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From Sample to Signal in Laser-Induced Breakdown Spectroscopy

Permanent Link: http://ufdc.ufl.edu/UFE0022048/00001

Material Information

Title: From Sample to Signal in Laser-Induced Breakdown Spectroscopy An Experimental Assessment of Existing Algorithms and Theoretical Modeling Approaches
Physical Description: 1 online resource (291 p.)
Language: english
Creator: Herrera, Kathleen
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2008

Subjects

Subjects / Keywords: alloy, aluminum, annealing, breakdown, calibration, carlo, cf, free, induced, laser, libs, monte, plasma, simulated, standard, standardless, vacuum
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: In recent years, laser-induced breakdown spectroscopy (LIBS) has become an increasingly popular technique for many diverse applications. This is mainly due to its numerous attractive features including minimal to no sample preparation, minimal sample invasiveness, sample versatility, remote detection capability and simultaneous multi-elemental capability. However, most of LIBS applications are limited to semi-quantitative or relative analysis due to the difficulty in finding matrix-matched standards or a constant reference component in the system for calibration purposes. Therefore, methods which do not require the use of reference standards, hence, standard-free, are highly desired. In this research, a general LIBS system was constructed, calibrated and optimized. The corresponding instrumental function and relative spectral efficiency of the detection system were also investigated. In addition, development of a spectral acquisition method was necessary so that data in the wide spectral range from 220 to 700 nm may be obtained using a non-echelle detection system. This requires multiple acquisitions of successive spectral windows and splicing the windows together with optimum overlap using an in-house program written in Q-basic. Two existing standard-free approaches, the calibration-free LIBS (CF-LIBS) technique and the Monte Carlo simulated annealing optimization modeling algorithm for LIBS (MC-LIBS), were experimentally evaluated in this research. The CF-LIBS approach, which is based on the Boltzmann plot method, is used to directly evaluate the plasma temperature, electron number density and relative concentrations of species present in a given sample without the need for reference standards. In the second approach, the initial value problem is solved based on the model of a radiative plasma expanding into vacuum. Here, the prediction of the initial plasma conditions (i.e., temperature and elemental number densities) is achieved by a step-wise Monte Carlo optimization of calculated synthetic spectra in order to obtain a close correlation with experimentally measured ones. The two approaches were applied to the laser-induced breakdown spectra of different types of samples: aluminum alloys, brass, soil, and powder alloys. Experiments were performed under atmospheric and vacuum conditions. Spatially- and temporally-resolved studies were also carried out. From the results obtained with CF-LIBS, the technique can be considered semi-quantitative to quantitative depending on the experimental parameters used and the type of samples analyzed. Comparison of CF-LIBS with conventional calibration curves was also carried out and the results obtained from CF-LIBS agree well with certified values. From the simulations performed using the Monte Carlo approach, relatively high correlation coefficients between synthetic and calculated spectra were obtained (R > 0.9).
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 Kathleen Herrera.
Thesis: Thesis (Ph.D.)--University of Florida, 2008.
Local: Adviser: Winefordner, James D.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2009-02-28

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2008
System ID: UFE0022048:00001

Permanent Link: http://ufdc.ufl.edu/UFE0022048/00001

Material Information

Title: From Sample to Signal in Laser-Induced Breakdown Spectroscopy An Experimental Assessment of Existing Algorithms and Theoretical Modeling Approaches
Physical Description: 1 online resource (291 p.)
Language: english
Creator: Herrera, Kathleen
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2008

Subjects

Subjects / Keywords: alloy, aluminum, annealing, breakdown, calibration, carlo, cf, free, induced, laser, libs, monte, plasma, simulated, standard, standardless, vacuum
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: In recent years, laser-induced breakdown spectroscopy (LIBS) has become an increasingly popular technique for many diverse applications. This is mainly due to its numerous attractive features including minimal to no sample preparation, minimal sample invasiveness, sample versatility, remote detection capability and simultaneous multi-elemental capability. However, most of LIBS applications are limited to semi-quantitative or relative analysis due to the difficulty in finding matrix-matched standards or a constant reference component in the system for calibration purposes. Therefore, methods which do not require the use of reference standards, hence, standard-free, are highly desired. In this research, a general LIBS system was constructed, calibrated and optimized. The corresponding instrumental function and relative spectral efficiency of the detection system were also investigated. In addition, development of a spectral acquisition method was necessary so that data in the wide spectral range from 220 to 700 nm may be obtained using a non-echelle detection system. This requires multiple acquisitions of successive spectral windows and splicing the windows together with optimum overlap using an in-house program written in Q-basic. Two existing standard-free approaches, the calibration-free LIBS (CF-LIBS) technique and the Monte Carlo simulated annealing optimization modeling algorithm for LIBS (MC-LIBS), were experimentally evaluated in this research. The CF-LIBS approach, which is based on the Boltzmann plot method, is used to directly evaluate the plasma temperature, electron number density and relative concentrations of species present in a given sample without the need for reference standards. In the second approach, the initial value problem is solved based on the model of a radiative plasma expanding into vacuum. Here, the prediction of the initial plasma conditions (i.e., temperature and elemental number densities) is achieved by a step-wise Monte Carlo optimization of calculated synthetic spectra in order to obtain a close correlation with experimentally measured ones. The two approaches were applied to the laser-induced breakdown spectra of different types of samples: aluminum alloys, brass, soil, and powder alloys. Experiments were performed under atmospheric and vacuum conditions. Spatially- and temporally-resolved studies were also carried out. From the results obtained with CF-LIBS, the technique can be considered semi-quantitative to quantitative depending on the experimental parameters used and the type of samples analyzed. Comparison of CF-LIBS with conventional calibration curves was also carried out and the results obtained from CF-LIBS agree well with certified values. From the simulations performed using the Monte Carlo approach, relatively high correlation coefficients between synthetic and calculated spectra were obtained (R > 0.9).
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 Kathleen Herrera.
Thesis: Thesis (Ph.D.)--University of Florida, 2008.
Local: Adviser: Winefordner, James D.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2009-02-28

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2008
System ID: UFE0022048:00001


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1 FROM SAMPLE TO SIGNAL IN LASER-INDUCED BREAKDOWN SPECTROSCOPY: AN EXPERIMENTAL ASSESSMENT OF EXIS TING ALGORITHMS AND THEORETICAL MODELING APPROACHES By KATHLEEN KATE HERRERA A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2008

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2 2008 Kathleen Kate Herrera

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3 "I may not be there yet, but I'm clos er to my goal than I was yesterday." Anonymous

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4 ACKNOWLEDGMENTS I would like to express my deepest gratitude, fi rst and forem ost, to my research adviser, Dr. James D. Winefordner for all the support, guidance and advice he has given me all these years. I would not have made it this far if he had not encouraged me at a time when I felt that I could not go on much longer. I consider myself very fortunate and I am incredibly proud to have been a part of the Winefordner group. I woul d also like to acknowledge to Dr. Nicol F. Omenetto for patiently and enthusiastically fo llowing my research from beginning to end. I learned how to be a good and effective researcher from our regular meetings in his office. His passion for science is truly amazing and contagious. This research would not have been what it is now if not for all his wonderful scientific ideas. I am also gr ateful to Dr. Benjamin W. Smith for all the invaluable help he has provided in the lab and for all the insightful comments during group meetings. I have much appreciation for Dr. Igor B. Gornushkin for teaching me the Monte Carlo LIBS approach and LIBS in general. I am completely in awe of his knowledge about spectroscopy, mathematics, physics, and programming. I am greatly indebted to him for the time he has taken to modify the MATLAB program for me countless of times. I would also like to thank Dr. Elisabetta Tognoni from the Institute for Chemical-Physi cal Processes of CNR in Pisa, Italy for sharing with me her knowledge on CF -LIBS and for patiently corresponding with me through e-mail to answer all my questions on CF-LIBS. I thank all the previous and current members of the Winefo rdner-Omeneto-Smith research group, especially Dr. Galan Moore, Heh-Young Moon and Benit Lauly for all the insightful discussions on LIBS. Lastly, I would like to ex tend my sincerest gratitude to my family and friends for their unwavering support and encouragement.

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5 TABLE OF CONTENTS page ACKNOWLEDGMENTS...............................................................................................................4 LIST OF TABLES................................................................................................................. ..........9 LIST OF FIGURES.......................................................................................................................14 LIST OF ABBRE VIATIONS, CONSTANTS AND SYMBOLS.................................................19 Abbreviations..........................................................................................................................19 Constants.................................................................................................................................20 Symbols..................................................................................................................................20 Roman Symbols...............................................................................................................20 Greek Symbols................................................................................................................23 ABSTRACT...................................................................................................................................26 CHAPTER 1 BACKGROUND AND SIGNFICANCE............................................................................... 28 2 BRIEF OVERVIEW OF LASER-INDU CED BREAKDOWN SPECTROSCOPY ............. 35 Introduction................................................................................................................... ..........35 Historical Background.......................................................................................................... ..35 General LIBS Process........................................................................................................... ..37 Laser-Material Coupling.................................................................................................38 Ablation, Vaporization and Breakdown.......................................................................... 39 Expansion........................................................................................................................40 Emission....................................................................................................................... ...42 Cooling and Crater Formation.........................................................................................43 3 SPECTRAL LINE PROFILE, BROADENING MECHANISMS AND INSTRUMENTAL FUNCTION ............................................................................................ 49 Introduction................................................................................................................... ..........49 Line Broadening Mechanisms................................................................................................50 Doppler Broadening........................................................................................................50 Pressure Broadening........................................................................................................ 51 Van der Waals broadening....................................................................................... 51 Resonance broadening.............................................................................................. 52 Stark broadening......................................................................................................53 Self-Absorption Broadening............................................................................................53 Self-absorption check............................................................................................... 54 Duplication factor..................................................................................................... 56

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6 Instrumental Function.......................................................................................................... ...56 Influence of Slits............................................................................................................. .57 Influence of Aberrations.................................................................................................. 57 Spherical aberration.................................................................................................. 58 Coma........................................................................................................................58 Astigmatism.............................................................................................................58 Influence of Diffraction...................................................................................................59 Overall Line Profiles.......................................................................................................... .....59 4 EXPERIMENTAL CHARACTERIZATION OF INSTRUMENTAL SYSTEM AND OPTIMIZATION OF OPERATING CONDITIONS ............................................................ 67 Introduction................................................................................................................... ..........67 Experimental Set-up............................................................................................................ ...67 Calibration of the Mi cro meter Slit Dial.................................................................................. 69 Optimization of the Slit Width............................................................................................... 71 Development of a Method for Spectral Data Acquisition...................................................... 72 Determination of the Instrumental Function...........................................................................75 Determination of the Detector Spectral Efficiency................................................................ 77 Determination of the Effect of CCD Pixel Binning................................................................ 77 Optimization of the Number of Accumula ted Laser Shots and Sa mpling Procedure............ 78 5 QUANTITATIVE STANDARD-FREE ALGORITHMS IN LASER-INDUCED BREAKDOWN SPECTROSCOPY .......................................................................................94 Introduction................................................................................................................... ..........94 Calibration-Free Laser-Induced Breakdown Spectroscopy (CF-LIBS) ................................. 94 Working Hypotheses....................................................................................................... 94 Stoichiometric ablation............................................................................................ 95 Local thermodynamic equilibrium........................................................................... 98 Optically thin plasma.............................................................................................102 Measurement of Integrated Line Intensity.................................................................... 103 Determination of Electron Number Density.................................................................. 105 Saha-Boltzmann method........................................................................................ 105 Stark broadening method.......................................................................................105 Determination of Laser-Induced Plasma Temperature.................................................. 109 Boltzmann plot method.......................................................................................... 109 Saha-Boltzmann plot method................................................................................. 110 Determination of Relative Concentration and Experim ental Factor............................. 111 Monte Carlo Simulated Annealing Optimization Method for Laser-Induced Breakdown ..112 Spectroscopy (MC-LIBS).....................................................................................................112 Working Hypotheses and General Theoretical Considerations..................................... 112 Calculation of Total Number Density, Temp erature and Their Initial Distributions .... 113 Calculation of Number Density of Atom s, Ions and Electrons..................................... 116 Calculation of Emission Spectra l Radiance and Line Profile ....................................... 117

