.; Niemax, K. Fresenius Zeitschrift Fur Analytische Chemie,
1989, 334, 649-649.


[36] Quentmeier, A.; Sdorra, W.; Niemax, K. Fresenius Zeitschrift Fur Analytische
Chemie, 1989, 334, 650-650.


[37] Sdorra, W.; Quentmeier, A.; Niemax, K. Mikrochimica Acta, 1989, 2, 201-218.


[38] Ko, J. B.; Sdorra, W.; Niemax, K. Fresenius' Zeitschrift fuer Analytische Chemie,
1989, 335, 648-51.


[39] Leis, F.; Sdorra, W.; Ko, J. B.; Niemax, K. Mikrochimica Acta, 1989, 2, 185-99.


[40] Adrain, R. S.; Watson, J. Journal Of Physics D-Applied Physics, 1984, 17, 1915.


[41] Radziemski, L. J.; Cremers, D. A., 1989, pp.437.


250









[42] Radziemski, L. J. Microchemical Journal, 1994, 50, 218-34.


[43] Lee, Y.-I.; Song, K.; Sneddon, J. Lasers in Analytical Atomic Spectroscopy, 1997,
197-235.


[44] Rusak, D. A.; Castle, B. C.; Smith, B. W.; Winefordner, J. D. Critical Reviews in
Analytical Chemistry, 1997, 27, 257 290.


[45] Tognoni, E.; Palleschi, V.; Corsi, M.; Cristoforetti, G. Spectrochimica Acta, Part
B: Atomic Spectroscopy, 2002, 57B, 1115-1130.


[46] Lee, W.-B.; Wu, J.; Lee, Y.-I.; Sneddon, J. Applied Spectroscopy Reviews, 2004,
39, 27-97.


[47] Wallis, F. J.; Chadwick, B. L.; Morrison, R. J. S. Applied Spectroscopy, 2000, 54,
1231-1235.


[48] Cremers, D. A.; Barefield, J. E.; Koskelo, A. C. Applied Spectroscopy, 1995, 49,
857-860.


[49] Lazzari, C.; De Rosa, M.; Rastelli, S.; Ciucci, A.; Palleschi, V.; Salvetti, A. Laser
and Particle Beams, 1994, 12, 525-30.


[50] Ciucci, A.; Corsi, M.; Palleschi, V.; Rastelli, S.; Salvetti, A.; Tognoni, E. Applied
Spectroscopy, 1999, 53, 960-964.


[51] Mao, X. L. L.; Shannon, M. A.; Fernandez, A. J.; Russo, R. E. Applied
Spectroscopy, 1995, 49, 1054-1062.


[52] Castle, B. C.; Talabardon, K.; Smith, B. W.; Winefordner, J. D. Applied
Spectroscopy, 1998, 52, 649-657.


[53] Gornushkin, I. B.; Anzano, J. M.; King, L. A.; Smith, B. W.; Omenetto, N.;
Winefordner, J. D. Spectrochimica Acta, Part B: Atomic Spectroscopy, 1999, 54B,
491-503.


[54] Piepmeier, E. H.; Malmstadt, H. V. Analytical Chemistry, 1969, 41, 700.


251









[55] Scott, R. H.; Strasheim, A. Spectrochimica Acta Part B: Atomic Spectroscopy,
1970, 25, 311.


[56] Cremers, D. A.; Radziemski, L. J.; Loree, T. R. Applied Spectroscopy, 1984, 38,
721.


[57] Anglos, D.; Couris, S.; Fotakis, C. Applied Spectroscopy, 1997, 51, 1025-1030.


[58] Georgiou, S.; Zafiropulos, V.; Tomari, V.; Fotakis, C. Laser Physics, 1998, 8,
307-312.


[59] Georgiou, S.; Zafiropulos, V.; Anglos, D.; Balas, C.; Tornari, V.; Fotakis, C.
Applied Surface Science, 1998, 127, 738-745.


[60] Pallikaris, I. G.; Ginis, H. S.; Kounis, G. A.; Anglos, D.; Papazoglou, T. G.;
Naoumidis, L. P. Journal Of Refractive Surgery, 1998, 14, 655-660.


[61] Eppler, A. S.; Cremers, D. A.; Hickmott, D. D.; Ferris, M. J.; Koskelo, A. C.
Applied Spectroscopy, 1996, 50, 1175-1181.


[62] Miles, B.; Cortes, J. Field Analytical Chemistry and Technology, 1998, 2, 75-87.


[63] Theriault, G. A.; Bodensteiner, S.; Lieberman, S. H. Field Analytical Chemistry
and Technology, 1998, 2, 117-125.


[64] Milan, M.; Vadillo, J. M.; Laserna, J. J. Journal Of Analytical Atomic Spectrometry,
1997, 12, 441-444.


[65] Boulmer-Leborgne, C.; Hermann, J.; Dubreuil, B. Plasma Sources Science &
Technology, 1993, 2, 219-226.


[66] Callies, G.; Berger, P.; Hugel, H. Journal of Physics D: Applied Physics, 1995, 28,
794-806.


[67] Wen, S.-B.; Mao, X.; Greif, R.; Russo, R. E. Journal of Applied Physics, 2007,
101, 123105.


252









[68] Yalcin, S.; Crosley, D. R.; Smith, G. P.; Faris, G. W. Applied Physics B: Lasers
and Optics, 1999, 68, 121-130.


[69] Schittenhelm, H.; Callies, G.; Berger, P.; Hugel, H. Applied Surface Science,
1997, 109-110, 493.


[70] Singh, J. P.; Thakur., S. N. Laser-induced breakdown spectroscopy, Elsevier:
Amsterdam; Bostor; London 2007.


[71] Wen, S. B.; Mao, X. L.; Greif, R.; Russo, R. E. Journal Of Applied Physics, 2007,
101, 023115.


[72] Ng, C. W.; Ho, W. F.; Cheung, N. H. Applied Spectroscopy, 1997, 51, 976-983.


[73] Russo, R. E. Applied Spectroscopy, 1995, 49, 14A-28A.


[74] Thorne, A. P. Spectrophysics: London, Chapman and Hall; New York, Wiley,
1974, 402p.


[75] Aguilera, J. A.; Aragon, C. Spectrochimica Acta Part B-Atomic Spectroscopy,
2008, 63, 793-799.


[76] Griem, H. R., Plasma Spectroscopy; McGraw-Hill, New York, 1964, 580p.


[77] Lochte-Holtgreven, W.; Editor. Plasma Diagnostics 1968.


[78] Thorne, A. P.; Litzen, U.; Johansson, S. Spectrophysics: Principles and
Applications, Berlin; New York: Springer, cl999.

[79] Omenetto, N.; Winefordner, J. D.; Alkemade, C. T. J. Spectrochimica Acta, Part
B: Atomic Spectroscopy, 1975, 30B, 335-41.


[80] Konjevi6, N. Physics Reports-Review Section of Physics Letters, 1999, 316, 339-
401.


[81] El Sherbini, A. M.; El Sherbini, T. M.; Hegazy, H.; Cristoforetti, G.; Legnaioli, S.;
Palleschi, V.; Pardini, L.; Salvetti, A.; Tognoni, E. Spectrochimica Acta Part B:
Atomic Spectroscopy, 2005, 60, 1573-1579.

253









[82] Friedjung, M.; Muratorio, G. Astronomy and Astrophysics, 1987, 188, 100-8.


[83] Kastner, S. 0.; Kastner, R. E. Journal of Quantitative Spectroscopy & Radiative
Transfer, 1990, 44, 275-88.


[84] Irons, F. E. Journal Of Quantitative Spectroscopy & Radiative Transfer, 1979, 22,
1-20.


[85] Habib, A. A. M.; EI-Gohary, Z. Journal Of Quantitative Spectroscopy & Radiative
Transfer, 2002, 72, 341-347.


[86] Pestehe, S. J.; Tallents, G. J. Journal Of Quantitative Spectroscopy & Radiative
Transfer, 2002, 72, 853-878.


[87] Alkemade, C. T. J.; Hollander, T.; Snelleman, W.; Zeegers, P. T. T. International
Series in Natural Philosophy, Vol. 103: Metal Vapors in Flames 1982.


[88] Boumans, P. W. J. M. Analytical Spectroscopy Series, 1972, 1, Pt. 2, 1-254.


[89] Cowan, R. D.; Dieke, G. H. Reviews of Modem Physics, 1948, 20, 418-55.


[90] Fujimoto, T. Plasma Spectroscopy, Oxford University press 2004.


[91] Huddlestone, R. H.; Leonard, S. L.; Editors. Plasma Diagnostic Techniques (Pure
and Applied Physics, Vol. 21) 1965.


[92] Omenetto, N.; Winefordner, J. D. Progress in Analytical Atomic Spectroscopy,
1979, 2, 1-183.


[93] Bye, C. A.; Scheeline, A. Applied Spectroscopy, 1993, 47, 2022.


[94] Liu, H. C.; Mao, X. L.; Yoo, J. H.; Russo, R. E. Spectrochimica Acta, Part B:
Atomic Spectroscopy, 1999, 54B, 1607-1624.


[95] Bastiaans, G. J.; Mangold, R. A. Spectrochimica Acta, Part B: Atomic
Spectroscopy, 1985, 40B, 885-92.


254









[96] Fisher, V.; Bernshtam, V.; Golten, H.; Maron, Y. Physical Review A: Atomic,
Molecular, and Optical Physics, 1996, 53, 2425-32.


[97] Nicholson, J. P. Plasma Physics and Controlled Fusion, 1989, 31, 1433-41.


[98] Burgess, A.; Summers, H. P. Monthly Notices of the Royal Astronomical Society,
1987, 226, 257-72.


[99] Demtroder, W. Laser Spectroscopy: Basic Concepts and Instrumentation, 2nd
edition, Springer 1996.


[100] Ingle Jr, J. D.; Crouch, S. R. Spectrochimical Analysis, Prentice Hall 1988.


[101] Griem, H. R. Physical Review, 1963, 131, 1170-1176.


[102] Griem, H. R. Principles of Plasma Spectroscopy 1997.


[103] Barthelemy, 0.; Margot, J.; Laville, S.; Vidal, F.; Chaker, M.; Le Drogoff, B.;
Johnston, T. W.; Sabsabi, M. Applied Spectroscopy, 2005, 59, 529-536.


[104] Calzada, M. D. Memorie della Astronomica Italiana Supplement, 2005, 7, 198-
207.


[105] Capitelli, M.; Capitelli, F.; Eletskii, A. Spectrochimica Acta, Part B: Atomic
Spectroscopy, 2000, 55B, 559-574.


[106] Kruger, C. H.; Owano, T.; Gordon, M.; Laux, C. Pure and Applied Chemistry,
1992, 64, 607-13.


[107] Sola, A.; Calzada, M. D.; Gamero, A. Journal of Physics D: Applied Physics,
1995, 28, 1099-110.


[108] Zeng, X.; Mao, S. S.; Liu, C.; Mao, X.; Greif, R.; Russo, R. E. Spectrochimica
Acta, Part B: Atomic Spectroscopy, 2003, 58B, 867-877.


[109] Moon, H. Y.; Omenetto, N.; Smith, B. W.; Winefordner, J. D. In NORTH
AMERICAN SYMPOSIUM LIBS 2009: New Orleans, LA., USA, 2009.

255









[110] Amoruso, S. Applied Physics A: Materials Science & Processing, 1999, 69, 323-
332.


[111] Drawin, H. W.; Felenbok, P. Data for Plasmas in Local Thermodynamic
Equilibrium 1965.


[112] Torres, J.; Jonkers, J.; van de Sande, M. J.; van der Mullen, J. J. A. M.; Gamero,
A.; Sola, A. Journal of Physics D: Applied Physics, 2003, 36, L55-L59.


[113] Pupyshev, A. A.; Semenova, E. V. Spectrochimica Acta, Part B: Atomic
Spectroscopy, 2001, 56B, 2397-2418.


[114] McWhirter, R. W. P. Plasma Diagnostic techniques, New York Academic 1965.


[115] Fujimoto, T.; McWhirter, R. W. P. Physical Review A, 1990, 42, 6588-6601.


[116] Herrera, K. K.; Tognoni, E.; Omenetto, N.; Smith, B. W.; Winefordner, J. D.
Journal Of Analytical Atomic Spectrometry, 2009, 24, 413-425.


[117] Galmed, A. H.; Harith, M. A. Applied Physics B: Lasers and Optics, 2008, 91,
651-660.


[118] Simeonsson, J. B.; Miziolek, A. W. Applied Optics, 1993, 32, 939-47.


[119] Sabsabi, M.; Cielo, P. Applied Spectroscopy, 1995, 49, 499-507.


[120] Hermann, J.; Boulmer-Leborgne, C.; Hong, D. Journal of Applied Physics, 1998,
83, 691-696.


[121] Gornushkin, I. B.; Stevenson, C. L.; Smith, B. W.; Omenetto, N.; Winefordner, J.
D. Spectrochimica Acta, Part B: Atomic Spectroscopy, 2001, 56B, 1769-1785.


[122] Lazic, V.; Barbini, R.; Colao, F.; Fantoni, R.; Palucci, A. Spectrochimica Acta Part
B: Atomic Spectroscopy, 2001, 56, 807-820.


[123] Aragon, C.; Bengoechea, J.; Aguilera, J. A. Spectrochimica Acta Part B-Atomic
Spectroscopy, 2001, 56, 619-628.

256









[124] Bulajic, D.; Corsi, M.; Cristoforetti, G.; Legnaioli, S.; Palleschi, V.; Salvetti, A.;
Tognoni, E. Spectrochimica Acta Part B: Atomic Spectroscopy, 2002, 57, 339-
353.


[125] Amamou, H.; Bois, A.; Ferhat, B.; Redon, R.; Rossetto, B.; Ripert, M. Journal of
Quantitative Spectroscopy & Radiative Transfer, 2003, 77, 365-372.


[126] Ribiere, M.; Cheron, B. G.; Bultel, A. High Temperature Material Processes
(Redding, CT, United States), 2008, 12, 109-120.


[127] Aguilera, J. A.; Bengoechea, J.; Aragon, C. Spectrochimica Acta Part B-Atomic
Spectroscopy, 2003, 58, 221-237.


[128] Gouy, L. G. Comptes Rendus, 1879, 88, 418-421.


[129] Harrison, J. A. Proceedings of the Physical Society, London, 1959, 73, 841-8.


[130] Jentschke, H.; Schumacher, U.; Hirsch, K. Contributions To Plasma Physics,
1998, 38, 501-512.


[131] Lesage, A.; Konjevic, N.; Fuhr, J. R. AIP Conference Proceedings, 1999, 467,
27-36.


[132] Myeong, H. S.; Xichun, H.; Terry, A. m. Chemical physics, 1998, 228, 145-156.


[133] Zwicker, H.; Schumacher, U. Zeitschrift fuer Physik, 1965, 183, 453-71.


[134] Goto, T.; Mori, M.; Hattori, S. Applied Physics Letters, 1976, 29, 358-360.


[135] Ichikawa, Y.; Teii, S. Journal Of Physics D-Applied Physics, 1980, 13, 1243-1251.


[136] Kobilarov, R.; Konjevic, N.; Popovic, M. V. Physical Review A, 1989, 40, 3871-
3879.


[137] Santiago, I.; Calzada, M. D. Applied Spectroscopy, 2007, 61, 725-733.


257









[138] Gornushkin, I. B.; Heitmann, U.; Moore, G.; Omenetto, N.; Smith, B. W.;
Winefordner, J. D. In Poster presented at FACSS 2006: Orlando, Fl, 24-28, 2006,
pp. pp. 108-109, Abstract #167.


[139] De Galan, L.; Winefordner, J. D. Spectrochimica Acta, Part B: Atomic
Spectroscopy, 1968, 23, 277-89.


[140] Gautier, C. i.; Fichet, P.; Menut, D.; Lacour, J.-L.; L'Hermite, D.; Dubessy, J.
Spectrochimica Acta Part B: Atomic Spectroscopy, 2005, 60, 265.


[141] Gautier, C. i.; Fichet, P.; Menut, D.; Lacour, J.-L.; L'Hermite, D.; Dubessy, J.
Spectrochimica Acta Part B: Atomic Spectroscopy, 2004, 59, 975.


[142] Tognoni, E.; Palleschi, V.; Corsi, M.; Cristoforetti, G. Spectrochimica Acta Part B:
Atomic Spectroscopy, 2002, 57, 1115.


[143] Winefordner, J. D.; Gornushkin, I. B.; Correll, T.; Gibb, E.; Smith, B. W.;
Omenetto, N. Journal of Analytical Atomic Spectrometry, 2004, 19, 1061-1083.


[144] Miziolek, A.; Palleschi, V.; Schechter, I., 2006, pp. 516-538.


[145] Scaffidi, J.; Angel, S. M.; Cremers, D. A. Analytical Chemistry, 2006, 78, 24.


[146] Sattmann, R.; Sturm, V.; Noll, R. Journal of Physics D: Applied Physics, 1995, 28,
2181.


[147] St-Onge, L.; Detalle, V.; Sabsabi, M. Spectrochimica Acta Part B: Atomic
Spectroscopy, 2002, 57, 121.


[148] Rai, V. N.; Yueh, F.-Y.; Singh, J. P. Applied Optics, 2003, 42, 2094.


[149] Kuwako, A.; Uchida, Y.; Maeda, K. Appl. Opt., 2003, 42, 6052.


[150] Kraushaar, M.; Noll, R.; Schmitz, H. U. Applied Spectroscopy, 2003, 57, 1282.


[151] De Giacomo, A.; Dell'Aglio, M.; Colao, F.; Fantoni, R. Spectrochimica Acta Part
B: Atomic Spectroscopy, 2004, 59, 1431.

258









[152] Corsi, M.; Cristoforetti, G.; Giuffrida, M.; Hidalgo, M.; Legnaioli, S.; Palleschi, V.;
Salvetti, A.; Tognoni, E.; Vallebona, C. Spectrochimica Acta Part B: Atomic
Spectroscopy, 2004, 59, 723.


[153] Uebbing, J.; Brust, J.; Sdorra, W.; Leis, F.; Niemax, K. Applied Spectroscopy,
1991, 45, 1419.


[154] Stratis, D. N.; Eland, K. L.; Angel, S. M. Applied Spectroscopy, 2001, 55, 1297.


[155] Stratis, D. N.; Eland, K. L.; Angel, S. M. Applied Spectroscopy, 2000, 54, 1270.


[156] Stratis, D. N.; Eland, K. L.; Angel, S. M. Applied Spectroscopy, 2000, 54, 1719.


[157] Pearman, W.; Scaffidi, J.; Angel, S. M. Appl. Opt., 2003, 42, 6085.


[158] Cristoforetti, G.; Legnaioli, S.; Pardini, L.; Palleschi, V.; Salvetti, A.; Tognoni, E.
Spectrochimica Acta Part B: Atomic Spectroscopy, 2006, 61, 340.


[159] Sobral, H.; Villagran-Muniz, M.; Navarro-Gonzalez, R.; Raga, A. C. Applied
Physics Letters, 2000, 77.


[160] Ivarez-Trujillo, L. A.; Ferrero, A.; Laserna, J. J.; Hahn, D. W. Applied
Spectroscopy, 2008, 62, 1144.


[161] Alvarez-Trujillo, L. A.; Ferrero, A.; Laserna, J. J. Journal of Analytical Atomic
Spectrometry, 2008, 23, 885-888.


[162] Mermet, J. M.; Mauchien, P.; Lacour, J. L. Spectrochimica Acta Part B: Atomic
Spectroscopy, 2008, 63, 999.


[163] Poussel, E.; Mermet, J. M. Spectrochimica Acta Part B-Atomic Spectroscopy,
1996, 51, 75-85.


[164] Salin, E. D.; Horlick, G. Anal. Chem. FIELD Full Journal Title:Analytical
Chemistry, 1980, 52, 1578-82.


259









[165] Taylor, J. R. An Introduction to Error Analysis: The study of Uncertainties in
Physical Measurements 1982.


[166] Moon, H. Y.; Herrera, K. K.; Omenetto, N.; Smith, B. W.; Winefordner, J. D.
Spectrochimica Acta Part B: Atomic Spectroscopy, 2009, 64, 702-713.


260









BIOGRAPHICAL SKETCH

Heh Young Moon was born and raised in Seoul, South Korea. She is the oldest

daughter in a family that includes her parent Soon-Kee Moon and Jong-Rye An, three

sisters and one brother. Heh Young received bachelor's degree in chemistry from Sun

Moon University in March of 1995 and received a master's degree in physical chemistry

from Korea University in March of 1999. During this time, Heh Young earned a full

scholarship and fellowship: Excellent (top) scholarships from Sun Moon University and

Brain Korea 21 Fellowship from Korea University. She also worked as a graduate

student research assistant (GRA) in the Korea Research Institute of Standards and

Science (KRISS) in South Korea during the master degree program from 1999 to 2000.

After graduation, she also worked as general chemistry coordinator as well as part-time

lecturer in Korea University from 2000 to 2003. She married Dooho Park in December

of 2003 and then followed her husband in 2004 in order to join a PhD program at

University of Florida in Gainesville, Florida. She entered the University of Florida in the

fall of 2005 and joined Professor Nicolo6 Omenetto group to work on her doctoral degree

in physical chemistry.


261





PAGE 1

1 DIAGNOSTIC AND ANALYTICAL STUDIES OF LASER INDUCED PLASMAS By HEH YOUNG MOON A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2010

PAGE 2

2 2010 Heh Young Moon

PAGE 3

3 To my parents, my husband (D ooho Park ) and my lovely daughter (S uebin P ark )

PAGE 4

4 ACKNOWLEDGMENTS I would like to express my sincere appreciation to my mentor Dr. Nicol Omenetto f or his outstanding guidance and discuss ion, understanding, patience, and most importantly, his friendship during my graduate studies at University of Florida. It has been a wonderful experience to work in Dr. O menetto lab for that he has always created the best ever environment for us to conduct scientific experiments under his mentorship and insightful discussion I believe h e is a wonderful scientist and wonderful person I really respect his enthusiasm eagerness and deep knowledge to the research. When ever I felt that I could not go on much longer he had encouraged me all the time to not only grow as an experimentalist and a chemist but also as an instructor and an independent thinker so that I can focus on my research again done for me, Professor Omenetto, I would like to gratefully and sincerely thank you again. I would also like to acknowledge to Dr. James D. Winefordner for his all the insightful comments and support for my research in our regular meeting even thought he has a lready retired from the faculty at UF. I am also grateful to Dr. Benjamin W. Smith for his good guide and advice from his scientific experience and knowledge. He is also wonderful person and scientist. I think I have been very fortunate to have many resear ch co supervisors. I could never have been able to finish my dissertation without the guidance of them. I also thank my committee members, Dr. Philip Brucat, Dr. Nicolas Polfer and Dr. David Hahn. I would like to thank all the previous and current members in our group, especially Dr. K athleen Kate Herrera and Daniel Edward Shelby for all insightful discussion on LIBS and a good friendship. I also thank to Dr. Ben it Lauly Jonathan A. Mert en and Richard A. Warren for a good discussion and all the help

PAGE 5

5 Fi nally, and most importantly, I would like to thank my family for all of their love and support without which I could not have managed to complete my dissertation. I would like to thank my husband Dooho Park for understanding and love during the past few years His support, encouragement, patience and unwavering faith and love were in the end what made this dissertation possible. I also would like to thank to my daughter, Suebin Park (a source of unending joy and love), has been wonderfully understanding t hroughout the dissertation process and has been awaiting the day when I would be finished. Specially, I would also like to thank my parent for taking care of my daughter during two years in South Korea for helping me focus on my research. My mother always listened to me on the phone and encouraged me to continue on with the research whenever I was stressed and feeling down.

PAGE 6

6 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ .. 4 LIST OF TABLES ................................ ................................ ................................ ............ 9 LIST OF FIGURES ................................ ................................ ................................ ........ 10 L IST OF ABBREVIATIONS ................................ ................................ ........................... 19 LIST OF SYMBOLS AND CONSTANTS ................................ ................................ ....... 21 ABSTRACT ................................ ................................ ................................ ................... 28 CHAPTER 1 INTENT AND SCOPE OF STUDY ................................ ................................ .......... 30 2 FUNDAMENTAL OF LIBS ................................ ................................ ...................... 32 Introduction ................................ ................................ ................................ ............. 32 The Discovery of LIBS ................................ ................................ ............................ 32 General Principle of LIBS [1] ................................ ................................ ................... 36 LIBS Design (General) ................................ ................................ ..................... 37 Basics of Laser Matter Inte raction and Processes in Laser Induced Plasma ... 37 3 FUNDAMENTAL INVESTIGATION OF LASER INDUCED PLASMA ..................... 48 Introduction ................................ ................................ ................................ ............. 48 Spectral Emission from Plasma ................................ ................................ .............. 49 Width and Shape of Spectral Lines [74] ................................ ........................... 51 Determining Electron Densities from Spectral Line Widths .............................. 56 Plasma Opacity ................................ ................................ ................................ 57 Thermodynamic Equilibrium and Temperature ................................ ................. 61 4 LINE TO CONTINUUM INTENSITY RATIO IN LASER INDUCED BREAKDOWN SPECTROSCOPY AS AN EXPERIMENTAL CHECK TO LOCAL THERMODYNAMIC EQUILIBRIUM ................................ ........................... 72 Introduction ................................ ................................ ................................ ............. 72 Theory [107] ................................ ................................ ................................ ............ 74 Line to Continuum Intensity Ratio Method for Determining of T e ..................... 74 Experimental ................................ ................................ ................................ ........... 78 Results and D iscussion ................................ ................................ ........................... 79 Electron N umber D ensity (n e ) ................................ ................................ ........... 79 Excitation T emperature (T exc ) ................................ ................................ ........... 82

PAGE 7

7 Electron T emperature (T e ) ................................ ................................ ................ 83 Conclusion s ................................ ................................ ................................ ............ 88 5 ON THE USEFULNESS OF A DUPLICATING MIRROR TO EVALUATE SELF ABSORPTION EFFECTS IN LASER INDUCED BREAKDOWN SPECTROSCOPY ................................ ................................ ................................ 102 Introduction ................................ ................................ ................................ ........... 102 The Self absorption Correction Factor K ................................ ............................. 104 Experimental ................................ ................................ ................................ ......... 109 Results and Discussion ................................ ................................ ......................... 109 Evaluation of R C ................................ ................................ ............................. 109 Evaluation of R ................................ ................................ .............................. 110 Temporal Behavior of K ,corr and D ................................ ........................... 111 Self absorption Corrected Saha Boltzmann Plots ................................ .......... 113 Self absorpt ion Corrected Calibration Curves ................................ ................ 114 Conclusions ................................ ................................ ................................ .......... 115 6 A COMPARISON OF SINGLE VERSUS DOUBLE PULSE LASER INDUCED BREAKDOWN SPECT ROSCOPY ................................ ................................ ....... 134 Introduction ................................ ................................ ................................ ........... 134 Experimental ................................ ................................ ................................ ......... 136 Laser and D etector S ystem ................................ ................................ ............ 136 Triggering S ystem ................................ ................................ .......................... 139 Results and D iscussion ................................ ................................ ......................... 139 Opt imization ................................ ................................ ................................ ... 139 Time gated, Spectrally Resolved, One direction Images in Single and Orthogonal Double Pulse Pre ablation Scheme ................................ .......... 146 Spectroscopic Study of the Factors Concurring to the Intensity Enhancement in Double pulse LIBS ................................ ........................... 150 Conclusions ................................ ................................ ................................ .......... 159 7 CONSIDE RATION ON THE SPECTRAL FLUCTUATION APPROACH IN LASER INDUCED BREAKDOWN SPECTROSCOPY ................................ .......... 195 Theory ................................ ................................ ................................ ................... 196 Standard Deviation Limiting Cases ................................ ............................. 199 Relative Standard Deviation Limiting Cases ................................ ................ 203 Experimental ................................ ................................ ................................ ......... 206 Results and Discussion ................................ ................................ ......................... 207 Conclusion s ................................ ................................ ................................ .......... 218 Appendix ................................ ................................ ................................ ............... 241 Glossary ................................ ................................ ................................ ......... 241 8 CONCLUSION AND FUTURE WORK ................................ ................................ .. 243 Summary ................................ ................................ ................................ .............. 243

PAGE 8

8 Future Work ................................ ................................ ................................ .......... 247 LIST OF REFERENCES ................................ ................................ ............................. 248 BIOGRAPHICAL SKETCH ................................ ................................ .......................... 261

PAGE 9

9 LIST OF TABLES Table page 2 1 Significant milestones in the development of LIBS as an analytical technique applicable to a variety of samples and circumstance s [1] ................................ ... 46 2 2 Advantages and disadvantages of laser induced breakdown spectroscopy ....... 47 4 1 Selected spectral lines and corresponding spectroscopic information of the investigated elements (a) ................................ ................................ .................... 100 4 2 Gating and laser energy parameters used for temporal characteristic and line to continuum intensity ratio method of pure copper metal: (a) at the short delay times with laser puls e energy 50 5 mJ and (b) at long delay times with laser pulse energy 90 5 mJ ................................ ................................ .... 101 5 1 Elemental percentage composition of South African aluminum alloy standards disks (APEX Smelter Co., Sou th Africa) [166]. ................................ 132 5 2 Selected spectral line and corresponding spectroscopic information of the investigated elements (a) [166] ................................ ................................ ........... 133 6 1 Concentration of several elements in NIST Al SRM 603 and South African Al alloy standards AA1 and D28 (APEX Smelter Co., South African) ................... 190 6 2 Selected spectral lines and correspon ding spectroscopic information of the investigated elements (a) ................................ ................................ .................... 191 6 3 All parameter values mentioned in Eq. 6 11 at different delay times (pre ablation air spark scheme) ................................ ................................ ............... 192 6 4 Plasma temperature and electron number density in both single and orthogonal pre ablation air spark double pulse configuration at different delay times. ................................ ................................ ................................ ................ 193 6 5 All parameter values mentioned in Eq. 6 11 at different delay times (reheating scheme) ................................ ................................ ........................... 194 6 6 Plasma temperature and electron number density in both single and orthogonal reheating double pulse configuration at different delay times. ........ 194 7 1 Factors affecting quantitative analysis using LIBS. ................................ ........... 239 7 2 Elemental percentage composition of South African aluminum alloy standards disks (APEX Smelter Co., South Africa). ................................ ......... 240 7 3 Elemental percentage composition of NIST brass standards. .......................... 240

PAGE 10

10 LIST OF FIGURES Figure page 2 1 Diagram of a typical laboratory LIBS apparatus. ................................ ................ 42 2 2 A s ummary of laser ablation (LA) processes and various mechanisms occurring during each process. Inserted figure shows the schematic diagram of expanding laser produced plasma into ambient gas in detail. The plasma plume is divided into several zones having h igh density hot and low density cold plasma. The farthest zone from the target has minimum plasma density and temperature. The laser is absorbed in low density corona [70]. .................. 43 2 3 Timing of th e physical phenomenon observed during the plasma expansion and two major types of laser absorption wave schemes [68, 71]. ....................... 44 2 4 (a) Relevant time periods after plasma formation during which e mission from different species predominate. The box represents the time during which the plasma light is monitored using a gatable detector. (Here, t d is the delay time and t w is the gate pulse width.) (b) Relevant timing periods for a double pulse configu ration. (Here, t is interpulse delay time between two lasers.) [2] ........... 45 3 1 Energy level scheme and associated excitation/de excitation processes. The symbols shown above the arrows represent t he rate constants for the transition: i.e., C ( l ): excitation rate coefficient; F( l ): de excitation rate coefficient; A( l A coefficient or transition probability for l ; S( l ): ionization rate coefficient; ( l ): three body recombination rate coefficient; ( l ): radiative recombination rate coefficient; ( l ): ionization potential of level l (adapted from ref [90]). ................................ ................................ ....................... 68 3 2 Spectral line profile. Here 0 is the central wavelengt h, 1 and 2 are the wavelength whose intensity is half of the maximum intensity I 0 the full width at half maximum (FWHM) (adapted from [99]). ............................. 69 3 3 Normalized spectral profile s versus relative frequency for pure Doppler (D), pure Lorentzian (L) distributions of equal full width at half maximum (FWHM), and the resulting Voigt (V) profile (adapted from ref [100]). ................................ 70 3 4 Spectral line profile as a function of gradually increasing atomic concentration (a h). Note that the center of the line reaches the blackbody radiation limit at high atom densities (adapted from ref [100]). ........................... 71 4 1 Experimental LIBS set up ................................ ................................ ................... 90 4 2 (a) L ine broadening and (b) the electron number density calculated from Stark broadened line widths of the Ba II line at 252.84 nm at 90 5 mJ laser pulse energy as a function of delay time. ................................ ........................... 91

PAGE 11

11 4 3 (a and b) Saha Boltzmann plots and (c) Boltzmann plot in different delay times. (d f) Corresponding excitation temperatures versus delay times show in the figure. ................................ ................................ .............................. 92 4 4 Electron temperature versus (a b) free free bound correction factor and (c d) free bound continuum correction factor as a function of delay time. ................... 93 4 5 Normalized line profiles of Cu atomic transition at 282.44 nm (a) at 50 ns t d 500 ns delays (laser pulse energy 50 5 mJ and gate width 50 ns) and (b) at 500 ns t d 15000 ns dela ys (laser pulse energy 90 5 mJ and gate width 100 ns). ................................ ................................ ................................ .............. 94 4 6 (a and c) T emporal evolution of the excitation and electron temperature s at 282.44 nm Cu I line from copper metal (b and d) The l ine profile in the figures correspond s to the Voigt profile fit of the emission lines at different delays from plasma creation. ................................ ................................ .............. 95 4 7 (a) T emporal evolution of the excitation temperature and electron temperature at 296.12 nm Cu I line of Al alloy sample (Z8) (b) T he line profile in the figures correspond s to the Voigt profile fit of the emission lines at different delays from plasma creation. ................................ ............................ 96 4 8 T emporal evolution of the excitation temperature and electron temperature for Cu atomic lines at 282.44, 296.12 and 510.55 nm in a copper metal for (a) short delay times (100 ns t d 500 ns) and (b) long delay time (500 ns t d 15000 ns) ................................ ................................ ................................ ...... 97 4 9 Time resolved emission spectra from laser induced plasma of Ba II lines. The spectra were recorded at 90 5 mJ pulse energy and the gate time of the intensity was set by 0.1 s. ................................ ................................ ........... 98 4 10 (a) T emporal evolution of the excitation temperature and electron temperature at 252.84 nm Ba II line of Al alloy sample (Z 8) (b) T he line profile in the figures correspond s to the Voigt profile fit of the emission lines at different delays from plasma creation. ................................ ............................ 99 5 1 (a) Scheme of the set up used, with the addi tion of an external spherical mirror; (b) Schematic representation of the plasma images on the slit with and without the mirror, which is located at a distance from the plasma equal to its radius of curvature; (c) zero order plasma images obtained with and without the mirror [166]. ................................ ................................ .................... 118 5 2 Magnesium, copper, and iron compositions in the 9 aluminum alloy samples used. The insert represents the magnesium composition used to obtain the calibratio n plots [166]. ................................ ................................ ....................... 119