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7 Rough approximation............................................................................................. 117 Detailed approximation.......................................................................................... 119 Spectral line profile................................................................................................ 120 Solution to the Inverse Problem.................................................................................... 121 6 COMPARATIVE STUDY OF TWO STAN DARD-FREE APPROACHES IN LASERINDUCE D BREAKDOWN SPECTROSCOPY.................................................................. 129 Introduction................................................................................................................... ........129 Experimental................................................................................................................... ......131 Results and Discussion......................................................................................................... 132 Standard-Free Analysis of Aluminum Alloys...............................................................132 General assessment of procedure........................................................................... 132 Determination of electron numb er density and temperature. ................................. 135 Determination of relative composition................................................................... 138 Spatially-Resolved Standard-Free Analysis of Alum inum Alloy................................. 141 Spatially-resolved emission spectra....................................................................... 141 Determination of electron numb er density and temperature. ................................. 144 Determination of relative composition................................................................... 147 Conclusion............................................................................................................................149 7 SEMI-QUANTITATIVE ANALYSIS OF DIFFERENT SAMPLES BY CALIBRATION-FREE LASER-INDUC ED BREAKDOWN SPECTROSCOPY ............. 200 Introduction................................................................................................................... ........200 Experimental................................................................................................................... ......203 Results and Discussion......................................................................................................... 204 Temporally-Resolved Analys is of Alum inum Alloys................................................... 204 Quantitative Analysis of Brass......................................................................................208 Calibration-free LIBS.............................................................................................208 CF-LIBS versus conventional LIBS......................................................................210 Quantitative Analysis of Aluminum Alloys.................................................................. 211 Calibration-free LIBS.............................................................................................211 CF-LIBS versus conventional LIBS......................................................................214 Quantitative Analysis of Soils....................................................................................... 215 Quantitative Analysis of Different Types of Alloys......................................................217 Conclusion............................................................................................................................219 8 CONCLUSION AND FUTURE WORK............................................................................. 258 Summary and Concluding Remarks.....................................................................................258 Future Research Directions...................................................................................................261 APPENDIX A CALCULATION OF RADIAL EXPANS ION VELOCITY PROP ORTIONALITY CONSTANT IN MC-LIBS...................................................................................................264

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8 B CALCULATION OF THE TOTAL ELEMENT NUMBER DENSITY I N MC-LIBS....... 267 C CALCULATION OF PLASMA TEMPERATURE IN MC-LIBS...................................... 270 D CALCULATION OF ATOM, ION AND ELEC TRON NUMBER DE NSITIES IN MCLIBS......................................................................................................................................274 E CERTIFIED CONCENTRATION VALUES OF REFERENCE STANDARDS ............... 277 LIST OF REFERENCES.............................................................................................................279 BIOGRAPHICAL SKETCH.......................................................................................................291

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9 LIST OF TABLES Table page 4-1 Results of the calibration of the m icrometer slit dial......................................................... 92 4-2 Calculated central wavelengths for s pectral data acquisition............................................ 93 5-1 Calculated FWHM of reduced Stark pr ofiles in nm per cgs field strength unit .............. 128 6-1 List of spectral lines used in th e CF-LIBS analysis of Al alloy B8 ................................. 182 6-2 List of spectral lines used in th e CF-LIBS analysis of Al alloy D33 ............................... 183 6-3 List of spectral lines used in th e CF-LIBS analysis of Al alloy S4 ................................. 184 6-4 List of spectral lines used in th e CF-LIBS analysis of Al alloy SM10 ............................ 185 6-5 List of spectral lines used in th e CF-LIBS analysis of Al alloy V14 ............................... 186 6-6 List of spectral lines used in th e CF-LIBS analysis of Al alloy Z8 ................................. 187 6-7 List of spectral lines used in the Monte Carlo L IBS simulations.................................... 189 6-8 Electron number density (in cm-3) and temperature (in K) values calculated using MC-LIBS and CF-LIBS for 6 Al alloy standards............................................................ 190 6-9 Relative concentration values and relativ e erro rs (in %) calculated from CF-LIBS analysis of aluminum alloys B8 and D33........................................................................ 190 6-10 Relative concentration values and relativ e erro rs (in %) calculated from CF-LIBS analysis of aluminum alloys S4 and SM10...................................................................... 190 6-11 Relative concentration values and relativ e erro rs (in %) calculated from CF-LIBS analysis of aluminum alloys V14 and Z8........................................................................ 191 6-12 Number densities (in cm-3) calculated from MC-LIBS analysis of six different aluminum alloys...............................................................................................................191 6-13 Relative concentration values and relativ e erro rs (in %) calculated from MC-LIBS and CF-LIBS analysis of Al alloy B8.............................................................................. 191 6-14 Relative concentration values and relativ e erro rs (in %) calculated from MC-LIBS and CF-LIBS analysis of Al alloy D33............................................................................192 6-15 Relative concentration values and relativ e erro rs (in %) calculated from MC-LIBS and CF-LIBS analysis of Al alloy S4.............................................................................. 192

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10 6-16 Relative concentration values and relativ e erro rs (in %) calculated from MC-LIBS and CF-LIBS analysis of Al alloy SM10......................................................................... 192 6-17 Relative concentration values and relativ e erro rs (in %) calculated from MC-LIBS and CF-LIBS analysis of Al alloy V14............................................................................192 6-18 Relative concentration values and relativ e erro rs (in %) calculated from MC-LIBS and CF-LIBS analysis of Al alloy Z8.............................................................................. 193 6-19 Atomic masses (in g) of different elements in the aluminum alloy sample..................... 193 6-20 Electron number density (in cm-3) and temperature (in K) values calculated using MC-LIBS and CF-LIBS for Al alloy standa rd D33 at different spatial positions...........193 6-21 Sigmoidal fitting parameters for the spatial evolution of temperature............................ 194 6-22 Sigmoidal fitting parameters for the spatial evolution of electron number density......... 194 6-23 Relative concentration values (in %) cal culated from CF-LIBS analysis of aluminum alloys D33 at different spatial positions...........................................................................195 6-24 Relative errors (in %) of calcu lated CF-LIBS concentration values at different spatial positions...................................................................................................................... .....195 6-25 Relative concentration values, relative errors (in %) and number densities (in cm-3) calculated from MC-LIBS and CF-LIBS analysis of Al alloy D33 at spatial position A.......................................................................................................................................196 6-26 Relative concentration values, relative errors (in %) and number densities (in cm-3) calculated from MC-LIBS and CF-LIBS analysis of Al alloy D33 at spatial position B.......................................................................................................................................196 6-27 Relative concentration values, relative errors (in %) and number densities (in cm-3) calculated from MC-LIBS and CF-LIBS analysis of Al alloy D33 at spatial position C.......................................................................................................................................196 6-29 Relative concentration values, relative errors (in %) and number densities (in cm-3) calculated from MC-LIBS and CF-LIBS analysis of Al alloy D33 at spatial position E.......................................................................................................................................197 6-30 Relative concentration values, relative errors (in %) and number densities (in cm-3) calculated from MC-LIBS and CF-LIBS analysis of Al alloy D33 at spatial position F.......................................................................................................................................197 6-31 Relative concentration values, relative errors (in %) and number densities (in cm-3) calculated from MC-LIBS and CF-LIBS analysis of Al alloy D33 at spatial position G.......................................................................................................................................198

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11 6-32 Relative concentration values, relative errors (in %) and number densities (in cm-3) calculated from MC-LIBS and CF-LIBS analysis of Al alloy D33 at spatial position H.......................................................................................................................................198 6-33 Relative concentration values, relative errors (in %) and number densities (in cm-3) calculated from MC-LIBS and CF-LIBS analysis of Al alloy D33 at spatial position I........................................................................................................................................198 6-34 Relative concentration values, relative errors (in %) and number densities (in cm-3) calculated from MC-LIBS and CF-LIBS analysis of Al alloy D33 at spatial position J........................................................................................................................................198 6-35 Relative concentration values, relative errors (in %) and number densities (in cm-3) calculated from MC-LIBS analysis of Al alloy D33 at spatial position K...................... 199 7-1 Electron number density, temperature and re lative standard devi ation ca lculated for aluminum alloy B8 at 5 different delay times.................................................................. 248 7-2 Electron number density, temperature and re lative standard devi ation ca lculated for aluminum alloy SM10 at 6 different delay times............................................................. 248 7-3 Relative concentration values (in %) cal culated from CF-LIBS analysis of aluminum alloy B8 at 5 diffe rent delay times...................................................................................248 7-4 Relative concentration values (in %) cal culated from CF-LIBS analysis of aluminum alloy SM10 at 6 different delay times.............................................................................. 249 7-5 Relative errors (in %) calculated from CF -LIBS analysis of alum inum alloy B8 at 5 different delay times........................................................................................................ 249 7-6 Relative errors (in %) calculated from CF -LIBS analysis of alum inum alloy SM10 at 6 different delay times.....................................................................................................249 7-7 Relative concentration values and relativ e erro rs (in %) calculated from CF-LIBS analysis of 10 NIST brass standards................................................................................ 250 7-8 Temperature, electron number density and m inimum electron number density for LTE calculated from CF-LIBS analysis 10 NIST brass standards.................................. 250 7-9 Spectroscopic parameters of Zn spectral lin es used in the calibration curves for brass analysis .............................................................................................................................251 7-10 Zn calibration curve parameters and limits of detection.................................................. 251 7-11 Relative concentration of Zn (in %) ca lculated using CF-LIBS and conventional LIBS approaches ..............................................................................................................251 7-12 Relative errors (in %) in calculated Zn concentration ..................................................... 251

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12 7-13 Electron number density and minimum electron nu mber density for LTE calculated for 6 Al alloy standards at different ambient pressures...................................................252 7-14 Laser-induced plasma temperatures calcula ted f or 6 Al alloy standards at different ambient pressures............................................................................................................. 252 7-15 Relative concentration values and relativ e erro rs (in %) calculated from CF-LIBS analysis of aluminum alloy B8 at 3 different pressures................................................... 253 7-16 Relative concentration values and relativ e erro rs (in %) calculated from CF-LIBS analysis of aluminum alloy SM 10 at 3 different pressures.............................................. 253 7-17 Relative concentration values and relativ e erro rs (in %) calculated from CF-LIBS analysis of aluminum alloy D33 at 2 different pressures................................................. 253 7-18 Relative concentration values and relativ e erro rs (in %) calculated from CF-LIBS analysis of aluminum alloy S4 at 2 different pressures................................................... 254 7-19 Relative concentration values and relativ e erro rs (in %) calculated from CF-LIBS analysis of aluminum alloy V14 at 2 different pressures................................................. 254 7-20 Relative concentration values and relativ e erro rs (in %) calculated from CF-LIBS analysis of aluminum alloy Z8 at 2 different pressures................................................... 254 7-21 Spectroscopic parameters of spectral lines used in the calibration curves for Al alloy analysis .............................................................................................................................255 7-22 Cu and Si calibration curve para m eters and limits of detection...................................... 255 7-23 Relative concentration of Cu (in %) ca lculated using CF-LIBS and conventional LIBS approaches ..............................................................................................................255 7-24 Relative errors (in %) in calculated Cu concentration ..................................................... 255 7-25 Relative concentration of Si and relative erro rs (in %) calculated using CF-LIBS and conventional LIBS approaches........................................................................................255 7-26 Relative concentration values and relativ e erro rs (in %) calculated from CF-LIBS analysis of Montana soil NIST SRM 2711 and Estuarine sediment NIST SRM 1646... 256 7-27 Relative concentration values and relativ e erro rs (in %) calculated from CF-LIBS analysis of Buffalo River sediment NIST SRM 2704 and Montana soil NIST SRM 2710..................................................................................................................................256 7-28 Relative concentration values and relativ e erro rs (in %) calculated from CF-LIBS analysis of Canadian soils SO-2 and SO-3......................................................................256 7-29 Temperature, electron number density and m inimum electron number density for LTE calculated from CF-LIBS anal ysis of 6 soil standards............................................ 256

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13 7-30 Relative concentration values and relativ e erro rs (in %) calculated from CF-LIBS analysis of Ti alloy pellet Alfa Ae sar 88395 and Ti alloy metal NIST SRM 654b......... 257 7-31 Relative concentration values and relativ e erro rs (in %) calculated from CF-LIBS analysis of Zn alloys NIST SRM 627 and 629................................................................257 7-32 Relative concentration values and relativ e erro rs (in %) calculated from CF-LIBS analysis of Ni alloy pellet NIST SR M 882 and Cu-Ni alloy metal NIST SRM 1276a... 257 7-33 Temperature and electron number density calculated from CF-LIBS analysis of 6 alloy standards.................................................................................................................257 E-1 Elemental percentage composition of South African alum inum alloy standards............ 277 E-2 Elemental percentage compos ition of NIST brass standards ........................................... 277 E-3 Elemental percentage composition of NIST and Canadian soil standards ...................... 278 E-4 Elemental percentage compositi on of different alloy standards ......................................278

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14 LIST OF FIGURES Figure page 2-1 Diagram of a typical laboratory LIBS apparatus............................................................... 44 2-2 Schematic representation of the main processes in LIBS.................................................. 45 2-3 Schematic illustration of the laser-indu ced plasm a and various interaction zones............ 46 2-4 Timing of the different p hysical phenom ena observed dur ing the plasma expansion....... 47 2-5 Temporal history of the laser-induced plasm a showing the different predominant emitting species............................................................................................................... ...47 2-6 Simplified energy level diagram showing the dif ferent transitions which produce the continuum and line emissions............................................................................................ 48 3-1 Line profile, half-width, kern el and wings of a spectral line ............................................. 61 3-2 Spectral line profiles as a function of increasing atom ic concentration............................ 62 3-3 An example of a self-reversed spectral line profile........................................................... 62 3-4 Self-absorption check...................................................................................................... ...63 3-5 Convolution of the entrance and exit slit widths............................................................... 64 3-6 Effect of spherica l aberration on a lens .............................................................................. 64 3-7 Effect of coma....................................................................................................................64 3-8 Effect of astigmatism on a concave mirror used off-axis.................................................. 65 3-9 Effect of diffraction...................................................................................................... ......65 3-10 Overall spectral line profile............................................................................................. ..66 4-1 Experimental LIBS set-up for experim ents under atmospheric conditions....................... 81 4-2 Schematic diagram of cable connections and the corresponding tim ing sequence used in the experimental system................................................................................................. 82 4-3 Experimental LIBS set-up for experiments under vacuum conditions.............................. 83 4-4 Ray diagram for Fraunhofer diffraction by a single slit and the corresponding intensity distribution and im ag e of the diffraction pattern................................................. 84 4-5 Experimental set-up used in the ca lib ration of the micrometer slit dial............................ 85

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15 4-6 Experimental set-up used in the optimizat ion of the slit width and m easurement of the instrumental function................................................................................................... 85 4-7 Effect of slit width on the normalized intensity distribution and full width at half m aximum...........................................................................................................................86 4-8 Example of a merged spectrum.......................................................................................... 87 4-9 A schematic diagram of the components of a Czerny-Turn er-based spectrometer and the respective rays and angles formed when light enters the slit....................................... 87 4-10 Determination of the instrumental function....................................................................... 88 4-11 Determination of the de tector spectral efficiency .............................................................. 89 4-12 Effect of binning................................................................................................................90 4-13 Effect of laser shot accumulation....................................................................................... 91 5-1 Temporal evolution of the H line at 656.272 nm .......................................................... 123 5-2 Boltzmann plot obtained using Fe I lines in an alum inum alloy sample......................... 123 5-3 Energy levels of atomic (I) and ionic (II) species............................................................ 124 5-4 Saha-Boltzmann plots of different elements.................................................................... 125 5-5 Illustration of the coordinate system used in the sem i-empirical vacuum plasma expansion model.............................................................................................................. 126 5-6 Correlation between the experi m ental and simulated spectrum......................................126 5-7 Extrema of a func tion in an interval ................................................................................ 127 6-1 Section of laser-induced breakdown sp ectra of different alum inum alloys..................... 153 6-2 Images of laser-induced plasmas obtaine d from different aluminum alloy samples....... 153 6-3 Effect of the number of iterations pe r param eter on the correlation coefficient R and computer run time of a 3.1 GHz PC................................................................................ 154 6-4 The Stark broadened hydrogen alpha lin e at 656.272 nm in the aluminum alloy spectra used for electron number de nsity determination in CF-LIBS............................. 155 6-5 Saha-Boltzmann plots of selected elem ents in aluminum alloy sample.......................... 156 6-6 Spatial and temporal evolution of temperature and elec tron nu mber density obtained using the MC-LIBS approach for aluminum alloy samples............................................ 157

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16 6-7 Spatial evolution of temporally-integra ted tem perature and electron number density obtained using the MC-LIBS approach for aluminum alloy sample............................... 159 6-8 Comparison of electron number densities and plasm a temperatures calculated using MC-LIBS and CF-LIBS approaches................................................................................160 6-9 Relative elemental compositions of aluminum alloy samples obtained with CF-LIBS com pared with certified values........................................................................................ 161 6-10 Relative percentage errors of the elem ental compositi on calculated using CF-LIBS..... 162 6-11 Comparison of experimental spectra of alum inum alloys and the best-fit simulated spectra calculated with MC-LIBS.................................................................................... 163 6-12 Relative concentration values obtained using MC-LIBS and CF-LIBS compared with certified values (black bars) .............................................................................................164 6-13 Relative errors of calculated concentrat ion values obtained using MC-LIBS and CFLIBS .......................................................................................................................... ......165 6-14 Image of the laser-induced plasma obtaine d from an Al alloy D33 using a delay time of 50 ns and gate width of 100 ns under 0.1 m bar pressure............................................. 166 6-15 Spatially-resolved spectra of differe nt neutral and singly-ionized lines. .........................167 6-16 Spectrally-integrate d intensities of different neut ral and singly-ionized lines at various spatial positions ...................................................................................................168 6-17 Spatial frequency distribution profile of different species in the alum inum alloy plasma..............................................................................................................................169 6-18 Electron number density and temperatur e values calculated at different spatial position s using CF-LIBS and MC-LIBS......................................................................... 170 6-19 Saha-Boltzmann plots of selected elem ents in alum inum alloy sample D33 at different spatial positions.................................................................................................171 6-20 Spatial and temporal evolution of temperature and electron nu m ber density obtained using the MC-LIBS approach for aluminum alloy sample D33...................................... 172 6-21 Spatial evolution of temporally-integra ted tem perature and electron number density obtained using the MC-LIBS approach for aluminum alloy sample D33....................... 176 6-22 Relative concentration values at different sp atial positions calculated with CF-LIBS... 177 6-23 Comparison of experimental spectra of alum inum alloy D33 and the best-fit simulated spectra calculated with MC-L IBS at different spatial positions...................... 178

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17 6-24 Number densities (cm-3) of different elements in th e alloy sample calculated at different spatial positions using MC-LIBS......................................................................179 6-25 Relative concentration values calculated at different spatial positions using MCLIBS and CF-LIBS compared with certified values ........................................................ 180 6-26 Relative errors of calculated concentrat ion values at different spatial positions calculated using MC-LIBS and CFLIBS........................................................................181 7-1 Section of the wide spectral range data of alum inum alloy samples at different delay times.......................................................................................................................... .......221 7-2 Temporal evolution of the number of iden tified neutral lines a nd singly-ionized lines for the different elem ents present in the aluminum alloy samples.................................. 222 7-3 Temporal evolution of laser-induced plasm as obtained from the aluminum alloy samples.............................................................................................................................224 7-4 Temporal evolution of the electron num ber density calculated using the H line at 656.272 nm for the alumi num alloy samples................................................................... 225 7-5 Saha-Boltzmann plots of selected lines at different delay tim es..................................... 226 7-6 Temporal evolution of temp erature calculated for selected e lements in the aluminum alloy samples....................................................................................................................228 7-7 Temporal evolution of av eraged plasm a temperatures.................................................... 229 7-8 Elemental concentrations of the aluminum alloy sam ples calculated from CF-LIBS at different delay times........................................................................................................ 230 7-9 Relative errors calculated from CF-LIBS results of th e aluminum alloy samples.......... 232 7-10 LIBS measurements of 10 NIST brass standards............................................................ 233 7-11 Results of the CF-LIBS analysis of 10 NIST brass standards ......................................... 234 7-12 Calibration curves constructed for the quantitativ e analysis of Zn in brass sam ples......235 7-13 Images of the laser-induced plasma obt ained from different alum inum alloys at different ambient pressures.............................................................................................. 236 7-14 Section of laser-induced breakdown spect ra of the alum inum alloy samples at different ambient pressures.............................................................................................. 237 7-15 Calculated electron number density and te m perature values for different aluminum alloys under different ambient pressures.........................................................................238

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18 7-16 Relative elemental concentrations of the alum inum alloy samples at different ambient pressures............................................................................................................. 239 7-17 Relative errors of calculated elemental c oncentrations of the al um inum alloy samples at different ambient pressures..........................................................................................240 7-18 Calibration curves constructed for the quantitative analys is of Cu and Si in the alum inum alloy samples.................................................................................................. 241 7-19 LIBS measurements of 6 soil standards........................................................................... 242 7-20 Relative elemental concentrations of soil standards calculated from CF-LIBS.............. 243 7-21 The relative errors of calculated elementa l concentrations of soil standards and the calculated electron num ber density and temp erature values of the laser-induced plasmas.............................................................................................................................244 7-22 LIBS measurements of 6 different alloy standards ..........................................................245 7-23 Relative elemental concentrations of alloy standards calculated from CF-LIBS............ 246 7-24 The relative errors of calculated elementa l concentrations of al loy standards and the calculated electron num ber density and temp erature values of the laser-induced plasmas.............................................................................................................................247 8-1 A general schematic diagram of CF-LIBS and MC-LIBS analysis from sample to signal ................................................................................................................................263

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19 LIST OF ABBREVIATIONS, CONSTANTS AND SYMBOLS Abbreviations AES Atomic emission spectroscopy CF-LIBS Calibration-free laserinduced breakdown spectroscopy CNR Consiglio Nazionale delle Richerche GF-AAS Graphite furnace atomic absorption spectroscopy IB Inverse bremsstrahlung ICCD Intensified charge-coupled device ICP-AES Inductively-coupled plasma atomic emission spectroscopy ICP-MS Inductively-coupled plasma mass spectrometry IPCF Istituto per i Processi Chimico-Fisici LA Laser ablation LA-OES Laser ablation optical emission spectroscopy LIBS Laser-induced breakdown spectroscopy LIPS Laser-induced plasma spectroscopy LSS Laser spark spectroscopy LTE Local thermodynamic equilibrium LTSD Lens-to-sample distance MC-LIBS Monte Carlo simulated anneali ng optimization method for laser-induced breakdown spectroscopy MPI Multiphoton ionization RSD Relative standard deviation SAC Self-absorption correction S/N Signal-to-noise ratio

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20 Constants c Speed of light in vacuum 2.9979 108 m s-1 e Elementary charge 1.6022 10-19 C 0 Permittivity of free space 8.8542 10-12 C2 N-1 m-2 h Plancks constant 6.6261 10-34 J s kB Boltzmann constant 1.3807 10-23 J K-1 me Electron mass 9.1094 10-31 kg NA Avogadros number 6.0221 1023 mol-1 Stefan-Boltzmanns constant 5.6705 10-8 W m-2 K-4 Symbols Roman Symbols Aki Transition probability for spontaneous emission between states k and i s-1 a Width of the beam emerging from the dispersion element, mm a( r,t ) Line damping parameter, dimensionless bbB Blackbody spectral radiance, (J s-1 cm-2 sr-1 nm-1) j luB Einstein coefficient for absorption transition, cm3 erg-1 s-1 Hz Cs Relative number density of species s D Duplication factor, dimensionless d Laser spot diameter, cm d Groove spacing, nm groove-1 E Energy difference, eV Ei Energy of lower level i Ek Energy of upper level k F CF-LIBS experimental factor, cm-3

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21 Fabs Absolute spectral efficiency Fdet Optical efficiency of detection system Frel() Optical efficiency of detection system f Focal length of the spectrometer, mm fik transition oscillator strength, dimensionless G Free-free Gaunt factor, dimensionless G Number of grooves per millimeter, grooves mm-1 gi Statistical weight of lower level i dimensionless gk Statistical weight of upper level k dimensionless j Plasma constituent kion Ionization rate coefficient, cm3 s-1 l Optical path length, cm I Wavelength-integrated intensity of emitted light, W cm-3 kiI Integrated line intensity, photons cm-3 s-1 kiI Corrected experimental integrated line intensity measkiI, Measured integrated line intensity, counts 1I Measured line profile wi thout the spherical mirror 2I Measured line profile with the spherical mirror I Radiation spectral radiance, erg s-1 cm-2 Hz-1 sr-1 M Atomic or molecular weight, g mol-1 or amu m Mass, kg m Diffraction order, dimensionless Npixel Number of column pixels nD Number of particles in the Debye sphere, cm-3

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22 ne Electron number density, cm-3 nI, j an Neutral atom number density, cm-3 nII, j in Singly-ionized number density, cm-3 trnj, Total number density of constituent j as a function of radial coordinate r and time t, cm-3 ntot Total particle number density, cm-3 s kn Number density of species s at level k, cm-3 s totn Total number density of species s, cm-3 j luP,P Normalized line profile, dimensionless p Pressure, dyne cm-2 q Energy loss due to radiation per unit volume per unit time, erg cm-3 s-1 R Correlation coefficient, dimensionless R Interparticle distance, cm R Outer boundary of plasma R Ratio of spectral line intensities with two plasma lengths, dimensionless Rc Ratio of intensities of continuum radiation with two plasma lengths, dimensionless Rd Reciprocal linear dispersion, nm mm-1 r Radial coordinate of particle in the plasma, cm s Atomic species Te Electron temperature, K Texc Excitation temperature, K TeV Temperature, eV Tion Ionization temperature, K TK Temperature, K