PAGE 12

12 5 3 (a) Observed spectral profile of the copper atomic line at 510.55 nm for different delay times from the onset of the plasma. (b) Experimental evaluation of R and R C in the case of the copper atomic line at 510.55 nm. The delay time is 1.0 s and the gate width 0.1 s [166]. ................................ 120 5 4 Experimental ratio (R C ) of the continuum radiation with and without the mirro r observed at different delay times. The measurements refer to the 510.55 nm Cu line. The average value of R C over the delay times is 1.60 [166]. ............... 121 5 5 Calculated dependence of the correctio n factor K ,corr as a function of R C for different values of R e.g., for different degree of self absorption [166]. .......... 122 5 6 (a) Calculated values of R as a function of wavelength along the line profiles; (b) Correction factor K ,corr as a function of wavelength and self absorption corrected line profiles (c) Voigt profile fit of the emission lines obtained with and without the mirror and after correction for self absorption. All cases refer to the Cu I transition at 510.55 nm and to measurements taken at 1.0 s delay time. The average value of R C (1.6) was used here [166]. ...................... 123 5 7 Temporal behavior of the correction factor K ,cor r (evaluated at the line center) for three Cu atomic lines at 510.55 nm, 324.75nm and 327.40 nm as a function of different delay times after plasma formation. The error bars reported were calculated assuming a maximum error of 10 % for each correction fact or (see text for discussion) [166]. ................................ ............... 124 5 8 Temporal behavior of the correction factor, K ,corr (evaluated at the line center) for three Mn lines at 403.08 nm, 403.31 nm and 403.45 nm as a function of different delay times after plasma formation [166]. ......................... 125 5 9 Cu I emission profil es observed at 510.55 nm with and without the mirror, together with corresponding calculated duplication factor D at different delay times [166]. ................................ ................................ ................................ ....... 126 5 10 Saha Boltzmann plots constructed usi ng atomic and ionic lines of Al and Cu measured in the spectra of two different alloy samples. The data were obtained at 1.0 s delay time. Plots (a) and (c) show all the data while plots (b) and (d) result after exclusion of the transitions affected by se lf absorption [166]. ................................ ................................ ................................ ................ 127 5 11 Saha Boltzmann plot constructed using Fe atomic and ionic lines: (a) 1.0 s delay time, and (b) 3.0 delay time. The two slopes result from the data uncorrected (o pen squares) and corrected (open circles) for self absorption. The lines correspond to the best linear fitting of the data [166]. ....................... 128 5 12 Saha Boltzmann plot constructed using Cu atomic and i onic lines at 5.0 s delay time. The two slopes result from the data uncorrected (open squares) and corrected (open circles) for self absorption. The lines correspond to the best linear fitting of the data. The transitions used (nm) are indicated [166]. .... 129

PAGE 13

13 5 13 Experimental calibration plots of Mg using eight Al alloy standard samples with and without correction for self absorption at (a) Ionic line 280.27 nm and (b) atomic line 285.21 nm. Gat e width: 0.1 s; delay time: 2.0 s; pulse energy 90 5 mJ. The dotted lines connecting the uncorrected data are meant as a visual aid while those drawn through the corrected data correspond to the best linear fit [166]. ................................ ................................ ..................... 130 5 14 Variation of the calculated correction factor K ,corr (evaluated at the line center) for the Mg atomic (open squares) and ionic (open triangles) lines for each Al alloy sample measured. The insert indicates the magnesi um content of each sample. The error bars reported were calculated assuming a maximum error of 10 % for each correction factor (see text for discussion) [166]. ................................ ................................ ................................ ................ 131 6 1 Common pulse configurati ons. (a) Collinear configuration, in which the first and second laser pulses are both focused on/or into a sample. In orthogonal configuration, a single ablative pulse is coupled with either (b) a pre ablation air spark that is parallel to and up to severa l millimeters above the sample surface or (c) a reheating pulse [70]. ................................ ................................ 161 6 2 ( a) Scheme of the set up showing LIBS system for both single and double pulse operation. ................................ ................................ ................................ 162 (b) Timing and triggering system used for both pre ablation air spark and reheating double pulse scheme s ................................ ................................ ..... 162 6 3 LIBS signal enhancement at the several different transition lines for the s everal elements (Al II, Mg I and II and Cr II) versus the interpulse delay time 100 s) at several different distances ( d 0.3 2.5 mm ) in SRM 603 sample. ................................ ................................ ................................ ...... 163 6 4 Pre ablation air spark double pulse configuration signal enhancement versus the interpulse delay time (= t) in (a) NIST Al SRM 603 and (c) South African Al AA1 sample and signal enhancement versus the distance (= d mm) from t he sample surface to air spark above the sample in (b) NIST Al SRM 603 and (d) South African Al AA1 sample. ................................ .............................. 164 6 5 Spectra showing Al II 281.62 nm and Mg I 285.21 nm emission lines of interes t in terms of delay time in Al alloy sample (SRM 603) in both (a) single pulse and (b) orthogonal pre ablation air spark double pulse configuration. (c) For each emission line, graphs of LIBS signal enhancement with use of the double pulse irradiation vers us several delay times from 0.5 s to 10 s ................................ ................................ ................................ ....... 165 6 6 Signal to noise (S/N) ratio as a function of delay times for each Al II and Mg I emission line. ................................ ................................ ................................ .... 166

PAGE 14

14 6 7 Triggering scheme for the time resolved study of plasma evolution in the reheating double pulse scheme (a) with short gate width of 0.1 s and (b) long gate width of 30 s (averaged measuring) of plasma in the triggering system initiated by the Quantel Brillant laser. ................................ ................... 167 6 8 LIBS signal enhancement versus interpulse delay in the reheating double pulse scheme (a) with short gate width of 0.1 s and (b) long gate width of 30 s (averaged measuring) of plasma in the triggering system initiated by the Quantel Brillant laser ................................ ................................ ................. 168 6 9 Plasma images in (a) double pulse, (b) single pulse and (c) only air spark (without sample plasma) at the center wavelength of 259.09 nm in aluminum alloy AA1 sample. (d) Intensity enhancement compared to only air spark (without ablation) laser pulse as well as the LIBS signal from the ablation laser pulse only. ................................ ................................ ................................ 169 6 10 (a) Time sequence for the time resolved study of plasma evolution in the reheating double pulse scheme. The acquisition time after the ablating laser pulse is about 3.0 s (t w :0.1 s; t d : 1.0 s). (b) Peak intensity as a function of decay time of plasma for selected neutral and ionic lines (t w :0.1 s; t d : 1.0 s; d :3.0 mm) and inserted figure shows a log log scale plot of the same data. ................................ ................................ ................................ ........ 170 6 11 (a) Time sequence of the experimental set up in the case of the reheating double pulse scheme. (b) Timing between laser output pulse and HV gate pulse (PG 200 Delay Trigger out) at the different delay time t d (c) LIBS signal enhancement (log scale) of Al II 281.62 nm as a function of the delay time t d ................................ ................................ ................................ .............. 171 6 12 LIBS signal enhancemen t versus the interpulse delay time (= t) at the several distances (= d mm) from the air spark to sample surface in a selected line (a) Mg II 279.08 nm and (b) Al II 281.62 nm and (c) at the maximum distance ( d = ~ 3.0 mm) for several transition lines i n the reheating double pulse configuration. ................................ ................................ .............. 172 6 13 LIBS signal enhancement versus the delay between the two laser pulses in the reheating double pulse scheme for selected neutral and ioni c lines s; d : 3.0 mm). ................................ ........... 173 6 14 Signal to noise (S/N) ratio as a function of delay times for each Al II and Mg I emission line. ................................ ................................ ................................ .... 174 6 15 Time gated, spectrally resolved, one directional images of the laser induced plasma of a Al alloy sample (603), obtained in the single (left images) and in the orthogonal pre ablation air spark double pulse mo de (right images). The gate width and interpulse delays between two laser pulses were kept by constants (0.1 s and 30 s respectively), and the ICCD gate delays were 0.5 (a,g), 1.0 (b,h), 2.0 (c,i), 3.0 (d,j), 5.0 (e,k) and 8.0 (f,l). .............................. 175

PAGE 15

15 6 16 Time gated, spectrally resolved, one directional images of the laser induced plasma of a Al alloy sample (603), obtained in the single (left images) and in the orthogonal reheating double pulse mode (rig ht images). The gate width and ICCD gate delays were kept by constants (0.1 s and 1.0 s respectively), and interpulse delay times ( t) between two laser pulses were 0.5 (a,g), 1.0 (b,h), 1.5 (c,i), 2.5 (d,j), 4.0 (e,k) and 6.0 (f,l). .............................. 176 6 17 Spatial intensity profiles of atomic and ionic emission lines of Al, Mg, Cr at d ifferent delay times from 0.5 s to 8.0 s in the pre ablation air spark scheme. The acquisition time (= t w ) and interpulse delay time ( t) between two laser pulse was fixed at 0.1 s and 30s. ................................ .................. 177 6 18 Spatial intensity profiles of atomic and ionic emission lines of Al, Mg, Cr at different delay times from 0.5 s to 6.0 s in the reheating scheme. The gate width and ICCD gate delays were kept by constants (t w : 0.1 s and t d : 1.0 s respectivel y). ................................ ................................ ................................ .... 178 6 19 SEM images of craters produced 50 consecutive samplings of Al alloy sample (a) in the single pulse and (b) in the double pulse ( t = 20 s) using the orthogonal pre ablation air spark mode, and (c) in the single pulse and (d) in the double pulse ( t = 5.0 s) using the orthogonal reheating mode. ..... 179 6 20 Signal enhance ment versus delay times at the different Mg atomic (solid dots) and ionic (open dots) lines (a) In orthogonal pre ablation air spark and (b) in reheating scheme LIBS. ................................ ................................ .......... 180 6 21 Logarithmic plot s of neutral and ionic line enhancements at the different delay times from (a) 0.5 s to (i) 10 s (in the pre ablation air spark scheme). 181 6 22 (a) LIBS spectra in both single (black color ) and double pulse (gray color) at the different delay times for the pre ablation air spark scheme ( center = 281.5 nm, t = 30 s and t w = 0.1 s). ................................ ................................ .... 182 (b) LIBS spectra in both single (blac k color) and double pulse (gray color) at the different delay times for the pre ablation air spark scheme ( center = 292 nm, t = 30 s and t w = 0.1 s). ................................ ................................ .... 183 6 23 (a) Plasma temperature obt ained from Saha Boltzmann plot, (b) temperature difference ( T = slope) and intercept (= q) from the logarithm plots of neutral and ionic line enhancements, (c) electron number density using Stark broadening (Al II 281.62 nm) and (d) The enhancement of tot al number density of atoms and ions in plasma from Eq. 6 11 at the different delay times. ................................ ................................ ................................ ................ 184 6 24 Saha Boltzmann plot in both (a) single and (b) orthogonal pre ablation air spark double pulse configuration and (c) single and (d) orthogonal reheating double pulse configuration. ................................ ................................ .............. 185

PAGE 16

16 6 25 SEM images of craters produced 50 consecutive samplings of Al alloy sample (a) in the single pul se and (b) in the double pulse ( t = 20 s) using a pre ablation air spark. Spectrally resolved one directional images of the laser induced plasma of a Al alloy sample, obtained (c) in the single and (d) in the double pulse ablation mode (t d = 2.0 s; t w = 0.1 s; t = 30 s). ........... 186 6 26 Logarithmic plots of neutral and ionic line enhancements at the different delay times from (a) 0.5 s to (f) 9.0 s (in the reheating scheme). ................. 187 6 27 (a) LIBS spectra in both single (black color) and double pulse (gray color) at the different delay times for the reheating scheme ( center = 281.5 nm, t d = 1.0 s and t w = 0.1 s). ................................ ................................ ........................... 188 (b) LIBS spectra in both single (black color) and double pulse (gray color) at the different delay times for the reheating scheme ( center = 292 nm, t d = 1.0 s and t w = 0.1 s). ................................ ................................ ........................... 188 6 28 (a) Plasma temperature obtained from Saha Boltzmann plot, (b) temperature difference ( T = slope) and intercept (= q) from the logarithm plots of neutral and ionic line enhancements, (c) electron number density using Stark broadening (Al II 281.62 nm) and (d) The enhancement of total number density of atoms and ions in plasma from Eq. 6 11 at the different delay times. ................................ ................................ ................................ ................ 189 7 1 An example of the descr iption of net signal: i.e., the simplest signal measurement consists of the peak intensity ( ) at the central wavelength of the analyte line and an off peak measurement of the background at a single position ( ) ................................ ................................ ................ 221 7 2 In standard deviation (SD) limiting cases, simulated shapes of the plot SD versus wavelength. ................................ ................................ ........................... 222 7 3 In relative sta ndard deviation (RSD) limiting cases, simulated shapes of the plot RSD versus wavelength. ................................ ................................ ............ 223 7 4 (a) 3D LIBS spectra for 55 laser shots in an Al alloy (D28) sample and (b) a 55 shot ensembl e averaged LIBS spectrum (black line) with both associated standard deviation (red line) and relative standard deviation (blue line). Used gate delay time and gate width are 2.0 s and 0.1 s, respectively. ................ 224 7 5 Zn and Cu atomic emission lines for both (a and c) 55 single shot ensemble averaged spectra and (b and d) associated standard deviation curves at the same spectral range in Al alloy sample (D28) and NIST brass standard (1113) respec tively. In both samples, the settings on the detection system were 2.0 us and 0.1 s for the gate delay time and gate width, respectively Each full width at half maximum value of Cu I resonance line at 324.7 nm was obtained by fitting a Voigt profile (see the blue arrows). ............................ 225

PAGE 17

17 7 6 (a and b) 55 single shot LIBS spectra at the peak of Zn I 330.3 nm in both Al alloy sample (D28) and NIST brass standard (1113), respectively. (The used gate delay t ime and gate width were 2.0 s and 0.1 s, respectively.) Each correlation factor between two major noise sources was calculated at the peak of Zn I 330.3 nm by using Eq. 7 7. In Al alloy sample (D28), is 0.527, while in NIST brass stan dard (1113), is 0.871. ................................ ............. 226 7 7 (a and b) LIBS spectra for the several Mg compositions in Al alloy samples ( S quare box indicates the region for zoom in) and (c and d) e x perimentally calculated correlation factor as a function of both concentration and standard deviation of the background measured near Mg I 285.21 nm respectively Either a single pixel or 20 pixels measurement was used for the determination of the standar d deviation of the background measured. ............ 227 7 8 (a) LIBS spectra (ensemble averaged) showing the Mg I and II lines and Al II line and (b) standard deviation curves for 50 laser shots in 6 Al a lloys samples. (c) Relative standard deviation (RSD) curves as calculated from the quotient of the standard deviation (square box indicates the region for zoom in) (d) RSD curves showing the increase of Mg composition. ......................... 228 7 9 (a) LIBS spectra (ensemble averaged) showing the Cu I and Zn I lines and (b) standard deviation curves for 50 laser shots in 7 NIST brass standards. (c) Relative standard deviation (RSD) curves as calculated from the quo tient of the standard deviation (square box indicates the region for zoom in) (d) RSD curves showing the increase of Cu composition. ................................ ..... 229 7 10 (a and b) LIBS spectra and standard deviation cur ves as a function of wavelength for different delay times at Mn II 259.37 nm in Al alloy (AA1) sample. (c) The plot of correlation factor versus delay time. ......................... 230 7 11 Th e plot of a relative standard deviation versus wavelength for different delay times at Mn II 259.37 nm in Al alloy (603) sample. ................................ ........... 231 7 12 (a and b) The ensemble averaged spectra for Ba II in B aCl 2 pallet at 0.5 us and 3.0 us delay times, respectively with each RSD curve and (c and d) associated SD curves. ................................ ................................ ...................... 232 7 13 The ensemble averaged spectra for several elements in Al alloy (S5) sample at (a) 0.5 us and (c) 5.0 us delay times, respectively with each RSD curve (blue line) and (c and d) associated SD curves. ................................ ............... 233 7 14 (a) LIBS spectrum at 2.0 us delay time in Al alloy (A A1) sample including 0.540 % of Mn and (b) the standard deviation curve only near Mn II 259.37 nm line. (c) LIBS spectrum showing Mn ionic emission line at 259.37 nm The region A, B, C and D indicate the region selected for RMS noise calculation. (d) Expe rimental values of the correlation factor as a function of standard

PAGE 18

18 deviation of the background measured by 10 pix els (the region A,B ,C and D : black squares ) and single pixel (the region A~C, blue dots). ........................... 234 7 15 Experimental percent RSD of the net signal (% RSD net ) as a function of the analyte concentration (a) at Mg I 285.21 nm line in 7 Al alloy samples an (b) at Zn I 330.26 nm line in 6 NIST brass standards. ................................ ............ 235 7 16 The log of the signal to noise (S/N) ratio as a function of the log of net signal for (a) Mg I 285.21 nm in 5 Al alloy samples and (b) Zn I 330.26 nm in 7 NIST brass standards. ................................ ................................ ...................... 236 7 17 (a and c ) LIBS spectr a and (c and d) associated SD curves at both 0.5 us and 3.0 s delay time s, respectively in Al alloy ( SM10 ) sample ...................... 237 7 18 (a and b) LIBS spectra and associated SD curves at Mg I 285.21 nm in the samples containing two extreme concentrations such as Al alloy D28 (0.004 % of Mg) and S11 (1.11 % of Mg). ................................ ........................ 238

PAGE 19

19 L IST OF A BBREVIATIONS AAS Atomic Absorption Spectrometry AES Atomic Emission Spectroscopy Blank signal CCD Charge Coupled Device DP Double Pulse FWHM Full Width at Half Maximum fs femtosecond IB Inverse Bremsstrahlung ICCD Intensified Charge Coupled Device ICP AES Inductively Coupled Plasma Atomic Emission Spectrometry ICP MS Inductively Coupled Plasma Mass Spectrometry IR Infrared LA Laser Ablation LIBS Laser Induced Breakdown Spectroscopy LIF Laser Induced Fluorescence LIPS Laser Induced Pl asma Spectroscopy LOD Limit of Detection LSC Laser Supported Combustion LSD Laser Supported Detonation (waves) LSR Laser Supported Radiation LTE Local Thermodynamic Equilibrium LTSD Lens to Surface Distance mJ milli Joule Nd:YAG Neodymium Yttrium Aluminum Garnet

PAGE 20

20 NIST National Institute of Standards and Technology nm nanometer ns nanosecond P/B Peak to Base PC Personal Computer PMT Photomultiplier Tube ps picoseconds R MS Root Mean Square RSD Relative Standard Deviation S/B Signal to Background Ratio S/N Sign al to Noise Ratio SP Single Pulse SEM Scanning Electron Microscopy TE Thermodynamic Equilibrium s microsecond

PAGE 21

21 LIST OF SYMBOLS AND CONSTANTS Roman Symbols Analyte (element) in plasma e.g. A Mn Einstein transition probability of spontaneous emission between upper level ( ) and lower level ( ), s 1 Einstein transition probability of spontaneous emission between up per excitation level ( ) and lower excitation level ( ) of the ion s 1 F irst Bohr radius nm Line damping parameter, dimensionless Blackbo dy spectral radiance, J s 1 cm 2 sr 1 nm 1 Blackbody radiation distribution or Planck s distribution function W cm 2 sr 1 nm 1 Blackbody radiation distribution or Wien s distribution function, W cm 2 sr 1 n m 1 E xcitation rate coefficient cm 3 s 1 Duplication factor, dimensionless Sample to lens distance Energy of lower level eV Energy of upper level eV E xcitation energy of lower level of the ionic line eV Ionization potential of the neutral species in its ground state, e V E xcitation energy of lower level of the ionic line eV Energy separation between level and eV Energy differenc e, eV

PAGE 22

22 C orrection of ionization energy (or lowering correction parameter) eV Electric field strength of the plasma microfield kg m s 3 A 1 De excitation rate coefficient, cm 3 s 1 Focal length of the spectrometer, mm or cm Oscillator strength for transition D etection function cm 3 counts photon 1 s Excitation/ionization function leading to atomic/ionic emission Initial interaction function between the sample and the laser leading to ablation/vaporization of solid material The calibration function which describes the plasma characteristics in terms of optical depth Free free Gaunt factor, dimensionless reflection and absorption losses of the duplication mirror Statistical weight of lower level dimensionless Statistical weight of upper level dimensionless or Integrated line intensity, photons cm 3 s 1 Intensity at the center of the line profile photons cm 3 s 1 integrated net intensity Total angular momentum Self absorption correction factor, dimensionless Ionization rate coefficient cm 3 s 1 Absorption coefficient, cm 1

PAGE 23

23 Net absorption coefficient, cm 1 Optical path length cm Atomic or molecular weight, g mol 1 or amu Quantum number representing the component of the total angular moment um Number of column pixels on ICCD camera Boltzmann distribution/ or population density for analyte in the excited level Number of particles in the Debye sphere, cm 3 Electron number density, cm 3 Electron number density in DP or SP, cm 3 N umber density in the excited state cm 3 or Number density of neutral atom ic species, cm 3 or Number density of single ionized species, cm 3 T ot al number density of atoms and ions for the analyte in the plasma cm 3 T otal number density of atoms and ions in the plasma in DP and SP, cm 3 Ratio of two emission intensities Ratio of continuum ra dia t ion with and without duplicating mirror Double pulse/single pulse i ntensity ratio for neutral lines

PAGE 24

24 Double pulse/single pulse i ntensity ratio for ionic lines Uncertainty associated with the ratio of two emission intensities Radial coordinate of particle in the plasma, cm Analytical net signal counts Ensemble average net signal counts Slit width, m Spectral profile of the line, cm 1 P lasma excitation temperature in SP and DP, K Electron temperature, K Excitation temperature, K Ionization temperature, K Temperature difference, K Delay time, s Gate width, s Partition function, dimensionl ess or P artition function of the analyte in neutral or singly ionized state plasma volume cm 3 the excitation volume seen by a detector, cm 3 Lennard Jones potential ( ~ 1/r 6 ) Nuclear charge which acts on the optical electron Spectroscopic symbol

PAGE 25

25 Ionization stage Greek Symbols ion broadening para meter N eutral fraction of the atoms of the analyte in the plasma S ingly ionized fraction of the atoms of the analyte in the plas ma Emission coefficient Continuu m emission coefficient or Correlation factor between major noise sources in a LIBS measurement Absorption coefficient, cm 1 Wavelength, nm or Instrumental spectral band width, nm Stark line width, nm Stark line width at FWHM of the experimental spectral line, nm RMS n oise from the background sig nal RMS n oise from the blank signal RMS n oise from the dark current and amplifier readout system RMS n oise in the analytical net signal T otal root mean square ( RMS) noise Radiation damping constant, s 1 fraction of the plasma volume included in the detector field of view Frequency, Hz

PAGE 26

26 Frequency of line center Doppler broadening Life time of a classical oscillator, s P hoton energy of the transition at frequency J Free bound continuum correction factor, dimensionless Optical depth, dimensionless Plasma velocity, 10 5 10 6 cm s 1 Electron impact half width, nm Pixel s ize, m Lorentzian width nm Gaussian width nm M olar fraction of the analyte in the plasma for DP or SP Ionization potential, eV Lowe ring of the ionization potential, eV Overall detection efficiency, count photon 1 s Constants Speed of light in vacuum 2.9979 10 8 m s 1 Elementary charge 1.6022 10 19 C Permittivity of free space 8.8542 10 12 C 2 N 1 m 2 Planck s constant 6.6261 10 34 J s or Boltzmann Constant 1.3807 10 23 J K Electron mass 9.1094 10 31 kg

PAGE 27

27 Avogadro s number 6.0221 10 23 mol 1 Gas constant 8.3145 J/mol K

PAGE 28

28 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy DIAGNOSTIC AND ANALYTICAL STUDIES OF LASER INDUCED PLASMAS By Heh Young Moon August 2010 Chair: Nicol Omenetto Major: Chemistry Since its early applications, Laser Induced Breakdown Spectroscopy (LIBS) has been recognized as a useful tool for solid state chemical a nalysis due to its numerous attractive advantages as an analytical tool: e.g., simultaneous multi element detection capability, no sample preparation rapid or real time analysis, and allowing in situ analysis requiring only optical access to the sample. However, the quantitative accuracy of the technique depends on the complex fundamental processes involved in laser induced plasma formation, ablation, atomization, excitation and ion recombination. Thus, problems arising from laser target coupling, matrix effect s line interferences, fractionation in target vaporization the main assumptions of the methods, namely the optical ly thin emission of spectral lines and the existence of local thermodynamic equilibrium in the plasma should be properly addressed in order to obtain reliable quantitative results [1, 2] The general scope of this research encompasses two aspects related to the LI BS technique : one aspect is the fundamental study of the plasma characteristics and another is an improved use of the technique in quantitative analysis. The main project is to revisit and investigate some fundamental assumptions such as the existence of l ocal

PAGE 29

29 thermodynamic equilibrium (LTE) and optically thin plasma condition s (e.g., free of self absorption phenomenon) as mentioned above. Moreover, double pulse LIBS, which is one of the attractive spectroscopic methods for the diagnostics of the laser indu ced plasma due to lower detection limits and enhanced and longer sustained emission signals for analysis, was also investigated herein in order to understand the relative importance of the factors related to the intensity increases as well as the underlyi ng physical mechanisms. In general, LIBS signal enhancemen t is commonly attributed to an increase of ablated mass from the target or to plasma reheating. Furthermore, signals in LIBS measurement are influenced by the presence of spurious signals or noise s Some types of noise s are fundamental to a given exp eriment, and although they may not be entirely eliminated, it is often possible to minimize them if the limiting noise can be determined The study of noise forms a part of the discussion of errors in an alytical measurement The root mean square (RMS) value of a noise source and the signal to noise (S/N) ratio are useful parameters to describe figures of merit of the analytical procedure. In addition, the relative standard deviation (RSD) is also related to the precision of the measurement. The general ly useful S/N ratio expression will be discussed with respect to analytical measurements in this study The noise expression occurring in LIBS measur e ment will be also exp licitly discussed and evaluated with some information about the type of noise present.

PAGE 30

30 CHAPTER 1 INTENT AND SCOPE OF STUDY Since the 1960s, soon after the first report of laser action in ruby [3] it was realized that when the laser radiation was focused, the intense light beam was capabl e of vaporizing and exciting solid material into a plasma, which is known as Laser I nduced Breakdown Spectroscopy (LIBS) based on the optical emission s pect roscopy of Laser I nduced Plasmas (LIPs) It has been used as a powerful tool for fundamental studies and numerous applications in analytical spectroscopy because it seems to be fairly simple; the vaporization atomization, and excitation processes are carried out in one step by the laser pulse and setting up an apparatus with minima l /no sample preparatio n to perform a LIBS measurement is quite simple. However, the basic physical and chemical processes involved are not so simple Thus, the importance of fundamental study in LIBS has been increasingly recognized for better understanding in this field Fro m the beginning, C hapter 2 provides a brief chronological overview of laser indu ced breakdown spectroscopy ; it can be explained in terms of experimental aspect s based on th e recent literature dealing with the fundamentals and its applications with LIBS Ch apter 3 presents a basic physical study on the use of LIBS for quantitative analysis. In addition, the chapter includes a discussion of the theoretical assumptions on the state of plasma for achieving accurate quantitative analysis Subsequently, C hapter 4 and 5 focus on the experimental investi gations of laser induced plasma s In an attempt to simplify a very complex phenomenon of plasma, most of the methods developed for LIBS diagnostic studies assume the following : t he plasma volume under observation is in Local Thermodynamic E quilibrium (LTE) and the spectral lines measured are optically thin, i.e., free from self absorption. Th e s e chapters (C hapter s 4

PAGE 31

31 and 5) describe the introduction of a novel approach ( Line to continuum intensity ratio method) for ch ecking the validity of the LTE assumption and for the first time, the usefulness of a duplication mirror for ev aluating self absorption effect s on the emission line Chapter 6 illustrates the use of double pulse irradiation and its advan ta ges In this cha pter the optimal conditions in our experimental system are described in terms of the temporal and spatial evolution of plasma. The chapter discusses our effort s to explain the coupling of the laser radiation with the plasma based on the use of spectroscop ic diagnostics of the plasma origina ted by a double pulse laser The possible dynamic and physical mechanisms in the single and double pulse configuration responsible for the enhancement of emission lines are investigated, and the o pti mal conditions found in each case are also studied Finally, Chapter 7 dea ls wit h considerations on the spect ral fluctuation approach in laser induced breakdown spectroscopy For t his approach, within the simplifying assumptions made and the validity of these assumptions ; i.e ., all noise sources present in a measurement are independent it is argued that the behavior observed by plotting the standard deviation and relative standard deviation of each spectral element (pixel) versus wavelength can indeed be informative regarding the characteristic aspects of the measurement. In addition, the chapter describes how the approach can provide some information about the type of noise present in a LIBS measurement and the limiting noise of the measurement

PAGE 32

32 CHAPTER 2 FUNDAMENTAL OF LIBS Introduction Laser induced breakdown spectroscopy (LIBS) is one method of atomic emiss ion spectroscopy (AES) based on the fact t hat lasers tightly focused on solid, liquid or gas es (the target) create a plasma from which atoms and molecules emit. In principle, t he purpose of AES is to determine the elemental composition of a sample (a solid, liquid, or a gas); examination of the emitted light provides the analysis because each Thus, t he intensity of the emitted radiation and the frequencies at which the emission is observed serve to identify and provide information on the number of atoms responsible for the emission. The intensity of the radiation is proportional to the number of emitting atoms as long as the atomic number density is low. The chapter presents a brief overview of the history of LIBS followed by a description of its basic principle and the current experimental ap proaches as well as a summary of physics and phy sical chemistry regarding laser induced plasm as. The D iscovery of LIBS Light emitting plasmas have been studied since the 1920s, and laser induced plasma since the 1960s [4] The first published report as a potential spectroscopic technique was a meeting abstract by Brech and Cross in 1962 [5] but initially the LIBS plasma found greatest value as a micro sampling source for an electrode ge nerated spark In 1963, with the development of the first pulsed Q switched ruby laser [6] the first analytical use for spectrochemical analysis of surfaces was reported by Debras Gu don and Liodec [7] This was the birth of laser induced breakdown spectroscopy. In

PAGE 33

33 1964, Marker et al. reported the first observation of optically induced breakdown in a gas [8] and Runge et al. discussed the use of the pulsed Q switched ruby laser for direct spark excitation on metals such as Ni and Cr in iron [9] T he first LIBS instrument was introduced in 1967 followed by the development of several commercial LIBS instruments by Jarrell Ash Corp. (USA), VEB Carl Zeiss Jena Co. (Germany) and J EOL Ltd (Japan). Although these instruments could be operated with the laser plasma generating the spectral emissions, they could not typically compete in both precision and accuracy with the development of high performance elemental analysis technique suc h as inductively coupled plasma spectroscopy (ICP) and conventional spark spectroscopy. In the early 1970s much of the research on the laser plasma and its uses appeared in the Russian literature [10 13] and th e classic book by Raizer, Laser induced Discharge Phenomena [14] In the same time period it was first recognized by Cerrai and Trucco [15] and Marich et al. [16] that physical and chemical matrix effects in laser sampled spectrochemical analysis exist It is now acc epted that a variety of physical and chemical effects play important roles in signal strength, and repeatability. In the middle to late 1970s, aerosols became a subject of research. Lencioni discussed the effects of dust and particles in the beam, which in fluenced breakdown [17] Several studies were performed for spectrochemical analysis of aerosols [18 20] During the 1980s, as lasers and other LIBS components became s maller and the drive for more portable and versatile instruments increased, LIBS experienced a rebirth. The potential of LIBS as a more convenient atomic emission technique became apparent to both industrial and academic laboratories. In 1981, two papers w ere

PAGE 34

34 published for Los Alamos National Laboratory: the time integrated [21] and time resolved [22] forms of the technique in gases. During that period Los Alamos scientists studied the detection of toxic materials on various chem ical states (solid, liquid or gas) with the use of this technique [23 29] Some research also focused on diagnostics and enhancements. Initial interest focused on the acoustic effect produced by plasm a [30, 31] In the late 1980 s interest in creased in making LIBS more quantitative. Niemax et al. contributed much work during this period [32 37] K o, et al. mentioned the usefulness of internal standardization [38] They concluded that internal standardization was not a given in all cases, but the conditions for its use needed to be established for each situation. In the mean time, the atomization and propagatio n properties of the plasma plume were investigated by Leis et al. [39] Since the 1990s, applications a nd fundamental studies have developed rapidly. In particular, during the past 2 0 years, the LIBS technique has made significant progress. Many useful books and review articles have appeared [1, 2, 27, 40 46] In particular, the power of LIBS as a qualitative and quantitative elemental analysis technique is well addressed from several groups in the US and the other countries such as Italy, Australia, Canada a nd Spain. During this period, commercial instrument s for coal analysis in the Chadwick group [47] (Australia) and remote analysis by LIBS using a fiber optical cable [48] at Los Alamos were demonstrated In this time, quantitative LIBS studies also continued. Palleschi s group in Pisa (Italy) disc ussed applications to pollutant detection [49] In particular the devel opment of the calibration free LIBS (CF LIBS) procedure in 1999 has made much a useful contribution for quantitative LIBS analysis [50] In addition, Mao et al. in Russo s group at Lawrence Berkely Laboratory studied the

PAGE 35

35 process of laser ablation [51] ; otherwise, Winefordn er a n the discussion of the variables influencing the precision of LIBS measurements by Castle et al in 1998 [52] Gornushkin et al. reported on a curve of growth methodology applied to laser induced plasma emission spectroscopy [53] Moreover, t he dou ble pulse approach first suggested by Piepmeier et al. [54] in 1969 and Scott et al. [55] in 1970 resurfaced in this period In 1984, Cremers et al. [56] performed a detailed study of the possible applicati ons of the laser double pulse technique for analytical purposes. Research regarding sources and applications of these enhancements has continued with many advances in each area. As the field proceeded into the 1990s, applications to art and biologic al analysis, i n particular, received much attention [3, 57 60] Detect ion of element al contaminants in soils also received considerable attention [40, 61 63] Mor eover, there has been a significant improvement of the instrumentation in LIBS, which can be attributed to the ava ilability of more robust, smaller, faster and less costly laser sources, the development of sensitive gated imaging detector s (e.g. intensified charge coupled devices, ICCD) and the advent of high resolution spectrometers (e.g. the compact echelle spectrom eter) [64] Since the late 1980s, the number of publication s involving LIBS increased exponentially each year [1] due to the unique advantages of LIBS: remote sensing capabilities, in situ analysis, little to no sample preparation, micro destructive nature, applicability to all media, simultaneous multi element detection cap ability and rel atively simple instrumentation. Table 2 1 briefly describes some of the more important milestones in LIBS development. Because LIBS is one of the most versatile analytical

PAGE 36

36 method s many applications studied in the early development of LIBS h ave re surfaced due to increased needs or improved instrumental capabilities. General P rinciple of LIBS [1] In LIBS, the vaporizing and exciting plasma is produced by a high power focused laser pulse. As most commonly used and shown schematically in Fig. 2 1, a typical LIBS system consist s of a neodymium doped yttrium aluminum garnet (Nd:YAG) solid state laser and a spectrometer with a wide spectral range and a high s ensitivity, fast response rate and time gated detec tor. This is coupled to a computer which can r apidly process and interpret the acquired data. Each firing of the laser generate s a single LIBS measurement. Typically, however, the signals from multiple laser shots are added or averaged to increase repeatab ility and precision and to average out non uniformity in sample composition [1] The LIB S instrument has many distinct advantages compared with the conventional AES based analytical method An overview of the advantag es and disadvantages of LIBS is listed in T able 2 2 As such LIBS is one of the most experimentally simple spectroscopic analytical techniques, making it one of the cheapest to purchase and to operate. One merely focuses a laser pulse in or on a sample, which can be gas, liquid, aerosol or solid, to form micro plasm a. The spectra emitted are used to determine the of plasma formation and evolution are not so simple. The re ason for the complexity is due to critical parameters that influence the ablation proces s: laser irradiance, wavelength, pulse temporal duration and shape, physical / chemical properties of the target material and composition/pressure of the surrounding en vironment. G eneral information on fundamental principles and instrumental aspects of laser induced plasma

PAGE 37

37 emission relevant to analysis in particular, of solid sample s will be covered in this section LIBS Design ( G eneral) A simplified experimental appa ratus required for LIBS analysis is shown in Fig.2 1. T he two basic components of the apparatus include the excitation source and spectrometer with the detector. In general, a Nd:YAG laser which generates energy in the near infrared region of the electroma gnetic spectrum, with a wavelength of 1064 nm, is used as the excitation source The pulse duration is ~ 10 ns generating an irradiance which can exceed 1GW cm 2 at the focal point. The spectrometer consists of either a monochromator (scanning) or a polych romator (non scanning) and a photomultiplier tube (PMT) or charge coupled device ( CCD ) detector that converts the incident photon flux into a measurable electrical signal. The most common monochromator is the Czerny Turner type whil e the most common poly chromator i s the Echelle type E ven so the Czerny Turner configuration can be used to disperse the radiation onto a CCD effectively making i t a polychromator. T he polychromator spectrometer is the type most commonly used in LIBS as it allows simultaneous acquisition of the entire wavelength range of interest. Spectrometer response is typically from 1100nm (near infrared) to 170 nm ( a deep ultraviolet), the approximate response range of a CCD detector. The energy resolution of the spectrometer can also a ffect the quality of the LIBS measurement. A high resolution system can separate spectral emission line s effectively resulting in reducing line interference and increasing spectral selectivity. Basics of L aser M atter I nteraction and P rocesses in L aser I nd uced P lasma Understanding the laser matter interaction will a llow ablation of stoich iometric vapor and control of the laser induced plasma properties for optimum LIBS performance.