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23 tdelay Delay time, s texp Plasma expansion time, s tgate Gate width, s tion Ionization time s U(T) Partition function, dimensionless u(r,t) Radial expansion velocity, cm s-1 V Perturbation of energy level, J V(t) Velocity of plasma boundary, cm s-1 w Electron-impact half-width, nm w Slit width, m wpixel Pixel size, m z Charge number, dimensionless Greek Symbols Incidence angle Ion-broadening parameter, dimensionless Polarizability, m3 Target absorptivity, cm-1 1/2 Reduced Stark profile, nm j Ratio of specific heat capacities of species j, dimensionless Diffraction angle Internal energy per unit mass, erg g-1 c, Non-integrated continuu m radiation intensity, W cm-3 nm-1 t Proportionality coefficient between collective velocity of particles and radius, s-1 Grating rotation angle

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24 Polar angle (), Absorption coefficient, cm-1 Total absorption coefficient, cm-1 mean Planck mean absorption coefficient, cm-1 ff Free-free absorption coefficient, cm-1 fb Free-bound absorption coefficient, cm-1 bb Bound-bound absorption coefficient, cm-1 t Line shift normalized by Doppler width, dimensionless Wavelength, nm Spectral line width, nm D Doppler line width, nm d Diffraction-limited spectral bandpass, nm G Gaussian line width, nm I Instrumental line width, nm L Lorentzian line width, nm range Spectral range, nm res Resonance line width, nm s Geometric spectral bandpass, nm Stark Stark line width, nm Stark shift Stark line shift, nm V Voigt line width, nm VDW Van der Waals line width, nm VDW shift Van der Waals line shift, nm j Atomic mass of species j, g

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25 Frequency, Hz Free-bound continuum correc tion factor, dimensionless z Factor for electron atom structure, dimensionless Generalized number density of species, cm-3 () Optical depth, dimensionless Exit or take-off angle Plasma expansion velocity, 105 106 cm s-1 Ionization potential, eV Lowering of the ionization potential, eV Solid angle, sr

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26 Abstract of Dissertation Pres ented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy FROM SAMPLE TO SIGNAL IN LASER-INDUCED BREAKDOWN SPECTROSCOPY: AN EXPERIMENTAL ASSESSMENT OF EXIS TING ALGORITHMS AND THEORETICAL MODELING APPROACHES By Kathleen Kate Herrera August 2008 Chair: James D. Winefordner Major: Chemistry In recent years, laser-indu ced breakdown spectroscopy (LIBS) has become an increasingly popular technique for many diverse applications. This is mainly due to its numerous attractive features including minimal to no sample prepar ation, minimal sample invasiveness, sample versatility, remote detection capability and si multaneous multi-elemental capability. However, most of LIBS applications are limited to semi -quantitative or relative analysis due to the difficulty in finding matrix-matched standards or a constant reference component in the system for calibration purposes. Therefore, methods which do not require th e use of reference standards, hence, standard -free, are highly desired. In this research, a general LIBS system wa s constructed, calibrated and optimized. The corresponding instrumental function and relative spectral efficiency of the detection system were also investigated. In additi on, development of a spectral acquisition method was necessary so that data in the wide spectral range from 220 to 700 nm may be obtained using a non-echelle detection system. This requires multiple ac quisitions of successive spectral windows and splicing the windows together wi th optimum overlap using an in-house program written in Qbasic.

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27 Two existing standard-free approaches, the ca libration-free LIBS (CF-LIBS) technique and the Monte Carlo simulated annealing optimiza tion modeling algorithm for LIBS (MC-LIBS), were experimentally evaluated in this researc h. The CF-LIBS approach, which is based on the Boltzmann plot method, is used to directly eval uate the plasma temperature, electron number density and relative concentrations of species present in a give n sample without the need for reference standards. In the second approach, th e initial value problem is solved based on the model of a radiative plasma expa nding into vacuum. Here, the prediction of the initial plasma conditions (i.e., temperature and elemental number densities) is achieved by a step-wise Monte Carlo optimization of calculated synthetic spectra in order to obtain a close correlation with experimentally measured ones. The two approaches were applied to the laserinduced breakdown spectra of different types of samples: aluminum alloys, brass, soil, and powder alloys. Experiments were performed under atmospheric and vacuum conditions. Spatiallyand temporally-resolved studies were also carried out. From the results obtained with CF -LIBS, the technique can be considered semiquantitative to quantitative depending on the expe rimental parameters used and the type of samples analyzed. Comparison of CF-LIBS with conventional calibration curves was also carried out and the results obtained from CF-LIB S agree well with certified values. From the simulations performed using the Monte Carlo approach, relatively high correlation coefficients between synthetic and calculat ed spectra were obtained (R > 0.9).

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28 CHAPTER 1 BACKGROUND AND SIGNFICANCE Laser-induced breakdown spectroscopy (LIBS) is a fast and useful qualitative [1, 2] and sem i-quantitative [3, 4] technique for the dete rmination of elemental composition of a wide range of materials, such as metal alloys [5-7], glasses [8-10], liquids [11-13], aerosols [14-16], painted artworks [17-19], archaeological arti facts [20-22], etc., unde r various analytical conditions. LIBS is based on th e spectral and time-resolved analysis of atomic and ionic emission from a laser-induced plasma (LIP), obtained by focusing an intense laser pulse onto the sample surface [23]. The material present in the focal volume undergoes instantaneous ablation and vaporization accompanied by rapid dissociation in to atoms and ions in excited states, as well as free electrons [24]. During the expansion and the cooling of the plasma in the ambient atmosphere or in vacuum, several simultaneous processes occur whic h produce the continuum and line emission: bremsstrahlung (free-free transitions), radiative recombination (free-bound transitions), and radiative relaxation of excited atoms, ions or molecules (bound-bound transitions) [25]. Temporal resolution is required for discrimination between early plasma continuum and delayed atomic and ionic line emissions. The latter allow for a qualitative identification of species in the plasma while th eir relative line intensities give a quantitative measure of the concentration of the corresponding elements [26]. The increasing popularity of LIBS over more conventional methods of atomic spectroscopy, such as GF-AAS and IC P-AES, is due to its several attr active features [27]. It is a simple and relatively non-invasive technique, because both the ablation and excitation processes are performed in a single step, in situ and in real time, and only a very small amount of the sample is vaporized. Sample preparation is of ten unnecessary; therefore, the risk of sample contamination is reduced and measurement time is shortened. The sample versatility and

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29 simultaneous multi-elemental capability of LIBS make this method suitable for a number of diverse applications, such as space explora tion [28-30], environmental monitoring [31-33], forensic analysis [34-36], military and homeland security [37-39], cultural heritage [20-22], and production control and qual ity assurance [40-42]. In spite of the numerous advantages of LI BS, there are a few drawbacks which limit the applicability of the method, particularly for quantitative analysis. The most relevant are its poor figures of merit (accuracy, precisi on, detection limits) in comparis on to conventional techniques. According to Castle et al. [43], the unsatisfactory analytical performance of LIBS is due to several factors, including sample inhomogeneity, s hot-to-shot variability of the laser pulse, and matrix effects. The latter is one of, if not th e most challenging aspect in LIBS quantitative analysis and is characterized by the strong depe ndence of atomic emission spectra on relatively small variations in sample composition [44]. Matrix effects can be minimized by calibration with proper reference samples having the same matrix composition or by normalization of the analyte signal by a reference signal [23]. Howe ver, in the case of hi ghly variable or fully unknown matrices, these approaches would limit the method to semiquantitative analysis [26]. It should also be emphasized that in many appli cations it is difficult to find matrix-matched standards or a constant reference component in the system. Hence, methods which do not require the use of reference standard s (standard-free) are highly desired. Detailed investigations of the various types of matrix effects have been carried out in order to maximize the potential of LIBS for qua ntitative measurements. Wisbrun et al. [45] studied the effect of persistent aerosols produced above so il and sand samples. Their results show that aerosol production is dependent on laser repetition rate. They also demonstrated that a linear dependence exists between particle size and analy tical signal as predicted by their zero order

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30 model. Eppler et al. [46] investigated the effects of ch emical speciation a nd matrix composition on lead and barium measurements using soil an d sand matrices. Their results suggest that analyte emission is dependent on both factors. Suggestions to explain this dependency were given but no definite conclusi ons were made. Bulatov et al. [47] employed LIBS to investigate the matrix effects of sand/soil mixtures th rough a combination of spatial and temporal resolutions. They noted that there is an op timum distance from the surface for obtaining the highest trace element sensitivity in a given matr ix. The same group performed further matrix effect studies by shockwave propagation and concl uded that matrix effects can be characterized by the amount of energy coupled into the plasma [48]. Gondal et al. [49] investigated the role of different binding materials for tr ace Mg analysis using LIBS and determined that KBr gives the highest LIBS sensitivity, largest ablated mass a nd deepest crater compared to starch, poly(vinyl alcohol), silver and aluminum. They attributed these to the differences in latent heat of vaporization for various elements in th e binder and the grain size of matrix. Several solutions to the matrix effects problem have been proposed in recent years. Chaleard et al. [50] developed an analytical procedure which enables matrix effects correction for quantitative multi-matrix analysis. Their approach is based on the assumption that intensities of emission lines are a function of the ablated mass and the plasma excitation temperature, which were evaluated by acoustic wave measurements and two-line intensity ratio, respectively. In their results, normalization of the net intensities with respect to these two parameters yielded a single slope calibration curve for a series of samples with varying matrices. Xu et al. [51] established a method which compensates for the pul se-to-pulse fluctuations in LIBS based on the assumption that a similar variation pattern is obser ved for both the signal in tensity and baseline. They applied their model to the analysis of 50 single-shot spectra of Zn-contaminated aerosols

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31 and obtained a linear relationship between the corre cted intensities and Zn concentration. They noted that their method provides absolute con centrations and does not require an internal reference standard, although standard samples ar e still necessary to c onstruct the calibration curves. However, according to Gornushkin et al [52], the method proposed by Xu et al. lacks generality in its applicability based on their own experimental results and the underlying analytical and physical interpreta tion of the single-shot model. They argued that although the method has been shown to work for the analysis of Zn in particulate matt er, the success of the application might be restricted to very few matrices or might ha ve been fortuitous. Gornushkin et al. [53] then proposed a surface density-based calibration met hod for the determination of magnesium in powdered samples in which a m echanical effect was assumed to strongly influence the emission intensities. The authors recommended the technique for the analysis of various types of finely ground samples where ~10% precision and ~10-20% relative error are acceptable. The aforementioned studies are just few of th e numerous investigations that various groups have done on matrix effects; each can be regarded as a research tool for the progress of LIBS in quantitative applications and possibly towards the realization of the ultimate goal in analytical spectroscopy, i.e., absolute analysis. Nevertheless, there is still a need for a procedure that will completely take into account the adverse influence of matrix effects on LIBS quantitative analysis or, at least, alleviat e the difficulties related to the requirement of matrix-matched reference standards, particularly for very complex cases, such as multi-elemental determinations in a priori unknown conditions. Accordingly, Ciucci et al. [54-57] developed and patented an innovative LIBS algorithm that el iminates the use of reference st andards and calibration curves. This calibration-free method (CF-LIBS) allows quantitative information to be obtained by

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32 interpretation of the experiment al results using the basic physics of the laser-induced plasma, assuming that some fundamental conditions, su ch as local thermodynamic equilibrium (LTE), stoichiometric ablation, and optical ly thin plasma, are verified. In close relation to the goal of absolute analysis, several publications on theoretical modeling of laser-induced plasma expansion ha ve an inherent yet untapped analytical significance. Some models are capable of predic ting the detailed spectral distribution of plasma radiation. Mazhukin et al. [58] ma thematically analyzed the influe nce of radiative transfer on the dynamics of laser-induced plasma of aluminum vapor using two-dimensional radiation gas dynamics with multi-group diffusion approximation to describe the plasma radiation transfer. The model was able to predict the plasma spectrum not only in a wide spectral region but also in a narrow energy window. The latter has great si gnificance in real plasma spectroscopy because observations are usually done in narrow spectral regions where the details of line profiles are more evident. De Giacomo et al. [59] perfor med a temporal evolution study of electron, atom and ion population densities in the plasma produced by KrF excimer laser on TiO and TiO2 targets. The authors proposed a state-to-state collisional radiative model to describe kinetic processes and obtained good quantit ative agreement with the experimentally determined particle number densities and temperature. Furthermore, Casavola et al [60] developed a fluid dynamic model with chemical kinetics and determined the e ffect of different initial parameters, such as temperature, pressure, plume size and expansion velocity on the plasma expansion. Using the model, the authors were able to predict temporal evolution of titanium con centration at a specific distance from the target. In a rather similar as pect to that of CF-LIB S, a radiative, semiempirical model of laser-induced plasma v acuum expansion proposed by Gornushkin et al. [6164] also has the capabilit y of providing quantitative analytical information. This is based on the

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33 unique aspect of the model which allows for the prediction of initial conditions of the plasma expansion by a direct correlation of calculated synthetic spectra with experimentally measured ones using the Monte Carlo simulated ann ealing optimization approach (MC-LIBS). As previously mentioned, there is an apparent need for a proc edure or procedures that can be applied to samples of varying degrees of complexities without prior knowledge of its environment. The possibility of having reliable standard-free routines for quantitative LIBS analysis that could lead to absolute measur ements opens up several avenues for the general applicability of LIBS to any type of samples under different anal ytical situations. In the present study, two out of several existing st andard-free approaches in the literature were experimentally evaluated, the CF-LIBS and MC-LIBS approaches Neither technique requires reference standards nor calibration curves. Each method was evaluated for its applicability in the quantitative analysis of different certified samples, such as alum inum alloy, brass, soil, powdered alloys, etc., in both atmospheric and vacuum conditions. CF-LIBS and MC-LIBS approaches were also applied to the anal ysis of spatially-reso lved measurements performed under vacuum conditions. Development of a method for an efficient spectral data acquisition was also carried out in order to obtain an experi mental spectrum with wide wave length coverage using a gated, non-echelle LIBS system. The latter addressed the problem of the narrow wavelength range capability of the detection system used in this research. The assessment of the two approaches involved the optimization and calibration of several experimental parameters and the determination of the spectral efficiency and inst rumental function of the detection system. In addition, each method was generally classified as quantitative, se mi-quantitative or qualitative with quantitative estimates [65] depending on the relative percentage errors obtained from the

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34 analysis of the standard samples. Limitations in the applicability of each method were also assessed based on the results of the experimental evaluation.