PAGE 38

38 When a short pulse laser beam is focused onto the sample surface, the surfac e temp erature of the sample increases and then a small vol ume of the solid is ablated a process known as Laser Ablation (LA). This ablate d mass further interacts with the laser beam to form a highly energetic plasma that consists of free electrons excite d atoms and ions. Laser ablation will be divided into three main processes for discussion in this section: bond breaking and plasma igni tion plasma expansion and cooling and particle ejection and condensation. Fig ure 2 2 shows a summary of the three proc esses and various mechanisms occurring during each process. During the plasma ignition process, the mechanisms and plasma properties strongly depend on the laser irradiance and pulse duration. However, the scope of this study was limited to a nanosecond la ser pulse; thus, the dominant mechanism in the plasma ignition is thermal vaporization: that is, the temperature of the solid surface increases, and a well defined phase transition occurs from solid to liquid, liquid to vapor, and vapor to plasma. As the n ext process, plasma expansion begins after the plasma ignition process (see in the middle picture of Fig. 2 2 ). The plasma expansion process will be governed by the initial plasma properties (e.g. electron number density, temperature and expansion speed) w hich are strongly dependent on the laser properties. In addition, it will be related to the initial mass and energy in the vapor plume, and the surround ing gas where the free electrons present in the plasma modify the propagation of laser light The hot ex panding plasma interacts with the surrounding gas mainly by two mechanisms: (i) the expansion of the high pressure plasma compresses the surrounding gas and drives a shock wave and (ii) during this expansion, energy is transferred to ambient gas by the com bination of thermal conduction, radiative transfer and heating by the shock wave. Since vaporization

PAGE 39

39 and ionization take place during the initial f r action of the laser pulse duration, the rest of the laser pulse energy is absorbed in the vapor and in the ex panding plasma plume. This laser absorption in the expanding vapor/plume generates three different types of waves laser supported combustion (LSC) waves, laser supported detonation (LSD) waves and laser supported radiation (LSR) waves (for I laser > G W/c m 2 ) as a result of the different mechanisms of propagation of the absorbing front into the cool transparent gas atmosphere [65 67] At the low irradiances used in LIBS experiment s the models that most closely match experiment are LSC and LSD. The LSC wave occurs at low irradia tion ( 1 0 4 10 7 W/cm 2 ), and the precursor shock is separated from the absorption zone and plasma (see Fig. 2 3). Fresh shocked gas ingested by the LSC wave rapidly heats The LSC wave velocity is lower than that of the shock wave a nd the plasma stays confined to the vapor and the surrounding ambient gas. Otherwise, LSD waves occur at intermediate irradiation (10 7 10 9 W/cm 2 ), the precursor shockwave is sufficiently strong so that the shocked gas is hot enough to begin absorbing the laser radiation without requiri ng additional heating by energy transport from the plasma. Thus, the laser absorption zone follows directly behind the shockwave and moves at the same velocity. As can be seen in Fig. 2 3, t he LSD wave is typically observed to form ahead of a target before it has even started to evaporate. Yal in et al. [68] also studied the influence of ambient conditions on the laser air spark and found evidence in support of a laser supported radiation wave (LSRW) model. According to this model after the initial breakdown, the plasma is heated to the point where it is opaque to the laser. A region closer to the laser source is then heated by the UV emission from the hot plasma and wh en sufficient electrons are generated laser radiation is absorbed again via electron

PAGE 40

40 ion inverse B remsstrahlung. As a result, a heating wave propagates into a cold gas in a direction opposite to the laser direction, as sh own schematically in Fig. 2 3 Fi nally, du ring the plasma cooling process nano sized particles will be formed from condensation of the vapor. Actually, condensation starts when the vapor plum e temperature reaches the boiling temperature of the target material and stops at the condensation temperature of the material. As discussed above, l aser ablation involves complex, non linear physical and chemical mechanisms that span several orders of magnitude in time with respect to the different predominant emitting speci es under ambient condition s as well as the different physical phenomena obser ved during the plasma expansion. Because the laser plasma is a pulsed source, the resulting spectrum evolves rapidly in time. A schematic overview of the temporal history of a LIBS plasma initiated by a si ngle laser pulse is shown in Fig. 2 4 (a) Between its initiation and decay, the plasma evolves through several transient phases [68 69] as it grows and interacts with the surroundings. The initiation of plasma formation over a target surface is dominated by strong continuum emission because ionization is high. T his light is caused by bremsstrahlung and recombination from the plasma as free electrons but when sufficient electrons are generated, the dominant laser absorption mechanisms makes a transition to electron ion inverse Bremsstrahlung Photo ionization of excited states can also contribute in the case of interactions with sho rt wavelength radiations. The same absorption processes also are responsible for the absorption by the ambient gas. When the laser pulse terminates, the plasma starts to cool down. During the plasma cooling process, the electrons of the atoms and ions at t he excited electronic states decay into natural ground states, causing the plasma to

PAGE 41

41 emit light with discrete spectral peaks. Throughout there is a background continuum that decays with time more quickly than the spectral lines. For this reason, LIBS measu rements are usually carried out using time resolved detection. In this way the strong continuum emission at early times can be removed from the measurements by turning the detector on after this continuum emission has significantly subsided in intensity bu t atomic emissions are still present (see Fig. 2 4 (a)). The majority of LIBS measurement is conducted by using a single pulse in which a series of individual laser sparks are formed on the sample at the laser repetition rate. In some cases, double pulse or multiple pulses for LIBS, in a various configuration s have been used because i t can result in large enhancements in signal intensities [27] Figure 2 4 (b) illustrates the timing between two pulses, where t represents the temporal difference between two laser pulses. Note that t d is measured from the second laser pulse in this case. More detail for double pulse LIBS will be described in Chapter 6

PAGE 42

42 Figure 2 1. Diagram of a t ypical laboratory LIBS apparatus. Spectrograph Array detector 0.100 s Detector controller Gating electronics Computer Lens Lens 2 f 2 f Laser

PAGE 43

43 Figure 2 2. A summary of laser ablation (LA) processes and various mechanisms occurring during each process. Inserted figure shows the schematic diagram of expanding laser produced plas ma into ambient gas in detail. The p lasma plume is divided into several zones having high density hot and low density cold plasma. The farthest zone from t h e target has minimum plasma density and temperature. The l aser is absorbed in low density coron a [70] Target Target Plasma ignition fs laser (10 12 10 17 W/cm 2 ) Electronic excitation and ionization (10 15 10 17 s) Coulomb explosion (10 13 s) Electron lattice he ating (10 12 s) ns laser (10 7 10 11 W/cm 2 ) Thermal vaporization (10 9 10 8 s) Non thermal ablation (10 9 10 8 s) Plasma shielding (10 9 10 8 s) Plasma expansion And cooling Shockwave propagation Plasma expansion (10 11 10 6 s) Plasma radiation cooling (10 6 10 4 s) Particles ejection and condensation Nano particles formation (10 4 10 3 s) Ejection of liquid droplet (10 8 10 6 s) Solid exfoliation (10 6 10 5 s) Shock wave in ambient gas Lase r Target Cold plasma Line emission Hot plasma Bremsstrahlung Continuum emission Target

PAGE 44

44 Figure 2 3. Timing of the physical phenomenon observed during the plasma expansion and two major types of laser absorption w ave schemes [68, 71]

PAGE 45

45 Figure 2 4. (a) Relevant time periods after plasma formation during which emission from different species predominate. The box represents the time during which the plasma light is monitored using a gatable detector. (Here, t d is the d elay time and t w is the gate pulse width.) (b) Relevant timing periods for a double pulse configuration. (Here, t is interpulse delay time between two lasers.) [2]

PAGE 46

46 Table 2 1 Significant milestones in the development of LIBS as an analytical technique applicable to a variety of samples and circumstance s [1] Yea r Significant milestones 1960 Ted Maiman develops the first pulsed laser 1963 First analytical use of a laser plasma on surfaces, hence the birth of laser induced breakdown spectroscopy 1963 First report of a laser plasma in a gas 1963 Laser micro spec tral analysis demonstrated, primarily with cross excitation 1963 Laser plasma in liquids were initially investigated 1964 Time resolved laser plasma spectroscopy introduced 1966 Characteristics of laser induced air sparks studied 1966 Molten metal dir ectly analyzed with the laser spark 1970 Continuous optical discharge reported 1970 Q switched laser use reported, results compared with normal laser pulses 1971 Biological materials investigated with LIBS 1972 Steel analysis carried out with a Q switc hed laser 1978 Laser spectrochemical analysis of aerosols reported 1980 LIBS used for corrosion diagnostics in nuclear reactors 1982 Initial use of the acoustic properties of the laser induced spark 1984 Analysis of liquid samples and hazardous aerosol s demonstrated 1988 Attempts made to enhance intensities through electric and magnetic fields 1989 Metals detected in soils using laser plasma method 1992 Portable LIBS unit for monitoring surface contaminants developed 1992 Stand off LIBS for space ap plications demonstrated 1993 Underwater solid analysis via dual pulse LIBS demonstrated 1995 Demonstration of fiber optic delivery of laser pulses 1995 Multiple pulse LIBS reported for use on steel samples 1997 LIBS use in applications in painted works of art and illuminated manuscripts 1998 Subsurface soil analysis by LIBS based cone penetrometers shown 1998 Reports on the use of echelle spectrometers coupled with CCD detectors 1999 Trace metal accumulation in teeth observed with LIBS 1999 Pulses f rom different lasers used to enhance LIBS performance 1999 Calibration free LIBS introduced 2000 Report on commercial instrument for coal analysis 2000 Demonstration of LIBS on a NASA Mars rover 2000 First International Conference on LIBS Pisa, Italy 2002 Second International Conference on LIBS Orlando, FL 2004 Third International Conference on LIBS Malaga, Spain 2004 LIBS approved for 2009 Mars mission 2006 Forth International Conference on LIBS Montreal Canada 2008 Fifth International Con ference on LIBS Berlin, Adlershof Germany

PAGE 47

47 Table 2 2 Advantages and disadvantages of laser induced breakdown spectroscopy Advantages Disadvantages Simultaneous multi element detection capability Difficulty in obtaining matrix matched standards Min imal or no sample preparation Variation in the mass ablated caused by significantly inhomogeneous as a result of either bulk or surface non uniformity Simplicity Poor precision, typically 5 10 % Rapid or real time analysis Relatively higher detection l imits than standard solution techniques (e.g., ICP OES) Capable of i n situ analysis requiring only optical access to the sample Standard emission disadvantages: e.g., spectral interference depending upon the instrumental resolution and the existence of se lf absorption of some lines. Only very small amount of material is vaporized Possibility of optical component damage from high energy power of laser Capability of some elements difficult to monitor with conventional AES methods Complexity of laser ablat ion under variety experimental conditions Ability to all states of materials, e.g., gases, liquids and solids Variety of measurement scenarios

PAGE 48

48 C HAPTER 3 FUNDAMENTAL INVESTIG ATION OF LASER INDUCED PLASMA Introduction The aim of this chapter is to pr ovide basic information on the use of the technique of laser induced breakdown spectroscopy (LIBS) for quantitative analysis. The interaction of high power laser light with a target material has been an active topic of research not only in plasma physics b ut also in the field of material science, chemical physics and particularly analytical chemistry [41] When this high power laser beam is focused on a target (solid, liquid or gas), it produces a plasma, which is a local assembly of atoms, ions and free electrons Plasmas are characterized by a variety of parameters, the most basic being the degree of ionization. A weakly ionized plasma is one in which the ratio of electrons to other species is less than 1 0 %. At the other extreme, highly ionized plasma may have atoms stripped of many of their electrons, resulting in very high electron to atom/ion ratios. LIBS plasmas typically fall in the category of weakly ionized plasmas [70] In LIBS, the vapo rizing and exciting plasma from a sample expands either in the vacuum or in the ambient gas depending on the experimental condition s As a result of the laser matter interaction, various processes may occur: e.g. ablation of material, target acceleration, high energy particle emission, generation of various parametric instabilities as well as emission of radiation ranging from the visible to hard X rays depending on the intensity of the laser. These processes h ave many applications, but only the spectrosco pic study of optical emission from the laser induced plasma known as LIBS, on a solid target will be studied herein. The following sections will briefly describe the plasma physics relevant to laser induced breakdown spectroscopy that are

PAGE 49

49 essential to und erstand this study and the applicability of LIBS. The chapter also includes a discussion of the theoretical assumptions on the state of the plasma for achieving precise quantitative analysis by LIBS Spectral E mission from P lasma In a plasma, atoms and ion s undergo transitions between their quantum state through radiative and non radiative processes. Non radiative process involve s collisions and radiative processes involve emission, absorption, and fluorescence of radiation. Figure 3 1 shows schematically t ransitions in an atoms or ion s These transitions are [90] : (spontaneous radiative transition) (excitation by electron impact) (de excitation by electron impact) (radiative recombination) (ionization by electron impact) (three body recombination) In the above, levels and are of the atoms or ions in the ioniz ation stage ( ) and is the ground state of the ions in the next ionization stage. The letter in the initi al state (left hand side) indicates the incident electron inducing the transition ; otherwise, in the final state (right hand side) represents the scattered electrons. The photon with frequency emitted in the transition. The symbols shown above the arr ows represent the rate constants with the units for the transitions. Among these processes, the most important are spontaneous radiative transitions and collisional transitions induced by electron impact (collisions). In laser induced

PAGE 50

50 plasma, in particula r, plasma emission is not a direct consequence of the photo excitation mechanism because the duration of the plume is relatively long in comparison with both the radiative lifetimes of the emitting species and the laser pulse duration Rather, the impact e xcitation by thermal electrons can be adapted to explain the phenomenon [72] Laser induced plasma emission consists of atomic and ionic spectral lines and a broad band continuum that is t he result of electron ion recombination (radiative recombination) and free free interaction (Bremsstrahlung) Identification of the spectral lines and measurement of their intensities provide both qualitative and quantitative information, but qu antitative analysis is not simple due to the complexity of the determination of quantitative line intensity [73] The e mission signal (counts photon) of a particular atomic or ionic line of an element is given by the product of the excited state number density, the spontaneous transition probability of the transition chosen and the detection function, [2] (3 1) where is the excitation volume seen by the detector, (no units) is the calibration function, which describes the plasma characteristics in terms of optical depth such as self absorption/or self reversal effects and is the overall detection efficiency. This equation can be e xpressed by three interrelated functions, describing the initial interaction between the sample and the laser leading to ablation / vaporization of solid material, the exci tation/ionization mechanisms leading to

PAGE 51

51 atomic/ionic emission, and the characterization of the radiation environment, (thin or thick plasma): (3 2) These functions are related to the fundamental assumptions for simplifying a very complex phenomenon in quantitative LIBS analysis as follows : the compositions of the plasma volume under observatio n is representative of the sample composition (stoichiometric ablation) the plasma volume under observation is in Local Thermodynamic Equilibrium (LTE), and the spectral lines measured are optically thin. When the above conditions are satisfied, the repro ducibility of the quantitative results is assured in most cases. W idth and S hape of S pectral L ine s [74] The main diagnostic technique for plasma involves the r elationship between plasma properties and spectral line characteristics. In general, t here are two major reasons for determining the line shapes of spe ctral li ne s originating in plasma. The first reason is the use of measured line shapes to determine physi cal properties of emitting plasma such as the charged particle densities and temperature. The second reason is to determine the absorption and induced emission coefficients which depend on the oscillator strength and densities of emitting atoms in addition to the line shape. Figure 3 2 shows a hypothetical spectral line profile and identifies the different features. The studies presented herein only deal with the physical properties from t he line shapes of spectral li nes originating in plasma. In addition, line shapes and shifts can be a diagnostic for the p rinciple broadening mechanisms. In LIBS plasma, three different

PAGE 52

52 processes may contribute to the finite width of a spectral line: natural broadening, Doppler br oadening, and interactions with neighboring particles (e.g. Stark broadening) I n the solid state the last interaction may take many different forms but if the discussion is limited to free atoms and molecules, the interactions with other particles may be treated under the heading of pressure broad ening. Furthermore, in investigating line broadening processes in emission it is essential to check for optically thin ness in the line and to make appropriate corrections for self absorption if required because it affects the line broadening. Natural broad ening. Spectral line profiles are determined by the dominant broadening mechanisms In the ideal case of a free atom the radiated intensity of a line profile is spread over a frequency dependent Lorentzian profile having the form (3 3) where is the intensity at the center of the line profile and is the radiation damping constant of (3 4) The lifetime of a classical oscillator is the inverse of damping constant (3 5) This spread of intensity over a range of frequencies is called natural broadening of the spectral line and ( ) is called ful l width at half maximum (FWHM). Doppler broadening. However, except at very low atomic densities the ideal condition is never realized in practice and natural broadening is always accompanied by Dopp l er broadening which dominates the line shape near its center. Doppler broadening arises due to random thermal motions of the emitting atoms

PAGE 53

53 In general, a source moving towards an observer causes the wavelength to decrease (blue shift) and a source moving away from an observer causes it to increase (red shift). A large n umber of atoms having different velocities will e mit a spread of wavelengths, i e., a broadened line. Thus, the resulting line profile by Doppler broadening is given by a Gaussian profile : (3 6a) with FWHM (3 6b) where is the frequency of line center, and are the actual atomic or molecular mass and the universal gas constant, respectively and is the equilibrium temperature. Often the two are of comparable magnitude The resulting profile obtained by convolution of the two is called the Voigt prof ile. Figure 3 3 compares the characteristics of Gauss and Lorentz profiles of equal full width at half maximum (FWHM), and the resulting Voigt profile. As shown in Fig. 3 3 t he Gaussian will do minate close to the line center; the Lorentz in the line wings Thus, the combination of both types of profile functions (Voigt profile) depends on the relative strength of the two effects. Pressure broadening [74] The p r esence of nearby particles will affect the radiation emitted by an individual particle causing a frequency disturbance and a phase shift There are two limiting cases by which this occurs: Impact pressure broadening : T he collision of other partic les with the emitting particles interrupts the emission process. The duration of the collision is much shorter than the lifetime of the emission. This effect depends on both the density

PAGE 54

54 and temperature of the gas. The broadening effect is described by a Lorentzian profile and there may be an associated shift. Quasistatic pressure broadening : The presence of other particles shifts the energy levels in the emitting particle, thereby altering the frequencies of the emitted radiation. The duration of the collision is m uch longer than the lifetime of the emission process. This effect depends on the density of the gas, but is rather insensitive to temperature. The form of line profile is determined by the functional form of the perturbing force with respect to distance fr om the perturbing particle. There may be a shift in the line center. Pressure broadening may also be classified by the nature of the perturbing force as follows: (i) L inear Stark broadening occurs via the linear Stark effect which results from the interac tion of an emitter with an electric field, which causes a shift in energy which is linear in the field strength ( ; (ii) R esonance broadening occurs when the perturbi ng particle is of the same type as the emitting particle, which int roduces the possibilit y of an energy exchange process ( and the lines are symmetrically broadened and unshifted. [75 77] ; (iii) Q uadratic Stark broadening occurs via the quadratic Stark effect which r esults from the interaction of an emitter with an electric field, which causes a shift in energy which is quadratic in the field strength. ( ; (iv) Van der Waals broadening occurs when the emitting particle is being perturbed by van d er Waals forces Specifically, a fluctuating dipole in the radiating atom induces a dipole to the neutral ground state atom and the corresponding interaction causes line broadening. The energy shift as a function of distance is given in the wings by e.g. the Lennard Jones potential ( [78] Actually, line shift s takes place only for quadratic stark and Van der Waals interactions, n =4 or 6. In general, Van der Waals and resonance broadening mechanisms are important in weakly ionized plasma; Stark broadening otherwise is most important in highly

PAGE 55

55 ionized and high density plasmas where the strong electric field from the charged species produce s a broadening of the transitions between the split atomic levels. Thus, among the pressure broadening mechanisms Stark broadening which is the major broadening effect in laser induced plasmas will be described here in in detail. When the emitting species (atoms or ions) in a plasma are under the influence of an electric field by fast moving electrons and relatively low moving ions both of the above broadening mechanisms are completely negligible in comparison to the broadening cau sed by the charged particles (Stark broadening) Thus, Stark line broadening from collisions of charged s pecies is the primary mechanism influencing the emission spectra in conventional LIBS experiments. The interaction between the atom and this electric f ield is described by the Stark effect which splits and shifts the energy levels of the atom. However, only the hydrogen atom and H like ions exhibit the linear Stark effect proportional to ; whereas all other atoms exhibit the quadra tic Stark effect proportional to and hence to Thus, it is obvious that the extent of Stark effect will be negligibly small for a large distance from an ion or electron. I n the Stark ef fect degenerated sublevels identified by the quantum number representing the component of the total angular momentum are partially or completely split, leading either to an unresolved, broadened, and shifted level, or a resolved series of sublevels. Selection rules on the transitions between the sublevels allow one to predict the intensity of the resulting line. The linear Stark effect splits the energy levels symmetrically, resulting in a symmetric line pattern; the quadratic Stark effect, otherwise, splits t he energy levels asymmetrically with a shift, usually towards the red, of the center of gravity of the line pattern.

PAGE 56

56 Determining E lectron D ensities from S pectral L ine W idths The most powerful spectroscopic technique for determining the electron density of a plasma comes from the measurement of the stark broadening of a spectral line. In this method absolute int ensities of spectral li ne s are not required, merely line shapes and FWHM are sufficient. Both the linear and the quadratic Stark effect are encountered in spectroscopy. However, only the hydrogen atom and H like ions exhibit the linear Stark effect, whereas all other atoms exhibit the quadratic Stark effec t. This is the reason that ideally information about electron density is extracted from the lines of H or H like ions, where the half w idth of the line profile can be calculated easily with a greater accuracy. In the case of the linear Stark effect, the re lation between electron density and the line width is given by a simple relation [76] : (3 7) w here is the FWHM and the parameter depends (only weakly) on and which can normally be treated as being constant. The constant for the H Balmer lines is available in the litera ture [76] The first choice for electron density determination in LIBS plasma containing hydrogen is the H line (with an error of 5%) [76] because of its large intensity and sufficiently large line broadening, which can be measured precisely using a spectrometer of moderate resolution. The possibility of self absorption in this case is relatively small. The second best choice among the B al mer series is the H line. The H line is suitable in the case where the electron density is not too high ( ), because at higher electron densities this strong line is quite susceptible to self absorption, which severely distorts the line profile. In th e case of non H like

PAGE 57

57 atoms, where the quadratic Stark effect is dominant, the relation between the electron density and the line width [76] is (3 8) The firs t term in the brackets gives the contribution from electron broadening, and the second term stems from ion broadening. Here is the electron impact parameter at and is the ion broadenin g parameter. The parameter s and can be found easily from the literature [76] Since the second term in Eq. 3 8 is normally small, the expression reduces to (3 9) which is normally used for calculations in the case of plasmas generated from solid targets. In general, Stark width and shifts will be largest for the upper levels closer to the ionization limit and for upper levels that originate in electron configurations that have opti cal electrons with high angular momentum. Hence f levels are affected more than d levels and so on. As one goes higher in atomic mass, the Doppler widths get smaller. Hence, even for many strong lines that originate from upper levels that are still far from the ionization limit, Stark broadening can dominate. Regarding shifts in wavelengths, except for high f levels, these are typically less than 0.1 nm. Whether the Stark widths and shifts of li ne s from LIBS plasma are observable depends on the optical and spectral resolving powers of the spectrometer detector system. Plasma O pac ity Having introduced the concepts of line profile and line width, we can now discuss the opacity of a plasma. Fundamentally, a plasma is optically thin when the emitted

PAGE 58

58 radiation traverses and escapes from the plasma without significant absorption or scat tering. The (thermal) spectral radiance of a transition emitted from a plasma is given by [79] : (3 10) where is the spectral radiance (W cm 2 sr 1 nm 1 ) of the emission line, is the transition probability (s 1 ), is the Planck constant (J s), is the population of the excited level (cm 1 ) is the velocity of light (cm s 1 ), is the spectral profile of the line ( cm 1 ), is the emission (absorption) path length in the direction of the observation (cm), and is the net absorption coefficient, defined by the difference in the population of the lower and upper levels of the transition. Note that Eq. 3 10 is the result of integration over the emission line of sight, assuming a spatially homogeneous atomic distribution. As c learly shown in Eq. 3 10 the formula contains the self absorption term, given by the last ratio in the right hand side of equation. If this term is multiplied and divided by one obtains by series expansion (3 11a) wh ere the parameter is defined as (3 11b) In Eq. 3 11b, the parameter is identical to that used by Konjevi [80] evaluated at the line center ( ), is also identical to the so called self absorption

PAGE 59

59 coefficient (SA) derived by El Sherbini et al. [81] Finally, i f one uses the definition of the optical depth (see, for example, [74] p. 294), (3 12) T he last term in Eq. 3 10 becomes (3 13) Thus, Eq. 3 11a can be obtained by substituting Eq. 3 11b into Eq. 3 10 It is worth pointing out that this correction factor is the same as that reported in astrophysics work [82, 83] and appropriate to the c hosen physical emission/absorption model [84 86] Finally, when E q. 3 11a is integrated over wavelength, after making use of the relations between the Einstein coefficients and the absorption oscillator strength of the transition, and of the Boltzmann ratio for the atomic populations, valid under local thermodynamic equilibrium conditions (LTE), one obtains the well known expre ssion for the thermal emission as given by the radiation theory [74, 87 92] e.g., (3 14a) (3 14b) w here is the spectral radiance of the blackbody radiation given by the Planck or by the Wien laws at (W cm 2 sr 1 nm 1 ) and the integral terms are the expression of the total absorption factors, is related to the emission coefficient ( ) by the valid for LTE. The ratio [90] ) In the case o f negligible self absorption i e ., if the

PAGE 60

60 optical thickness over the whole wavelength range of the line profile, then one obtains (3 15a) In the optically thin condition, therefore, grows linearly with the wavelength integrat ed absorption coefficient, which in turn is directly related to the atom number density. Otherwise, in the other extreme (optically thick) condition, e.g., one obtains (3 15b) Under very strong self absorption, the observed line intensity then reaches the limit of black body radiation at the temperature and then the line los es its characteristic shape, i e. the observed line intensity no longer follows linearly the absorption coefficient and the stron ger lines effectively saturat e Moreover, the line profile cannot be recovered. Figure 3 4 show s an example of emission lines with varying optical thickness. For intermediate cases, i e ., if the optical depth ( ) is not too large, the line profile that would have been observed for the optically thin case may be recovered by us ing as a correction factor, defined in Eq. 3 11b In quantitative LIBS, the subtle onset of self absorption poses a problem for converting line intensities to concentrations. Self absorption is also a major problem for calibration f ree LIBS (CF LIBS). More detai l will be described in Chapter 5 In this chapter, A method will be presented to detect self absorption easily in the laboratory by using a spherical mirro r behind the plasma and comparison of the intensity of a given line wi th and without the mirror in place.

PAGE 61

61 Thermodynamic E quilibrium and T emperature Definition of thermodynamic equilibrium in laser induced plasma [2, 74] I f thermodynamic equilibrium ex ists, then plasma properties, such as the relative populations of energy level s and the distribution of the speed of the particles, can be described through the concept of temperature. Complete thermodynamic equilibrium would exist when all forms of energ y distribution are described by the same temperature. In fact, however, complete thermodynamic equilibrium is rarely achieved so physicists have settled for a useful approximation, Local Thermodynamic Equilibrium (LTE). In this state, the collision rates must exceed the radiative ones by at least one order of magnitude [76] so that the non equilibrium of radiative energy can be neglected, while for every point it is still possible to find a temperature parameter that satisfies the Boltzmann, Saha and Maxwell distributions. Thus, the plasma electronic excitation temp erature T and electron density which can be derived from the plasma emission data, can be used to describe the plas ma characteristics [74] In laser induced plasma the LTE assumption must be checked for LIBS analytical applications aimed to quantitative analyses, since the cu rrent data processing completely relies on their validity. Under LTE conditions characteristic line emission spectra are detected mostly from the atomic and first ionic excited species produced. Thus, only neutral and singly ionized species will be consid ered in the following. Provided that the radiative processes negligibly alter the balances of the collisional ones, the populations density and plasma ionization are ruled by Boltzmann and Saha equilibrium relations [52] This is the case of electron excitation kinetics driven p lasma in LTE, which is characterized by only one thermodynamic temperature, e.g. the electron

PAGE 62

62 temperature T e Under LTE conditions, the population of the excited levels for each species follows a Boltzmann distribution: (3 16) where and indicate the population density of the excited level of analyte (or species) and the total number density of the species in th e plasma respectively, and are the excitation energy of the level and the statistical weight of the levels ( ) respectively is the total angular quantum number o f the term, is 16 erg K), is the absolute temperature, and is the partition function of the species A at temperature T: (3 17) Similar considerations lead to Saha equation for atom/ion equilibrium as follow s (3 18) where is the plasma electron density, and are number densities of the neutral atomic species and the single ionized species, respectively, is the ionization potential of the neutral species in its ground state, is the electron mass and is Planck s constant. In this equation is a small correction of ionization energy due to small scale polarization of the plasma, or the tendency of electrons and ions to be surrounded by particles of the op posite charge [76] For checking the validity of LTE, experimentally, the line to continuum intensity ratio metho d will be described in chapter 4 One investigate s whether the plasma

PAGE 63

63 excitation tempera ture T exc obtained from a Boltzmann or Saha Boltzmann plot is different from the electron temperature T e resulting from the measurement of the intensity of plasma continuum. By maintaining T exc T e in the theoretical expression for the intensity ratio, any deviation from LTE condition can be assessed. Measurement of plasma t emperature. As described previously, under LTE conditions only one temperature describes the distribution of species in energy levels, the population of ionization stages or the kineti c energy of electrons and heavier particles. There are many methods for determining the plasma temperature based on the absolute or relative line intensity (two line method or Boltzmann plot /or Saha Boltzmann plot ), the ratio of line to continuum intensity etc. One of these methods may be chosen under the appropriate experimental conditions. Under the assumption of local ther modynamic equilibrium (LTE), the totally integrated intensity (W m 3 sr 1 ) corresponding to the transition between the upper level and the lower level is given by (3 19) where and are the wavelength, the transition probability and the statis tical weight for the upper level, respectively; is the speed of light and the other sym bols have already been defined in the list of symbols Provided that the LTE hypothesis described above is fulfilled, the plasma temperature can be calculated from the intensity ratio of a pair of spectral li ne s originating in different upper levels of the same element and ionization state. For the two line method, and of the same species, characteri zed by different values of

PAGE 64

6 4 the upper level energy ( ), the relative intensity ratio can be used to calculate the plasma temperature as follow s : (3 20) Assuming that the intensity values are t he only facto rs affected by the experimental error, the uncertainty in the temperature determination can be expressed by (3 21) where is the difference in energy of the two states observed, is the measured ratio of emission intensities and is the uncertainty associated with the ratio. When selecting a line pair, it is advisable to choos e two li ne s as close as possible in w avelength and as far apart as possible in excitation energy to reduce the effect of varying spectral response of the instrument as well as the sensitivity to small fluctuations in emission intensity. In Eq. 3 21 large values of wil l minimize the effect of the uncertainty in R on the uncertainty in T [87] However, relative intensities are not easy to measure precisely. A way to improve temperature values is to use many emission lines corresponding to different energy level s of a certain sp ecies in the plasma. Under the assumptions that the plasma is both in LTE and optically thin, the population of the excited levels for each species f ollows a Boltzmann distribution (see Eq. 3 1 6 ). We rearrange Eq. 3 1 9 into the form: or (3 22)

PAGE 65

65 where all symbols have been already defined. This is the equation of a straight line with slope of Hence, if one plots the quantity on the left against (of th e upper state for emission), and if there is a Boltzmann distribution, a straight line is obtained. Therefore, the plasma temperature can be obtained via linear regression, without knowing or To improve this method, the use of many lines in some sense literature exhibit a significant degree of uncertainty (from 5 to 50 %). Because emission lines from different ionizatio n stages are usually present in laser I nduced plasma, a combination of the Saha ionization and Boltzmann excitation distributions can be used to measure the electron temperature under LTE assumption [68] The most common form of the coupled Saha Boltzmann relation takes the form of the ionic/atomic emission radiance ratio (3 23) The superscripts I and II denote atomic and ionic parameters, respectively. Here is the first ionization potential and is the lowering correction parameter. The coupled form of the Saha Boltzmann distribution can be modified as in the case of the Boltzmann plot (3 24) Similar to the Boltzmann plot, this method allows for the determination of temperature from the slope of the line ( ) in Eq. 3 24 With the spread energy levels, the slope from a linear regression calculation is less sensitive to measurement noise. Furthermore,

PAGE 66

66 the electron density can now be obtained from the intercept. It should be noted that, in contrast to the B oltzmann plot alone, the intercept of the coupled Saha Boltzmann plot does not require an absolute intensity calibration because the geometric factors cancel out in the ratio [93] In fact, an independent measurement of electron density can be made via the Stark broadening technique which does not require the plasma to be in LTE. For the diagnosis of early phase plasma, for instance, Liu et a l [94] used the line to continuum intensity ratio, because line and continuum intensities are typically comparable at the start of plasma evolution. Under the assumption of local thermal equilibrium (LTE), the plasma temperature T can be determined by the line to continu um intensity ratio where is the continuum emission coefficient and is the integrated emission intensity over the line spectral profile [95] : (3 25a) (3 25b) where the G factor is the free free Gaunt factor [96 98] and factor is the free bound continuum correction factor which is analogous to the G factor, and all parameters are identified in the list of symbols When the continuum emission becomes weak, the plasma temperature calculated from ratio of line to continuum is not accurate. The plasma temperature in this case, can be estimated by using a Boltzmann plot or Saha Boltzmann plot mentioned above based on measuri ng the relative intensities of lines

PAGE 67

67 with known transitio n probabilities and degenerac ies Thus, all methods mentioned above can be complementary to each other under the appropriate experimental conditions.