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35 CHAPTER 2 BRIEF OVERVIEW OF LASER-INDU CED BREAKDOWN SPECTROSCOPY Introduction The laser-induced breakdown spectroscopy (LIB S) technique, also referred to as laserinduced plasma spectroscopy (LIPS), laser spark spectroscopy (LSS) or la ser ablation optical emission spectroscopy (LA-OES), falls under th e category of atomic emission spectroscopy (AES). In LIBS, the plasma is formed when a high-powered pulsed laser is focused onto or into a small volume of the sample, producing an i rradiance inside the volume exceeding several megawatts per centimeter squared (106-109 W cm-2). LIBS has been considered as one of the simplest and most convenient analytical methods for trace elemental analysis of solid, liquid and gaseous samples because the laser-induced plas ma is used as vaporization, atomization, excitation and ionization source. In this chapter, a succinct summary of the hist orical development of LI BS is described, as well as a general overview of the basic principles and characterist ics of LIBS. The scope of the discussion of pertinent LIBS processes and mechanis ms is limited to analysis of solid materials at high irradiances (>109 W cm-2). In addition, a brief review of recent applications of LIBS to solid analysis is presented herein. Historical Background The develop ment of LIBS has been summarized and discussed in great detail in Ref. [66] and several excellent review arti cles [67-76] which deals with di fferent aspects of the technique have appeared in the past decade, hence, only the most significant events are included here. In 1960, Maiman [77] constructed the first optica lly-pumped ruby laser a nd shortly thereafter, Brech and Cross [78] observed and reported the fi rst ruby laser-produced spectra. However, in their work and in most of the research which en sued, the laser was used mainly for ablation and

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36 vaporization and an auxiliary electrical spark wa s required for cross-excitation to further enhance the signal intensity. In 1963, the first analyt ical application of laser-induced plasma for spectrochemical analysis of surfaces was dem onstrated by Debras-Gudon and Liodec [79], who used a giant pulse or Q-switched laser which produced cr aters with diameters of 100 m. In 1964, Runge et al. [80] and Ferguson et al. [81] carried out similar experiments on metals and powdered solids, respectively. In the same year, temporal re solution was introduced through the introduction of streak cameras and rotating mirrors in the detection system in order to discriminate the early plasma continuum emission from late atomic and ionic line emissions. Also during this time period, commercial inst ruments were being manufactured by Carl Zeiss Jena Co. (Germany), Jarrell-Ash Corp. (USA) a nd JEOL Ltd. (Japan) but were discontinued by the late 1970s since they could not compete in accuracy and precision with conventional spark spectroscopy [66]. Following the initial investigations on laser-induced plasmas, more fundamental studies and applications of LIBS had been carried out, although most of the research works were published in the Russian literature [82-85]. Subsequently, the very first studies on matrix effects began in the late 1970s [86-88]. The initial findings showed that physical conditions and chemical composition play significant roles in LIBS signal intensities and repeatability. Since the mid-1980s, there has been a continuous increase in research activity in LIBS which can be attributed mainly to the availability of more robust, smaller, faster and less costly laser sources, the development of sensitive gated imaging detectors, such as the intensified charge coupled devices (ICCD) and the advent of high-resolution dispersion optics, such as echelle-based spectrographs [74]. As LIBS adva nced further into the last decade of the 20th century, more research groups emerged in the US Australia, Canada, Spain and Italy. It was

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37 also during this period that remote elemen tal analysis and portable instruments were demonstrated [89, 90]. In 1999, the Palleschi research group developed and patented the calibration-free LIBS (CF-LIBS) procedure for quan titative analysis with out the requirement of reference standards or ca libration curves [56, 57]. The development of LIBS from the invention of the first ruby laser to its recent adoption for planetary geological application on a mission to Mars in 2009 demonstr ates the high-level of maturity that LIBS has achieved over the past seve ral years. There is also an increasing interest in LIBS as an analytical method due to its high versatility. This is ev ident in the number of publications related to fundamentals and applications of LIBS that reached about 1,200 in the last five years. An exponential trend in the progression of LIBS publications is predicted to happen in the years to come [66]. General LIBS Process In LIBS, the plasm a is generated when a lase r pulse of sufficient energy is focused on the sample surface. A typical laboratory LIBS system is shown in Fig. 2-1. The plasma emission is collected using a lens, as shown in Fig. 2-1, or by a fiber optic cable. The collected plasma emission is spectrally resolved by a dispersive wa velength selection system and then analyzed by a detector. A single laser shot corresponds to one LIBS measurement. Generally, LIBS signal intensities from multiple laser shot s are either accumulated or averaged. Previous studies have shown that this improves the analytical figures of merit of the measurement and averages out any slight inhomogeneity in the sample composition [91]. The laser-induced plasma is weakly ionized and consists of excited atoms and ions and free electrons. It is electri cally neutral and the char ged species often act in a collective manner [66]. The mechanisms of plasma formation and evol ution consist of several complex phenomena

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38 which are dependent on critical parameters such as laser irradiance, wavelength and pulse width, thermo-optical properties of the material and the pressure and composition of surrounding atmosphere [75, 92]. A simplifie d schematic representation of the main processes involved is shown in Fig. 2-2 [75] and a detailed discussion of each step and several related processes is presented herein. Laser-Material Coupling The initial step is characterized by the coupli ng of the optical energy into a small area of the solid (Fig. 2-2a). The amount of laser energy absorbed within the material is determined by the absorption and reflectance coe fficients of the targ et, particularly in metals [93, 94]. The target absorptivity in cm-1, which is critical in the determin ation of the breakdown threshold of metals, is expressed as: n 4 (2-1) where is the laser wavelength (cm), n is the imaginary part of the bulk refractive index and 1/ is the absorption length (cm) which determines the real interaction thickness between laser irradiance and the target. The reflectance, on the other hand, has been reported to decrease under laser irradiation due to th e apparent shortening of collis ion time between electrons and lattice. However, surface contamination, e.g. presence of absorbates or oxide layers, or macroscopic defects, e.g. flakes, pits or craters, lowers the refl ectance of the surface compared to the bulk material. The presence of these impurities and defects actually a ffects the laser-material coupling to a great extent as they decrease the la ser irradiance threshold to initiate vaporization of the surface [94].

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39 Ablation, Vaporization and Breakdown According to Russo [92], at irradiances higher than 109 W cm-2, using lasers operating in the nanosecond regime or shorter, the absorption of energy results in an e xplosion or ablation of the material in the focal volume (Fig. 2-2b). Th e material removal is due to the instantaneous heating of the surface past its vaporization temperature. Ener gy dissipation through vaporization from the surface is relatively slow compared to the laser pulse duration and the pressure above the surface prevents further vaporization until the underlying material reaches a critical temperature. Once the temperature of the subs trate is raised beyond its critical value through heat conduction, the surface then explodes and le ads to the formation of a rapidly expanding vapor plume in front of the sample. Wen et al. [95] also pointed out that the rate of vaporization of the material at this point in the process is dependent only on the background gas pressure and not on the type of background gas. Chan and Russo [96] also considered the ablation process to be stoichiometric in this regime because of the more uniform non-thermal heating and the more explosive release of the ejected material. This implies that the composition of the latter is representative of the com position of the sample. Consequently, the plasma formation is initia ted when the breakdown threshold is reached and is generally a two-step proce ss. The initial step is mainly influenced by the pressure above the surface and the laser wa velength. At low pressures, or at short wavelengths, where collision effects are considered neglig ible, the predominant mechanis m is multiphoton ionization (MPI) which can be expressed as: eM M mhv (2-2) where m is the number of photons. This results when the number of photons simultaneously absorbed is greater than the ionization potential of an atom [97, 98]. Alternately, at high

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40 pressures, or at long wavelengths, the plasma is initiated by inverse br emsstrahlung (IB) where electrons gain sufficient energy by absorption of la ser radiation during collisions with neutrals. For this process to occur, an initial or seed el ectron in the focal volume must be present. As stated by Weyl [98], the presence of aerosols in the focal volume initiates breakdown since these particles heat up under laser irradi ation and could create seed el ectrons by thermionic emission. Electrons can also be created when laser irra diances are high since the electric field may be strong enough to pull an el ectron in an outer shell out of its orbital thr ough the tunnel effect. Also, electrons can be produced from a small amo unt of ionization which can be attributed to cosmic rays and natural radioa ctivity of the earth [98]. The second step in the plasma initiation is aval anche ionization, also referred to as cascade ionization or electron cascade growth, where th e electrons formed by MPI or the energetic electrons produced by IB can impact ionize an atom or molecule through the reaction: e2MM e (2-3) This will lead to a cascade breakdown causing an exponential increase in the number of free electrons [98]. Once the plasma formation is initiated, the incoming energy from the laser pulse can sustain a high-temperature plasma in which the species in the vapor ized material undergoes excitation. Expansion Descriptively, the plasma that is initially form ed appears as a bright flash of intense light followed by a loud snapping sound due to the shoc kwave produced as it undergoes expansion outward in all directions from the focal volume as depicted in Fig. 2-2c. As the plasma propagates and interacts with its surroundings, it evolves thro ugh several different transient phases which are very well described in the literat ure [95, 99, 100]. A schematic drawing of the

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41 laser-induced plasma and various interaction zones is presented in Fig. 2-3 [101, 102]. The corresponding timing of the different physical ph enomena observed during the plasma expansion is illustrated in Fig. 2-4 [95]. The initial rate of plasma expansion is on the order of 105 m s-1 and is greatest towards the focusing lens of the laser beam since this is the so urce direction of optical energy into the plasma. This creates an el lipsoidal-shaped plasma due to non-isotropic expansion [76]. The propagation of the high-temperature and high-pressure plasma causes compression of the background gas producing an external shoc kwave which strengthens when the vapor plume reaches a critical electron number density (Fig. 24) [95, 100]. The heated gas layer then begins to strongly absorb a significant fraction of the laser energy and rapidly heats to plasma conditions. This begins a self-s ustaining absorption process that results in plasma propagation into the ambient gas [99]. According to Root [ 99], the energy transfer from the plasma to the atmosphere during the expansion is a combinati on of thermal conduction, radiative transfer and shockwave heating, all of which are dependent on one or more of the following experimental parameters: laser energy, target vapor compos ition, ambient gas composition and pressure and laser wavelength [95, 103-105]. In viewpoint of Fig. 2-3, several regions and discontinuities ar e present during the expansion due to the interaction between the plasma and the ambient atmosphere and brief descriptions of each are given herein. The plasma core, which is the densest part of the plasma, only exists for the first several ns. In the si mulated model developed by Wen et al. [100], the vapor plume region is considered the unshocked part of the laser-indu ced plasma since it is not in direct contact with the external shockwave. Th e internal shockwave, which occurs from the end of the laser pulse until about 100 ns (Fig. 2-4), is formed in the outer region of the vapor plume

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42 due to the high backpressure created by the external shockwave. Wen et al. [95, 100] pointed out that for a supersonic vapor plume expansion, the internal shockwave is necessary for satisfying the pressure and velocity contin uity conditions at the contact su rface. In their simulation, the internal shockwave was shown to propagate b ack and forth between the contact surface and sample surface. The contact front simply descri bes the transition from material gas to ambient gas. It also illustrated in Fig. 2-3 that the inner region of the external shockwave is highly ionized compared to the outermost region. This is clearly due to heating of the atmosphere caused by the highly energetic plasma. Emission The resulting spectrum evolves rapidly in time due primarily to the pulsed nature of the laser-induced plasma (Fig. 2-2d). A schematic re presentation of the te mporal history of the laser-induced plasma concerning the different predominant emitting species is illustrated in Fig. 2-5 [66]. The timescales shown in Fig. 2-4 and Fi g. 2-5 are valid for a plasma initiated at 1 atm using a 1064 nm Nd:YAG laser with a pulse widt h between 4 and 10 ns. During the onset of the plasma formation when ionization is high, an intense broadband continuu m of light dominates the plasma emission until about 300 ns after the laser pulse has been fired. This continuum emission is a result of bremsstrahl ung or free-free (ff) transitions and radiative recombination or free-bound (fb) transitions. Line emissions, on the ot her hand, are due to ra diative relaxation of atoms and ions in excited states. These tran sitions are called bound-bound transitions (bb). The simplified energy level diagram for all these tran sitions is shown in Fig. 2-6 [25]. In the bremsstrahlung process, photons are emitted wh en high energy electrons decelerate through collisions. Radiative recombination, on the othe r hand, occurs when a free electron is captured into an atomic or ionic energy level and liberat es its excess kinetic energy in the form of a

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43 photon [25]. Also, more neutral atoms begin to form as electron-ion recombination proceeds throughout the plasma lifetime. Some neutrals may also recombine to form molecules [66]. Temporal resolution is usually carried out in LIBS measurements in order to discriminate the early plasma continuum from late atom ic and ionic line emissions. The important experimental parameters for time-resolved detection are delay time, tdelay and gate width, tgate, where delay time is the time between the initiatio n of the laser pulse and the beginning of the gate width and the latter is the integration windo w during which the plasma emission is recorded (Fig. 2-5) [91]. Cooling and Crater Formation The plasma starts to cool as its component s liberate more energy through radiation or conduction. The cooling process also helps in the formation of polyatomic aggregates and clusters which are deposited toge ther with molten material aro und the crater after a given time (Fig. 2-2e) [75]. The crater (Fig. 2-2f) that forms after the plasma has ceased has shape and dimensions which are dependent on the properties of the target material and the characteristics of the laser used (energy, puls e width and wavelength).

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44 350 360 370 380 390 0 2000000 4000000 6000000 Intensity (counts)Wavelength (nm) Spectrograph Spectrograph Laser Laser Array Detector Array Detector Gating Electronics Gating Electronics Computer Computer Plasma Plasma Target Target Lens Lens Lens Lens Translation Stage Translation Stage 350 360 370 380 390 0 2000000 4000000 6000000 Intensity (counts)Wavelength (nm) 350 360 370 380 390 0 2000000 4000000 6000000 Intensity (counts)Wavelength (nm) Spectrograph Spectrograph Laser Laser Array Detector Array Detector Gating Electronics Gating Electronics Computer Computer Plasma Plasma Target Target Lens Lens Lens Lens Translation Stage Translation Stage Figure 2-1. Diagram of a typica l laboratory LIBS apparatus.

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45 Figure 2-2. Schematic representation of the main processes in LIBS: (a) laser-material coupling, (b) ablation, vaporization and breakdown, (c) expansion and shockwave formation, (d) emission, (e) cooling and (f) crater fo rmation (Adapted from Ref. [75]).

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46 Figure 2-3. Schematic illustration of the laser-induced plasma and various interact ion zones (Adapted from Ref. [101]).

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47 Figure 2-4. Timing of the differe nt physical phenomena observe d during the plasma expansion (Adapted from Ref. [95]. Figure 2-5. Temporal history of the laser-induced plasma showing the different predominant emitting species (Adapted from Ref. [66]).

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48 Figure 2-6. Simplified energy level diagram showing the different transitions which produce the continuum and line emissions. Free-free (ff) transitions or bremsstrahlung correspond to loss or gain of energy by an el ectron in the field of an ion. Free-bound (fb) transitions, also called radiative recombination, occu r when an ion captures an electron and makes a radiative transition to a bound state. Bound-bound transitions (bb) correspond to the radiat ive relaxation of excited atoms, ions or molecules. and are the kinetic and ionization energies, resp ectively. (Adapted from Ref. [25])

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49 CHAPTER 3 SPECTRAL LINE PROFILE, BROADENING MECHANISMS AND INSTR UMENTAL FUNCTION Introduction During the lifetime of a laser-induced plasma, atoms and ions in the excited states undergo relaxation and radiation at char acteristic wavelengths (or frequencies) is released. When emission is recorded, spectral lines with fini te widths are obtained. Different broadening mechanisms may contribute to the finite width of a spectral line. Thes e processes result in a spectral distribution of photons in the vicinity of the central wavelength, 0 [25, 106]. A hypothetical line profile, I (), and the different spectral features ar e illustrated in Fig. 3-1 [107]. In brief, the line kernel is the spectral region within the half-width and the line wings are the spectral regions outside the kernel where < 1 and > 2. The wavelength interval, between the two wavelengths 1 and 2 at which the intensity is equivalent to half the maximum intensity, I0 is known as the full width at half maxi mum (FWHM) of the line. It is also sometimes referred to as half-width or line width. The complete shape of the line profile de pends on particular broadening process or processes and the importance of any line broadening mechanism is usually measured by the full width at half maximum. However, it should be noted that the FWHM does not necessarily impart information about the wings of the line [ 25]. In spectrochemical analysis, the spectral line profile is fundamental in the selection of lin e for analysis, especially if spectroscopic and quantitative information are desire d. It also plays an important part in the comprehension of spectral interferences and in the general performance of the analyt ical calibration function. In addition, the analysis of line profiles is an essential diagnostic tool in the study of physical conditions of the plasma such as temperature and number densities of electrons, atoms and ions.

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50 Only the major broadening effects that are commonly encounte red in laser-induced plasmas, e.g., Doppler broadening, pressure broadening and self-absorption, are described herein. In addition, a comprehensive section is devoted to the instrumental function since spectral line profiles are highly c onvoluted and knowledge of th e instrumental broadening is crucial in the determination of sp ectral line widths due to the atom ic system under investigation. Line Broadening Mechanisms Doppler Broadening Doppler broadening is the dominant broadeni ng mechanism several microseconds after the initiation of the laser-induced plasma at low pressures assuming the medium is not optically thick [25, 107]. Doppler broadening is the result of the so-called Doppler effect which is the apparent shift in wavelength of the signal fr om a source moving towards or away from the observer. 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). Hence, a large number of emitting and absorbing atoms along the optical path length which have different velocities will emit a spread of wave lengths [25]. For a D oppler-broadened spectral line the intensity distribution has a Gaussian profile and the statistical distribution of velocities is described by Maxwells law if the motion is in thermal equilibrium. The full width at half maximum for Doppler broadening can be expressed as [106]: 2 02ln8 mc TkB D (3-1) where T is the absolute temperature (K), m is the mass of radiating atom (kg), kB is Boltzmanns constant (J K-1) and c is the speed of light (m s-1). Evaluation of the constants in Eq. 3-1 and expressing m by the atomic or molecular weight M = mNA where NA is the Avogadros number (mol-1), the Doppler width simplifies to [106]:

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51 M TD 0 71016.7 (3-2) Pressure Broadening This broad type of broadening, also called coll isional broadening, is due to the interaction of the emitters with different types of perturbers The type of interaction can be expressed in terms of perturbation of energy levels, V which varies with the interparticle distance R as given by [108]: x x R C RV (3-3) where the value of x and the interaction constant Cx depend on the type of interaction considered. When collisions are between neutral particle s, the broadening is called van der Waals broadening and x = 6. When the interactions are between similar atoms, the broadening is called resonance or Holtzmark broadening and x = 3. When the broadening is due to charged perturbers, the broadening is called Stark broadening and x = 2 or 4 for linear or quadratic Stark effect, respectively [25, 106, 108]. Van der Wa als and resonance broadening mechanisms are important in weakly ionized plasmas while Stark broadening is most important in highly-ionized and high density plasmas where th e strong electric field from th e charged species produces a broadening of the transitions betw een the split atomic levels. Van der Waals broadening. This broadening is attribut ed to the interaction between neutral species. Specifically, a fluctuating dipole in the radiating atom induces a dipole to the neutral ground state atom and th e corresponding interaction causes line broadening. This dipoleinduced dipole interaction can be expressed as [108]: 6 6 6 0 21 4 R C R p RV (3-4)

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52 where is the polarizability of the perturber in m3, p2 is the mean square dipole moment, and 0 is the permittivity of free space. The negative sign indicates that the force is attractive. In addition, the mean square dipole moment is larg est for most highly excited levels which implies that the perturbation undergoes a red shif t. However, for small values of the force becomes repulsive and the perturbation is a blue shift. The value of x in this case is 12 which is described by the Lennard-Jones potential [108]. The corresponding broadening and shift (in m) due to van der Waals interaction, according to the impact approxima tion, are given by [109]: c nCVDW2 5/35/2 671.2 (3-5) c nCshiftVDW2 5/35/2 6 ,98.0 (3-6) where is the transition wavelength in m, is the relative velocity in m s-1, n is the number density of perturbing particles (m-3) and C6 is the interaction constant in m6 s-1, as given in Eq. 3-4. Resonance broadening. This broadening mechanism is also known as Holtzmark broadening and occurs only between identical species. Also, res onance broadening is restricted to lines with the upper or lower level with an electric dipole transition to the ground state (resonance lines). This takes the form of a dipole-dipole interact ion which results to symmetrically broadened and unshifted lines [25] The FWHM in m can be expressed as [109]: n cm fe g ge ik k i res 2 0 2 23 0 2/116 3 (3-7) where gi and gk are the statistical wei ghts of the lower and upper states, respectively, e and me are elementary charge (C) and ma ss (kg) of the electron, fik is the transition oscillator strength

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53 (dimensionless) and the rest of the variables have already been defined and can also be found in pp. 19-23. Stark broadening. The perturbation of the ener gy levels of a radiating atom by microscopic electric field of i ons or electrons is called the Stark effect and it contributes significantly to line width broadening under ty pical LIBS conditions. For hydrogenic ions, where x =2, the Stark effect is linear which causes the symmetrical splitting of energy levels. The result is a symmetrically broadened, unshifted spectral line [25]. For non-hydrogenic elements, on the other hand, the interaction is de scribed by a quadratic Stark effect where the pert urbation is proportional to 1/ R4. The quadratic Stark effect splits the energy levels asymmetrically and also shifts their center of gravity downwards [25]. The shift is usually towards the red and is the same for ions or electrons. The FWHM of a Stark-broadened line and the corresponding shif t (in m) are given by [109]: 2/16/1 4/16 220068.01 1053.51102 Tn N wne e e Stark (3-8) ) 0068.01( 1032.6 1012/16/1 4/16 22 ,Tn n w d wne e e shiftStark (3-9) where ne is the electron number density in m-3, w is the electron impact half-width in m, d/ w is the ratio of shift to width (dimensionless) and is the ion-broadening parameter (dimensionless). Self-Absorption Broadening When a significant fraction of photons emitted by excited atoms is absorbed by atoms in the lower level along the optical path between emission volume and detector, self-absorption occurs. This is common for transitions involvi ng ground or near ground states, i.e., resonance or near-resonance transitions, respectiv ely. Self-absorption distorts and broadens the line profile as shown in Fig. 3-2 [106]. At low atomic concen trations, the entire li ne profile grows with

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54 concentration. However, as self -absorption occurs, the line profile begins to saturate and attains a flat-top shape (Fig. 3-2). A related phenomenon to self-absorption is sel f-reversal which is char acterized by a dip at the center of the line profile (Fig. 3-3). Th is usually occurs if the media does not have homogeneous temperature distribution, i.e., a hot inner core is enveloped by a cooler outer layer of much lower electron number density where the line center can be strongly absorbed [106]. Although, it is very easy to rec ognize a self-reversed line because of the dip in the line center, it is oftentimes difficult to determine if a line suffers from self-absorption due to the good adherence of Stark-broadened line prof iles to dispersion shapes [110]. Self-absorption check. A straightforward experimental check for self-absorption is described by Konjevic [110] where a concave or spherical mirror is plac ed at the radius of curvature, rc which is twice the focal length of the mirror. This particular configuration, as shown in Fig. 3-4a, doubles the path length which implies that if a line is not self-absorbed, the signal intensity should double as we ll. In practical terms, line profiles are recorded with and without the spherical mirror and then one observes whether the profiles are proportional everywhere to the same factor [ 110]. If the proportionality fact or is not preserved for the high intensity region at or near the line center but in stead becomes smaller, then self-absorption is present. If the product of the absorption coefficient () and path length l is not large (() l < 1), the measured intensity may be corrected to the limit of an optically thin layer (() l 1) [110]. However, if absorpti on is extremely large, i.e., () l 1, the intensity of the plasma radiation approaches that of a blackbody and the line profile ca nnot be recovered. Konjevic [110] described in detail the st eps involved in the eval uation of correction fo r self-absorbed line