PAGE 68

68 Figure 3 1. Energy level scheme and a ssociated excitation/de excitation processes The symbols shown above the arrows represent the rate constants for the transition: i.e., C ( l ): excitation rate coefficient; F( l ): de excitation rate coefficient; A( l ): Einstein s A coefficient or transi tion probability for l ; S( l ): ionization rate coefficient; ( l ): three body recombination rate coefficient; ( l ): radiative recombination rate coefficient; ( l ): ionization potential of level l (adapted from ref [90] )

PAGE 69

69 Fig ure 3 2. Spectral line profile. Here 0 is the central wavelength, 1 and 2 are the wavelength whose intensity is half of the maximum intensity I ( 0 ), and is the full width at half maximum (FWHM) (adapted from [99] )

PAGE 70

70 Figure 3 3 Normalized spectral profiles versus relative frequency for pure Do ppler (D), pure Lorentzian (L) distributions of equal full width at half maximum (FWHM), and the resulting Voigt (V) profile (adapted from ref [100] )

PAGE 71

71 Figure 3 4. Spectral line profile as a function of gradually increasing atomic concentration (a h). Note that the center of the line reach es the blackbody radiation limit at high atom densities (adapted from ref [100] )

PAGE 72

72 CHAPTER 4 LINE TO CONTINUUM INTE NSITY RATIO IN LASER INDUCED BREAKDOWN SPECTROSCOPY AS AN E XPERIMENTAL CHECK TO LOCAL THERMODYNAMIC EQUILIBRIUM Introduction The concept of local thermodynamic equilibrium (LTE) plays a vital role in plasma physics and plasma spectroscopy. In the LTE mod el it is assumed that collision induced transitions and reactions are more frequent than r adiative ones [76, 101, 102] If space and time variations are sufficiently small so that at each point and instant a local steady state population is established, the assumption of local thermodynamic equilibrium will always be valid as long as radiative rate processes are small compared with collision al processes. Thus, although the plasma temperature and density may vary in space and time, the distribution of pop ulation densities at any instant and point in space depends entirely on local values of temperature, density, and chemical composition of the plasma. With this assumption of local thermodynamic equilibrium all particle number densities neutral particles as well as ions can be calculated from total number densities and temperature, and they are allowed to be a function of time if the relaxation time for the establishment of thermodynamic equilibrium is smaller than the time variation of the densities and temperature. Therefore, it is very important to assess the existence of local thermodynamic equilibrium as examining time resolved plasma phenomena. The uncertainties in predictions of s pectral line intensities from a LTE model plasma depend on the uncerta inties in the values of these plasma parameters as well as the atomic transitions probabilities. The aim of this proposed research is to investigate several diagnostic methods in order to examine time resolved plasma phenomena, with emphasis on the evalua tion of

PAGE 73

73 the existence of equilibrium conditions at various stages of plasma evolution in LIBS For this purpose, the most interesting plasma diagnostic indicator s are the electron temperature T e a nd the electron number density n e since one can predict fro m these two parameters the extent of local thermodynamic equilibrium (LTE) which exists in the plasma. Most studies in this field have been performed under the assumption of the existence of such LTE conditions [68, 94, 103, 104] The reason is that if the LTE condition is ver ified it is possible to characterize the plasma by a unique temperature which considerably simplifies the description of the plasma properties. Few studies, however, have been devoted to the experimental evaluation of this assumption [101, 105 107] One of the approaches that can be used for the evaluation of the LTE condition is the Line to continuum intensity ratio method [94, 95, 107, 108] This approach has been described in the case of a high pressure, argon surface microwave plasma [94, 95, 107, 108] and, to the best of our knowledge has not yet bee n applied to laser induced plasma. In this approach, the theoretical ratio between the intensity of selected transitions, considered to be optically thin, and the underlying spectral continuum is used. In these expressions, the excitation temperature and t he electron temperature are purposely kept different from each other. Experimentally, the plasma excitation temperature, T exc is obtained from a conventional Boltzmann /or Saha Boltzmann plot, and the ratio between the spectrally integrated line intensity and the continuum intensity is measured By inserting these two experimental values into the theoretical expression, one can check whether the electron temperature derived in t his way is equal or different from the excitation temperature provided by the Bo ltzmann plot. In this way, any deviation from LTE conditions can then be assessed [109]

PAGE 74

74 Theory [107] Under the assumption of local thermal equilibrium (LTE), the elec tron temperature T e can be assumed equal to the excitation temperature T exc namely T e = T exc = T. However, putting T exc equal to T e in the expression for the ratio of the integrated emission intensity to the continuum intensity does not provide an accurate determination of T e when some deviation from LTE can be expected. Therefore, as suggested by Sola et al. [107] in t he case of an argon surfatron plasma, we propose to maintain T exc e in the line to continuum ratio expression (see below) in the laser induced plasma and to compare the value of T e obtained when the experimentally determined T exc and line to continuum ratio are used in the theoretical expression. Line to Continuum I nt ensity Ratio Method for D etermining of T e Under the assumption of local ther modynamic equilibrium (LTE), the totally integrated radiant emissivity (W m 3 sr 1 ) can be expressed as a function of the excitation temperature T exc and an experimentally measura ble transition probability as given below: (4 1) where all parameters have been already defined in Chapter 3 A practical and useful form can be obtained by using Sa ha equation for atom/ion equilibrium i e ., (4 2) where all parameters are also identified in Chapter 3 By combining Eq. (4 1) and Eq. (4 2) one obtains the integrated line radiation as the following expression:

PAGE 75

75 (4 3a) ( kg m 5 s 2 K 3/2 ) (4 3b) where all parameters are identified in the list of symbols equation implies LTE, one assumes that T ion = T e = T exc However, i n the proposed approach, t he assumption that the ion temperature T ion is equal to t he electron temperature T e was kept [110] but we keep the assumptio n of the electron temperature T e different from the excitation temperature T exc Equation (4 3a), thus, can be rewritten by (4 4) Continuum radiation from the LTE model plasma arises from the interaction of initially free electron s with the positive ions or atoms that are present. The interactions may be either free free transitions (Bremsstrahlung) or free bound transitions (recombination radiation) [76, 90, 102] This calculation yields a semi classical expression for multiplied by correction factors such as the free free Gaunt factor ( ) and free bound continuum correctio n factor ( ) derived from quantum mechanical considerations (see below ), i.e ., (4 5a) ( kg m 5 s 2 K 1/2 ) (4 5b)

PAGE 76

76 Thus, taking the ratio of the frequency integrated lin e intensity to the non integrated continuum intensity one obtains (4 6a) (s K ) (4 6b) In addition, Eq. 4 6a can be further simplified by examining the term containing the correction factors and This factor is the free free Gaunt factor which is a weak function of temperature and electron density, and improves the theoretical descrip tion of the free free continuum. Unfortunately, Accurate quantum mechanical calculation of Gaunt factors exist only for hydrogenic species [98] Numerically, the value of is approximately unity [96, 97] so that the exponential term including in Eq 4 6a can be negligible if T e bound transitions dominate the continuum. The factor is t he free bound continuum correction factor which is analogous to the factor. It corrects the semi classical expression for free bound continuum radiation. In the approach, t he effect of and on the calculation of the electron temperature in the theoretical expression (see Eq 4 6a) will be discussed below Moreover, the lowering of the ionization energy is required to get an electron temperature in the expression of Eq. 4 6a. is a small correction of ionization energy due to small scale polarization of the plasma, or the tendency of electrons and ions to be surrounded by particles of the opposite charge. Generally, this

PAGE 77

77 factor has been calc ulated by several methods. One of the methods was suggested by Uns o ld [111] who has derived a simple formula for estimation of (eV) (4 7) where n e is the electron density and Z eff is nuclear char ge which acts on the optical electron. (e.g. Z eff =1 for neutral hydrogen, Z eff =1 also for neutral helium, Z eff =2 for one fold ionized helium etc). The other method was suggested by Griem [76, 77, 102] with the following formula for estimation of (4 8 a ) If one considers the shielding for heavy particles (ions or neutrals) by ions and electrons in a thermal plasma, the Debye (or shielding) radius is in principle given by the formula: ( 4 8b) According to above two Eq 4 8a and 4 8b we can simply get the formula in terms of the temperature and electron density: (eV) (4 9) The theoretical expression of line to continuum intensity ratio method in Eq 4 6 a, th erefore, is only a function of temp erature and known or calculable constants. The experimental values of the ratio and of T exc can then be inserted into Eq 4 6 a to calculate T e Experimentally, what is measured from the continuum intensity is the intensi ty over a finite spectral band width ( ). For this reason, the experimental continuum intensity

PAGE 78

78 should be expressed by or This expression is agreement with units of both sides in Eq. 4 6a. Thus, the final equation relating the ratio of experimentally observed line to continuum intensity is: (4 10a) (4 10b) Experimental A schematic of the apparatus for plasma emission measurements is shown in Fi g 4 1. A Nd YAG laser (Brilliant, 360 mJ maximum pulse energy at 1064 nm and maximum repetition frequency of 10 Hz) was focused on the sample surface with a quartz lens (10 cm focal length). In this work, the laser was operated at 1 Hz and was characterized by a pulse energy of 90 5 mJ of 6ns of duration. All measurements were performed at atmospheric pressure. A positioning system consisting of a helium neon laser was used to optimize the sample to focusing lens distance. For all measurem ent, the target was moved with a three dimensional stage (x, y and z transition stage) and translated horizontally every 10 laser shots. A controlled stream of air was used to carry away the dust plume formed during the interaction. A 5.0 cm diameter quart z lens, with a focal length of 7.5 cm, was used to collect the plasma emission and to produce a one to one image of the plasma onto the entrance slit of the monochromator. An adjustable iris was positioned close to the lens

PAGE 79

79 in order to match the F number o f the spectrometer (F/6.5 system). A 35 um slit width was used in all cases. The spectrometer (Acton triple grating, 0.5 m focal length) was equipped with three gratings (1200, 2400 and 3600 grooves / m m), providing a reciprocal linear dispersion of 1.57, 0.72 and 0.41 nm / mm, respectively. In the present work, the 2400 grooves / mm grating was used. The spectrometer has a typical spectral coverage of 10 nm and a spectral resolution of 0.03 0.05 nm. The detector is an intensified CCD (ICCD 5764 / RB E, Pri nceton instruments) with a photosensitive area of 576 384 pixels, corresponding to (12.7 8.4) mm 2 The spectral coverage by a single pixel varies from 0.016 nm at 282 nm to 0.014 nm at 428 nm. The ICCD is operated by its controller (ST 138, Princeton Instruments) and by a pulse generator (PG 200, Princeton Instruments), allowing the choice of the gate width and of the delay time for time resolved acquisition The gate width and the delay time between the laser pulse and the beginning of the acquisition could then be adjusted in order to maximize the signal to background and the signal to noise ratio. A delay time of 1 s was experimentally found to represent a good compromise between the necessity of measuring accurately the continuum and of providing a satisfactory signal to noise ratio for the transitions chosen. The data acquisition was controlled with the Winspec32 software (Version 2.5.18.2, Princeton Instruments). Results and D iscussion Electron N umber D ensity (n e ) The emission spectra revealed n oticeable line broadening, which is important for the determination of the electron number density (see Fig. 4 2a ). Major line broadening mechanisms are Stark broadening (Lorentzian profile), Doppler broadening (Gaussian profile), and pressure broadening a s mentioned in the chapter 3 Stark line broadening

PAGE 80

80 from collisions of charged species is the primary mechanism influencing the emission spectra in these experiments. The determination of the electron density using Stark broadening has the advantage of not requiring the validity of LTE condition. The electron number density related to the full width at half maximum (FWHM) of stark broadening lines is given by the expression [68, 94, 103, 104, 112] (4 1 1 a ) w here B is a coefficient equal to 1.2 and 0.75 for ionic and neutral lines, respectively and is the number of particles in the Debye sphere and is estimated from (4 11b) The first term in Eq 4 11a r efers to broadening due to the electron contribution whereas the second term is attributed to the ion broadening. Since the contribution of the ionic broadening is normally very small, it can be neglected and Eq 4 11a reduces to a much simpler form as see n below: (4 12) In the above Ea. 4 11a is the electron impact parameter and is the ion broadening parameter; and are function of temperature and are approximated by second order polynomials [113] The chosen spectral line was fi tted by a Voigt profile and the Lorentzian width ( ) of the line was taken as (FWHM exp of the experimental spectral line) while the Gaussian width ( ) is the instrumental line broadening that is predetermined using the

PAGE 81

81 line width of a Hg hollow cathode lamp at Hg I 294.263 nm with 35 m slit width, = 0.5 The line broadening was calculated by the equation as seen below, (4 13) In this way, it was possible to eliminate the instrumental broadening. Over the tim e scale investigated, the measured electron densities were found to have a trend, where n e decreases exponentially with the delay times, which vary from the order of ~ 10 19 cm 3 to ~ 10 18 cm 3 in a delay range (100 ns to 3000 ns) as shown in Fig. 4 2b The corresponding lower limit of electron density is given by the McWhirter criterion which has been used for assessing LTE conditions [114, 115] (4 14) where is the electron temperature in K elvin and is the largest energy transition in eV It is assumed that the distribution of population densities of the ele ctrons is determined by collisions with other particles rather than by radiative processes. In general, it is only at later times that the electron density values converge toward this lower limit. In our study, the McWhirter criterion appeared to be fulfi lled in the whole studied delay time range due to the significant laser fluence (90 5 mJ laser pulse energy). The measured electron densities, that is, are higher than the lower limit, which varies from ~ 10 19 cm 3 to 10 17 cm 3 for the range of obtained temperature (for T = 18,000 7,500 K and E < 5.0 eV) as shown in Fig. 4 2. However, one should note that the McWhirter criterion is necessary but not a sufficient condition for a plasma to be in LTE due to the evolution of plasma in space and time. Thus, it is important to study the local

PAGE 82

82 thermo dynamic equilibrium (LTE) conditions in the plasma, and then assess any derivation from LTE conditions in order to determine the best conditions at which they are satisfied. This was done by comparing the excitation temperature ( T exc ) and electron temperat ure (T e ) in the line to continuum intensity ratio method as a function of the delay ti me for an experimental assessment of LTE In the study, the plasma seems to reach the LTE state around 5.0 s after its formation as shown by the agreement between T exc and T e in the theoretical expression of the line to continuum intensity ratio method. Experimentally, in the beginning of the relaxation, in general, the electron temperatures appear to be high er than the excitation temperature s due to its fast evolution and the plasma being heated by inverse Bremsstrahlung. This means that some time is required after the plasma formation in or der to reach LTE. More studies pressented in the following sections. Excitation T emperature (T exc ) The Boltzmann plot is a well known method for determining the excitation temperature ( T exc ) of the plasma using the Boltzmann equilibrium relationship without knowledge of the concentration (or number densities) and the par tition function in terms of temperature. The Boltzmann plot method allows plasma temperature to be determined through a simple linear regression with the slope by representing log (I ul / g u A ul ) against the upper energy level E u in eV, provide d that the tra nsition probabilities (A ul ) from a given excitation state are known as shown in Eq. 3 22 However for high temperature, the energy spread in a single ionization state is not large enough to provide accurate temperature values.

PAGE 83

83 On the other hand, the Saha equation provides a relationship between transition line intensities from different ionization stages. Using both equations together has some advantages for determining temperatures in plasmas. First, it combines the improved statistics of the Boltzmann p lot due to the use of many emission lines with the greater accuracy of the Saha analysis because of the larger energy spread available ( see, for example, [68, 116] ) In other words, with a large range of energy values in the abscissa, the p resence of one or two outliers is not expected to significantly affect the slope of the overall plot. For the evaluation of the plasma temperature with this approach the Boltzmann plot and Saha Boltzmann plot methods were used in the spectral profiles of the transitions chosen. It is important to note that the measurements correspond to line of sight averages and therefore one should be aware that spatial resolution is not taken into account here. Figure 4 3 shows excitation temperatures obtained from bot h Boltzmann and Saha Boltzmann plots for several elements such as copper and barium used in our work. Table 1 lists some spectral lines and their constants used in the study (transition probabilities and statistical weights of these lines). Electron T emper ature (T e ) The electron temperature (T e ) was calculated by taking the ratio of the frequency integrated line intensity to the experimental continuum intensity multiplied by spectral band width ( ), namely the line to continuum intensity ratio method (see Eq. 4 10). As mentioned above, the electron temperature can be calculated by keeping T exc e in the theoretical expression.

PAGE 84

84 As pointed out in the theory section, provided that the fre e free Gaunt factor and free bound continuum factor can be explained, Eq. 4 10 can be further simplified and then the electron temperature T e can be calculated more precisely. For the study, the Cu atomic line at 282.44 nm in pure copper metal was consider ed As mentioned in the theory section, since it is difficult for the correction factors and to be calculated precisely, arbitrary values from 0.01 to 1 for both and were inserted into Eq. 4 10 in order to c heck how these values affect the calculation of T e as a function of delay time, as can be shown in Fig 4 4. After 0.5 s delay time, the calculated electron temperature was identical for arbitrary values of within an error range (about ~ 20 %), which can be attributed to uncertainty in the Einstein transition probability (see in Fig. 4 4a and b) Otherwise, for the free bound continuum correction factor the calculated electron temperatures show ed a significant difference for different values of as a function of delay time (see in Fig 4 4c and d). In the extreme case, e.g., at the shortest delay time (t d = 500 ns), the difference in electron temperatures was so pronounced that the correction factor increases from 0.01 to 5 ; i.e., it is out of the error range ( > ~ 50 %), which can be attributed to the Einstein transition probability In our work, however, and values of 1, respectively, in Eq. 4 10 were used for simplifying of the complex calculation It is worth nothing that this approach can assess the existence of local thermod ynamic equilibrium in examining time resolved plasma phenomena, a lthough some error in calculation of electron temperature depending on correction factor can be expected The study was performed on three different samples such as a pure copper metal (9 9.99 % Cu) and a luminum alloy sample (16.05% Cu) for copper and a BaCl 2 p e llet for

PAGE 85

85 barium Emission lines to be used for the line to continuum intensity ratio method were selected according to the following criteria: (1) the line shoul d be free of interference with other lines, (2) it should be on a strong continuum radiation even at l ong delay time s and (3) it should be free from self absorption Experimental results for Cu I n the case of copper metal, we used two different gating a nd laser energy parameters (see Table 4 2) at short delay and long delay times, respectively If the experimental condition of the gating and energy parameters used at long delay time is kept at short delay time e.g. t d < 300 ns the ICCD camera is satur ated in the cases of ion sp ecies because the ionic emission is very strong at the short delay time. F or the purpose of spectrochemical analysis, especially the line to continuum intensity ratio method, neutral atoms are more suitable, because they are more sensitive and observable o ver a longer period of time. For this reason, the Cu atomic line at 282.44 nm in pure copper metal (Fig. 4 5 and 4 6 ) and 296.12 nm in the Al alloy (Z8) sample (Fig. 4 7 ) were selected for analyzing signal to background ratio bec ause it is the highest signal to continuum intensity ratio as well as the best resolved line even at long delay t ime s As the delay time increase d from to the excitation temperature decrease d as seen in Fig. 4 6 However, for short delay tim es (t d < 300 ns ) after the laser pulse, the excitation temperature could not be measured accurately because the line emission can be imbedded in the continuum emission as seen in Fig. 4 5 a In addition, during this period, 50 5 mJ laser pulse energy was us ed due to saturation of the ICCD camera. Galmed et.al [117] showed th at LTE conditions are fulfilled only in the cases of 75 100mJ laser pulse energies. Thus, it is very hard to describe the trend

PAGE 86

86 of the excitation temperature during this time period ( t d < 300 ns ) as can be seen in Fig. 4 6a The excitation temperature exhibit ed an initial f ast decay from 22, 328 K at 0.5 as shown in Fig. 4 6c Finally, the Cu lines disappear after th is time (see Fig. 4 6d) While it should be noted that the electron temperature also decreased exponenti ally as the delay time increased until delay time, but increased again after due to the small signal to continuum intensity ratio. Moreover, at the short delay time (t d < 100 ns, see Fig. 4 6c), Stark shifts as well as Stark line b roadening were observed. Based on this result, p lasmas seem to reach LT E formation, as shown by the agreement between the excitation and electron temperatures (see in Fig. 4 6c). A s imilar result of plasma temperature was also observed in the case of the aluminum alloy sample (Z8) ( see Fig. 4 7 ) For verification of this approach, it should also be checked whether the electron temperature s measured at the Cu I 282.44 nm line are coincident with that measured at different lines (e.g., Cu I 510.55 nm, Cu I 296.12 nm etc.) of the same eleme nt (e.g., Cu) in the copper metal Figure 4 8 clearly shows that this approach worked successfully ; i.e., the electron temperatures calculated at th re e different lines are very similar to each other Base d on the result, i t can be explained that i n the beginning of the relaxation, the electron temperature is much higher than the excitation temperature due to the plasma being he ated by inverse Bremsstrahlung but after a certain delay time (in our work aft thermodynamic equilibrium Thus, it is necessary to study the local thermodynamic equilibrium (LTE) condition in the plasma and determine

PAGE 87

87 the best conditions at which they are satisfied in order to analyze the emission spect rum of the laser induced plasma. Experimental results for Ba II. The spectroscopic information of the barium ionic lines which were used has been already represented in Table 4 1. Figure 4 9 shows the time resolved emission spectra from laser induced plas ma of Ba II l ines at the several delay times ( t d 3.0 As observed before, the emission of ionic species seems to decay much faster compared to that of atomic species. In the study, the Ba II lines as well as the continuum radiation disappear ed after a means it is very difficult to get high signal to continuum intensi ty ratio after this delay time. However, w e have also observed a very similar trend in the case of Ba II lines (compared to the result for Cu lines ) within a certain range of delay times For the study the Ba ionic line at 252. 84 nm in BaCl 2 pellet was selected. In Fig. 4 10 a t short delay time s the difference of the excitation and el ectron temperature was fairly considerable due to the fast evolution of the plasma as well as inverse Bremsstrahlung during this time p eriod. However, this difference decreased gradually with increasing delay time, so that the plasma seems to reach LTE after its formation (see Fig. 4 10 a ). I t should be noted herein that the delay time period for achievin g L TE was shorten ed in the case of the ionic species compared with that of the atomic species This result makes us think that in the case of the ionic species the evolution of the plasma decay s rapidly and the plasma can reach the equilibrium state at a r e latively sho r t delay time. In general, because the ion ic species are i n high l ying energy levels, the excitation temperature can be comparable to the electron temperature at sho r t delay time s

PAGE 88

88 Conclusion s The concept of local thermodynamic equilibrium ( LTE) has been widely used to simplify the interpretation of spectral line inten sities from laboratory and astrophysical plasmas. If LTE is a good approximation of the plasma state, the plasma temperature and electron density which can be easily derived fro m the emission spectra can be used to describe the plasma characteristics and plasma analysis becomes possible. Thus, there are many circumstances where it is important to have rather precise criteria to identify the plasma conditions under which it is saf e to assume LTE in order to carry out a successful analysis T he proposed method, namely line to continuum intensity rati o method, is very useful to evaluate experimentally the existence of local thermodynamic equilibrium conditions at various stages of p lasma evolution with the overall goal of reaching a better understanding of the chemistry and dynamics of the laser induced plasma. The experimental results presented demonstrate well the usefulness of this approach by the following results : The approach a llows experimental checking of the existence of local thermodynamic equilibrium conditions in time resolved plasma. The McWhirter criterion appeared to be fulfilled in the whole studied delay time range, but is not sufficient condition for LTE. In our re sult, t he electron temperature was always higher than the excitation temperature due to the plasma being he ated by inverse Bremsstrahlung but after a certain delay time (in our work between 3.0 and 5.0 ), plasmas reach the local thermodynamic equilibrium state ; i.e. the electron temperature is consistent with the excitation temperature after that time T he delay time period for ac hieving the LTE condition was shorten ed in the case of the ionic species compared with that of the atomic species due to the high lying energy level s of ionic species.

PAGE 89

89 On the other hand it should be also stressed that this method has some limitations on the calculation of electron temperature due to the uncertainty from E ins t ein transition probabilities free free Gaunt factor s and free bound continuum correction factor s As mentioned above, although some error in calculation of electron temperature, in particular, depending on correction factor can occur it can be worth while to assess the existence of local thermodynamic equilibrium within time resolved plasma phenomena.

PAGE 90

90 Figure 4 1. Experimental LIBS set up

PAGE 91

91 Figure 4 2. (a) L ine broadening and (b) the electron number density calculated from Stark broadened line widths of the Ba II line at 252.84 nm at 90 5 mJ laser pulse energy as a function of delay time.

PAGE 92

92 Figure 4 3. (a and b) Saha Boltzmann plots and (c) Bol tzmann pl ot in different delay times. (d f) Corresponding excitation temperatures versus delay times show in the figure

PAGE 93

93 Figure 4 4. Electron temperature versus (a b) free free bound correction factor and (c d) free bound continuum correction factor as a f unction of delay time.

PAGE 94

94 Figure 4 5 Normalized line profiles of Cu atomic transition at 282.44 nm (a) at 50 ns t d 500 ns delays (laser pulse energy 50 5 mJ and gate width 50 ns) and (b) at 500 ns t d 15000 ns delays (laser pulse energy 90 5 mJ a nd gate width 100 ns).

PAGE 95

95 Figure 4 6 (a and c) T emporal evolutio n of the excitation and electron temperature s at 282.44 nm Cu I line from copper metal (b and d) The l ine profile in the figures corresp ond s to the Voigt profile fit of the emission lines at different delay s from plasma creation

PAGE 96

96 Figure 4 7 (a) T emporal evolution of the excitation temperature and electron temperature at 296.12 nm Cu I line of Al alloy sample (Z8) (b) T he line profile in the figures correspond s to the Voigt profile fi t of the emission lines at different delays from plasma creation

PAGE 97

97 Figure 4 8. T emporal evolution of the excitation temperature and electron temperature for Cu atomic lines at 282.44, 296.12 and 510.55 nm in a copper metal for (a) short delay times (100 ns t d 500 ns) and (b) long delay time (500 ns t d 15000 ns)

PAGE 98

98 Figure 4 9 Time resolved emission spectra from lase r induced plasma of Ba II lines. The spectra were recor d ed at 90 5 mJ pu lse energy and the gate time of the intensity was set by 0.1 s.

PAGE 99

99 Figure 4 10 (a) T emporal evolution of the excitation temperature and electron temperature at 252.84 nm Ba I I line of Al alloy sample (Z8) (b) T he line profile in the figures corresp ond s to the Voigt profile fit of the emission lines at different delays from plasma creation

PAGE 100

100 Table 4 1. Selected spectral lines and corresponding spectroscopic information of the investigated elements (a) Species Wavelength, 0 ( nm ) E l ( eV ) E u ( eV ) g u A ul ( 10 8 s 1 ) Cu I 261.84 1.39 6.12 4 0.31 Cu I 282.44 1.39 5.78 6 0.08 Cu I 296.12 1.39 5.58 8 0.04 Cu I 324.75 0.00 3.82 4 1.37 Cu I 327.40 0.00 3.79 2 1.36 Cu I 465.47 5.08 7.74 8 0.42 Cu I 510.55 1.39 3.82 4 0.02 Cu I 515.32 3.79 6.19 4 0.60 Cu I 521.82 3.82 6.19 6 0.75 Cu I 578.29 1.64 3.79 2 0.02 Cu II 221.02 3.26 8.86 5 1.58 Cu II 221.81 2.83 8.42 3 3.41 Cu II 222.88 2.98 8.54 1 4.11 Cu II 224.27 3.26 8.78 5 1.58 Cu II 224.70 2.72 8.23 5 3.70 Cu II Cu II Ba II Ba II Ba II Ba II Ba II Ba II Ba II Ba II Ba II Ba II Ba II Ba II Ba II 227.63 229.43 230.42 233.53 234.76 252.84 263.48 277.14 389.18 413.06 416.60 452.49 455.41 489.99 493.41 2.98 2.83 0.60 0.70 0.70 2.51 2.72 2.72 2.51 2.72 2.72 2.51 0.00 2.7 2 0.00 8.42 8.23 5.98 6.01 5.98 7.41 7.43 7.19 5.70 5.72 5.70 5.25 2.72 5.25 2.51 3 5 6 8 6 4 6 2 4 6 4 2 4 2 2 0.60 0.25 0.52 0.81 0.11 0.69 0.73 0.04 2.17 2.18 0.35 0.66 1.11 1.04 0.95 (a ) From NIST Atomic Spectra Database, http://physics.n5ist.gov/Phys.Ref Data/ASD/html.ref.html

PAGE 101

101 Table 4 2. Gating and laser energy parameters used for temporal characteristic and line to continuum intensity ratio method of pure copper metal: (a) at t he short delay times with laser pulse energy 50 5 mJ and (b) at long delay times with laser pulse energy 90 5 mJ (a ) Delay time ( = t d ) Gate width ( = t w ) 50 ns 50 ns 100 ns 50 ns 200 ns 50 ns 300 ns 50 ns 400 ns 50 ns 500 ns 50 ns (b) Delay time ( = t d ) Gate width ( = t w ) 500 ns 100 ns 1000 ns 100 ns 1500 ns 100 ns 2000 ns 100 ns 2500 ns 100 ns 3000 ns 5000 ns 8000 ns 10000 ns 15000 ns 100 ns 100 ns 100 ns 100 ns 100 ns

PAGE 102

102 CHAPTER 5 ON THE USEFULNESS OF A D UPLICATING MIRROR TO EVALUATE SELF ABSORPTION EFFECT S IN LASER INDUCED BREAKDOWN SP ECTROSCOPY Introduction This Chapter is mostly taken from our publication, which appeared in 2009 [166]. Tables and figures were reproduced with permission of Elsevier. The concept of self absorption an d its extreme case of self reversal for inhomogeneous temperature distributions, is intrinsically related to the measurement of line intensities as mentioned in C hapter 3. When re absorption of the emitted species by the laser light becomes noticeable, the observed intensities will depart from the expected values. In order words, starting with the most intense liens, it approaches a flat topped profile, evidence of self absorption. Moreover, self absorption has been considered in the characterization of spe ctroscopic emission sources and used to evaluate population densities in different sources [90] Since the advent of LIBS as an analytical technique, in various works the effort for correcting the self absorption effect of spectral line has been reported in a number o f papers [29, 53, 81, 118 126] R ecently, several methods were proposed for evaluating the reduced line intensities by self absorption. Bulajic et al applied on algorithm for self absorption correction to the procedure for calibration free quantitative element al analysis, which have alre ady been developed by [50] The theory was based on the Curve of Growth (COG) method, which was first proposed by Gornushkin et al [53] in laser induced breakdown spectroscopy. In LIBS calibration plots, a simple method which takes into account the effects responsible fo r non linearity in the relationship between line intensity and elemental concentrations was also presented [122] For qualifying the effect of self absorption, El Shelbini et al [81] proposed the evaluation of

PAGE 103

103 self absorption coefficients of aluminum emission lines in LIBS measurement. The method was performed by comparing the measurement of the line width of the self absorbed lines with that of the corresponding non self absorbed lines in order to evaluate self absorption coefficient. The electron density can be also evalua ted by relating the line width affected by self absorption to the electron density. It was shown that the use of the self absorption correction method leads to more accurate temperature values. Moreover, several authors established new methods for a satisf actory fit between the theoretically and experimentally spectral lines strongly deformed by self absorption in Al resonant lines [121, 125 127] However, the mentioned methods require the necessity of changing the sample concentration or calculation a curve of growth and some modeling or equilibrium hypothesis of plasma parameters in LIBS. Among the existing experimental approaches, one that seems to have been [128] which has been amply described in flame work [87] and also for plasma work [80, 129 133] Alternative methods have also been described [134 137] and claimed to have the advantage that the knowledge of the mirror ref lectivity is not required. In this chapter, one illustrates the use of the duplicating mirror in LIBS, which have been yet appeared in the field of LIBS, and prove s its usefulness in characterizing the effect of self absorption and its temporal behavior d uring the evolution of plasma. It is shown that this simple expedient provides a quick check for the existence of optically thick plasma conditions, and one to follow the temporal evolution of the plasma optical depth from the early decay of the continuum emission to the end of the plasma lifetime.

PAGE 104

104 Moreover, the presence of the continuum emission is itself a way to measure mirror losses, as pointed out by Konjevi [80] The usefulness of this method will be checked in the Saha Boltzmann plot for the evaluation of the plasma temperature and correcting the deviation from linearity at increasing concentrations in the calibration curve. The Self ab sorption C orrection F actor K As mentioned in the previous section, can be evaluated by placing a mirror behind the plasma [80, 129 133] Alternative methods have also been described [134 137] In the case of a laser induced plasma, this method appears more convenient than that of placing an identical plasma directly behind the original plasma on the optical axis, as done, for example, in flame work [87] or changing the length of the plasma d ischarge axially viewed [134 136] or comparing transversal and longitudinal observations of the plasma [137] By u sing a spherical mirror located at twice the value of its focal length from the plasma, two line profiles (with and without the mirror) can be obtained and used for the determination of In order to evaluate correction for self abs orption, the pertinent equations illustrating the parameters relevant to the experiment can be derived as shown by Konjevi [80] The expression for the intensity of radiation from the homogeneous plasma layer (optical length, ) in LTE can be represented: (5 1 a ) (5 1b) (5 1c)

PAGE 105

105 where is the spectral radiance (W cm 2 sr 1 nm 1 ) of the equilibrium radiat ion (or blackbody radiation ) at temperature, suffices 1 and 2 refer to measurements taken without and with the mirror, respectively and is the absorption coefficient which is related to Kirchhoff s law of radiation by for LTE. In addition, the parameter G includes reflection and absorption losses at the mirror, as well as imperfect matching of solid angles, and can be evaluated by rationing the signal obtained for the intensity of the plasma continuum, where is equal to zero, e.g., (5 1d) Usually, ratio could also be determined at the line wings where absorption is negligible; the continuum radiation, otherwise, should be chosen for more accurate result. In the expression of Eq. 5 1a, one can distinguish three cases depending upon the value of : If the line profile is in the condition of negligible self absorption, e. g., optical thickness << 1 over the wavelength range of the line, then one obtains by series expansion (5 2) In the other extreme condition, >> 1 R Eq. 5 1a may be written as e.g., observed line intensity reaches a black body radiation of temperature T, and the line loses its characteristic shape, which means the observed line intensity no longer follow the absor ption coefficient. Moreover, the line profile cannot be recovered. However, if optical depth, <1, is not too large, the line profile for the optical thin case may be recovered by u sing a correction factor of Eq. 3 11b.

PAGE 106

106 The expression of optical depth (see Eq. 3 12) can be also modified by the pertinent equations illustrating the parameters relevant to the experiment : e.g., (5 3) Thus, the experimental correction factor can be obtained by inserting Eq. 5 3 into Eq. 3 11b for making to the useful equation in terms of the experimental ratios and : (5 4) The correction factor can be then multiplied on the line profile to retrieve the optically thin line profile. As pointed out [80] the met hod cannot be used for high values of the optical depth, since the true line profile cannot be retrieved (see the extreme case, >>1). From an experimental point of view, it is useful to consider the effect of variation in the plasma optical depth on the correction factor. In the range of optical depths where the method can be applied, it can be shown from Eq. 3 11b and Eq. 3 12 that the relative error in (see Eq. 3 11b) is a function of e.g.,: (5 5a)

PAGE 107

107 From Eq. 5 5a, one obtains the correlation function between the relative error of correction factor and that of optical depth as below: (5 5b) The above equations indicate that the relative error affecting the correction factor is smaller than that affecting the optic al depth since and It means the majority of the relative error affecting the correction factor is from the optical depth. Experimentally the relative error which is able to affect the correction factor is always less than 10%. For values of above ~3 for instance, (within approximately 10%) and any variation in will directly affect the precision in determining of Of even more practical significance is the behavior of the relative error in as a function of the experimental ratios and As seen from Eq. 3 11b, for >>1, one can be expressed as ( 5 6a) From Eq. 5 3, one also can be expressed as ( 5 6b) (5 6c) Thus, the relative error can be expressed as

PAGE 108

108 (5 7) By comparing Eq. 5 7 with Eq. 5 5a, one can see that, since Y function (= ) grows much faster than the experimental error affecting Y will have an even less relevant effect on From the experimental data, one can also calculate the Duplication Factor expressed by the following relation [28, 87] : (5 8) As seen in the expression, represents the relative increase in line intensity, or integral absorption, caused by doubling the product ( ), and takes the asymptotic values of 1 (at low optical depths) and 0.415 (at high optical depths) [87] This qua ntity was used in flame work [87] and was shown to provide complementary information to that obta ined by the c urves of growth [87, 138] The measured signal called intensity in most of the literatures has the form multiplied by the optical conductance of the system (optics and monochromator) and the instrumental fu nction or slit function of the monochromator [100, 139] For the measurement of the integr ated intensity, the instrumental function can be made larger than the spectral profile of the line. However, when calculating the correction factor wavelength by wavelength (or pixel by pixel), it must be much smaller that the line width. Since the line pr ofiles decreases as the delay time of observation increases, this last condition is valid at early delays, but fails to hold at longer delays.

PAGE 109

109 Experimental The experimental LIBS set up used in all measurements have already been described in detail in Chap ter 4. Only different thing is the spherical mirror which was placed behind the plasma at a distance equals to its radius of curvature (see Fig. 5 1 ). An optical shutter inserted between the sample stage and the spherical mirror allowed spectra to be obtai ned with and without the mirror. In particular, the zero order plasma images obtained with and without the mirror were checked repeatedly, and merged carefully together, before changing any of the experimental parameters, such as the time delay and the spe ctral positioning of the grating. The result of s uch procedure is shown in Fig. 5 1c. Nine Al alloy samples D28, V14, D33, B8, AA3, S4, R14, Z8, SM10 of known composition (South Africa) were used. The compositions of the major components and the spectral information pertinent to the transitions used in th is work are reported in Tables 5 1 an d 5 2 and in Fig. 5 2, respectively. Results and D iscussion Evaluation of R C For an accurate evaluation of the parameter a relatively strong continuum radiation at the far wings of the line (approximately five times the full width at half maximum) was measured. Moreover, since the continuum emission dominates initially, as can be seen in Fig. 5 3 a, the ratio can be dete rmined at short delay times. Fig. 5 3b illustrates a typical example of how this ratio was determined and calculated in the case of the copper atomic line (510.55 nm). The calculated at 1.0 s delay time is 1.67, indicating that the reflection and absorption losses are about 30 % in our work

PAGE 110

110 (see Fig. 5 4). Figure 5 5 also shows the calculated values of self absorption correction factor, for various values of and For the value of found experimentally, it is clear that, as the ratio approaches 1, the line is strongly self absorbed, resulting in a relatively high correction factor, This condi tion is, of course, expected from Eq. 5 1c. Evaluation of R Three elements, namely Cu, Fe and Mn, were considered and repeated measurements performed with and without the mirror on selected spectral lines as a function of the delay time after the laser pulse. In the previous section, Fig. 5 3 reported a typical example of calculating from the ratio of peak intensities at a given wavelength under line profile. The results obtained for Cu are collected in Fig. 5 6, together with th e wavelength behavior of the factors involved, e.g., in Fig. 5 6a and in Fig. 5 6b. As expected, the center of the emission profile saturates at a much faster rate than the line wings when the plasma length is doubled, as can be seen in Fig. 5 6a. The ratio was evaluated pixel by pixel (e.g., wavelength interval by wavelength interval) in order to obtain an accurate value of the correction factor for each spectr al resolution element within the line profile, thus following the different effects of the optical thickness on the different spectral intervals under the overall emission profile. The calculated correction factor, obtained for ea ch wavelength interval, was then applied to the data obtained without the mirror in order to retrieve the corrected line profile, as shown in Fig. 5 6c.