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55 profiles using the config uration described in Fig. 3-4 and only the pertinent steps are briefly discussed herein. Assuming that the plasma is in local thermodynamic equilibrium (LTE), the intensity of radiation I() can be expressed as: l BIbb exp1 (3-10) where bbB is the blackbody spectral radiance as given by Plancks law (Eq. 3-11). 1/exp 1 25 2 Tkhc hc BB bb (3-11) At the optically thin case where () l 1, the term exp(-() l ) can be simplified to 1() l hence, Eq. 3-10 becomes: lBIbb (3-12) The correction factor K is then given by taking the ra tio of Eq. 3-12 and Eq. 3-10: l l K exp1 (3-13) The corrected line profile is then obtained by multiplying the self-absorbed profile with the correction factor K Experimentally, K can be determined by recording I2() and I1() which are the spectral line profiles recorded with and with out the spherical mirror, respectively (Fig. 3-4b). From the spectra recorded, the ratio R can be determined by: l G I I R exp11 2 (3-14) where G is a factor which takes into account the mirro r reflectivity and geometrical effects. For the continuum radiation, () = 0 and G I I Rc c c 11 2 (3-15)

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56 () l can be solved by combining Eqs. 3-14 and 3-15: 1 1 lnR R lc (3-16) Hence, the correction factor K may be expressed as: 1 1 1 1 1 lnc cR R R R K (3-17) Duplication factor. A parameter also related to self-absorption is the duplication factor, D which has previously been defined by Alkemade [111] as the relative increase in line intensity (or integral absorption) caused by doubling the product nafikl where na is the atomic number density. lfnI lfnIlfnI Dika ika ika 2 (3-18) This means that when the optical path length is doubled, as in the cas e described previously when a spherical mirror is used and the medium is optically thin, the duplication factor is unity. However, at the optically thick limits, D approaches a value e qual to 0.415 [111]. Instrumental Function If a source emits radiation which consists of a single monochromatic wavelength 0 and is detected by a perfect spectrometer the output should be identical to the spectrum of the emission which is a perfect line at exactly 0. But in reality, spectrometers are not ideal and they produce an apparent spectral broadening of the purely monochromatic wavelength. The line profile now has a finite width and is known as the instrument al line profile or instrumental function. It is crucial to have knowledge of the instrumental function since emission wavelengths are usually in the same order of magnitude or even narrower than the instrumental profile that the

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57 latter determines its shape. In general, it is always best to virtually eliminate the contribution of instrumental broadening by using high-resolution spectrometer whose instrumental width is of the order of one-tenth or less than the observed experimental pr ofile [110]. Unfortunately, that is not possible in several cases, hence, the next alternative is to dec onvolute the line profile and that requires experimental determination of the instrumental function. The shape of the instrumental profile is a function of various parameters such as: width of the entrance slit width of the exit slit or the size of pixel in the case of a multi-channel array detector diffraction effects aberration effects quality of the components a nd alignment of the system Influence of Slits If the slits are of finite widths and there ar e no other contributing eff ects to broaden the line then the contribution of the slit to the overall instrume ntal line profile is the convolution of the entrance and exit slit images. Examples of the convolution of the entrance and exit slits depending on their respective widths are illustrated in Fig. 3-5. The FWHM in this case is equal to the geometric spectral bandpass s except at very narrow slit widths where aberration and diffraction effects must be c onsidered. The geometric spectral bandpass is given by [106]: slitdswR (3-19) where Rd is the reciprocal linear dispersion (nm mm-1) which is a property of the detection system and represents the number of wavelength intervals contained in each interval of distance along the focal plane and wslit is the slit width. Influence of Aberrations Several different forms of aberrations affect th e instrumental profile. These aberrations are deviations of the optical elements from ideal or first-order behavior. In actual practice,

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58 aberrations occur in combinations rather than alone. The three most common aberrations for optical systems are spherical aberration, coma and astigmatism. Spherical aberration. Spherical aberration is the result of rays emanating away from the surface of an optical surface. For converging elem ents, off-axis or marginal rays are focused closer to the element than paraxial rays. Parall el rays produce a circle in the focal plane [106]. This phenomenon is illustrated in Fig. 3-6. In addition, spherical aberration is dependent on lens shape, orientation and conjugate ratio, as well as on the index of refraction of the materials present [112]. Generally, this form of aberrati on can be reduced by placin g an aperture stop in front or behind the lens to block off-axis rays but this also causes reduction in the irradiance of image. Coma. Coma arises from differences in the op tical path lengths of various rays to the focal plane in an off-axis system. Parallel rays which are striking the lens at a slight angle causes the image to develop a comet-like tail, as show n in Fig. 3-7a. This skewing of rays in the focal plane results in the broadening of the base on one side of a spectral line, as depicted in Fig. 3-7b [106]. As with spherical ab erration, correction can be achieved by using multiple surfaces. Also, a clearer and sharper image may be obtained by placing an aperture in the optical system to eliminate more off-axis rays [112]. Astigmatism. Another type of aberration usuall y encountered in optical systems is astigmatism. It arises when the point object is co nsiderably off-axis and results in two distinct focal lengths for rays in two different planes (tan gential and sagittal), as shown Fig. 3-8. The figure illustrates that tangential ra ys from an object come to a focus nearer to the lens than do rays in the sagittal plane [112]. In other word s, when an image is evaluated at the tangential

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59 focus, a line in the sagittal direction is obser ved and vice versa. Astig matism causes blurring of the image which can result in a loss of wa velength resolution (b roadening) [113]. Influence of Diffraction Diffraction, which is defined as the deviation of light from rectilinear propagation when it encounters an obstacle, is another optical phe nomenon which affects the instrumental function [106]. If the slit widths are infinitesimally na rrow and aberrations are negligible, the resulting instrumental line profile is that of a classic diffraction pattern. Diffraction affects the shape of the intensity distribution profile by broadening the image by d and rounding off the corners as illustrated in Fig. 3-9. d is the diffraction-limited spectral bandpass which can be expressed as [107]: a f RwRdddd 2 (3-20) where wd is the diffraction-limited slit width, f is the focal length of the spectrometer and a is the width of the beam emerging from the dispersion element [106]. Although spectral resolution is limited by aperture diffraction (e.g., grating or pris m) not by slit diffraction, it is the latter which imposes a limitation on the transmitted intensity at small slit widths, hence, a lower limit to the useful width of the entrance slit given by wd in Eq. 3-20 [107]. Overall Line Profiles Doppler and instrumental line profiles usually have a Gaussian distribution and collisional processes follow a Lorentzian function. When bo th pressure and Doppler broadening are present along with a substantial contribution from instrument al broadening, the resulting line profile is a combination of Lorentzian and Gaussian line sh apes. Assuming that the three broadening types are independent processes, the overall line profile is obtained by convoluting the three profiles. The result is a Voigt profile with a FWHM given by:

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60 2 222G L L V (3-21) where L and G are the line widths of the Lorentzian and Gaussian profiles, respectively. Furthermore, the wings of a Voigt profile are almost entirely determined by the Lorentzian component and the central part of the Voigt and its FWHM are essentially determined by the Gaussian component, as illustrated in Fig. 3-10. It is also very important to note that a Gaus sian profile may be itself a convolution of two or more Gaussian profiles, e.g. Doppler and inst rumental line profiles, th e FWHM in this case is given by: 2 2 I D G (3-22) where I is the line width of the instrumental profile Similarly, a Lorentzian profile may also be a convolution of two or more Lorentzian prof iles and the resultant FWHM can be expressed as: 2, 1, L L L (3-23)

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61 Figure 3-1. Line profile, half -width, kernel and wings of a spectral line. The function I () in the vicinity of 0 is the line profile. The wavelength interval = 2 1 between the two wavelengths 1 and 2 is the full width at ha lf maximum (FWHM) of the line. The line kernel is the spectral region within the half-width and the line wings are the spectral regions outside the kernel where < 1 and > 2. (Adapted from Ref. [107])

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62 Figure 3-2. Spectral line profiles as a function of increasing atomic concentration (a through h). The line center reaches the blackbody intensity limit at high atom densities. (Adapted from Ref. [106]) Figure 3-3. An example of a self-reversed spectral line profile.

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63 Figure 3-4. Self-absorption check. (a) A spherical mirror is placed at the radius of curvature and the corresponding (b) spectral line profiles I1() and I2() with single and double plasma le ngth, respectively, are recorded (Adapted from Ref. [110])

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64 Figure 3-5. Convolution of the entrance and exit slit widths. (a) Equal entrance and exit slit widths results in a triangul ar-shaped instrumental prof ile and (b) Unequal entrance and exit slit widths results in a trapezoidal-shaped profile. Figure 3-6. Effect of spheri cal aberration on a lens. The corresponding image formed on the focal plane is a circle with blurre d edges. (Adapted from Ref. [106]) Figure 3-7. Effect of coma: (a) on an image a nd (b) on the spectral distribution (Adapted from Ref. [114]).

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65 Figure 3-8. Effect of astigmatism on a concave mirro r used off-axis. If the image plane is at the tangential focus, Ft, sagittal astigmatism occurs and if the image plane is at the sagittal focus, Fs, tangential astigmatism occurs. (Adapted from Ref. [114]) Figure 3-9. Effect of diffraction. The instrumental line profile is broadened by d due to diffraction spreading.

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66 Gaussian Gaussian Lorentzian Lorentzian Intensity ( Intensity ( a.u a.u .) .) Voigt Voigt GL Gaussian Gaussian Lorentzian Lorentzian Intensity ( Intensity ( a.u a.u .) .) Voigt Voigt Gaussian Gaussian Lorentzian Lorentzian Intensity ( Intensity ( a.u a.u .) .) Voigt Voigt GL Figure 3-10. Overall spectral line profile. The convolution of Gaussian (blue) and Lorentzian profiles (red) results in a Voigt (green ) profile. (Adapted from Ref. [107])

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67 CHAPTER 4 EXPERIMENTAL CHARACTERIZATION OF INSTRUMENTAL SYSTEM AND OPTIMIZATION OF OPERATING CONDITIONS Introduction Complete characterization of the experimental set-up and data acquisition is important in any system to enhance accuracy and precision, partic ularly if quantitative information is desired. Several parameters were optimized and calibrated in this research which included the slit width, instrumental function, detector spectral efficiency, grating rota tion angle, number of vertical CCD pixels for binning, and the num ber of laser shots accumulated. Experimental Set-up The schematic diagram of the experimental sy stem used for LIBS experiments performed under atmospheric conditions is depicted in Fig. 4-1. It consisted of a laser, a spectrometer, an intensified charge-coupled device (ICCD), det ector gating and control electronics, and a computer for control and data acquisition. A Q-switched Nd:YAG laser (Brilliant T27; Quantel USA) delivered a maximum pulse energy of 360 mJ at the fundamental wavelength of 1064 nm and produced a 5.3 ns duration pulse at a maxi mum repetition frequency of 10 Hz. The pulsed laser beam was focused to a 0.070 cm diameter s pot on the target by using a 3.5 cm diameter, 10 cm focal length lens. For the present research, a pulse energy of 90 mJ was used which provided an incident laser irradiance of 5 GW cm-2. A simple positioning system consisting of a helium-neon laser, a photodiode detector and a multi-meter was used to monitor the position of the target surf ace with respect to the laser focusing lens. The positioning system was optimized so that half the value of the voltage read when there was no sample indicated the correct lens-to-sample distance (LTSD). This allowed samples of varying thicknesses to be anal yzed without compromising reproducibility. Movement of the sample was accomplished by usi ng an x, y, z translation stage. For all

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68 measurements, the sample was translated every 10 laser shots. A controlled stream of air was also blown across the surface of the sample to carry away the dust plume formed by the laser radiation shockwave. Plasma emission was collected by a 5 cm diameter lens with a focal length of 7.5 cm. An adjustable iris was attached to the lens in order to correctly match the F-number of the spectrometer which is an F/6.5 system. The diameter of the aperture used was 2.3 cm. The 1:1 image of the plasma was focused onto a 35m wide entrance slit of a 0.5 m focal length CzernyTurner-based spectrometer (SpectraPro-500i; Ac ton Research Corp.) equipped with three gratings: 1200, 2400 and 3600 grooves mm-1 grating. However, only the 2400 grooves mm-1 grating was used in this research since it provided a good compromise between spectral resolution and spectral window size The system was coupled to a two-dimensional intensified charge-coupled device (ICCD-576S/RB-E; Princet on Instruments) and it s controller (ST-138; Princeton Instruments) and a programmable pulse delay generator (PG-200; Princeton Instruments) was used to gate the detection. Th e firing of the laser flas h lamp was triggered by a boxcar (SR250; Stanford Research Systems) and the corresponding Q-switch output served as the trigger for the pulse generator. The re petition frequency was kept at 1 Hz for all measurements. The data acquisition was c ontrolled using Winspec32 software (Version 2.5.18.2; Princeton Instruments) installed on an Intel Pentium 4 1.80 GHz computer. A schematic of the cable connections and the corresponding timing sequence are shown in Figs. 4-2a and 4-2b, respectively. In this part icular timing mode, the laser acted as the master and sends out a trigger to the pulse generator to op en the shutter and to begi n the gated detection. An oscilloscope (TD 520A, Tektronix, Inc.) was used to measure the sequence of acquisition which began from the output trigger sent out by the boxcar to th e laser flash lamp.