PAGE 111

111 The profiles shown in this figure have not been corrected for the instrumental slit function of the mo nochromator. As mentioned in the theoretical considerations, the accuracy of the evaluation of relies on the assumption that the spectral bandwidth of the monochromator is much smaller than the line profile to be measured. In our ca se, the full width at half maximum (FWHM) of the profile measured at 1 s delay time with and without the mirror varies from 143 pm to 122 pm, respectively. With an experimentally measured bandwidth of 3 pm, assuming both Gaussian functions, the error is t herefore less than 5 %. Temporal B ehavior of K ,corr and D ( ) The temporal evolution of the correction factor, is given in Fig. 5 7. Three copper line (510.55 nm, 324.75 nm and 327.40 nm) were considered here, our choice being motivated by their relatively significant corre ction factor resulting from the comparison of the mirror / no mirror spectra. As shown in this figure, it is evident that all three lines are affected by self absorption and that the effect increases with the delay time. This is in general expected for tra nsitions involving the ground level (324.75 nm and 327.40 nm) since the population of this level grows in the recombining stage of plasma evolution. Also expected is the result shown that the transition at 510.55 nm, whose lower level is 1.39 eV above the ground level (see Table 5 2), is the least affected. The error bars affecting the measurements can be explained by the fact that at early delays the continuum emission is strong and the line emission is weak (and the line is embedded in the continuum see Fig. 5 3), thus affecting the evaluation of while at longer delays the continuum intensity decreases significantly, and therefore affecting the measurement of Moreover, as pointed out before, since the pro files

PAGE 112

112 are not corrected for the instrumental response, the accuracy in the calculation of the values was left uncorrected. A similar behavior was observed for the three resonance transitions of Mn around 400 nm (see Table 5 2), as s hown in Fig. 5 8. It is also worth noting that our results agree qualitatively with those published by El Sherbini et al. [81] As discu ssed in the previous section, an additional, rela ted method of checking the degree of self absorption at the line center and in the wings involves the calculation of the Duplication Factor, This can be done again, as described before, using the duplicating mirror and calculating from Eq. 5 8. Figure 5 9 shows the data obtained for the Cu line at 510.55 nm at different delay times. As shown, self absorption starts affecting the line profile at about 1 s delay time and its effect increases as the time delay progresses. As expected, the effect is stronger at the center of the profile. At delay times shorter than 1 s, has an approximately uniform value (about 0.8), as shown in Fig. 5 9a. These results are in agreeme nt with those reporte d in Fig. 5 6 for the same Cu transition. Similar considerations and cautioning remarks regarding the variable accuracy of the data, due to the narrowing of the line profile at longer delays also apply here. In conclusion, within the accuracy limits of ou r calculations, the data shown justify our statement about the usefulness of the mirror approach, and show that the temporal evolution of self absorption can be easily followed during the plasma expansion and recombination.

PAGE 113

113 Self absorption Corrected Saha Boltzmann P lots A logical test to prove the usefulness of the mirror and the resulting correction factor is its application to the study of the spectral profiles of the transitions chosen in the Boltzmann and Saha Boltzmann plots for the evaluation of the temperature of the plasma. Self absorbed lines will give intensity values lying below the line corresponding to the best fit in these plots. The mirror approach will therefore quickly identify outliers, allowing one to either exclude them from the fit or t o apply appropriate corrections factors. On the other hand, it is important to note that the measurements correspond to line of sight averages and therefore one should be aware that spatial resolution is not taken into account here. It seems that, since m ost temperature evaluations are made with the Saha Boltzmann plot (see, for example, [68, 81, 116] ), and therefore with a large range of energy values in the abscissa the presence of one or two outliers is not expected to significantly affect the slope of the overall plot. In other words, it seems worthwhile to note that the sensitivity of the temperature plot to self absorption effects is not as pronounced, provided that many lines of widely different uppe r state energy are used, which should be the case of the Saha Boltzmann approach [68] In the case of a double pulse experiment, and for temperature values in the range 11,000 K 12,000 K, El sherbini et al. [81] reported temperature differences of about 700 K when the data were corrected for self absorption, e.g., a difference of about 5 6 %. Fig ure 5 10, 5 11 and 5 12 report our results obtained on different elements, different samples and at different delays. It should also be noted that the data were obtained over a period of time of more than a year. The elements considered were Cu, Al and Fe This choice was mainly dictated by our previous experience with these

PAGE 114

114 samples [116] Strong lines for Al (308.22 nm, the unresolved doublet at 309.28 nm, 394.40 nm and 396.15 nm), Fe (371.99 nm) and Cu (324.75 nm and 327.40 nm) were used to magnify the effect. Figure 5 10 shows the data o btained at 1 s delay for Al and Cu in two different alloy samples. As seen from the comparison of Fig s 5 10a and 5 10b, when the strongly self absorbed Al lines are removed from the significantly larger than the expected error in the measurements. On the other hand, when the same pr ocedure is applied to copper, as shown in Figs. 5 10c and 5 10d, the difference in temperature is not so pronounced. Similar reason can be applied to the data obtained at different delay times for Fe and Cu, shown in Figs. 5 11 and 5 12. The temperature decreases as the delay time increases as expected, and the corrected plots show a consistently lower temperature when compared to the uncorrected one. From the trend observed in Figs. 5 11 and 5 12, one can conclude that self abs orption effects become more important at longer delays: this can be seen from the difference between the corrected and non corrected values for Fe at 1 s and 3 s, and in particular for Cu (Fig. 5 12), where the longest delay time of 5 s was used. Self a bsorption C orr ected Calibration C urves Another logical test for assessing the usefulness of the correction approach is to apply it to the calibration curves obtained with standards whose concentration is high enough to make the plasma optically thick. Inde ed, in this case, the curves of growth show the classical non linear behavior where the spectrally integrated intensity versus concentration starts bending towards the abscissa at a given critical concentration [53, 123]

PAGE 115

115 In our work, experimental calibration curves were obtained for th e Mg I line at 285.21 nm and the Mg II lines at 279.08, 279.55, 279.80 and 280.27 nm, in 8 Al alloy samples with Mg concentrations ranging from 0.004 to 1.27 %. The spectroscopic characteristic of the lines and the concentration of the magnesium in the Al alloy samples were reported in Table 5 2 and shown in Fig. 5 2, respectively. The strong resonance atomic and ionic lines at 285.21 nm and 280.27 nm were chosen ad hoc to emphasize the effect As expected, the calibration plots shown in Fig. 5 13 clearly indicate the presence of strong self absorption, the deviation from linearity starting with sample alloy S4, containing 0.35 % of Mg. Figure 5 14 reports the calculated values of the correction factor, of both lines for the all th e Al alloy samples investigated, showing again that the correction factor is higher for the two most concentrated samples (Z8 and R14) The lowest correction factor was obtained for sample D28 (0.07 % of Mg), and in fact with this sample the line intensity practically doubled when the mirror was used. As in the case of the temperature plots, was used for correcting the effect of self absorption of the line profiles. The corrected profiles were integrated and used in calibration plot The results of such procedure are also shown in Fig. 5 14. For both Mg lines, linearity was restored. Conclusions The theoretical co nsiderations given in this chapter and the experimental results presented demonstrate that the use of a duplicating mirro r in laser induced plasma experiments is characte rized by the following features [166]: It allows a quick checking of self absorption without the necessity of changing the sample concentration or calculating a curve of growth.

PAGE 116

116 It gives the possibility of f ollowing the time evolution of the optical depth of the plasma. This allows seeing when self absorption sets in during the plasma evolution and how relevant its effect is on the transitions used for the construction of the calibration curves. It allows the simultaneous observation of the effect of the duplication on a selected transition and the associated continuum background. This allows correcting for the mirror reflectivity losses and solid angle mismatch. It provides a way to correct for self absor ption (provided that the line is not strongly self absorbed). One can also use the wings of the transition if the continuum is absent. A line profile is needed in this case. It allows identifying outliers in the Boltzmann plot used for temperature measure ments and improving the linearity of the analytical calibration curves. Finally, it may also alert the analyst of the potential existence of spectral interferences The rationale behind this assertion is the following: Suppose that one emission line in the spectr um of element A is self absorbed and is also simultaneously affected by a coincident spectral line emitted by element B. Suppose that the line of element B is not self absorbed. The duplication factor will have a much higher value (closer to unity) than that expected from a self absorbed transition. In fact, the signal from element A will increase with the square root while the signal from B will increase linearly. It should also be stressed that one should not overemphasize the achievements obtaine d by the use of the duplicating mirror. This statement is based upon the following that were made in our work: The data provide only some kind of average line of sight information. This is clearly relevant when one refers to parameters such as number densi ty or optical depth and temperature, since their physical significance can be no better than the validity of the assumptions made in the derivation of the expressions. One of these assumptions is that the plasma layer is homogeneous. The plasma is expandin g, therefore setting a limit to the duplication of the same original volume seen without the mirror. The limit will be imposed by the expansion speed of the plasma and the plasma mirror distance. For example, if the plasma mirror distance is 30 cm and the expansion speed is 10 6 cm s 1 in the 2 ns roundtrip of the radiation, the plasma has moved vertically by 20 m. If 2 mm of plasma height are imaged on the slit, about 1 % of the plasma re sampled by the mirror will be new plasma. This situation will hol d for all the delay times investigated. As a consequence, the minimum spatial resolution and the continuum delay time (assuming experimental feasibility) will be 20 m and 2 ns, respectively

PAGE 117

117 In its simplest arrangement, such as that used in the present wo rk, the measurements taken with and without the mirror will not interrogate the sample plasma. In fact, the measurements are taken sequentially. The results will therefore be conditioned by the reproducibility of the laser interaction with the target as we ll as by the stability of the detection electronics It is also important to realize that, due to the temperature inhomogeneity of the laser induced plasma several strongly self absorbed transitions can also show self reversal, e.g., a dip in the line ce nter. Except in this extreme case, such dip may pass unobserved when a low spectral resolution monochromator is used and spatially and temporally integrated measurements are performed. If that is the case, the use of mirror will not help distinguishing bet ween self absorbed and self reversal lines. In spite of the last considerations, one has to realize that the measurements reported in this paper reflect the majority of the analytical experiments reported in the LIBS literature. It is felt that the simpli city of the experimental set up will make the duplicating mirror a useful addition to most LIBS experiments, allowing at least a quick check for the existence of self absorption. We therefore hope that it will find a more widespread use among the LIBS comm unity.

PAGE 118

118 (a) (b ) (c ) Figure 5 1. (a) Scheme of the set up used, with the addition of an external spherical mirror; (b) Schematic representation of the plasma images on the slit with and without the mirror, which is located at a distance from the p lasma equal to its radius of curvature; (c) zero order plasma images obtained with and without the mirror [ From ref. 166 reproduced with permission ]

PAGE 119

119 Figure 5 2. Magnesium, copper, and iron compositions in the 9 aluminum allo y samples used. The insert represents the magnesium composition used to obtain the calibration plots [From ref.166, reproduced with permission].

PAGE 120

120 Figure 5 3. (a) Observed spectral profile of the copper atomic line at 510.55 nm for differen t delay times from the onset of the plasma. (b) Experimental evaluation of R and R C in the case of the copper atomic line at 510.55 nm. The delay time is 1.0 s and the gate width 0.1 s [From ref.166, reproduced with permission].

PAGE 121

121 Figure 5 4. Experimental ratio (R C ) of the continuum radiation with and without the mirror observed at different delay times. The measurements refer to the 510.55 nm Cu line. The average value of R C over the delay times is 1.60 [From ref.166, reproduced with permission].

PAGE 122

122 Figure 5 5. Calculated de pendence of the correction factor K ,corr as a function of R C for different values of R e.g., for different degree of self absorption [From ref.166, reproduced with permission].

PAGE 123

123 Figure 5 6. (a) Calculated values of R as a function of wavelength along the line profiles; (b) Correction factor K ,corr as a function of wavelength and self absorption corrected line pr ofiles (c) Voigt profile fit of the emission lines obtained with and without the mirror and after correction for self absorption. All cases refer to the Cu I transition at 510. 55 nm and to measurements taken at 1.0 s delay time. The average value of R C (1.6) was used here [From ref.166, reproduced with permission].

PAGE 124

124 Figure 5 7. Temporal behavior of the correction factor K ,corr (evaluated at the line center) for three Cu ato mic lines at 510.55 nm, 324.75nm and 327.40 nm as a function of different delay times after plasma formation. The error bars reported were calculated assuming a maximum error of 10 % for each correction factor (see text for discussion) [From ref.166, repr oduced with permission].

PAGE 125

125 Figure 5 8. Temporal behavior of the correction factor, K ,corr (evaluated at the line center) for three Mn lines at 403.08 nm, 403.31 nm and 403.45 nm as a function of different delay times after plasma formation [From ref.166, reproduced with permission].

PAGE 126

126 Figure 5 9. Cu I emission profiles observed at 51 0.55 nm with and without the mirror, together with corresponding calculated duplication factor D at different delay times [From ref.166, reproduced with permission].

PAGE 127

127 Figure 5 10. Saha Boltzmann plots constructed using atomic and ionic lines of Al and Cu measured in the spectra of two different alloy samples. The data were obtained at 1.0 s delay time. Plots (a) and (c) show all the data while plots (b) and (d) result after exclusion of the transitions affected by self absorption [From ref.166, repro duced with permission].

PAGE 128

128 Figure 5 11. Saha Boltzmann plot constructed using Fe atomic and ionic lines: (a) 1.0 s delay time, and (b) 3.0 delay time. The two slopes result from the data uncorrected (open squares) and corrected (open circles) for self a bsorption. The lines correspond to the best linear fitting of the data [From ref.166, reproduced with permission].

PAGE 129

129 Figure 5 12. Saha Boltzmann plot constructed using Cu atomic and ionic lines at 5.0 s delay time. The two slopes result from the data unc orrected (open squares) and corrected (open circles) for self absorption. The lines correspond to the best linear fitting of the data. The transitions used (nm) are indicated [From ref.166, reproduced with permission].

PAGE 130

130 Figure 5 13. Experimental calibration plots of Mg using eight Al alloy standard samples with and without correction for self absorption at (a) Ionic line 280.27 nm and (b) atomic line 285.21 nm. Gate width: 0.1 s; delay time: 2.0 s; pulse energy 90 5 mJ. The dotted lines connecting the uncorrected data are meant as a visual aid while those drawn through the corrected data correspond to the best linear fit [From ref.166, reproduced with permission].

PAGE 131

131 Figure 5 14. Variation of the calculated correctio n factor K ,corr (evaluated at the line center) for the Mg atomic (open squares) and ionic (open triangles ) lines for each Al alloy sample measured. The insert indicates the magnesium content of each sample. The error bars reported were calculated assumin g a maximum error of 10 % for each correction factor (see text for discussion) [From ref.166, reproduced with permission].

PAGE 132

132 Table 5 1. Elemental percentage composition of South African aluminum alloy standards disks (APEX Smelter Co., South Africa) [Fro m ref.166, reproduced with permission]. D28 V14 D33 B8 AA3 S4 R14 Z8 SM10 Al 81.55 86.74 84.92 87.98 69.14 83.79 79.59 78.79 84.67 Si 9.66 6.2 8.54 2.33 17 1.03 14 0.84 2.92 Mg 0.004 0.025 0.038 0.076 0.2 0.35 0.87 1.27 1.08 Cu 1.76 4.05 2.89 6.95 8 2 .64 2.05 16.05 2.8 Zn 3.6 0.42 0.59 0.52 3.2 10.9 0.48 0.79 5.45 Fe 0.98 0.9 1.15 0.8 1.77 0.119 0.63 1.09 1.96 Mn 0.59 0.58 0.4 0.4 0.21 0.38 0.92 0.26 0.295 Ni 0.43 0.33 0.5 0.5 0.106 0.18 0.97 0.53 0.065 Ti 0.033 0.17 0.055 0. 16 0.078 0.12 0.16 0.1 7 0.055 Cr 0.21 0.18 0.047 0. 17 0.1 0.13 0.11 0.15 0.2 Sn 0.3 0.28 0.048 0.155 0.12 0.15 0.12 0.26 Pb 0.34 0.14 0.165 0.08 0.13 0.1 0.245

PAGE 133

133 Table 5 2. Selected spectral line and corresponding spectroscopic information of the investigated elements ( a) [From ref.166, reproduced with permission]. Species Wavelength, 0 ( nm ) E l ( eV ) E u ( eV ) g u A ul ( 10 8 s 1 ) Cu I 282.44 1.39 5.78 6 0.08 Cu I 296.12 1.39 5.58 8 0.04 Cu I 324.75 0.00 3.82 4 1.37 Cu I 327.40 0.00 3.79 2 1.36 Cu I 465.47 5.08 7.74 8 0. 42 Cu I 510.55 1.39 3.82 4 0.02 Cu I 578.29 1.64 3.79 2 0.02 Cu II 221.02 3.26 8.86 5 1.58 Cu II 221.81 2.83 8.42 3 3.41 Cu II 222.88 2.98 8.54 1 4.11 Cu II 224.27 3.26 8.78 5 1.58 Cu II 224.70 2.72 8.23 5 3.70 Cu II Cu II Fe I Fe I Fe I Fe I Fe I Fe I Fe I Fe II Fe II Fe II Mg I Mg II Mg II Mg II Mg II Mn I Mn I Mn I 227.63 229.43 358.12 361.88 371.99 373.49 373.71 374.56 411.85 258.59 259.94 261.18 285.21 279.08 279.55 279.80 280.27 403.08 403.31 403.45 2.98 2.83 0.86 0.99 0.00 0.86 0.05 0. 09 3.57 0.00 0.00 0.05 0.00 4.42 0.00 4.43 0.00 0.00 0.00 0.00 8.42 8.23 4.32 4.42 3.33 4.18 3.37 3.40 6.58 4.79 4.77 4.79 4.35 8.86 4.43 8.86 4.42 3.08 3.07 3.07 3 5 13 7 11 11 9 7 13 8 10 8 3 4 4 6 2 8 6 4 0.60 0.25 1.02 0.73 0.16 0.90 0.14 0.12 0.58 0.8 1 2.20 1.10 4.91 4.01 2.60 4.79 2.57 0.17 0.17 0.16 (a ) From NIST Atomic Spectra Database, http://physics.n5ist.gov/Phys.RefData/ASD/html.ref.html

PAGE 134

134 CHAPTER 6 A COMPARISON OF SINGLE V ERSUS DOUBLE PULSE LASER INDUCED BREAKDOWN SPECTROSCO PY Introduction Laser induced breakdown spectroscopy (LIBS) is a u seful tool for determining the multi elemental composition of a solid or liquid sample Especially, the interaction of a pulsed laser bea m with solid materials is attractive to the scientific community for its potential application s including material treatment, physical and chemical analysis, photo deposition, depth profiling and many other a reas du e to its advantages such as fast respons e, high sensitivity and the wide range of material s that can be investigate d with simple sample preparation and experimental set up. Despite the apparent simplicity of the experimental apparatus used and of the work devoted to the spectroscopic study, the processes involved in the interaction of laser with solid matter are rather complex, up to now not completely understood and still under intensive investigation Moreover one of the main limitations of LIBS concerns its lack of sensitivity [140, 141] when compared to several competing atomic spectroscopic techniques such as inductively coupled plasma atomic emission spectrometry (ICP AES) or inductively couple d plasma mass spectroscopy (ICP MS) Double pulse LIBS is one way to overcome this pro blem where the laser pulses are separated by a short delay time of the order of microseconds and has been introduced without any loss of reliability [142, 143] In some cases, it is exp ected that the use of the double pulse method can lead to lower dete ction limits, enhanced and longer sustained emission signals [144, 145] and internal standardization [146] The double pulse approach was first suggested by Piepmeier et al [54] in 1969 and Scott et al. [55] in 19 70. They suggested that, because a large portion of laser

PAGE 135

135 energy is ab sorbed by the plasma plume, the second laser pulse could lead to further excit ation of species in the plasma. In 1984, Cremers et al. [56] performed a detailed study of the possible applications of the laser double pulse technique for analytical purposes. Since the initial study by Cremers et al. [56] many efforts have been devoted to characterization of the mechanisms of the double pulse signal enhancement. Several geometries of the laser beams ha ve been considered Most representative/ common double puls e geometries have been based on collinear beams [56, 146 152] and on ortho gonal beams [141, 153 157] as shown in Figure 6 1 In the so called collinear geometry the two laser pulses have the same axis of propagation. Otherwise, i n the orthogonal geometry the two laser beams are directed by 90 deg ree with respect to each other. I t has been also differentiated by two configurations: the reheating scheme and the pre ablation air spark double pulse scheme depending on which of the laser pulses first reach the sample surface. In the reheating scheme, the second pulse paralle l to the target surface reheat s the plasma induced by the first laser pulse [141, 153] Otherwise, i n the pre ablation spark double pulse scheme [154 157] the first laser pulse is used to create a n air spark above the s a mple surface resulting in a rarified ambient environment in which the plasma generated by the second laser pulse can expand to a larger size [140, 141, 153, 158] These two configurations have been successfully used to improve LIBS sensitivity for various matrices such as liquids [56, 148, 149] and a variety of solid sa mples [150] such as steel [146] aluminum [147] brass [153] and glass [156] The papers dealing with the collinear geometry demonstrated an increase in intensity of emiss ion lines, ranging from a factor of 2 [146] up to 100 [147]

PAGE 136

136 The enhancement in spectral line emission intensity of double p ulse LIBS depends on sever al parameters: laser wavelength, interpulse delay time between the laser pulses ranging from a few tens of ns to several tens of s the distance between the sample surface to the air spark, plasma density, etc. In particular, t h e time delay between the two pulses is one of the most useful parameter s to effectively tailor the experimental conditions and to properly take advantage of different physical characteristic s of the expanding plume as observing the long relaxation time of the plasma, even in the milliseconds scale [159] While readily implemented, the mechanisms and phy sics associated with double pulse LIBS that account for enhanced signal intensity are not yet clearly understood The aim of this work, based on the use of spectroscopic methods for the diagnostics of the laser induced plasma originated by a double pulse l aser beam, is to study the coupling of laser light with plasma, to find the optimal conditions for the enhancement of emission lines as a function of several parameters and to study possible dynamical and physical mechani sms in single and double pulse co nfiguration. In particular, the derivation for the expression of the emission intensity for a given line in a LIBS plasma and the ratio of the double pulse to the single pulse intensity in terms of the fundamental plasma parameters can be used to obtain us eful physical information on the change of plasma conditions between single and double pulse irradiation Experimental Laser and D etector S ystem An expe rimental diagram for the double pulse LIBS system used in all measurements is shown in Fig. 6 2 a In order to analyze the processes of laser ablation and plasma formation obtained in the orthogonal double pulse LIBS configuration, two

PAGE 137

137 different types Nd:YAG lasers were used. The laser used for sample ablation (Quantel Brilliant Q switched Nd:YAG laser, 36 0 mJ maximum pulse energy at 1064 nm, maximum repetition frequency of 10 Hz, and pulse dura tion of 6 ns) with approximately 90 5 mJ/pulse was focused by a quartz lens (10 cm focal length). The laser used for air spark beyond the sample surface ( Laser pho tonics, YQL 102+ of pulsed Nd:YAG laser, 200 mJ maximum pulse energy at 1064 nm and maximum repetition frequency of 20 Hz) with approximately 100 mJ/pulse in order to achieve the large sig nal enhancements reported here was directed parallel to the sample a nd focused by a quartz lens (5 cm focal length). Both lasers were operated at 1 Hz for the experiments described here. All measurements were performed at ambient pressure. A controlled stream of air was used to carry away the dust plume formed during the i nteraction. The delay time between two laser pulses was changed by means of a delay generator (SR250 Boxcar) and monitored using a n oscilloscope (Tektronix, TDS 3012B). The delay generator enabled the two las ers to be fired simultaneously or have a variab le delay introduced between the two pulses. The measured temporal jitter of each laser pulse with respect to the other was within 200 ns. The plasma generated by pre ablation air spark form ed in the air above the sample and did not come in contac t with the sample surface. The laser beam for pre ablation air spark was focused to a point above the sample surface that coincided with the plasma that was generated by the ablation beam from a samp le In the reheating scheme the air spark was created after plasma formation. The laser timing is often referred to as a negative time for the pre ablation air spark pulses prior to the arrival of the ablation pulse at the sample, but as a positive time f or

PAGE 138

138 reheating pulses after the ablation event. The distance from the sample surface to air spark (hereafter named d ) was varied in the range 0.1 4.5 mm by slightly shifting the lateral position of the parallel beam len s for making the air spark at a fi xed focal length distance for plasma ablation A 5.0 cm diameter quartz lens, with a focal length of 7.5 cm, was used to collect the plasma emission and to produce a one to one image of the plasma onto the entrance slit of the monochromator. An adjustable iris was positioned close to the lens in order to match the F numbe was used in all cases. The spectrometer (Acton triple grating, 0.5 m focal length) was equipped with three gratings (1200, 2400, and 3600 grooves/mm), providing a reciprocal linear dispersion of 1.57 0.72, and 0.41 nm/mm, respectively. In the present work, the 2400 grooves/mm grating was used. The spectrometer has a typical spectral coverage of ~ 10 nm and a spectral resolution of 0.03 0.05 nm. The detector is an intensified CCD (ICCD 5764/RB E, Prin ceton instruments) with a photosensitive area of 576384 pixels, corresponding to (12.78.4) mm 2 The ICCD is operated by its controller (ST 138, Princeton Instruments) and by a pulse generator (PG 200, Princeton Instruments), allowing the choice of the ga te width and of the delay time for time resolved acquisition. The gate width and the delay time between the laser pulse and the beginning of the acquisition could then be adjusted in order to maximize the signal to background and the signal to noise ratio The data acquisition was controlled with the Winspec32 software (Version 2.5.18.2, Princeton Instruments).

PAGE 139

139 Triggering S ystem In double pulse work the triggering system is more complicated than that used for single pulse experiment The pre ablation air s park an d reheating double pulse scheme have different triggering system s Figure 6 1b shows the different triggering diagram for each scheme. A more detailed explanation is given in the following section. Results and D iscussion Optimization Among configu rations o f multi pulse LIBS, we describe here an orthogonal double pulse LIBS technique: i.e., an orthogonal pre ablation air spark and an orthogonal reheating scheme For selection of optimal plasma conditions in the double pulse arrangement detailed anal ysis of the complex spatial and temporal structure of the laser induced plasma is needed. In particular, the time space plasma characterization is important for clarifying the ma in mechanisms of the plasma occurring by the se two double pulse configuration s The samples used in this study were NIST 603 aluminum standard reference materials (SRMs) and South African AA1 aluminum standard s For all measurements, the Al II line at 281.62 nm (59,852 95,351 cm 1 ), Mg II line at 279.08 nm (35,669 71,491 cm 1 ), 279.55 nm (0 35,761 cm 1 ), 280.27 nm (0 35,669 cm 1 ) and 292.86 nm (35,669 69,805 cm 1 ) and Mg I line at 277.83 nm (21,850 57,833 cm 1 ) 277.98 nm (21,870 57,833 cm 1 ), 278.30 nm (21,911 43,371 cm 1 ) 285.21 nm (0 35,051 cm 1 ), Mn II lines a t 257.61 nm (0 38,807 cm 1 ), 259.37 nm (0 38,543 cm 1 ), 260.57 nm (0 38,366 cm 1 ), 293.31 nm (9,473 43,577 cm 1 ), 293.93 nm (9,473 43,485 cm 1 ) and 294.92 nm (9,473 43,371 cm 1 ) and Mn I lines at 279.48 nm (0 35,770 cm 1 ), 279.83 nm (0 35,7 26 cm 1 ), 401.81 nm (17,052 41,932 cm 1 ), 403.08 nm (0 24,802 cm 1 ),

PAGE 140

140 and 405.55 nm (17,282 41,933 cm 1 ) were chosen for the optimization study. The compositions of the major components and spectral information pertinent to the transitions used in thi s work are reported in Table s 6 1 and 6 2 In our work, the laser pulse energy for ablation from the sample was set at 90 5 mJ; the laser pulse energy for the air spark above the sample surface was changed to obtain the highest signal enhancement (100 5 mJ) and then all measurements were performed with the two fixed laser pulse energies at atmospheric pressure. Therefore, the major parameters for optimization were only for the distance (= d ) fro m a sample surface to air spark above a sample and interpu lse delay time (= t) between the two lasers. Optimization for pre ablation air spark double pulse scheme In the orthogonal pre ablation air spark double pulse scheme the detector (ICCD 5764/RB E, Princeton instruments) was controlled by the Quantel Brillant Nd:YAG laser u sed for plasma formation from a solid sample (see Fig. 6 2 b ). The time resolved studies were performed by controlling the small gate width t w (time during which the spectra were integrated), the gate delay time t d (time from which the spectra were acquired by the detector) and the delay between two laser pul t by delay generators (SR250 Boxcar) at the optimum distance d In t he study, the laser pulse for plasma formation (or ablation pulse) was used as the time reference and hence pre abla t i on air spark pulses were described with a negative sign, while re heating pulses were positive relative to the ablation pulses. LIBS signal up to 100 s ) for the several different distance s ( d 0.3 2.5 mm ) is reported in Fig. 6 3 for the NIST Al

PAGE 141

141 SRM 603 sample The si gnal enhancement strongly depends on the distance ( d ) and as shown in Fig. 6 3 These t wo experimental parameters significantly affected the LIBS signal enhancement in our result. From the result large enhancement s were observed around the inte rpulse delay time of 30 s and distance d of 0.5 mm from the sample surface for several spectral lines (see the region of the highlighted gray color in Fig. 6 3 ). For checking the reproducibility of the signal enhancement, similar experim ent s were also performed for the Al alloy AA1 sample Fig ure 6 4 shows the LIBS signal enhancements of several spectral lines at the optimized parameters in both NIST aluminum SRM 603 and South African aluminum AA1 sample The reproducibility of the line i ntensity was 10 2 % depending on the distance (= d ) and interpulse delay time When the pre ablation air spark was brought in too early before the ablation pulse ( e.g., between 100 and 5 when the two pulses were too close together in time ( e.g., between 5 and smaller enhancements we re observed as shown in Fig. 6 4 a and 6 4 c At short delay times in pre ablation air spark double pulse LIBS, the high electron densities formed early by air plasma interrupt plasma formation from a sa mple because they can absorb a large fraction of second laser pulse (or ablation pulse from a sample) before it reaches the sample surface. Otherwise, at the optimum interpulse delay time, where large enhancement are observed, the air spark formed by the f irst pulse can have appropriate time to expand and cool before the ablative pulse is fired resulting in large LIBS signal enhancements However, if the time interval between the two laser pulses is too long, no enhancement will be observed since decrease d plasma shielding or the rarified air effect generated by the pre ablation air spark no longer exists.

PAGE 142

142 As mentioned above, i n our experimental conditions the largest enhancement s were observed at an interpulse delay time of in both samples. Optim ized distance d was in the range between 0.3 0.7 mm as can be seen from Fig. 6 4 b and 6 4 d We assume the lateral length of entire plasm a is approximately 1.0 1.5 mm which means the pre ablation air spark was focused to a point above the sample surfac e that coincide with the center of the sample plasma that was generated by the ablation laser beam. In ad dition, i t is very interesting point that neutral lines with low excitation energy levels e.g. Mg I lines at 285.21 nm (0 35,051 cm 1 ), and Mn I li ne at 279.48 nm (0 35,770 cm 1 ) have a relatively small enhancement compared to ionic lines with high excitation energy levels for the same interpulse delay ( Fig. 6 4 ) Under the optimized conditions (e.g., d ~ 0. 5 mm : t ~ 30 s: laser pulse energy f or plasma formation from a sample ~ 90 5 mJ: laser pulse energy for air ablation ~ 100 5 mJ), the use of orthogonal pre ablation air spark double pulse LIBS results in larger signal to noise ratio, corresponding to larger sensitivity and lower detectio n limits, as compared to conventional LIBS (single pulse LIBS) The Al II line at 281.62 nm (59,852 95,351 cm 1 ) and Mg I line at 285.21 nm (0 35,051 cm 1 ) in an Al alloy sample ( NIST SRM 603) were chosen for assessing of the improvement of signal to n oise ratio (S/N) wit h the use of double pulse LIBS. A significant LIBS signal enhancement i n the aluminum ionic line was recorded up to a 5.0 s delay time, as observed in Fig. 6 5. On the contrary the resonance line, Mg I line at 285.21 nm (0 35,051 cm 1 ), was found to have less enhancement Based on the results, the signal to noise (S/N) ratio was calculated for both atomic and ionic emission peaks at each delay time (from 0.5 s to10 s) For calculation of S/N ratio, t he analyte s ignal s averaged by

PAGE 143

143 5 0 laser shots were taken as net intensities at each emission peak, while the background noise s were taken from the root mean square (RMS) intensit ies of the featureless continuum emission adjacent to each peak for 50 laser shots For the Al II line at 281. 62 nm, the signal to noise (S/N) ratio was improved significantly by a factor of 6 at 2.5 s delay time; otherwise, for the atomic resonance line (Mg I line at 285.21nm), it led to a reduced S/N ratio and even wors e with less or no LIBS signal enhancement in Fig. 6 6 T hus, one can conclude that signal enhancement with orthogonal pre ablation air spark double pulse LIBS results in the improvement of signal to noise (S/N) ratio corresponding to larger sensitivity and lower detection limits but only for par ticular spectral lines Optimization for reheating double pulse scheme For the reheating double pulse scheme the detector (ICCD 5764/RB E, Princeton instruments) was controlle d by L aser P hotonics laser used for reheating of the plasma The reason why we have used the different triggering systems is that our interesting point is the time resolved study of plasma evolution in the reheating scheme as well as pre ablation air spark scheme. If the detector with some delay time, e.g. t d y the Quantel laser as the pre ablation air spark scheme we should have only large averaged measuring or integration time, e.g. t w for the time resolved study during the plasma decay (see Fig. 6 7 ) For example, f igure 6 8 shows the enhanced signa l intensities at the different interpulse delays with the shorter integration time (t w integration time (t w controlled by the Quantel laser As shown in Fig. 6 8 a, i f the shor t integration time, e.g. t w = 0.1 the Quantel laser there

PAGE 144

144 are no enhancements after the interpulse delay time of 2.0 s because time (t d ) from which the spectra were acquired by the detector was set b y 2 .0 s, which means there are no double d ) is set to 2.0 s (see Fig. 6 7a). If a large averaged integration time, e.g., t w = 30 s, is used, this problem can be solved. As sh own in Fig. 6 8 b an enhancement was still detected by a factor of 2 after an interpulse delay time of 2.0 s. However, our study focuses on time resolved plasma spectroscopy. In order to overcome this problem in our system, the L aser P hotonics laser used for the reheating or re exciting the plasma was used to control the detector (ICCD 5764/RB E, Princeton inst ruments), which means that the emission signal c ould be obtained after this laser fired (see Fig. 6 2b ) One of the advantages in this triggering sy stem is that we can easily check experimentally whether sample ablation from the laser pulse for reheating occurs or not The image of the air spark created in air a few millimeters from the sample surface can be observed with the ICCD camera even without plasma formation from the sample because the detector was controlled by the laser pulse for the air spark (see Fig. 6 9 ). Figure 6 10a shows a schematic of the time resolved plasma study (t w = 0. 1 s) with the triggering system controlled by the Laser phot onics laser with th e reheating double pulse scheme. As mentioned above, t his triggering system is very useful for the time resolved plasma study because we can easily reheat or re excite the plasma at specific decay time s during plasma evolution by changin g the interpulse delay time between the two pulses (see Fig. 6 10 ). In order words, on e can adjust/or determine selectively the re heated or re e xcited position by changing the interpulse delay in our system In our

PAGE 145

145 study the time resolved plasma study was performed at a fixed ICCD delay time (t d ), but at varia ble interpulse delay time s For optimization of the reheating scheme, the LIBS analyses were also undertaken with the NIST Al SRM 603 sample. As mentioned in Fig. 6 10 b it is very clear that as the interpulse delay between the two lasers increases, the plasma is gone between 20 and 30 s. As described above, t he time resolved studies were performed using a fixed gate width (t w = 0.1 s) and gate delay time (t d = 1.0 s) for all measurements. The Q switch in the Laser P hotonics laser some time delay. In our system for the reheating scheme, the laser output pulse ( reheating pulse) was generated at 800 ns after t he regular Q switching as shown in Fig. 6 11 This is why the gate delay time in the rehea ting scheme was chosen to be after 800 ns As mentioned above, the interpulse delay time d from the sample surface are important factors affectin g the LIBS signal enhancement Therefore, the distance d was changed for several interpulse delay times for the optimization of the reheating scheme as can be seen in Fig. 6 12 For all measurements, t he reproducibility of the line intensity was 5 0.5 % depending on the distance. The optimum distance ( d ) from the sample surface to air spark was about 3.0 mm. In the reheating double pulse scheme, the LIBS signal enhan cement was more affected by the distance d in comparison with the pre ablation air spark s cheme. In addition, a significant enhancement was observed with the increase of the interpulse delay time whatever the distances ( d ) and transition li ne s are as can be seen in Fig. 6 12 For checking the reproducibility of the signal enhancement, a simila r experiment was also performed for

PAGE 146

146 Mn I and II lines in the Al alloy D28 sample. From Fig. 6 1 3 it is evident that the interpulse delay time strongly affected the signal enhancement since a markedly high DP/SP value was observed as the interpulse delay t ime increased. It can be explained that the enhancement occurs at long delay time s of plasma because most atoms can be easily excited after plasma cools down. In addition, as observed in the pre ablation air spark scheme, neutral lines wi th low excitation energy levels e.g. M n I lines at 403.08 nm (3.075 eV), 401.81 nm (5.199 eV) and 405.55 nm (5.199 eV), have a relatively small enhancement compared to ionic lines with high excitation energy levels for the same interpulse delay in the reheating scheme in Fig. 6 13 For the reheating scheme, the greatly enhanced ionic emission intensities at the Al II 281.62 nm line at long delay time s (e.g., 9.0 s) also result in improved signal to noise (S/N) ratios as can be seen in Fig. 6 14. Time gated, Spectrally R eso lved, One direction Images in Single and Orthogonal D ouble Pulse Pre ablation S cheme For this study, detailed information about density distributions of excited atoms and ions in the expanding plasma of Al alloy sample was obtained by using the imaging det ection system in both the orthogonal pre ablation air spark and reheating scheme s Most of the emission lines detected were assigned to Mg, Al, Cr ions and atom s Spectrally resolved, t ime resolved one dimensional spatial (along the longitudinal direction from the target surface ) images of the expanding plasma from an Al alloy sample are shown in Fig 6 15 (for pre ablation air spark) and 6 16 (for reheating) The left side s of Fig 6 1 5 and 6 16 show images for plasma produced by single pulse ablation regime s ; while, images on the right side show the plasma ablated in the orthogonal double pulse pre ablation air spark and reheating scheme The vertical axis

PAGE 147

147 corresponds to the plasma expansion which is generated from the sample surface ( at z = 1.0 mm in Fig 6 1 5 and 6 16 ) ; the horizontal axis represents the wavelength of the emitted light. In the pre ablation air spark scheme the gate width (t w ) and interpulse delay time ( t) between the two laser beams were respectively 0.1 s and 30 s and the distance ( d ) from the sample surface to the air spark was about 0.5 mm I n the reheating scheme, the gate width (t w ) and ICCD delay time ( t d ) were 0.1 s and 1.0 s respectively a nd d was about 3.0 mm based on the previous experiment for the optimization The magnification of all images which was obtained by integrating the sliced plasma plume (10 pixels) along the line of sight was kept constant to assure compar ability of the re corded images. In the orthogonal double pulse pre ablation air spark scheme the different stages of the plasma expansion vertically from the sample surface (z = 1.0 mm) at the several delays can be seen from the Fig. 6 17 which was obtained from the images in Fig. 6 1 5 In the early stage of expansion (0.5 1.0 s delay time) with the single pulse regime the plasma plume shows strong continuum emission and remains in contact with the surface expanding above the sample surface as shown in Fig. 6 1 5 At the later stage of the plasma evolution each individual emission lines can be easily identified, and the plasma plume expands slightly The maximum value in terms of the vertical direction of the plasma plume was gradually increased by about 1.0 mm a s the delay time increase d from 0.5 s to 8.0 s in Fig. 6 15 Otherwise, the presence of the pre ablation air spark laser pulse caused significant changes both in plume dynamics and emission intensities of plasma. One of the interesting points is that in the double pulse configuration the plasma plume expands farther from the target surface at the early

PAGE 148

148 stage of expansion and then comes back to the target surface after some delay time (Se e in Fig 6 17 ) which is the opposite trend, in comparison with the si ngle pulse c onfiguration. This result can be explained with the fact that the plasma plume in the case of double pulse ablation is more separated from the sample surface in the beginning of plasma formation compared to the case of the single pulse ablation From the observed plume dynamics the enhancement factor for line emission strongly depend s on the spatial distribution of the plasma plume. Therefore, some well defined distances along the vertical plume should be used in order to quantify the enhanceme nt factor. For example, for the plasma zone (z = 2.5 mm region) located at a distance of 1.5 mm above the target surface (z = 1.0 mm) the enhancement factors depending on the delay time after plasma formation were changed by a factor of 1 to 4 in Fig. 6 17 That is, the enhancement factor had a tendency to decrease in the plasma zone near the target surface and to increase at some distance from it at all delay times. In addition, the recorded spectra in Fig 6 17 show the spatial distributions of the excite d atom and ions in the vertical direction of the plume expansion. The plume orig inated from double pulse beam farther from the target along the z axis. The faster expansion in the double pulse configuration most probably results from the rarefied ambient a tmosphere caused by the first laser pulse for the pre ablation air spark Lower gas density in air allows a larger plasma expansion and spatial dimension of the plasma plume within the same time interval. This indicates that the second laser pulse initiall y interacts with the sample surface under the good condition of rarefied ambient atmosphere, which is why the plasma plume expands farther from the target surface at the early stage of expansion in the orthogonal double pulse pre ablation air spark scheme. The plasma in air produced

PAGE 149

149 by first laser beam de cays within a few microseconds and its density will tend to be much higher Moreover, it is interesting to compare the expansion dynamics for different plasma species present in the plume. The lines with re latively low excitation energy levels, e.g. Mg I line at 285.21 nm (0 35,051 cm 1 ), have less enhancem ent compared to the lines having higher excitation energy levels. Similar experiment s were performed in the orthogonal reheating scheme. As mentioned a bove, F igure 6 1 6 shows time gated spectrally resolved one dimensional images in the single and orthogonal reheating double pulse scheme s ( t w = 0.1 s : t d = 1.0 s : d = ~ 3.0 mm ). A continuous spectrum for the reheating of the plasma plume could be observed above the individual emission lines (s ee the right side images in Fig 6 1 6(g) (l) ) because the optimized distance d from the sample surface to the ablation spark in air was about 3.0 m m From Fig. 6 1 8 a little bump in the plasma zone (z = 4.0 5.0 mm region) located at a distance of 3.0 4.0 mm from the target surface (z = 1.0 mm) is evidence of ablation in air. Contrary to the pre ablation a ir spark scheme, the maximum value in terms of the vertical direction of the plasma plume was kept constant (z = 2.0 3.0 mm region) in all interpulse delays as shown in Fig. 6 1 8 In addition the i mages taken at all delays were more homogeneous and t he plasma dimension remained approximately constant but the intensity of spectral lines gradually decreased with increasing delay time. T he enhancement of the emission lines did not occur until 2.5 s. However, after 4 .0 s a relatively strong increase in i ntensity could be observed. That is, the enhancement factor had a tendency to decrease in the beginning of plasma formation (short delay times) and then to increase after the plasma cool s down in the reheating scheme. The physical mechanisms involved in th e reheating scheme and in

PAGE 150

150 the pre ablation air spark double pulse scheme seems to be differ ent As the reheating pulse directed in the plasma does not abla te further matter, the observed enhancements may not be linked to an increase of ablated matter. Scan ning electron microscope (SEM) images in Fig 6 1 9 were used to verify the physical mechanism s between the reheating and pre ablation air spark scheme. I n the reheating scheme, the observed enhancements are related to something else, not an increase of abl ated matter due to a rarefied air as in the pre ablation air spark scheme As mentioned in the previous section, the reheating scheme induced improvements for lines coming from high excitation energy levels, whereas neutral lines originat ing from low excit ation energy levels experienced decreases in intensity (see Fig. 6 13) Details of the study for ablated mass will be discussed in the next section. Spectroscopic Study of the Factors Concurring to the Intensity Enhancement in D ouble pulse LIBS I n this sec tion, we focus on a spectroscopic study of the factors related to the intensity increases in order to understand the physical mechanisms. The origin of the LIBS signal enhancement is commonly attributed to an increase of ablated matter from the target or t o plasma reheating. It is worthwhile to derive both the expression of the emission intensity for a give n line in a LIBS plasma and the ratio of the double pulse intensity to the single pulse intensity in terms of the fundamental plasma parameters. The emis sion signal obtained with double and single pulse irradiation was here studied in the approximation of a homogeneous spherical plasma in LTE. Derivation of the analytical formula for the enhancement The intensity of a spectral line, integrated over the wavelength profile, can be written as follows :

PAGE 151

151 (6 1) where the meaning of symbols is defined on the list of symbols T he efficiency response of the instrument is neglected and the volume of plasma ( ) is set as unity Note that Eq. 6 1 is the result of integration over the emission line of sight, assuming a spatially homogeneous atomic distribution. T he following quantities are supposed to vary f rom single to double pulse case: (6 2) Therefore, the ratio of the double pulse to single pulse intensity of a neural line obtained from the same sample can be expressed as: (6 3) By taking the logarithm in Eq. 6 3 (6 4) where is a constant term for any line of the analyte is a constant term for any line of the neutral species of and b is a constant term for any line of any element in the plasma. Similarly, for an ionic line the intensity enhancement can be also expressed as follows: (6 5)

PAGE 152

152 where all symbols are also defined on the list of symbols By taking the logarithm in Eq. 6 5 the expression of the ratio c an be modified by the equation having the useful terms : (6 6) Here, the constants and are the same as in Eq. 6 4 The term is a constant for any line of the ionic species of the analyte A. The ionized fract ion of the analyte can also be expressed in terms of the corresponding neutral fraction under the assumption of plasma composed only by neutral and singly ionized atoms as follows: (6 7) where is the expression of the Saha equation : (6 8) The expression of the enhancement of a neutral line in Eq. 6 5 can be also modified by the usef ul expression with the constant terms e.g. and which are the same as define d in Eq. 6 4 by substituting Eq. 6 7 in to Eq. 6 5 as follows : (6 9) By inserting the expression of Saha equation in Eq. 6 8 into Eq. 6 9 : (6 10)

PAGE 153

153 By taking the logarithm in Eq. 6 1 0 the expression for the logarithm of the ionic line enhancement can be comparable to that for th e logarithm of the neutral line enhancement (see Eq. 6 4 ) as follow s : (6 11) In this expression, the constant terms and are the same as defined in Eq. 6 4 The constant only depends on tw o plasma parameters such as the temperature an d electron number density in both single and double pulse cases Therefore, the de rived expressions for the logarithm of the ionic and neutral line enhancements can be easily used to obtain useful physical information on the change of plasma conditions in between single and double pulse irradiation Plasma temperature and num ber densit y As mentione d above, the expression in Eq. 6 11 can be easily exploited to get useful information for plasma parameters such as plasma temperature and electron number density in passing from single to double pulse irradiation F or this study, some lines (which have different excitation energy levels) from the same analyte can be sel ected for the enhancement plot based on the logarithm of the experimental intensity ratio between single and double pulse irradiation As in the Saha Boltzmann plot, the slop e and i ntercept can be found by linear regression of the experimental points. First of all, the slop e in plot has some information about plasma temperature similar to the Boltzmann or Saha Boltzmann plot. However, the slope in this enhancement plot represe nts the difference of temperature between

PAGE 154

154 two plasmas occurring by single and double pulse irradiation Therefore, a positive slope means that the plasma temperature in the double pulse spectrum is higher than that in the single pulse spectrum as shown in Eq. 6 11 In addition, the constant term can be neglected in the hypothesis that both plasma temperature and electron number density do not change dramatically from SP to DP: that is, all constant terms (e.g. and ) in Eq 6 1 1 will be the same as defined in the expression for the logarithm of the neutral line enhancement (see Eq. 6 4 ). In this case, the intensity ratio of neutral and ionic lines of the same element can be plotted on the same graph, provided is used as the absciss a instead of in Eq. 6 6 Moreover, the y intercept of the linear regression of points in the enhancement plot (Eq. 6 11 ) is related to the degree of enhancement of the total number of analyte neutral atom s in the plasma, which may arise both from the variation of ionization equilibrium and from a variation in the ablated/atomized mass. In Eq. 6 11 the first constant term depends on the ratio of the number of analyte atoms in the DP and SP plasmas. If the ablation can be considered stoichiometric, one would expect that the analyte molar faction doesn t change from the SP to the DP spectrum. The second term depends on the ionization equilibrium and partition function It can be easily calculated, provided the plasma temperature (T) and electron number density ( ) are known. If this second term is calculated, the first term can be also calculated by difference from the slope obtained experimentally (e.g. a slope is equal to ). So me example s from the study will be given below

PAGE 155

155 Example: Results for NIST Al SRM 603 sample. Several mechanisms may be responsib le for the observed enhancement of emission plasma characteristics as a result of a double pulse laser effect. A number of suggestions in the literature addressing the mechanisms of enhancement of the double pulse LIBS signal have been proposed. However, further study is needed to understand the mechanisms of double pulse enhancement These examples are helpful for st udying how the physical conditions in the plasma are expect ed to vary as the plasma generate in time in both single and double pulse configu ration s The approach described in th is section gives information at a glance on the change of plasma temperature in passing from SP to DP irradiation in the same sample. The analytical lines used in the present work were centered at 282 nm both for Mg I 277 .83 nm, 277.98 nm, 278.3 0 nm and 285.21 nm and for Mg II 279.08 nm, 279.55 nm, 280.27 nm, and centered at 292 nm for Mg II 292.86 nm in NIST Al SRM 603 sample as listed in Table 6 2 Figure 6 20 shows the enhanced signal intensities at delay time s from 0.5 s to 10 s, where the double pulse intensity enhancement of both neutral and ionic Mg lines is apparent in (a) the pre ablation air spark scheme and (b) reheating scheme In the pre ablation air spark a ll measurements have been performed at the optimum co ndition s as described in the previous section for optimization in Fig. 6 4 T he ratio of DP/SP integral intensity reaches a factor of 8, depending on the distance from the sample surface and delay time as well as different excitati on line s in Fig 6 3 In addition, i t should be noted that the degree of the enhancement should be different, depending on the cho ice of the collection region of the plasma as mentioned in the previous study. In our study, the LIBS signal

PAGE 156

156 enhancement was o btained by spatial integration (the same pixels in single and double pulse) over the whole plume. Both neutral and ionic lines were used to build the logarithm enhancement plot, following the representation of Eq. 6 11 but neglecting the constant term as mentioned above The logarithm ic plots of neutral and ionic line e nhancements in the pre ablation air spark scheme are shown in Fig. 6 21 A slope ( = T) and y intercept ( = q) are presented in each plot. The corresponding spectra for b uilding the logarithm plots are shown in Fig. 6 22 (a center = 281.5 nm ) and (b center = 292 nm ) The temperature difference ( T) and y intercept (q) between single and double pulse in terms of the delay time are also presented in Fig. 6 23 b For the p re ablation air spark configuration i t should be noted that a relatively high temperature difference between the single and double pulse was detected at short delay time s This result corresponds to the enhancement plot in Fig 6 20 a Otherwise, the slope of the linear regression is negative at 10 s delay time (see Fig. 6 21 i and Fig. 6 23 b ) which means the increase of intensities observed in the double pulse case cannot be explained only by a change in the plasma temperature. It is of interest to note tha t the strong enhancement at short delay ti me s for the orthogonal pre ablation air spark configuration is related to an increase in the temperature but not at long delay time s Furthermore, the experimental y intercept values can be used to get information on the change of atomized mass. As me nti oned in the previous section, both constant term s and in Eq. 6 1 1 can be calculated from the y intercept of plot, provided the plasma temperature (T) and electron number density ( n e ) are known. Plasma temperat ure and electron number density were estimated by means of spectroscopic measurements. If the plasma is in LTE in each temporal window considered, then the

PAGE 157

157 population density of atomic and ionic electronic states is described by a Boltzmann distribution. B y measuring the relative line intensity it is then possible to estimate the temperature through the slope of a straigh t line in the Boltzmann plot In our study, a Saha Bolt zmann plot was used for deriving plasma temperature due to the advantage of using many lines of widely different upper state energy as shown in Fig. 6 2 4 As mentioned in Chapter 4, the method for the electron number density measurement using Stark broadening of selected line was used. The electron number density relationship to the f ull w idth at half maximum (FWHM) of S tark broadening lines has been given in Eq. 4 12. In this chapter, electron number density has been estimated for the Al II line at 281.62 nm in single and double pulse configuration (see Fig. 6 23 c ) The starting valu e of for plasma generated by the double pulse excitation is relatively lower than in the case of single excitation, but it also changes slowly with time. Overall the electron number densities in the double pulse irradiation are a l ittle bit higher over the delay time than that in the case of single pulse irradiation, but not very significant ly so. Therefore, a ll constants (e.g. and ) in Eq 6 1 1 could be calculated by inserting plasma temperature (T ) and electron number density ( ) estimated by means of spectroscopic measurements into Eq. 6 1 1 but neglecting the constant term S ummarized values for them are given in Table 6 3 and 6 4 as wel l as F ig ure 6 23 As shown in Fig. 6 23 d it is very clear that as the delay time increases, the enhancement of total number density of atoms and ions in the plasma was exponentially increased until 3 .0 s which is the time scale of limitation for an enhancement, and then gradually decreased after 3 .0 s. Thus, the observed enhancements in emission of Mg atomic and ionic lines for the orthogonal pre ablation air spark configuration may be the result

PAGE 158

158 of i ncreased temperature and total atomic and ionic number density as shown in Fig ure 6 23 and Table 6 3 It is evident that the pre ablation spark causes rarefaction in the air which leads to the increased plasma volume and enhanced ablation observed by the i maging of the produced plasma (see Fig. 6 2 5 c and 6 2 5 d ) and craters (see Fig. 6 2 5 1a and 6 2 5b ) in the single and doub le pulse configuration A s imilar experiment was also performed in the reheating configuration. Figure 6 12 shows the optimum condition for the reheating double pulse configuration The o ptimum distance (= d mm) from the sample surface to the air spark was set between 1.0 and 3.0 mm, which depends on the interpulse delay time. As the interpulse delay time decreases the optimum d istance is closer to 1.0 mm as shown in Fig. 6 12 However, a significant signal enhancement for two lines (see Fig. 6 12 a and 6 12 b)) was observed for distances d around 3.0 mm reaching a maximum enhancement of ~ 40 (@ Al II 281.62 nm) and ~ 16 (@ Mg II 2 70.08 nm) for the longer delay time. It is manifest that the distance d strongly affects the signal enhancement depending on the interpulse delay time. This behavior was also observed for several spectral lines by plotting the LIBS signal enhancement vs. i nterpulse delay time as shown in Fig. 6 12 c All measurements were performed under th e optimum conditions ( d = ~ 3.0 mm; t d = 1.0 s; t w = 0.1 s) The logarithm ic plots of neutral and ionic line enhancements and their corresponding spectra are shown in Fi g. 6 2 6 and 6 2 7, respectively The slope of the linear regression was negative until 1.5 s and then changed to positive as seen from Fig. 6 26 and 6 2 8b It can be explained that the enhancement occurs at the longer delay time because most atoms c an be easily excited after the plasma cools down. The temperature difference and y intercept between single and double pulse in terms of the

PAGE 159

159 delay time are also presented in Fig. 6 2 8 b Contrary to the pre ablation air spark configuration, as the delay ti me increase, the temperature difference between SP and DP also i nc reases, which means much stronger enhancement occur s at the longer delay time. As described above, p lasma temperature and electron number density were estimated by mea ns of spectroscopic mea surement (see Figure 6 2 4 and Table 6 6) Correlations between LIBS signal enhancement and plasma temperature were found. In other words, the increase of plasma temperature is possibly the main factor in the correlation between the excitation energy level s and the increase in emission intensity enhancement from Mg atoms. Based on known plasma temperature and electron number density, the change of atomized mass was also calculated for checking another cause of the enhancement factors as shown from Figure 6 2 8 d and Table 6 5. The interesting feature observable from Fig. 6 2 8 d is that no significant enhancement of the number density of atoms and ions in the plasma was detected Thus, the observed enhancements in emission of Mg atomic and ionic lines for the o rthogonal reheating configuration are most likely the result of increased temperature Conclusion s The aim of this study was to find the optimum experimental condition for the large enhancement of emission lines as a function of several parameters and to s tudy possible dynamical and physical mechanisms based on the use of spectroscopic methods for the diagnostics of the laser induced plasma originated by a double pulse laser beam The theoretical derivation of the emission lines in a LIBS plasma and the rat io of the double and single pulse intensity in terms of the fundamental plasma parameters were used to get useful physical information on the change of plasma

PAGE 160

160 condition as well as understand the LIBS enhancement. The experimental results are following : In our study, two different schemes in orthogonal double pulse configuration i.e., pre ablation air spark an d reheating double pulse scheme s, were used In both schemes, the optimum conditions for getting large enhancement were different and the interpulse delay time t and the distance from the sample surface to air spark d are the most important parameters affecting a LIBS signal enhancement. From the study of plume dynamics in laser induced plasma an enhancement factor for line emission strongly depends on the sp atial distribution of plasma plume Thus, some well defined distance along the vertical plume should be used in order to quantify the enhancement factor. The observed enhancements of emission lines for the double pulse pre ablation air spark scheme may be result of increased temperature and total atomic and ionic number density; otherwise, the LIBS signal enhancements for the double pulse reheating scheme result only in increased temperature.

PAGE 161

16 1 Figure 6 1. Common p ulse configurations. (a) Coll inear configuration, in which the first and second laser pulses are both focused on /or into a sample. In orthogonal configuration a single ablative pulse is coupled with either (b) a pre ablation air spark that is parallel to and up to several millimeters above the sample surface or (c) a reheating pulse [70]

PAGE 162

162 Figure 6 2 (a). Scheme of the set up showing LIBS system for both single and double pulse operation. Figure 6 2 (b). Timing and triggering system used for both pre ablatio n air spark and reheating double pulse scheme s

PAGE 163

163 Figure 6 3 LIBS signal enhancement at the several different transition lines for the s everal elements (Al II, Mg I and II and Cr II) versus the interpulse delay ti me 100 s) at several d ifferent distances ( d 0.3 2.5 mm ) in SRM 603 sample.

PAGE 164

164 Figure 6 4 P re abl ation air spark double pulse configuration signal enhancement versus the interpulse delay time (= t) in (a) NIST Al SRM 603 and (c) South African Al AA1 sample and signal enhanc ement versus the distance (= d mm) from the sample surface to air spark above the sample in (b) NIST Al SRM 60 3 and (d) South African Al AA1 sample.

PAGE 165

165 Figure 6 5. Spectra showing Al II 281.62 nm and Mg I 285.21 nm emission lines of interest in terms of delay time in Al alloy sample (SRM 603) in both (a) single pulse and (b) orthogonal pre ablation air spark double pulse configuration. (c) For each emission line, graphs of LIBS signal enhancement with use of the double pulse irradiation versus several delay times from 0.5 s to 10 s

PAGE 166

166 Figure 6 6. Signal to noise (S/N) ratio as a function of delay time s for each Al II and Mg I emission line.

PAGE 167

167 Figure 6 7 Triggering scheme for the time resolved study of plasma evolution in the reheating double pulse scheme (a) with short gate width of 0.1 s and (b) long gate width of 30 s (averaged measuring) of plasma in the triggering system initiated by the Quantel Brillant laser

PAGE 168

168 Figure 6 8 LIBS signal enhancement versus interpulse delay in the reheating double p ulse scheme (a) with sh ort gate width of 0.1 s and (b) long gate width of 30 s (averaged measuring) of plasma in the triggering system initiated by the Quantel Brillant laser

PAGE 169

169 Figure 6 9 Plasma images in (a) double pulse, ( b) s ingle pulse and (c) only air spark ( without sample plasma ) at the center wavelength of 259.09 nm in aluminum alloy AA 1 sample. (d) Intensity enhancement compared to only air spark ( without ablation ) laser pulse as well as the LIBS signal from the ablation laser pulse only.

PAGE 170

170 Figure 6 10 (a) Time sequence for the time resolved study of plasma evolution in the reheating double pulse scheme. The acquisition time after the ablating laser pulse is about 3.0 s (t w :0.1 s; t d : 1.0 s; t: 2.0 s). (b) Peak intensity as a function of decay time of plasma for selected neutral and ioni c lines (t w :0.1 s; t d : 1.0 s; d :3.0 mm) and inserted figure shows a log log scale plot of the same data.

PAGE 171

171 Figure 6 11 (a) Time sequence of the experimental set up in the case of the reheating double pulse scheme. (b) Timing between laser output pulse and HV gate pulse (PG 200 Delay Trigger out) at the different delay time t d ( c) LIBS signal enhancement ( lo g scale) of Al II 281.62 nm as a function of the delay time t d

PAGE 172

172 Figure 6 12 LIBS signal enhancement versus the interpulse delay time (= t) at the s eve ral distances ( = d mm) from the air spark to sample surface in a selected line (a) Mg II 279.08 nm and (b) Al II 281.62 nm and (c) at the maximum distance ( d = ~ 3.0 mm) for several transition lines in the reheating double pulse configur ation.

PAGE 173

173 Figure 6 1 3 LIBS signal enhancement versus the delay between the two laser pulses t in the reheating double pulse scheme for selected neutral and ionic lines (gate width delay time: 1.0 s; d : 3.0 mm).

PAGE 174

174 Figure 6 14. S ignal to noise (S/N) ratio as a function of delay times for each Al II and Mg I emission line.

PAGE 175

175 Figure 6 15 Time gated spectrally resolved one directional images of the laser induced plasma of a Al alloy sample (603), obtained in t he single (left images) and in the orthogonal pre ablation air spark double pulse mode (right images). The gate width and interpulse delays between two laser pulses were kept by constants (0.1 s and 30 s respectively), and the ICCD gate delays were 0.5 ( a,g), 1.0 (b,h), 2.0 (c,i), 3 .0 (d,j), 5.0 (e,k) and 8.0 (f,l ).

PAGE 176

176 Figure 6 16 Time gated spectrally resolved one directional images of the laser induced plasma of a Al alloy sample (603), obtained in the single (left images) and in the orth ogonal reheating double pulse mode (right images). The gate widt h and ICCD gate delays were kept by constants (0.1 s and 1.0 s respectively), and interpulse delay times ( t) between two l aser pul ses were 0.5 (a,g), 1.0 (b,h), 1.5 (c,i), 2 .5 (d,j), 4.0 (e,k) and 6.0 (f,l ).

PAGE 177

177 Figure 6 17 Spatial intensity profiles of atomic and ionic emission lines of Al, Mg, Cr at different delay times from 0.5 s to 8.0 s in t he pre ablation air spark scheme The acquisition time (= t w ) and interpulse delay time ( t) between t wo laser pulse was fixed at 0.1 s and 30s.

PAGE 178

178 Figure 6 1 8 Spatial intensity profiles of atomic and ionic emission lines of Al, Mg, Cr at different d el ay times from 0.5 s to 6.0 s in the reheating scheme The gate width and ICCD gate delays were kept by constants ( t w : 0.1 s and t d : 1.0 s respectively).

PAGE 179

179 Figure 6 1 9 SEM images of craters produced 50 consecutive samplings of Al alloy sample (a) in the single pulse and (b) in the double pulse ( t = 20 s) using the orthogonal pre ablation air spark mode, and (c) in the single pulse and (d) in the double pulse ( t = 5.0 s) using the orthogonal reheating mode.

PAGE 180

180 Figure 6 20 Signal enhancement versus delay times at the different Mg atom ic (solid dot s) and ionic (open dots) lines (a) In orthogonal pre ablation air spark and (b) i n reheating scheme LIBS

PAGE 181

181 Figure 6 21 L ogarithm ic plots of neutral and ionic line enhancements at the different delay times from (a) 0.5 s to ( i) 10 s (in the pre ablation air spark scheme ).

PAGE 182

182 Figure 6 22 (a) LIBS spectra in both single (black color) and double pulse (gray color) at the different delay times f o r the pre ablation air spark scheme ( center = 281.5 nm, t = 30 s and t w = 0.1 s).

PAGE 183

183 Figure 6 2 2 (b) LIBS spectra in both single (black color) and double pulse (gray color) at the different delay times for the pre ablation air spark scheme ( center = 292 nm t = 30 s and t w = 0.1 s).

PAGE 184

184 Figure 6 2 3 (a) Plasma temperature obtained from Saha Boltzmann plot, (b) temperature difference ( T = slope) and intercept (= q) from the logarithm plots of neutral and ionic line enhancements (c) electron nu mber density u sing Stark broadening (Al II 281.62 nm) and (d) The enhancemen t of total number density of atoms and ions in plasma from Eq 6 11 at the different delay times.

PAGE 185

185 Figure 6 2 4 Saha Boltzmann plot in both (a) single and (b) orthogonal pre ablat ion air spark double pulse configuration and (c) single and (d) orthogonal rehe ating double pulse configuration.

PAGE 186

186 Figure 6 2 5 SEM images of craters produced 50 consecutive samplings of Al alloy sample (a) in the single pulse and (b) in the doubl e pulse ( t = 20 s) using a pre ablation air spark. Spectrally resolved one directional images of the laser induced plasma of a Al alloy sample, obtained (c) in the single and (d) in the double pulse ablation mode (t d = 2.0 s; t w = 0.1 s; t = 30 s).

PAGE 187

187 Figure 6 2 6 L ogarithm ic plots of neutral and ionic line enhancements at the different delay times from (a) 0.5 s to (f) 9.0 s (in the reheating scheme).

PAGE 188

188 Figure 6 2 7 (a). LIBS spectra in both single (black color) and doubl e pulse (gray color) at the different delay times for the reheating scheme ( center = 281.5 nm, t d = 1.0 s and t w = 0.1 s). Figure 6 2 7 (b) LIBS spectra in both single (black color) and double pulse (gray color) at the different delay times for the reheating scheme ( center = 292 nm, t d = 1.0 s and t w = 0.1 s).

PAGE 189

189 Figure 6 28 (a) Plasma temperature obtained from Saha Boltzmann plot, (b) temperature difference ( T = slope) and intercept (= q) from the logarithm plots of neutral and ionic line enhancements (c) electron number density using Stark broadening (Al II 281.62 nm ) and (d) The enhancement of total number density of atoms and ions in plasma from Eq. 6 1 1 at the different delay times.

PAGE 190

190 Table 6 1. Concentration of several elements in NIST Al SRM 603 and South African Al alloy standards AA1 and D28 (APEX Smel ter Co., South African) Element SRM 603 South African AA1 South African D28 Al 97.69 69.57 81.55 Si 0.520 14.6 9.66 Mg 1.01 0.170 0.004 Cu 0.290 5.70 1.76 Zn 5.90 3.6 Fe 0.210 1.73 0.98 Mn 0.540 0.59

PAGE 191

191 Table 6 2. Selected spectral lines and corresponding spectroscopic information of the investigated elements (a) Species Wavelength ( nm ) A ( 10 8 1/s ) E lower ( cm 1 ) E lower ( eV ) g lower E upper ( cm 1 ) E upper ( eV ) g upper Al II 281.61 3.83 59,852 7.42 3 95,351 11 .8 1 Mn II 257.61 3.025 0 0 7 38,807 4.812 9 Mn II 259.37 2.636 0 0 7 38,543 4.779 7 Mn II 260.57 2.711 0 0 7 38,366 4.757 5 Mn II 293.31 1.959 9,473 1.18 5 43,557 5.401 3 Mn II 293.93 1.855 9,473 1.18 5 43,485 5.392 5 Mn II 294.92 1.859 9,473 1.18 5 43,371 5.378 7 Mn I 279.48 3.70 0 0 6 35,770 4.43 8 Mn I 401.81 0.254 17,052 2.11 10 41,932 5.20 8 Mn I 403.08 0.170 0 0 6 24,802 3.08 8 Mn I 405.55 0.431 17,282 2.14 8 41,933 5.20 8 Mg II 279.08 4.01 35,669 4.42 2 71,491 8.86 4 Mg II 279.55 2.60 0 0 2 35,761 4.43 4 Mg II 280.27 2.57 0 0 2 35,669 4.42 2 Mg II 292.86 1.15 35,669 4.42 2 69,805 8.65 2 Mg I 277.83 1.82 21,850 2.71 1 57,833 7.17 3 Mg I 277.98 1.36 21,870 2.71 3 57,833 7.17 3 Mg I 278.30 2.14 21,911 2.72 5 43,371 7.17 3 Mg I 285.21 4 .91 0 0 1 35,051 4.35 3 (a) From NIST atomic spectra Database, http://physics.nist.gov/PhysRefData/ASD/lines_form.html

PAGE 192

192 Table 6 3. All par ameter values mentioned in Eq. 6 11 at different delay times (pre ablation air spark scheme) Delay time ( s ) Y intercept ( = q ) 0.5 1.757 1.143 0.6139 0.4410 0.5413 1.0 0.987 1.191 0.2041 0.1726 1.226 1.5 0.645 0.9668 0.3218 0.1912 1.380 2.0 0.303 0.8345 0.5315 0.02944 1.701 3.0 0.206 0.4382 0.6442 0.03751 1.904 5.0 0.0944 0.4891 0.5835 0.05959 1.792 8.0 0.325 0.0 05991 0.3190 0.06621 1.376 10 1.019 0.6686 0.3504 0.1977 1.420

PAGE 193

193 Table 6 4 Plasma temperatu re and electron number density in both single a nd orthogonal pre ablation air spark double pulse configuration at different delay times. Plasma temperature ( K ) Electron number density ( 10 17 cm 3 ) SP DP SP DP 0.5 14017 245 15679 227 5.13 5.11 1 13316 168 15632 237 4.57 4.54 1.5 1 3052 155 14657 201 4.02 3.99 2 12630 155 14194 180 3.69 4.07 3 12408 141 13084 148 3.4 3.49 5 11582 158 12217 189 2.96 3.04 8 10715 148 10752 169 2.9 2.90 10 10259 137 9696 127 2.9 3.01

PAGE 194

194 Table 6 5. Al l par ameter values mentioned in Eq. 6 11 a t different delay times (reheating scheme) Table 6 6. Plasma temperatu re and electron number density in both single and orthogonal reheating double pulse configuration at different delay times. Delay time ( s ) Y intercept ( = q ) 0.5 0.3972 0.1265 0.2707 0.05759 1.3 11 1 0.5397 0.2455 0.2943 0.04247 1.342 1.5 0.3960 0.09525 0.3008 0.07828 1.351 2.5 0.1873 0.2420 0.05469 0.12697 1.056 3 0.4518 0.3657 0.08612 0.2457 0.9175 4 0.4172 0.6381 0.2209 0.1051 1.247 9 0.6664 0.9457 0 .2793 0.003432 1.322 Delay time ( s ) Plasma temperature ( K ) Electron number density ( 10 17 cm 3 ) SP DP SP DP 0.5 13077 151 12741 188 3.80 3.45 1 12883 171 12523 165 3.32 3.32 1.5 12754 158 12732 167 3.05 3.29 3 11748 137 12792 146 2.65 3.85 4 11607 171 12867 134 2.53 3.28 9 10041 148 11247 165 2.15 2.54

PAGE 195

195 CHAPTER 7 CONSIDERATION ON THE SPECTRAL FLUCTUATION APPROACH IN LASER INDUCED BREAKDOWN SP ECTROSCOPY The a cceptability of laser induced breakdown spectroscopy (LIBS) is still r elated to the problem of quanti z ation involving accuracy, i.e. repeatability and trueness In a LIBS analysis there are many parameters that affect the precision and accuracy of a measurement. Some of them can be controlled, such as the stabilit y of the laser pulse energy, and others are dependent on the sample. A list of important parameters that affect a LIBS analysis is presented in Table 7 1. The fluctuation s of emission signal can be influenced by these parameters. T hus the study of the fun damental noise characteristics in LIBS spectra is important for optimizing the analytical utility of the technique. S everal papers have been published in several fields regarding spectroscopic noise [160 164] lvarez Trujillo et al. compared a new spectral data processing scheme (i.e., the standard deviation of collected spectra) with the traditional ensemble averaging of LIBS for non homogeneous analyte system (e.g., aerosol system ) [160, 161] For comparison between two methods, signal to noise (S/N) ratio and relative standard deviation (RSD) were calculated and the limiting noise of the measurement was also studied as detailed by Ingle and Crouch [100] Poussel and Mermet [163] reported some correlation between background signals in inductively coupled plasma atomic emission spectrometry (= ICP AES) to study effects on precision, limit of detection and limit of quantitation. The shape of the RSD curve of the net signal as a function of the concentration was also studied from both a theoretical and practical aspect. It was argued that this analysis seems to show the relevance of the various noise types as well as the limiting noise of the mea surements [162]

PAGE 196

196 As shown in several studies, the standard deviation (i.e., the root me an square noise) of the background may be the result of several fluctuating factors such as plasma temperature, electron number density, laser energy fluctuations and mass ablated by laser pulse ( since it may be contributed to the electron number density a nd plasma temperature ) T hus, the behavior observed by plotting the standard deviation (SD) and relative standard deviation (RSD) of each spectral element (pixel) versus wavelength can indeed be informative. First of all, all possible limiting noises prese nt in a LIBS measurement will be simulated by making the plot mentioned above and then compared with the results obtained in our work for studying the relevance of the various noise types as well as the limiting noise of the measurements. A possible correl ation between the background fluctuation and the analyte signal will be also studied. In addition, as a complementary approach the plot of signal to noise (S/N) ratio versus signal (or concentration ) will be shown and discussed in this chapter since the S /N ratio is the reciprocal of the RSD. Theory The lowest signal intensity that can be detected is determined by the fluctuations of the background signal, denoted as noise. The study of noise forms a part of the discussion of errors in analytical measure ment Usually, noise includes fluctuations which do not obey a regular distribution law, such as those produced by spikes on the line voltage or other disturbances from electrical equipment in the vicinity. The causes of these noise sources may be found in the light sources, the absorbing medium, the detectors and the electronic measurement systems used in optical spectrometry. The noise intensity can be expressed as the standard deviation of the background signal

PAGE 197

197 measurements, denoted as the root mean squ are (RMS) noise, or the peak to peak value which is the difference between the minimum and maximum ba ckground signal In a typical LIBS experiment, the noise in a signal includes both the noise in the background and the noise in the signal. A priori one does not know whether two noises are correlated or uncorrelated On logical grounds, one could suppose that, at least at the beginning of the plasma formation or at early evolution times, the background continuum and the signal would show some correlation in view of the fact that the origin of the fluctuation (temperature, electron number density and ablated mass) are similar for both. Otherwise, at long delays, the continuum background decays and the signal fluctuation due to the sampling process will then become the dominating cause of noise, at least for signal levels not too close to the detection limit. When making measurements in LIBS, more than one noise source occur s and so must be considered whatever measurement system is being utilized for the si gnal measurement. To calculate the variance in q as a function of the variances in and we use the following (general derivation of the propagation of errors) [165] : (7 1a) In the above equation, is the covariance of Using the definition of the correl ation coefficient, (7 1b) We obtain the working expression: (7 1c)

PAGE 198

198 where is the correlation factor which takes into the account the possibility that the two variables are correlated or uncorrelated That is, if the correlation factor is zero ( it can be explained by totally uncorrelated noise sources in which the last term in Eq 7 1c is zero Otherwise, the correlation factor can also vary between +1 (totally correlated noise sources) and 1 (anti correlated noise sources) [100] In luminescence and emission measurements, the experimental spectral peak intensity ( ) consists of the sum of the analytical net signal ( ) plus the blank signal ( ) including contributions from the background signal (or plasma continuum ) and the dark signal ( ) Then, the net signal ( ) is obtained by subtracting the value of the blank signal ( ). An example of the description of net signal is shown in Fig. 7 1 That is, the simplest net signal measurement consists of the peak intensity at the central wavelength 0 of the analyte line and an off peak measurement of the background at a single position if the dark signal can be negligible It should be noted that the background is measured at some distance from the line center and assumed to be representative of the true background value present under the line peak, excluding any contribution from the line wings. In the Appendix we list all parameters measured experimentally and their meaning. Using the above definitions, the noise in the plasma background associated with analyte line and the noise measured at the line center, due to the contribut ions of both analyte line and plasma background, would be given by the following expression: (7 1d)

PAGE 199

199 and the root mean square noise in the total emission signal can be shown as follow s : (7 1e) If the net signal due to the an a lyte line is obtained by subtracting the background signal from the total signal the propagation of error caused by the background correction can be made as follow s : (7 1f) In order to simplify the writing, from now on we will indicate the net average signal to the analyte with the average plasma background with the noise in the background with the noise in the signal with the tot al noise with and the noise of the difference with Standard Deviation Limiting Cases Case a 1: In this case, it is assumed that the noise in the signal is much less than the noise in the background. In other words, the measurement is background noise limited. Note that this is not likely to be the case in reality, although it may hold when the signal level is very low and the background is still high (e.g., close to the limit of de tection and at short delay times). Whatever the reason might be, if Eq. 7 1e simplifies to: (7 2) The last approximation holds whenever Should this be the case, the plot of the standard deviation versus wavelength, simulated in Fig. 7 2 a should remain at

PAGE 200

200 the same level as that corresponding to This will hold irrespective of whether the two noises are correlated or not. Case a 2: The noise in the background and the noise in the signal are of comparable magnitude, i.e., it is assumed that Note that one does not measure directly, since In this case, Eq. 7 1e becomes (7 3a) i) If and noises are completely uncorrelated, i.e., if the total noise will be given by (7 3b) As a consequence, when the standard deviation is plotted as a function of wavelength, one should observe an increase of a factor 1.414 at the locatio n of the spectral lin es (see in Fig. 7 2 b). ii) In this case, Eq. 7 1e can be simplified as follow: (7 3c) iii) In anti correlated case, (7 3d) Figur e 7 2 c and 7 2 d show the simulated plots when respectively.

PAGE 201

201 Case a 3: This is the case in which the noise in the signal dominates over that of the background, i.e., When this is true, the resulting total noise expression will be given by (7 4) The last approximation holds whenever Note that, in analytical practice, the signal is measured at moderately long delay times, when the plasma continuum has decayed to a negligible (or low) level. The fluctuations in the signal (due to the sampling process and the inherent signal noise) are t hen expected to dominate those of the background. The simulated plot of the standard deviation versus wavelength shown in Fig. 7 2 e should then b e characterized by an increase observed at the locations of the analyte peaks: e.g., such increases should corr espond to the ratio ( For example, if the increase will be a factor of 10. Note that changes with ( it increases with ), although the exa ct nature of the change is not known, since the type of noise is unknown. As shown in the previous background noise limited case, the above outcome holds irrespective of the value of the correlation coefficient. Case a 4 : This is the most general cases, i n which and can assume any value. The total standard deviation then becomes: (7 5 a ) As pointed out before, is not m easurable directly. In the case in which the noises are totally uncorrelated one can write: (7 5b)

PAGE 202

202 can be calculated by the difference betwe en two experimentally measured values. However, when the noises are correlated, cannot be calculated without which is unknown. In fact, the resulting quadratic equation below cannot be solved. (7 5c) In order to be able to calculate one can adopt the following procedure. The standard deviation of the difference between and i.e., can be experimentally evaluated from the measurement. For each spectrum (laser pulse), the total counts due to are measured simultaneously with is then subtracted from and the resulting is obtained for each spectrum. Repeating this operation for all N spectra, one can calculated the standard deviation of i.e., In practice, what is done is the following: (7 6a) with the result that (7 6b) In Eq. 7 6b, the only unknown is which can then be calculated by the following relation: (7 7) It can be seen that similar arguments as those already discussed before apply here. In fact: if we have

PAGE 203

203 (7 8) It can be calculated experimentally since the background in this case has been measured twice. From Eq. 7 6b it should be noted that if all noise sources are totally uncorrelated, the noise of the net signal can be simply calculated from Eq. 7 8 because and are known values experimentally and then compared with the experimentally measured noise of the net signal in Eq. 7 6a The high difference between the calculated and measured noise (= ) implies a high correlation between noise sources because the assumption about the correlation between noise sources from Eq. 7 7 c is not valid, which means t hat 0. Thus, it will be worth while to compare the difference between the calculated and measured SD s of net signal with the correlation factor in order to understand the multiplicative nature of noises Relative Standard Deviation Limiting Cases It is r elatively straightforward to extend the previous considerations and discuss the spectral behavior of the relative standard deviation (RSD) of the various signals defined before. By definition RSD can be defined as: (7 9a) (7 9b) Case b 1: Here, the following relations apply:

PAGE 204

204 (7 10a) (7 10b) (7 10c) In this case, in the plot of the relative standard deviation versus wavelength, the total analyte peak i ntensity at 0 should decrease with respect to the relative standard deviation of the background, since (S+B) > B. This is shown in the simulated Fig. 7 3 a. Case b 2: The pertinent equations in this case are: (7 11a) (7 11b) i) The pertinent equations in this case are: (7 12a ) (7 12b) The total RSD will decrea se compared to the but not as much as in Case 1 (a factor of 1.414 less, see simulated Fig. 7 3 b). ii) (7 13)

PAGE 205

205 In this case, if the signal and background have the same magnitude, the RSD plot will show no features at each peak (see simulated Fig. 7 3 c). iii) In this case, the will be z ero, since (see simulated Fig. 7 2 d). Case b 3: (7 14a) (7 14b) It can therefore be seen that the plot o f the RSD versus wavelength will either present no features, decreases or increases depending upon the values of the ratios in Eq. 7 14. In the peculiar case in which the noise ratio ( ) is equal to the ratio the RSD will be a flat featureless line when plotted versus wavelength One can argue that, at reasonable plasma decays (several microseconds), the first ratio will have a predominant effect, since while at early plasma decays and therefore the RSD plot should show an increase at the location of the spectral lines. It should be noted that in this limiting case, it is irrelevant whether In other words, correlation between the various n oises should play no role. Case b 4: General Case. (7 15) i) (7 16a)

PAGE 206

206 (7 16b) Here, one should take advantage of the procedure outlined in the previous section to calculate (after evaluating ). It should be also noted that Eq. 7 16 reverts Eq. 7 14 and Eq. 7 10 in the cases where is much greater or much smaller than respectively. ii) (7 17a) (7 17b) iii) (7 18a) (7 18b) Experimental The LIBS experimental system has already been described in detail in Chapter 4. The sch ematic of the set up is illustrated in Fig. 4 1. In our study, simultaneous measurements have been performed using the spectrometer (Acton triple grating, 0.5 m focal length) equipped with the intensified CCD detector (ICCD 5764/RB E, Princeton instruments ). All me asurements in this study were carried in atmospheric pressure and

PAGE 207

207 performed with a fixed laser pulse energy of 90 5 mJ. The experimental conditions and samples used for each study will be described in detail in the next section. Results and D is cussion As mentioned above all measurements were acquired with a grating monochromator equipped with and intensified CCD and the following consideration s should b e also mentioned before we make a discussion for consideration on the spectral fluctuation st udy in LIBS : The different spectral windows are considered to consist of a few isolated spectral lines, superimposed on a flat background continuum, reflecting the elemental composition of the sample. The spectra can be obtained at different delay times from the onset of the plasma at a fixed integration time Each spectrum is the result of a single laser shot fired on the same location of the sample. The data are not spatially resolved and the entire plasma height is binned ( pixel column ) For each sp ectral window considered, a certain number of single pulse s pectra are obtained For each pixel (or equivalently for each spectral resolution element) the average signal levels for the background, single plus background, net signal are computed, together w ith their corresponding standard deviation and relative standard deviation values (see Fig. 7 4 ) The background and the signal plus background are acquired simultaneously and may therefore show some correlation The only noises considered are background noise and signal noise: therefore, the dark current noise is neglected, together with excess detector noise and readout noise in the study Several experiments were performed under various experimental conditions in different samples to understand the li miting type of noise present in a measurement. Figure 7 5 shows Zn and Cu at omic emission lines for both 55 single shot ensemble averaged spec tra and their standard deviation curves at the same spectral window in

PAGE 208

208 both Al alloy sample (D28 ) and NIST brass s tandard (1113). T he standard deviation s of the spectra collected represent the variability i n the analyte signal s on a pixel column by pixel column basis across the CCD array. Based on the simulated shape of the plot of SD versus wavelength illustrated in the previous section they are close to the case i n which the noise in the signal dominates over that of the background because changes proportionally with a signal i.e., case a 3; (see Eq. 7 4). F igure 7 6 s hows 55 single shot LIBS s pectra at the peak of Zn I 330.3 nm in both Al alloy sample (D28) and NIST brass standard (1113) and each correlation factor value between two major noise sources was represented on the figures. The gate wi dth and delay time were 0.1 s and 2.0 s respectively with the laser pulse energy of 90 5 mJ For 55 single shot spectra, t he total noise was obtained by the experimental standard deviation at the line center of Zn I 330.3 nm and the background noise was obtained by RMS noise at some distance on either side of the Zn I emission line and then the experimental standard deviation of net signal was obtained by correction of the background contribution under the Z n atomic line (see Eq. 7 6 a ) Each valu e calculated is 0.527 and 0.871 respectively in both Al alloy D28 sample (3.60 % of Zn) and NIST brass 1113 standard (4.808 % of Zn ) At a relatively high concentration ( e.g., 4.808 % of Zn in NIST brass standard) a high degree of correlation was observed This result may suggest that the correlation between noise sources depends on analyte concentrations. For further study correlation factor values were also calculate d as a function of increasing Mg concentration in South African Al alloy samples as shown in Fig. 7 7 W hen the composition of Mg in Al alloy sample s increased, a high correlation factor was obtained In particular, at the minimum c oncentration of Mg (0.004 % of

PAGE 209

209 Mg), a correlation factor is close to zero ( ~ 0.014, see Fig. 7 7 c), which means no correlation between noise sources at a low concentration. It would be explained that at a low concentration, the continuum background decays significantly and signal fluctuation due to the sampling process may be a major cause of the total noise. On the other hand, the hig h degree of correlation between the noise in the background and the noise in the signal at a high concentration of the analyte would be due to the origin of the fluctuations, e.g., plasma temperature, electron number d ensity and ablated mass For further study, the RSD approach was used for the examination of the spectral behavi or of the relative standard deviation of the various signals. It is very useful even if only approximately, to the identification of the limiting noise and to the different role s played by the limiting noises during the lifetime of the plasma. Several lim iting cases simulated in the theory section were studied by plotting of the relative standard deviation (RSD) versus wavelength in several samples under d ifferent experimental conditions. O ne of the interesting points is that as the concentration of analyt e in the sample increases, the RSD value starts to decrease around the peak of the analyte. For instance, Figure 7 8 and 7 9 clearly shows some changes of the RSD curves with increasing of Mg and Cu compositions in South African Al alloy samples and NIST b r ass standards, respectively, at f ixed delay time and gate width; i.e., 2.0 s delay time and 0.1 s gate width They would be applied to case b 3 because in the plot of standard deviation versus wavelength in both figures the SD curves were characterized by an increase at the line center in comparison with the background intensities in all samples (see Fig. 7 8 b and 7 9 b ) ; in other words In this case, the plot of the RSD versus wavelength depends upon the ratios of the right hand side in Eq. 7 14b as

PAGE 210

210 mentioned before (see Fig 7 3 d). As examples, Figure 7 8 d and 7 9 d show clearly the dependence of the ratios in Eq. 7 14b. At high concentration s of Mg and Cu, the RSD value s around the peak s shows a decreasing trend compared to the p lasma background intensity because (see the values of the ratios in Eq. 7 14b) In contrast, as the concentration of the anal yte decreases, the RSD value of the background emission is relatively smaller than that of the line emissio n Temporal evolution of limiting noises. As an illustration of the above discussion, limiting noises also depend strongly upon the temporal evolution of the plasma as well as the analyte composition in a sample A logica l test for checking the temporal d ependence of limiting noises was performed at the Mn II 259.37 nm line for several delay times in an Al alloy sample (AA1) as shown in Fig. 7 1 0 Each spectrum measured for several delay times from 0.5 s to 8.0 s at a fixed gate width of 0.1 s was ave raged from 50 laser shots The standard deviation curves at each delay time were also plotted as a function of wavelength in Fig. 7 1 0 b. The r esult corresponds to the shape simulated in Fig. 7 2 e of the case a 3 i.e., Let s consid er a more general case by using case a 4. As mentioned above, the correlation factor values between two major noise sources can be calculate d by using Eq. 7 7 for each delay time. In Fig. 7 1 0 c as the delay time increas es, a low co rrelation was found That is a t short delay time, a high correlation was observed due to the reduction of the contribution of the shot noise to the total noise compared to the background noise, since it is well known that shot noises are uncorrelated ; at long delay time. On the other hand a low correlation was observed due to a significant decrease of the background intensity.

PAGE 211

211 Further study, as mentioned above was also performed by plotting the relative standard deviation (RSD) as well as the standard deviation (SD) as a function of wavelength (a pixel column by pixel column basis across the CCD array) because the RSD approach is very useful e specially to the different role s played by the limiting noises during the lifetime of the plasma. Figure 7 1 1 sh ows the RSD curves which correspond to Fig. 7 1 0 at the Mn II 259.37 nm line in the Al alloy sample (AA1) for different delay times As the delay time increa ses, the RSD curves, which show no enhancing features at the spectral positions of the analyte li nes, are characterized by an increase observed at the locati on of the an a lyte peak (e.g., at Mn II 259.37 nm) For other instances Figure 7 1 2 and 7 1 3 show the data sets obtained at extreme delay times such as short delay and long delay time s for the Ba II line in a BaCl 2 pe llet and for several analyte peaks in the Al alloy sa mple (S5), respectively. At long delay time s in both samples, the relative standard deviation at the analyte peak (e.g., see the Ba II line at 3.0 s delay time) was characterized by an increase compared to the RSD in the plasma background ; while at short delay time s it show no features in the entire spectral region. At the short delay time in which the strong plasma continuum emission appears due t o Bremsstrahlung and recombination radiation, the RSD value does not reveal any significant difference between line emission and plasma continuum emission, which would suggests some similar correlation in the degree of shot to shot variability over the ent ire spectral range including the Ba ionic line and plasma continuum radiation as shown in Fig. 7 1 2 a A similar result was observed in the data obtained from the Al alloy (S5) sample, as shown in Fig. 7 1 3 Thus, a t the beginning of the plasma the limiting noi se in a measurement may be characterized by case b 2 ( ) s imulated in the

PAGE 212

212 theory section because as shown in Fig. 7 1 3 b Case b 2 is valid only when the signal and background intensities are same magnitude in order to get flat featureless lines in the entire spectral region. However, there was very little difference between the signal and backgro und intensities at short delay time, but not a noticeable difference when compared to that at long delay time of plasma. At the beginning of the plasma, therefore continuum emission i s very dominant, and it can be comparable with line emission. In other words, at early evolution time s one could suppose that the continuum emission and line emission are correlated wi th each other (case b 2 ; i.e., ) In contrast, at long delay time s the continuum emission decays to a negligible level and the fluctuation s in the signal due to the sampling process and the inherent signal noise would be the dominat ing sources of noise. This would suggest that the signal fluctuation at the analyte peak dominate s in comparison with that at the continuum emission; hence this case can be characterized by case 3 ( ). The standard deviation curves i n Fig. 7 1 2 d a nd 7 1 3 d support the above discussion at long delay time s Of course, in this case, the RSD curves depend upon the values of the ratios and in Eq. 7 14b. As discussed in the theory section, i t s hould be noted that in these limiting cases, it is irrelevant whether is equal to 0, +1 or 1. In other words, correlation between the various noises should play no role at long delay time s As discussed above, the background correc tion for getting the net signal is not ideal because in the study, it was assumed that an off peak measurement of the plasma background is equal to the background intensity at the analyte peak ( see Fig. 7 1 ). Thus, the main limitation of the procedure is related to the accuracy of the

PAGE 213

213 background correction. We performed logical tests in order to know how different pixel sizes and positions for a background selection can affect the calculation of a correlation f actor because depends on the shape of the background (whether it is flat or not) and the selection of the background location First of all, the correlation factor was plotted as a fun ction of standard deviation as well as concentration for different pixel sizes, such as a single wavelength (or 1 pixel) at 284.748 nm as well as the one averaged by 20 pixel s as shown in Fig. 7 7 The result for both pixel sizes showed significantly simi l ar values except for 0.004% Mg (see Fig. 7 7 d) Moreover, several regions (e.g., A, B, C and D ) of the background intensity near the peak of Mn II 259.37 nm were selected and compared with a single pixel of the background region A ~ C in order to study the dependence of the background selection on the calculation of a correlation factor in Fig. 7 1 4 Each value calculated shows a slight discrepancy with the overall average value of ~ 0.4, but it is not signifi cant whatever the background regions are or the pixel sizes are in our experiment. However, the line i ntensity may have been influenced by the contribution from the true continuum, such as that which originates from the plasma electrons, to the whole spect ra. Thus, it is important to select appropriate shape and location of the true background. However, even though the accuracy of a correlation factor depends on several factors, this study is valuable in order to show the relative de gree of correlation at the different experimental conditions (e.g., different delay times, laser pulse energies, different concentrations and so on). In addition, Figure 7 1 5 shows the experimental percentage RSD of the net line intensity ( % RSD net ) as a function of the analyte concentration. For the study, the Mg I 285.21 nm line in 7 Al alloy samples and the Zn I 330.26 nm line in 6 NIST brass standards

PAGE 214

214 were used. At low concentrations, the values of % RSD net were relativel y high compared to the high co ncentrations of the analytes. Thus, the background intensity used for correction can has a significant role in the accuracy of the approach at a low concentration. For instance, at low concentration, a correlation factor obtained by a single pixel measurem ent in the background region had a value of 0.46; for the me asurement averaged by 20 pixels. On the other hand, it had a value of 0.014 as shown in Fig. 7 7 d That is, the discrepancy of the correlation factor for the use of the different background s (e.g., different pixel size or location of background) was about 44.6 %. In contrast, the discrepancies at higher concentrations were within 10%. This discrepancy resulted in a high % RSD net at the low concentrati on. Therefore, any minor change in the shape of the background in the selected window and the matrix effect in a various samples will result in an inadequate background correction and a wrong RSD of the net signal, which may be the limitation in the determ ination of % RSD net at low concentrations. Characterization of the type of limiting noises. To provide some additional insight into the nature of spectral noise, a complementary approach aimed at identifying the type of noise affecting the measurement was used, i.e., it consists in repeating the above described procedures with a plot of the log of as a function of the log of the analyte net signal since the S/N rat io is the reciprocal of the RSD T his is equi valent to a plot of the relative standard deviation versus signal. From the results obtained on each sample, the plot of the sign al to noise versus signal (e.g, concentration of the analyte) will provide the information sought

PAGE 215

215 To study the dependence of t he S/N on the analyte signal, log was obtained with the Mg I line at 285.21 nm in the South African Al alloys containing increasing Mg concentration (Fig. 7 1 6 a). The delay time and gate width were fixed at 2.0 s and 0.1 s respec tively The curves show a linear respons e with a slope near 0.5 (slope ~ 0.460). If signal shot noise becomes d ominant, a log log slope is 0.5 because of the square root dependence of signal shot noise on signal, as detailed by Ingle and Crouch [100] Otherwise, if bac k ground and/or signal flicker noise is significant or dominant c ompared to signal shot noise at certain signal levels, a log log slope no longer follow s the square root dependence of signal shot noise on signal. In other words, the presence of signal flicker noise or bac k ground noise reduces the S/N to a value below th at achievable if onl y signal shot noise is present. Analysis of the S/N study revealed an agreement with the results obtained for the RSD study. From the result obtained for Al alloy samples at 2.0 s delay time, the limiting noise of the measurement can b e characterized by signal shot noise (due to the sampling process and the inherent signal shot noise) Otherwise Figure 7 16 b shows the case in which the log log slope in the plot is close to unity NIST brass standards were used for these experiments (at the Zn I 330.3 nm emission line) and t he delay time and gate width used was the same as above. As an illustration of the above, where background noise is dominant, the log log slope is unity [100] Thus, the assumption that all noise sources, in most cases, are totally uncorrelated, is not valid from our results. From the experi mental considerations mentioned in the previous discussion i t is hypothesized that the only noises considered are background noise and signal noise. That is, the dark current noise can be neglected, together with excess detector noise

PAGE 216

216 and readout noise. F or checki ng the hypothesis, we can also use the propagation of errors for two quantities by the method described above such as background noise and dark current noise: (7 19 a ) (7 19b) where is the correlation factor between plasma background noise and dark current noise Thus if the correlation factor is zero it can be assumed that the assumption in our approach is valid i.e., the dark current can be negligible In Eq. 7 19b we assumed that the two noise sources are totally uncorrelated ( i.e., =0) and then compared the values obtained from and with because these values could be obtained experimentally from the data sets If two noise sources are uncorrelated, should be equal to plus Since the correlation between the a nalyte signal and the background depends strongly upon the delay time chosen for the measurement, two extreme delay times, e.g., short delay time and long delay time, were chosen for the study as shown in Fig. 7 1 7 At the short delay time, the two noise sources are totally uncorrelated ; i.e., the values in both sides of Eq. 7 19b are of very similar magnitude ( i.e., = 1.105 10 8 and = 1.106 10 8 ) and is 44 times larger than ; while, at the long delay time, there is some discrepancy between and compared to that at the short delay time, but it is barely significant ( i.e., = 3.058 10 8 and = 2.624 10 8 ), and by 6.7 times. Thus, some

PAGE 217

217 correlation between the background and dark current can exist at long delay time because the background decays significantly. However, in this study, we conclude that the contribution of dark current can be considered negl igible for a reasonable delay time, but it should be checked due to the decrease of the plasma background during the lifetime of the plasma. Finally, this approach may also alert one to the existen ce of self absorption at analyte peaks from the st andard deviation curve. Fig. 7 5 shows that the standard deviation curve appears to scale with the ensemble averaged line profile across the entire spectral window in the Al ally sample (D28) ; otherwise, in the NIST brass sample (1113), it is not the same scale with the line profile For further study a full width at half maximum (FWHM) was determined by fitting a Voigt profile for the Cu I resonance line at 324.7nm for a comparison of the line width betwee n the SD curve and the line profile in each Al alloy and NIST brass sample as shown in Fig. 7 5 At a high concentration of Cu (95.19 % of Cu in NIST brass 1113 ), the FWHM values of line profile and SD curve showed a significant difference by ~ 0.07 nm (se e Fig. 7 5 c and d) In other words, the peak in the SD curve was broadened compared to that in the line profile. In contrast, at a low concentration of Cu (1.76 % of Cu in Al alloy D28 ), the FWHM values in both line profile and SD curve showed the same val ues (about 0.12 nm ) ; hence, the SD curve appears to scale with the line profile. From the se results, we found a very interesting point that it is possible to check for the existence of self absorption using only the SD curve In our study, this trend was a lso proved several times. For instance, the samples, e.g., Al alloy D28 (0.004 % of Mg) and S11 (1.11 % of Mg), containing two extreme concentrations wer e chosen based on ou r previous work (see Fig. 7 18 ); i.e., the mirror

PAGE 218

218 experiment for checking of self a bsorption [166] All results corresponded to those in the case of t he Cu I resonance line That is, the FWHM values in both the SD curve and line profile were different at a high concentration (1.11 % of Mg), but not at a low concentration (0.004 % of Mg). Thus, this approach is very informative for checking for s elf abso rption as well as for examining the limiting noise of measurement. Conclusion s All considerations made in the study relate to the signals and associated standard deviations and to the precision of the measurement; i.e., to the relative standard deviation Within the simplifying assumptions made and the validity of these assumptions, it is argued that the behavior observed by plotting the standard deviation of each spectral element (pixel) versus wavelength, as it results from a series of a number of single shot spectra, taken with a series of samples containing increasing concentration or a single sample in the same spectral window for different delay times, can indeed be informative with respect to the following characteristic aspects in a measurement: I t indicates the precisi on in a LIBS measurement and temporal evolution of plasma It assesses the degree of correlation between the plasma background and the analytical signal. It suggests, even if only approximately, the identification of the limiting no ise and to the different role s played by the limiting noises for temporal evolution of plasma as well as different concentrations. On the other hand, while being informative for the limiting noise in a measurement, the above considerations can also provid e some information about the type of noise present in a measurement. O ne can concluded that the measurement is affected by shot noise, since it is well known that s h ot noises are uncorrelated. In addition, a

PAGE 219

219 complementary approach aimed at identifying the type of noise affecting the measurement was also used. T he above described procedure using several samples containing increasing concentration of an analyte are very similar. From the results obtained on each sample, the plot of the S/N versus signal (or c oncentration) provides the information sought. Needless to say, this is equivalent to a plot of the RSD versus signal (concentration), since the S/N ratio is the reciprocal of the RSD. The experimental results in our study are characterized by the followi ng features: The correlation between the peak signal and the background depend s strongly upon the delay ti me chosen for the measurement. In the SD and RSD curve approach for instance, it was observed that there is no correlation between noise source s at l ong delay time; otherwise, there is some similar correlation between atomic emission and plasma background at short delay time. The correlation also depends upon the concentration of an analyte. At high concentrations, noise sources contributed around the emission line are strongly correlated with each other. The degree of correlation between major noise sources in LIBS measurement was calculated, as the correlation factor It allows quantitative analysis for the degree of correlat ion under different experimental conditions (e.g., different delay times, laser pulse energies, different concentrations and so on ) The accuracy of this approach can be limited in the background correction for getting the net signal because in the study, it was assumed that an off peak measurement s of the background ( ) is equal to the background measurement under the peak of the emission line ( ). Thus, it is important to select appropriate shape and location of the true background, in particular in the case of weak background s From the result of the correlation factor obtained, the high degree of correlation between noise sources is related to the reduction of the contribution of the sh ot noise to the total noise compared to background noise. Thus, it can be explained that at short delay time or high concentration, a high correlation was observed due to the reduction of the contribution of the shot noise by high background intensity. Fr om above results, the assumption that all noise sources, i n most cases, are totally uncorrelated, is not valid. In addition, f rom the plot of log (S/N) versus log (s), b oth signal shot noise and signal flicker noise / or background noise may be influencing each other on the measurement.

PAGE 220

220 This approach hints the existence of self absorption by comparison of a full width at half maximum (FWHM) of the line profile with the associated SD curve.

PAGE 221

221 Figure 7 1 An ex ample of the description of net signal: i.e., the simplest signal measurement consists of the peak intensity ( ) at the central wavelength of the analyte line and an off peak measurement of the background at a single position ( )

PAGE 222

222 Figure 7 2 In standa rd deviation (SD) limiting cases, simulated shape s of the plot SD versus wavelength.

PAGE 223

223 Figure 7 3 In relative standard deviation (RSD) limiting cases, simulated shape s of the plot RSD versus wavelength.

PAGE 224

224 Figure 7 4 (a) 3D LIBS spectra for 55 lase r shots in an Al alloy (D28) sample and (b) a 55 shot ensemble averaged LIBS spectrum (black line) with both associated standard deviation (red line) and relative standard deviation (blue line). Used gate delay time and gate width are 2.0 s and 0.1 s, re spectively.

PAGE 225

225 Figure 7 5 Zn and Cu atomic emission lines for both (a and c) 55 single shot ensemble averaged spectra and (b and d) associated standard deviation cu rves at the same spectral range in Al alloy sample (D28) and NIST brass standard (1113) r espectively In both samples, the settings on the detection system were 2.0 us and 0.1 s for the gate delay time and gate width, respectively Each full width at half maximum value of Cu I resonance line at 324.7 nm was obtained by fitting a Voigt profile (see the blue arrows).

PAGE 226

226 Figure 7 6 (a and b) 55 single shot LIBS spectra at the peak of Zn I 330.3 nm in both Al alloy sample (D28) and NIST brass standard (1113), respectively (The used gate delay time and gate width were 2.0 s and 0.1 s, respecti vely.) Each correlation factor between two major noise sources was calculated at the peak of Zn I 330.3 nm by using Eq. 7 7 In Al alloy sample (D28), is 0.527, while in NIST brass standard (1113), is 0.871.

PAGE 227

227 Figure 7 7 (a and b) LIBS spectra for the several Mg com positions in Al alloy samples ( S quare box in dicates the region for zoom in) and (c and d) e xperimentally calculated correlation factor as a function of both concentration a nd standard deviation of the background measured near Mg I 285.21 nm respectively Either a single pixel or 20 pixels measurement was used for the determination of the standard deviation of the background measured.

PAGE 228

228 Figure 7 8 (a) LIBS spectra (ensembl e averaged) showing the Mg I and II lines and Al II line and (b) standard deviation curves for 50 laser shots in 6 Al alloys samples. (c) Relative standard deviation (RSD) curves as calculated from the quotient of the standard deviation (square box in dicat es the region for zoom in) (d) RSD curves showing the increase of Mg composition.

PAGE 229

229 Figure 7 9 (a) LIBS spectra (ensemble averaged) showing the Cu I and Zn I lines and (b) standard deviation curves for 50 laser shots in 7 NIST brass standards. (c) Relat ive standard deviation (RSD) curves as calculated from the quotient of the standard deviation (square box in dicates the region for zoom in) (d) RSD curves showing the increase of Cu composition.

PAGE 230

230 Figure 7 1 0 (a and b) LIBS spec tr a and standard deviatio n curves as a function of wavelength for different delay times at Mn II 259.37 nm in Al alloy ( AA1 ) sample (c) The plot of correlation factor versus delay time.

PAGE 231

231 Figure 7 11 The plot of a relative standard deviation versus wave length for different delay times at Mn II 259.37 nm in Al alloy (603) sample

PAGE 232

232 Figure 7 12 (a and b) The ensemble averaged spectra for Ba II in BaCl 2 pallet at 0.5 us and 3.0 us delay times, respectively with each RSD curve and (c and d) associated S D curves.

PAGE 233

233 Figure 7 13 The ensemble averaged spectra for several elements in Al alloy (S5) sample at (a) 0.5 us and (c) 5.0 us delay times, respectively with each RSD curve (blue line) and (c and d) associated SD curves.

PAGE 234

234 Figure 7 1 4 (a ) LIBS spectru m at 2.0 us delay time in Al alloy (AA1) sample including 0.540 % of Mn and (b) the standard deviation cu rve only near Mn II 259.37 nm line. (c) LIBS spectrum showing Mn ionic emission line at 259.37 nm The region A, B, C and D indicate the region selecte d for RMS noise calculation. (d) Experimental values of the correlation factor as a function of standard deviation of the b ackground measured by 10 pix els (the region A,B ,C and D : black squares ) and single pixel (the region A~C, b lue dots).

PAGE 235

235 Figu re 7 1 5 Experimental percent RSD of the net signal ( % RSD net ) as a functi on of the analyte concentration (a) at Mg I 285.21 nm line in 7 Al alloy samples an (b) at Zn I 330.26 nm line in 6 NIST brass standards.

PAGE 236

236 Figure 7 16 The log of the signal to noise (S/N) ratio as a function of the log of net signal for (a) Mg I 285.21 nm in 5 Al alloy samples and (b) Zn I 330.26 nm in 7 NIST brass standards.

PAGE 237

237 Figure 7 1 7 (a and c ) LIBS spectr a and (c and d) associated SD curves at both 0.5 us and 3.0 s delay time s, respectively in Al alloy ( SM10 ) sample

PAGE 238

238 Figure 7 18 (a and b) LIBS s pectra and associated SD curves at Mg I 285.21 nm in the samples containing two extreme concentrations such as Al alloy D28 (0.004 % of Mg) and S11 (1.11 % of Mg).

PAGE 239

239 T able 7 1. Factors affecting quantitative analysis using LIBS. Source Factor Comments Laser Laser pulse energy, laser pulse power, repetition rate Typically stable to within a few percent for constant temperature operation Detector Detector gain Keep constant or calibrate response if gain in changed Linearity of response Operate in region of linear response or change gain to maintain linearity Sampling parameters Lens to sample distance May be maintained through an automated focusing system; less a problem for longer focal lengths ; use of a collimated beam to form the plasma can minimize effects Changes in optical path transmission to/from sample Change of atmosphere above sample Absorption/scattering of laser pulse over optical path to sample b y gases and aerosols Gas pressure and composition affect ablation and plasma properties Sample Uniformity of composition Uniformity of surface Sufficient averaging to obtain representative sample Sufficient averaging to obtain representative sample Chemical matrix effects Physical matrix effects Under certain experimental conditions, effect may be reduced Under certain experimental conditions, effect may be reduced

PAGE 240

240 Table 7 2 Elemental percentage composition of South African aluminum alloy standards disks (APEX Smelter Co., South Africa). Table 7 3. Elemental percentage composition of NIST brass standards Note: Certified values are obtained from the NIST standard reference materials database http://ts.nist.gov/measurementservices/referencematerials/index.c fm E lement D28 V14 D33 B8 AA3 S4 R14 Z8 SM10 Al 81.55 86.74 84.92 87.98 69.14 83.79 79.59 78.79 84.67 Si 9.66 6.2 8.54 2.33 17 1.03 14 0.84 2.92 Mg 0.004 0.025 0.038 0.076 0.2 0.35 0.87 1.27 1.08 Cu 1.76 4.05 2.89 6.95 8 2.64 2.05 16.05 2.8 Zn 3.6 0.42 0.59 0.52 3.2 10.9 0.48 0.79 5.45 Fe 0.98 0.9 1.15 0.8 1.77 0.119 0.63 1.09 1.96 Mn 0.59 0.58 0.4 0.4 0.21 0.38 0.92 0.26 0.295 Ni 0.43 0.33 0.5 0.5 0.106 0.18 0.97 0.53 0.065 Ti 0.033 0.17 0.055 0.16 0 .078 0.12 0.16 0.17 0.055 Cr 0.21 0.18 0.047 0.17 0.1 0.13 0.11 0.15 0.2 Sn 0.3 0.28 0.048 0.155 0.12 0.15 0.12 0.26 Pb 0.34 0.14 0.165 0.08 0.13 0.1 0.245 Element AA1 S5 S11 SM1 SM9 Al 69.58 74.95 89.20 96.46 85.34 Si 14.60 2.240 0.450 0.390 1.690 Mg 0.170 0.090 1.110 1.000 0.430 Cu 5.70 5.750 0.980 0.970 3.000 Zn 5.90 14.94 6.850 0.500 3.700 Fe 1.73 0.760 0.570 0.410 3.700 Mn 0.540 0.550 0.500 0.110 0.760 Ni 0.600 0.210 0.100 0.050 0.200 Ti 0.110 0.065 0.070 Cr 0.280 0.110 0.115 0.380 Sn 0.500 0.110 0.310 Pb 0.380 0.120 0.320 E lement 1107 1108 1110 1111 1112 1113 1114 1115 1116 Cu 61.210 64.950 84.590 87.140 93.380 95.030 95.450 87.960 90.370 Zn 37.340 34.420 15.200 12.810 6.300 4.800 3.470 11.730 9.440 Fe 0.037 0.050 0.033 0.010 0.070 0.043 0.017 0.130 0.046 Mn 0.025 Ni 0.098 0.033 0.053 0.022 0.100 0.057 0.021 0.074 0.048 P 0.009 0.008 0.009 0.005 0.008 Pb 0.180 0.06 3 0.033 0.013 0.057 0.026 0.012 0.013 0.042 Sn 1.040 0.390 0.051 0.019 0.120 0.064 0.027 0.100 0.044

PAGE 241

241 Appendix Glossary Average total counts due to dark signal, plasma background and signal, measured at the center of the line (line peak). Average total counts due to dark signal background and signal, spectrally integrated over the line width. Average net counts due to signal, measured at the center of the line (line peak). Average net counts due to signal, spectrally integra ted over the line width. Average total counts due to plasma continuum with dark signal measured at the center of line (line peak) Average total counts due to plasma continuum with dark signal, spectral ly integrated over the line width. Average counts due to plasma co ntinuum measured at the center of the line (line peak). Average counts due to plasma continuum, spectrally integrated over the line width Average counts due to dark signal measured at the center of line (line peak). Average counts due to dark current, spectrally integrated over the line width. Average total counts due to plasma continuum with dark signal measured at a wavelength in the vicinity of the line (off peak), but not in the line wings. Average total counts due to plasma continuum with dark current, spectrally int egrated over the same number of pixels used for but measured in the vicinity of the line (off peak), and not including the line wings. Average counts due to plasma continuum measured at a waveleng th in the vicinity of the line (off peak), but not in the line wings. Average counts due to plasma continuum, spectrally integrated over the same number of pixels used for

PAGE 242

242 but measured in the vicinity of the line (off peak), but not including the line wings. Average counts due to dark current measured at a wavelength in the vicinity of the line (off peak), but not in the line wings. Average counts due to dark current, spectrally integrated over the same number of pixels used for but measured in the vicinity of the line (off peak), and not including the line wings.

PAGE 243

243 CHAPTER 8 CONCLUSIO N AND FUTURE WORK Summary The general scope of my research involved largely two aspects related to the fundamental study and the analytical characterization of the technique Laser Induced Breakdown Spectroscopy (LIBS). Th is project revisit ed and investi gate d in more details some of the conditions and/ or assumptions commonly made in LIBS, such as the existence of local thermodynamic equilibrium (LTE) and of optically thin plasma condition s, i.e., the absence of the phenomenon of self absorption Moreover double pulse LIBS was also studied with the aim of understanding the relative importance of the factors concurring to the enhancement of the emission line intensity as well as the underlying physical mechanism. Finally, the spectral fluctuation approach, a novel way of data analysis in LIBS, was also investigated and proven to be very informative to determine the type of noise present in a measurement as well as the limiting noise of the measurement. Line to continuum intensity ratio method. Most studies i n LIBS measurements have been performed under the assumption of the existence of LTE conditions. The LTE state is a good approximation in describing the plasma conditions, but the reliability of the hypothesis is heavily dependent on various experimental f actors such as the temporal evolution of the plasma, and the spatial inhomogeneities associated with its transient behavior. Thus, it is essential to investigate the plasma parameters as thoroughly as possible in order to determine the existence of LTE con ditions or the extent of departure from it. To this purpose, a line to continuum intensity ratio method discussed in Chapter 4, was used for the evaluation of LTE. In this approach, the

PAGE 244

244 theoretical ratio between the intensity of selected transitions, cons idered being optically thin, and the underlying spectral continuum were used (see Eq. 4 6) In these expressions, the excitation temperature and the electron temperature were purposely kept different from each other. Experimentally, the plasma excitation t emperature, T exc was obtained from a conventional Boltzmann plot /or Saha Boltzmann plot and the ratio between the spectrally integrated line intensity and the continuum intensity was measured. By inserting these two experimental values into the theoretic al expression in Eq. 4 6 one could check whether the electron temperature derived in this way was equal or different from the excitation temperature provided by the Boltzmann plot therefore assessing any deviation from LTE conditions It was evident from the results that LTE is a good approximation in describing the plasma conditions usually after a delay time from the onset of the plasma of 2.0 s. In addition, it was found that the delay time necessary for achieving LTE was reduced in the case of the io nic species compared to that of the atomic species, due to the high lying energy level of ionic species. Self absorption. In LIBS, emission measurements are often affected by the phenomenon of self absorption i.e., the plasma conditions are optically t hick. Various ways of accomplishing this task are described in the plasma literature [29, 53, 81, 118 126] My research proposes the application of an old method [128] for quantifying the effect of self absorption on atom ic and ionic emission lines Chapter 5 illustrates this method, which is sim ple and quick to implement, does not need either changing the sample concentration or calculating a curve of growth [53] and uses an external mirror to double the optical path length of the plasma emission in direction of the

PAGE 245

245 monochromator. The calculation of the so called duplication factor as well as the comparison of the line profiles obtained wi th and without the mirror allowed not only to prove the existence of the self absorption effect but also to apply a correction factor and to retrieve the original profile Spectroscopic study of the factors concurring to the intensity enhancement in double pulse LIBS. One of the most attractive approaches to improve the LIBS sensitivity and reproducibility without losing its non selective behavior is to use the double pulse excitation scheme. For example, the matrix matched requirement, which is a well know n limitation of nanosecond laser ablation, can be partially reduced by using double pulse scheme. In Chapter 6 in agreement with the results of the literature, we observed a significant improvement of the signal to noise (S/N) ratio in the orthogonal doub le pulse (DP) scheme compared to the LIBS single pulse (SP) scheme. Several mechanisms may be responsible for the observed enhancement and a number of suggestions addressing the mechanisms of enhancement of the double pulse LIBS signal have been proposed. However, the mechanisms of the double pulse enhancement are not completely understood and the topic is still the subject of investigation In our study, two different schemes in orthogonal double pulse configuration (i.e., pre ablation air spark and rehe ating double pulse scheme) were optimized with the aim of achieving the largest enhancements. A novel spectroscopic approach to characterize the factors concurring to the enhancement was also performed in order to understand its physical mechanisms. The a pproach is based on the theoretical relation between the logarithm of the ionic and neutral line enhancements as a function of the excitation

PAGE 246

246 energy of the lines investigated (as shown in Eq. 6 11) Such approach gives information at first glance on the ch ange of plasma temperature, number density and neutral/or singly ionized fraction of the atoms of the analyte in the plasma when the sample irradiation conditions on the sample change from SP to DP. Noise analysis in LIBS In all analytical methods, and therefore in LIBS as well, the precision of a measurement is limited by noise/or fluctuation in the measured signals. Thus, the study of the noise in LIBS spectra is essential for understanding these fluctuations and their effect on the results. In Chapt er 7, we have simulated many possible limiting noise situations present in a LIBS measurement by observing the behavior of the plots of the standard deviation and relative standard deviation resulting from many single shot spectra on a pixel by pixel (wave length) basis. Moreover, a p ossible correlation between the noise in the background and the noise in the signal has been also studied. The degree of correlation between these noise sources in LIBS measurement was calculated experimentally and then the rel evance of the noises was evaluated by the correlation factor Finally, a complementary approach for identifying the type of noise affecting the measurement was also used, as detailed by Ingle and Crouch [100] This approach relies on the slope of the plots of the S/N as a function of the log of the signal (co ncentration). This procedure is equivalent to a plot of the relative standard deviation versus signal, since the S/N ratio is the reciprocal of the RSD. By carefully analyzing the results, it was clearly shown that the noise type as well as the limiting no ise source strongly depends on the delay time and on the measuring gate width, i.e., on the temporal evolution of plasma. Moreover, our results also indicated a

PAGE 247

247 temporal dependence of the degree of correlation between the line emission and the underlying b ackground continuum. Future Work The verification of the existence of local thermodynamic equilibrium by the line to continuum intensity ratio method should be continued and applied to different LIBS set ups and irradiation geometries. In fact, the reliab ility of the LTE assumption is heavily dependent not only on the temporal evolution of plasma, but also to various experimental factors in LIBS measurement, including the laser pulse energies and the environment. Similarly, the application of the mirror a pproach described in Chapter 5 for studying self absorption effects can be extended to double pulse LIBS as well. To the self absorption in double pulse LIBS. In our pr eliminary double pulse work, such effect was indeed observed for several lines, which were optically thin in the corresponding single pulse experiment. By applying the same correction procedure outlined in Chapter 5 the non linearity in the calibration cu rves (due to the effect of self absorption) can be accounted for, thus extending the linear dynamic range of the technique. Finally, the spectral fluctuation approach should be applied to a large variety of sample targets, illumination conditions and acqu isition settings (delay time and measuring gate width), as well as to different environments (air, other gases, reduced pressures, etc.). As a general conclusion, it appears that there is still ample room for improvement not only in the theoretical modeli ng of the LIBS pla smas, but also in devising more refined experimental set ups and no vel approaches to data analysis

PAGE 248

248 LIST OF REFERENCES [1] Cremers, D. A.; Radziemski, L. J. Handbook of laser induced breakdown spectroscopy John Wiley & Sons, Ltd 2006 [2] Miziolek, A. W. P., V.; Schechter, I. Laser Induced Breakdown spectroscopy:Fundamentals and Applications Cambridge, UK; Cambridge University Press 2006 [3] Maiman, T. H. Nature 1960 187 493 494. [4] Radziemski, L. J. Spectrochim ica Acta, Part B: Atomic Spectroscopy 2002 57B 1109 1113. [5] Brech, F.; Cross, L. Applied Spectroscopy 1962 16 59 62. [6] Maiman, T. H. British Communications and Electronics 1960 7 674 5. [7] Debras Guedon, J.; Liodec, N. Bulletin de la Societe Francaise de Ceramique 1963 No. 61 61 8. [8] Maker, P. D.; Terhune, R. W.; Savage, C. M. Proceedings of the 3rd International Conference on Quantum Electronics, Paris 1964 2 1559. [9] Runge, E. F.; Minck, R. W.; Bryan, F. R. Spectrochimica Acta 1964 20 733 6. [10] Raizer, Y. P. Breakdown and heating of gases under the influence of a laser beam 1966 [11] Afanas'ev, Y. V.; Krokhin, O. N. Soviet Physics JETP 1967 25 639 645. [12] Biberman, L. M.; Norman, G. E. Uspekhi Fizicheskikh Nauk 1967 91 193 246. [13] Buravlev, Y. M.; Nadezhda, B. P. Atom. spektroskopiya i spektr. analiz. 1974 292 5.

PAGE 249

249 [14] Raizer, Y. P. Laser induced Discharge Phenomena Consultants Bureau: New York 1977 [15] Cerrai, E.; Trucco, R. Energia Nucleare (Milan) 1968 15 581 7. [16] Marich, K. W.; Carr, P. W.; Treytl, W. J.; Glick, D. Analytical Chemistry 1970 42 1775 9. [17] Lencioni, D. E. Applied Physics Letters 1973 23 12 14. [18] Belyaev, E. B.; Godlevskii, A. P.; Kopytin, Y. D. Kvantovaya Elektronika (Moscow) 197 8 5 2594 601. [19] Edwards, A. L.; Fleck Jr, J. A. Journal of Applied Physics 1979 50 4307 4313. [20] Ivanov, A. K.; Kopytin, Y. D. Soviet Journal of Quantum Electronics 1982 12 355 357. [21] Loree, T. R.; Radziemski, L. J. Plasma Chemistry and Pla sma Processing 1981 1 271 9. [22] Radziemski, L. J.; Loree, T. R. Plasma Chemistry and Plasma Processing 1981 1 281 93. [23] Cremers, D. A. Applied Spectroscopy 1987 41 572 9. [24] Cremers, D. A.; Archuleta, F. L.; Martinez, R. J. Spectrochimica A cta, Part B: Atomic Spectroscopy 1985 40B 665 79. [25] Cremers, D. A.; Radziemski, L. J. Analytical Chemistry 1983 55 1252 6. [26] Cremers, D. A.; Radziemski, L. J. Applied Spectroscopy 1985 39 57 63. [27] Cremers, D. A.; Radziemski, L. J.; Loree, T. R. Applied Spectroscopy 1984 38 721 9.

PAGE 250

250 [28] Radziemski, L. J.; Cremers, D. A.; Loree, T. R. Spectrochimica Acta, Part B: Atomic Spectroscopy 1983 38B 349 55. [29] Radziemski, L. J.; Loree, T. R.; Cremers, D. A.; Hoffman, N. M. Analytical Chemistr y 1983 55 1246 52. [30] Belyaev, E. B.; Godlevskii, A. P.; Kopytin, Y. D.; Krasnenko, N. P.; Muravskii, V. P.; Shamanaeva, L. G. Pis'ma v Zhurnal Tekhnicheskoi Fiziki 1982 8 333 7. [31] Kitamori, T.; Yokose, K.; Suzuki, K.; Sawada, T.; Gohshi, Y. Jap anese Journal of Applied Physics, Part 2: Letters 1988 27 L983 L985. [32] Ko, J. B.; Sdorra, W.; Niemax, K. Fresenius Zeitschrift Fur Analytische Chemie 1989 335 648 651. [33] Lawrenz, J.; Niemax, K. Spectrochimica Acta Part B Atomic Spectroscopy 19 89 44 155 164. [34] Leis, F.; Sdorra, W.; Ko, J. B.; Niemax, K. Mikrochimica Acta 1989 2 185 199. [35] Leis, F.; Ko, J. B.; Niemax, K. Fresenius Zeitschrift Fur Analytische Chemie 1989 334 649 649. [36] Quentmeier, A.; Sdorra, W.; Niemax, K. Fresen ius Zeitschrift Fur Analytische Chemie 1989 334 650 650. [37] Sdorra, W.; Quentmeier, A.; Niemax, K. Mikrochimica Acta 1989 2 201 218. [38] Ko, J. B.; Sdorra, W.; Niemax, K. Fresenius' Zeitschrift fuer Analytische Chemie 1989 335 648 51. [39] Leis F.; Sdorra, W.; Ko, J. B.; Niemax, K. Mikrochimica Acta 1989 2 185 99. [40] Adrain, R. S.; Watson, J. Journal Of Physics D Applied Physics 1984 17 1915 [41] Radziemski, L. J.; Cremers, D. A., 1989 pp.437.

PAGE 251

251 [42] Radziemski, L. J. Microchemical Jour nal 1994 50 218 34. [43] Lee, Y. I.; Song, K.; Sneddon, J. Lasers in Analytical Atomic Spectroscopy 1997 197 235. [44] Rusak, D. A.; Castle, B. C.; Smith, B. W.; Winefordner, J. D. Critical Reviews in Analytical Chemistry 1997 27 257 290. [45] To gnoni, E.; Palleschi, V.; Corsi, M.; Cristoforetti, G. Spectrochimica Acta, Part B: Atomic Spectroscopy 2002 57B 1115 1130. [46] Lee, W. B.; Wu, J.; Lee, Y. I.; Sneddon, J. Applied Spectroscopy Reviews 2004 39 27 97. [47] Wallis, F. J.; Chadwick, B. L.; Morrison, R. J. S. Applied Spectroscopy 2000 54 1231 1235. [48] Cremers, D. A.; Barefield, J. E.; Koskelo, A. C. Applied Spectroscopy 1995 49 857 860. [49] Lazzari, C.; De Rosa, M.; Rastelli, S.; Ciucci, A.; Palleschi, V.; Salvetti, A. Laser and Particle Beams 1994 12 525 30. [50] Ciucci, A.; Corsi, M.; Palleschi, V.; Rastelli, S.; Salvetti, A.; Tognoni, E. Applied Spectroscopy 1999 53 960 964. [51] Mao, X. L. L.; Shannon, M. A.; Fernandez, A. J.; Russo, R. E. Applied Spectroscopy 1995 49 1054 1062. [52] Castle, B. C.; Talabardon, K.; Smith, B. W.; Winefordner, J. D. Applied Spectroscopy 1998 52 649 657. [53] Gornushkin, I. B.; Anzano, J. M.; King, L. A.; Smith, B. W.; Omenetto, N.; Winefordner, J. D. Spectrochimica Acta, Part B: Atomic Spectroscopy 1999 54B 491 503. [54] Piepmeier, E. H.; Malmstadt, H. V. Analytical Chemistry 1969 41 700.

PAGE 252

252 [55] Scott, R. H.; Strasheim, A. Spectrochimica Acta Part B: Atomic Spectroscopy 1970 25 311. [56] Cremers, D. A.; Radziemski, L. J.; Loree, T. R. Applied Spectroscopy 1984 38 721. [57] Anglos, D.; Couris, S.; Fotakis, C. Applied Spectroscopy 1997 51 1025 1030. [58] Georgiou, S.; Zafiropulos, V.; Tomari, V.; Fotakis, C. Laser Physics 1998 8 307 312. [59] Georgiou, S.; Zafiropulos, V.; Anglos, D.; Balas, C.; Tornari, V.; Fotakis, C. Applied Surface Science 1998 127 738 745. [60] Pallikaris, I. G.; Ginis, H. S.; Kounis, G. A.; Anglos, D.; Papazoglou, T. G.; Naoumidis, L. P. Journal Of Refractive Surgery 1998 14 655 660. [61] Eppler, A. S.; Cremers, D. A.; Hickmott, D. D.; Ferris, M. J.; Koskelo, A. C. Applied Spectroscopy 1996 50 1175 1181. [62] Miles, B.; Cortes, J. Field Analytical Chemistry and Technology 1998 2 75 87. [63] Theriault, G. A.; Bodensteiner, S.; Lieberman, S. H Field Analytical Chemistry and Technology 1998 2 117 125. [64] Milan, M.; Vadillo, J. M.; Laserna, J. J. Journal Of Analytical Atomic Spectrometry 1997 12 441 444. [65] Boulmer Leborgne, C.; Hermann, J.; Dubreuil, B. Plasma Sources Science & Techno logy 1993 2 219 226. [66] Callies, G.; Berger, P.; Hugel, H. Journal of Physics D: Applied Physics 1995 28 794 806. [67] Wen, S. B.; Mao, X.; Greif, R.; Russo, R. E. Journal of Applied Physics 2007 101 123105

PAGE 253

253 [68] Yalcin, S.; Crosley, D. R.; Smit h, G. P.; Faris, G. W. Applied Physics B: Lasers and Optics 1999 68 121 130. [69] Schittenhelm, H.; Callies, G.; Berger, P.; Hgel, H. Applied Surface Science 1997 109 110 493. [70] Singh, J. P.; Thakur., S. N. Laser induced breakdown spectroscopy E lsevier: Amsterdam; Bostor; London 2007 [71] Wen, S. B.; Mao, X. L.; Greif, R.; Russo, R. E. Journal Of Applied Physics 2007 101 023115 [72] Ng, C. W.; Ho, W. F.; Cheung, N. H. Applied Spectroscopy 1997 51 976 983. [73] Russo, R. E. Applied Spectro scopy 1995 49 14A 28A. [74] Thorne, A. P. Spectrophysics : London, Chapman and Hall; New York, Wiley, 1974 402p [75] Aguilera, J. A.; Aragon, C. Spectrochimica Acta Part B Atomic Spectroscopy 2008 63 793 799. [76] Griem, H. R., Plasma Spectroscopy ; McGraw Hill, New York, 1964 580 p [77] Lochte Holtgreven, W.; Editor. Plasma Diagnostics 1968 [78] Thorne, A. P.; Litzn, U.; Johansson, S. Spectrophysics: Principles and Applications Berlin; New York: Springer, c1999. [79] Omenetto, N.; Winefordner, J. D.; Alkemade, C. T. J. Spectrochimica Acta, Part B: Atomic Spectroscopy 1975 30B 335 41. [80] Physics Reports Review Section of Physics Letters 1999 316 339 401. [81] El Sherbini, A. M.; El Sherbini, T. M.; Hegazy, H.; Cristoforetti, G.; Legnaioli, S.; Palleschi, V.; Pardini, L.; Salvetti, A.; Tognoni, E. Spectrochimica Acta Pa rt B: Atomic Spectroscopy 2005 60 1573 1579.

PAGE 254

254 [82] Friedjung, M.; Muratorio, G. Astronomy and Astrophysics 1987 188 100 8. [83] Kastner, S. O.; Kastner, R. E. Journal of Quantitative Spectroscopy & Radiative Transfer 1990 44 275 88. [84] Irons, F. E. Journal Of Quantitative Spectroscopy & Radiative Transfer 1979 22 1 20. [85] Habib, A. A. M.; El Gohary, Z. Journal Of Quantitative Spectroscopy & Radiative Transfer 2002 72 341 347. [86] Pestehe, S. J.; Tallents, G. J. Journal Of Quantitative Spe ctroscopy & Radiative Transfer 2002 72 853 878. [87] Alkemade, C. T. J.; Hollander, T.; Snelleman, W.; Zeegers, P. T. T. International Series in Natural Philosophy, Vol. 103: Metal Vapors in Flames 1982 [88] Boumans, P. W. J. M. Analytical Spectroscopy Series 1972 1, Pt. 2 1 254. [89] Cowan, R. D.; Dieke, G. H. Reviews of Modern Physics 1948 20 418 55. [90] Fujimoto, T. Plasma Spectroscopy Oxford University press 2004 [91] Huddlestone, R. H.; Leonard, S. L.; Editors. Plasma Diagnostic Techniques (Pure and Applied Physics, Vol. 21) 1965 [92] Omenetto, N.; Winefordner, J. D. Progress in Analytical Atomic Spectroscopy 1979 2 1 183. [93] Bye, C. A.; Scheeline, A. Applied Spectroscopy 1993 47 2022. [94] Liu, H. C.; Mao, X. L.; Yoo, J. H.; Russo R. E. Spectrochimica Acta, Part B: Atomic Spectroscopy 1999 54B 1607 1624. [95] Bastiaans, G. J.; Mangold, R. A. Spectrochimica Acta, Part B: Atomic Spectroscopy 1985 40B 885 92.

PAGE 255

255 [96] Fisher, V.; Bernshtam, V.; Golten, H.; Maron, Y. Physical Review A: Atomic, Molecular, and Optical Physics 1996 53 2425 32. [97] Nicholson, J. P. Plasma Physics and Controlled Fusion 1989 31 1433 41. [98] Burgess, A.; Summers, H. P. Monthly Notices of the Royal Astronomical Society 1987 226 257 72. [99] Demtr der, W. Laser Spectroscopy: Basic Concepts and Instrumentation 2 nd edition, Springer 1996 [100] Ingle Jr, J. D.; Crouch, S. R. Spectrochimical Analysis Prentice Hall 1988 [101] Griem, H. R. Physical Review 1963 131 1170 1176. [102] Griem, H. R. Prin ciples of Plasma Spectroscopy 1997 [103] Barthelemy, O.; Margot, J.; Laville, S.; Vidal, F.; Chaker, M.; Le Drogoff, B.; Johnston, T. W.; Sabsabi, M. Applied Spectroscopy 2005 59 529 536. [104] Calzada, M. D. Memorie della Astronomica Italiana Suppleme nt 2005 7 198 207. [105] Capitelli, M.; Capitelli, F.; Eletskii, A. Spectrochimica Acta, Part B: Atomic Spectroscopy 2000 55B 559 574. [106] Kruger, C. H.; Owano, T.; Gordon, M.; Laux, C. Pure and Applied Chemistry 1992 64 607 13. [107] Sola, A.; Calzada, M. D.; Gamero, A. Journal of Physics D: Applied Physics 1995 28 1099 110. [108] Zeng, X.; Mao, S. S.; Liu, C.; Mao, X.; Greif, R.; Russo, R. E. Spectrochimica Acta, Part B: Atomic Spectroscopy 2003 58B 867 877. [109] Moon, H. Y.; Omenetto, N .; Smith, B. W.; Winefordner, J. D. In NORTH AMERICAN SYMPOSIUM LIBS 2009 : New Orleans, LA., USA, 2009

PAGE 256

256 [110] Amoruso, S. Applied Physics A: Materials Science & Processing 1999 69 323 332. [111] Drawin, H. W.; Felenbok, P. Data for Plasmas in Local Ther modynamic Equilibrium 1965 [112] Torres, J.; Jonkers, J.; van de Sande, M. J.; van der Mullen, J. J. A. M.; Gamero, A.; Sola, A. Journal of Physics D: Applied Physics 2003 36 L55 L59. [113] Pupyshev, A. A.; Semenova, E. V. Spectrochimica Acta, Part B: Atomic Spectroscopy 2001 56B 2397 2418. [114] McWhirter, R. W. P. Plasma Diagnostic techniques New York Academic 1965 [115] Fujimoto, T.; McWhirter, R. W. P. Physical Review A 1990 42 6588 6601. [116] Herrera, K. K.; Tognoni, E.; Omenetto, N.; Smit h, B. W.; Winefordner, J. D. Journal Of Analytical Atomic Spectrometry 2009 24 413 425. [117] Galmed, A. H.; Harith, M. A. Applied Physics B: Lasers and Optics 2008 91 651 660. [118] Simeonsson, J. B.; Miziolek, A. W. Applied Optics 1993 32 939 47 [119] Sabsabi, M.; Cielo, P. Applied Spectroscopy 1995 49 499 507. [120] Hermann, J.; Boulmer Leborgne, C.; Hong, D. Journal of Applied Physics 1998 83 691 696. [121] Gornushkin, I. B.; Stevenson, C. L.; Smith, B. W.; Omenetto, N.; Winefordner, J. D. Spectrochimica Acta, Part B: Atomic Spectroscopy 2001 56B 1769 1785. [122] Lazic, V.; Barbini, R.; Colao, F.; Fantoni, R.; Palucci, A. Spectrochimica Acta Part B: Atomic Spectroscopy 2001 56 807 820. [123] Aragon, C.; Bengoechea, J.; Aguilera, J. A. Spectrochimica Acta Part B Atomic Spectroscopy 2001 56 619 628.

PAGE 257

257 [124] Bulajic, D.; Corsi, M.; Cristoforetti, G.; Legnaioli, S.; Palleschi, V.; Salvetti, A.; Tognoni, E. Spectrochimica Acta Part B: Atomic Spectroscopy 2002 57 339 353. [125] Amamou, H.; Bois, A.; Ferhat, B.; Redon, R.; Rossetto, B.; Ripert, M. Journal of Quantitative Spectroscopy & Radiative Transfer 2003 77 365 372. [126] Ribiere, M.; Cheron, B. G.; Bultel, A. High Temperature Material Processes (Redding, CT, United States) 2008 12 109 120. [127] Aguilera, J. A.; Bengoechea, J.; Aragon, C. Spectrochimica Acta Part B Atomic Spectroscopy 2003 58 221 237. [128] Gouy, L. G. Comptes Rendus 1879 88 418 421. [129] Harrison, J. A. Proceedings of the Physical Society, London 1959 73 841 8. [130] Jentschke, H.; Schumacher, U.; Hirsch, K. Contributions To Plasma Physics 1998 38 501 512. [131] Lesage, A.; Konjevic, N.; Fuhr, J. R. AIP Conference Proceedings 1999 467 27 36. [132] Myeong, H. S.; Xichun, H.; Terry, A. m. Chemica l physics 1998 228 145 156. [133] Zwicker, H.; Schumacher, U. Zeitschrift fuer Physik 1965 183 453 71. [134] Goto, T.; Mori, M.; Hattori, S. Applied Physics Letters 1976 29 358 360. [135] Ichikawa, Y.; Teii, S. Journal Of Physics D Applied Physics 1980 13 1243 1251. [136] Kobilarov, R.; Konjevic, N.; Popovic, M. V. Physical Review A 1989 40 3871 3879. [137] Santiago, I.; Calzada, M. D. Applied Spectroscopy 2007 61 725 733.

PAGE 258

258 [138] Gornushkin, I. B.; Heitmann, U.; Moore, G.; Omenetto, N.; Smi th, B. W.; Winefordner, J. D. In Poster presented at FACSS 2006 : Orlando, Fl, 24 28, 2006 pp. pp. 108 109, Abstract #167. [139] De Galan, L.; Winefordner, J. D. Spectrochimica Acta, Part B: Atomic Spectroscopy 1968 23 277 89. [140] Gautier, C. i.; Fich et, P.; Menut, D.; Lacour, J. L.; L'Hermite, D.; Dubessy, J. Spectrochimica Acta Part B: Atomic Spectroscopy 2005 60 265. [141] Gautier, C. i.; Fichet, P.; Menut, D.; Lacour, J. L.; L'Hermite, D.; Dubessy, J. Spectrochimica Acta Part B: Atomic Spectrosc opy 2004 59 975. [142] Tognoni, E.; Palleschi, V.; Corsi, M.; Cristoforetti, G. Spectrochimica Acta Part B: Atomic Spectroscopy 2002 57 1115. [143] Winefordner, J. D.; Gornushkin, I. B.; Correll, T.; Gibb, E.; Smith, B. W.; Omenetto, N. Journal of An alytical Atomic Spectrometry 2004 19 1061 1083. [144] Miziolek, A.; Palleschi, V.; Schechter, I., 2006 pp. 516 538. [145] Scaffidi, J.; Angel, S. M.; Cremers, D. A. Analytical Chemistry 2006 78 24. [146] Sattmann, R.; Sturm, V.; Noll, R. Journal of Physics D: Applied Physics 1995 28 2181. [147] St Onge, L.; Detalle, V.; Sabsabi, M. Spectrochimica Acta Part B: Atomic Spectroscopy 2002 57 121. [148] Rai, V. N.; Yueh, F. Y.; Singh, J. P. Applied Optics 2003 42 2094. [149] Kuwako, A.; Uchida, Y. ; Maeda, K. Appl. Opt. 2003 42 6052. [150] Kraushaar, M.; Noll, R.; Schmitz, H. U. Applied Spectroscopy 2003 57 1282. [151] De Giacomo, A.; Dell'Aglio, M.; Colao, F.; Fantoni, R. Spectrochimica Acta Part B: Atomic Spectroscopy 2004 59 1431.

PAGE 259

259 [152] Corsi, M.; Cristoforetti, G.; Giuffrida, M.; Hidalgo, M.; Legnaioli, S.; Palleschi, V.; Salvetti, A.; Tognoni, E.; Vallebona, C. Spectrochimica Acta Part B: Atomic Spectroscopy 2004 59 723. [153] Uebbing, J.; Brust, J.; Sdorra, W.; Leis, F.; Niemax, K. Applied Spectroscopy 1991 45 1419. [154] Stratis, D. N.; Eland, K. L.; Angel, S. M. Applied Spectroscopy 2001 55 1297. [155] Stratis, D. N.; Eland, K. L.; Angel, S. M. Applied Spectroscopy 2000 54 1270. [156] Stratis, D. N.; Eland, K. L.; Angel, S M. Applied Spectroscopy 2000 54 1719. [157] Pearman, W.; Scaffidi, J.; Angel, S. M. Appl. Opt. 2003 42 6085. [158] Cristoforetti, G.; Legnaioli, S.; Pardini, L.; Palleschi, V.; Salvetti, A.; Tognoni, E. Spectrochimica Acta Part B: Atomic Spectrosco py 2006 61 340. [159] Sobral, H.; Villagrn Muniz, M.; Navarro Gonzlez, R.; Raga, A. C. Applied Physics Letters 2000 77 [160] lvarez Trujillo, L. A.; Ferrero, A.; Laserna, J. J.; Hahn, D. W. Applied Spectroscopy 2008 62 1144. [161] Alvarez Trujil lo, L. A.; Ferrero, A.; Laserna, J. J. Journal of Analytical Atomic Spectrometry 2008 23 885 888. [162] Mermet, J. M.; Mauchien, P.; Lacour, J. L. Spectrochimica Acta Part B: Atomic Spectroscopy 2008 63 999. [163] Poussel, E.; Mermet, J. M. Spectroch imica Acta Part B Atomic Spectroscopy 1996 51 75 85. [164] Salin, E. D.; Horlick, G. Anal. Chem. FIELD Full Journal Title:Analytical Chemistry 1980 52 1578 82.

PAGE 260

260 [165] Taylor, J. R. An Introduction to Error Analysis: The study of Uncertainties in Physi cal Measurements 1982 [166] Moon, H. Y.; Herrera, K. K.; Omenetto, N.; Smith, B. W.; Winefordner, J. D. Spectrochimica Acta Part B: Atomic Spectroscopy 2009 64 702 713.

PAGE 261

261 BIOGRAPHICAL SKETCH Heh Young Moon was born and raised in Seoul, South Korea. S he is the oldest daughter in a family that includes her parent Soon Kee Moon and Jong R ye An, three sisters and one brother. Heh Young received bachelor s degree in chemistry from Sun Moon University in March of 1995 and received a master s degree in physi cal chemistry from Korea University in March of 1999. During this time, Heh Young earned a full scholarship and fellowship: Excellent (top) scholarships from Sun Moon University and Brain Korea 21 Fellowship from Korea University. She also worked as a grad uate student research assistant (GRA) in the Korea Research Institute of Standards and Science (KRISS) in South Korea during the master degree program from 1999 to 2000. After graduation, she also worked as general chemistry coordinator as well as part tim e lecturer in Korea University from 2000 to 2003. She married Dooho Park in December of 2003 and then followed her husband in 2004 in order to join a PhD program at University of Florida in Gainesville, Florida. She entered the University of Florida in the fall of 2005 and joined Professor Nicol Omenetto group to work on her doctoral degree in physical chemistry.