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69 For experiments carried out in vacuum, the configuration was similar to that of Fig. 4-1 only with an aluminum vacuum cell instead of a sample stage. The schematic diagram is illustrated in Fig. 4-3. One end of the vacuum chamber was connected to a roughing pump and a Pirani pressure gauge and digita l controller (Edwards) through a three-way valve while the other end was connected to a needle valve for air flow control. This configuration allowed samples to be changed without turning off the vacuum pump in between measurements. All measurements were temporally resolved with a suitable delay interval and proper gate width to discriminate the early plasma continuum from late line emissions and to maximize the signal-to-noise ratio as well. Calibration of the Mi crometer Slit Dial Knowledge of the exact value of the slit width us ed in any type of spectrochemical analysis is critical in the determination of the contri bution of the instrumental broadening since the product of the slit width and reci procal linear dispersion gives th e geometric spectral bandpass. The importance of understanding the effects of instrumental broadening and other types of broadening mechanisms on spectral line profiles ha ve already been discussed in Chapter 3. Therefore, prior to any LIBS measurements, the slit dial of the spectrometer was calibrated to guarantee correct reading of the slit width. The calibration of the micrometer slit dial is based on the Fraunhofer diffraction pattern formed when parallel rays strike a slit aperture, as shown in Fig. 4-4. The rays from the slit that reach P0 have the same path lengths and the sinusoi dal waves are in phase and add to produce a larger-amplitude resultant due to constructive in terference [106]. Howeve r, in the case of the rays which reach P1, a minimum in irradiance results in destructive interference. The general formula for diffraction minima is given by: mw 'sin (4-1)

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70 where w is the slit width and m is the diffraction order. Based on the geometry in the schematic given in Fig. 4-4, the following relationship can be obtained: f x tan (4-2) where x is the distance from the central diffract ion maximum to a diffraction minima and f is the focal length. In general, for very small angl es, the small angle approximation can be applied, i.e., tan and sin and for focal lengths much larger than the slit widths, = hence: x fm w (4-3) which is the condition for diffraction minima. By extension, the general formula for successive maxima can be expressed as: 2 1 x fm w (4-4) where x is the distance from the central di ffraction maximum to another maximum. The slit dial calibration expe riment was carried out by focusing a helium-neon (He-Ne) laser onto the entrance slit of the spectrometer, as illustrated in Fig. 4-5. The exit slit was covered in case stray light reached the detector to avoid damaging the intensified charge-coupled device even though the system was not switched on. A small screen, e.g. a piece of paper, was placed at the first focal plane (right in front of the collimating mirror) for viewing and marking of the resulting diffraction pattern formed at differe nt slit widths. The image formed at the focal plane is depicted in Fig. 4-5. Due to the ease of marking the diffraction maxima rather than the minima, Eq. 4-4 was used to calibrate the slit dial at varying nominal slit widths. The value of f used in the calculations is not the nominal focal length of the spectrometer but the actual distance

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71 between the entrance sl it and the viewing screen which is equal to 48.5151 cm. The small difference is due to protective boundary that is in front of the collimating mirror. The value of is equal to the wavelength of the He-Ne laser beam which is 0.6328 m. The results of the calibration are summarized in Table 4-1. The of fset was calculated by ta king the absolute value of the difference between the calculated and nominal slit widths. From the results obtained, the zero of the micrometer slit dial corresponds to approximately 15.3 0.8 m. Optimization of the Slit Width The slit width was optimized in order to determine the minimum value that an entrance slit can be opened without compromising throughput or the maximum value that it can be opened without degrading the resolution. In other word s, diffraction and/or aberration-limited slit width have to be determined. The optimization was carried out by illuminating the entrance slit with a Hg hollow cathode lamp (Fisher Scientific Co.). Th e schematic of the set-up is illustrated in Fig. 4-6. The measurements were taken with the I CCD switched to shutter mode and the acquisition set to spectroscopy and free run modes. Differe nt exposure times were used depending on the wavelength under investigation to avoid saturation of the ICCD The hollow cathode lamp was maintained at a current of 15 mA. Several Hg li nes were recorded at 10 different slit widths starting from 15 m to 105 m at a 10 m interval. Triplicate measurements were carried out. One of the spectral lines used in the op timization was Hg I at 294.263 nm and the normalized spectra at different slit s widths are shown in Fig. 4-7a. The lines were fitted with a Gaussian function using an in-house fitting program written in MATLAB. The corresponding half widths determined from the fit were plotted against the slit widths and the result is shown in Fig. 4-7b. It can be observed that the FWHM incr eases in proportion to th e slit width at values greater than 35 m. However, at slit widths less than 35 m, the FWHM remains approximately

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72 constant and is larger than the calculated ge ometric spectral bandpass since the image of a given at the focal plane is no longer the width of the slit but larger. This is because the spectral bandpass is controlled by aberrations and diffraction as well as disp ersion. Other wavelengths of Hg I were also recorded and the pl ot of their half-widths against the slit width is shown Fig. 4-7c. It is evident from all wavelengths considered th at the resolution can no longer be improved even if the slit width is further decr eased to values lower than 35 m. Hence, the slit width used in all succeeding measurements is 35 m. Using the expression given in Eq. 3-20 [107] the diffraction-limited spectral bandpass, d, can be calculated for Hg I at equal to 294.263 nm using the following instrumental parameters: reciprocal linear dispersion, Rd = 0.7252 nm mm-1 focal length, f = 500 mm effective aperture width, a = 59.18 mm The result is approximately equal to 0.0036 nm which is much narrower than the experimental FWHM determined which is about 0.048 nm. This is because aside from diffraction and aberration effects, the main parameter which determines the limiting slit width or limiting resolution in this pa rticular case is the pixel size of the CCD. According to the Nyquist sampling theory, in order to assure perfect image reconstruction, the resolu tion must be calculated over 2.5 pixels. This implies that for a CCD with a pixel size of 22.5 m, the limiting resolution at 294.263 nm is 0.041 nm which is closer to the experimentally determined FWHM. Development of a Method for Spectral Data Acquisition In order to obtain quantitative elemental information using approaches which do not require the use of calibration curves or referen ce standards, the plasma emission spectrum must contain lines, ideally, from different ionization stages for all elemen ts present in the sample. In

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73 other words, a spectrum with a relatively wide sp ectral range is required. This can readily be achieved using an echelle spectrometer coupled to a CCD or an ICCD since they are designed to provide simultaneous recording of a wide wave length range spectrum in a single acquisition. However, in this research, a plane grating spect rometer coupled to an ICCD was used which has the shortfall of providing a ve ry narrow spectral window. Hence, development of a spectral acquisition method was necessary so that data in the wide spectral range from 220 to 700 nm may be obtained using a non-echelle detection system. This requi red multiple acquisitions of successive spectral windows and merging the win dows together with optimum overlap using an in-house merging program written in Q-Basic. An example of a merged spectrum is shown in Fig. 4-8 where different colors depict the spectral windows spliced together. A spectrum such as this one, with a spectral range from 220 to 700 nm required 67 individual spectral acquisitions. This also necessitated 67 grating rotations in order to move from one spectral window to the next. The size of the spectral window is not cons tant since dispersion varies with the wavelength as well. The spectral window size in the UV regi on is about 10 nm and decreases to about 6 nm at higher wavelengths for a 2400 grooves mm-1 grating. Knowledge of the angles and dispersion charac teristics of a plane grating spectrometer and the physical characteristics of the ICCD are pe rtinent in the proper se lection of the optimum central wavelength for successive spectral wi ndows in order to achieve optimum overlap (minimal to no gaps) in between windows when me rged together. Fig. 4-9 shows a schematic of the components of a Czerny-Turner-based gra ting spectrometer and th e respective rays and angles formed when light enters the slit. In brief, the rays emitted by the plasma are reflected off by the first mirror onto the collimating mirror. Th en, the collimated light strikes the grating and is dispersed onto the focusing mirror which focuse s the dispersed wavelengths at the focal plane

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74 for detection with an ICCD. The angle theta () that is formed between the axis of rotation and the axis normal to the grating is th e grating rotation angle. Alpha () is the angle of incidence or the angle formed between the incident ray and the normal axis and beta () is the angle of diffraction or the angle formed between the diffracted ray and the normal axis. Phi ( ) is the exit or take-off angle which is a constant value depending on the grating, in this case, is equal to 8.585. The distance between the en trance slit to the collimating mirror is the focal length f which is the same distance from the focusing mirror to the focal plane. The first step in the method development is th e determination of the grating rotation angle which can easily be solved using the grating equation: G d dm cossin 102cossin2sinsin6 (4-5) where m is the diffraction order, d is the groove spacing in nm groove-1 and G is the number of illuminated grooves in the grating. By simple manipulation, the grati ng rotation angle can be expressed as: cos102 arcsin6Gm (4-6) Once the grating rotation angle is known, the reciprocal lin ear dispersion for a specific wavelength is calculated. Using simple geometric relations, the reciprocal linear dispersion is given by: mfG mf d mf d dx d Rd 610)cos( cos cos (4-7) The third step in the method development is the determination of the spectral range, range, at a specific central wavelength. The spect ral range of the system varies with the

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75 reciprocal linear dispersi on and is also dependent on the pixel size of the CCD, wpixel, as well as the number of column pixels, Npixel, and can be calculated using the simple equation: pixel pixel d rangeNwR (4-8) Furthermore, since the central wave length of the first spectral window, c,1, is already predetermined and is equal to 225 nm, the starting wavelength, s,2, for the second spectral window can be calculate d using the equation: 21, 1,2, range cs (4-9) For a 10-pixel overlap between windows, the st arting wavelength can be adjusted accordingly using the following equation: pixeld sswR 102,2,' (4-10) Finally, the central wavelength for the subsequent window can now be determined once the adjusted starting wavelength s,2 is known: 22, 2,'2, range sc (4-11) The whole process can be repeated several times depending on the size of the spectral range desired. In this research, 67 central wavelengt hs were calculated for an optimum merging of spectral windows within the range of 220 to 700 nm. Table 42 lists the 67 cal culated central wavelengths used in all measurements. Determination of the Instrumental Function As previously discussed in Chapter 3, the dete rmination of the instrumental or slit function is fundamental especially in cases where the line wi dth of a spectral line profile is of comparable magnitude to the spectral bandw idth of the instrument. Th e resulting complex convolution

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76 integral can be analytically or numerically solved if the instrume ntal function has been completely characterized. In addition, the inst rumental function is required in plasma expansion modeling algorithms particularly if the calculated theoretical emission spectrum has to be compared to an experimentally acquired one. The same experimental configuration as in th e optimization of the slit width was used in order to determine the instrumental function (F ig. 4-6). The hollow cathode lamp which emits several spectral lines from both mercury and argon was used under a constant current of 5 mA. Triplicate measurements were carri ed out using an exposure time of 100 ms. All Hg and Ar lines detected between the spectral range of 220 and 700 nm were fitted with a pseudo Voigt function and the corresponding line widths were calculated fr om the fit. The spectra are shown in Fig. 410a and the plots of the FWHM versus waveleng th are shown in Fig. 4-10b. The resulting instrumental function was fitted with a secondorder polynomial fit using Origin 7.5. The average of the fits is shown in Fig. 4-10c, as well as the theoretical sp ectral bandpass calculated using a slit width of 35 m. The same decreasing trend can be observed between the experimentally determined spectra l bandwidth and the calculated theoretical spectral bandpass. Furthermore, the experimentally obtained values are significantly highe r since it does not only take into account the width of the slit but all the other optical components of the detection system. The experimental reciprocal linear disp ersion function can be easily evaluated from the instrumental function by dividing it by the slit width used in the experiment. The resulting second-order polynomial fit of th e dispersion is shown in Fi g. 4-10d and the corresponding polynomial equation for the disper sion function is given by: 271083987.9001.076486.1 dR (4-12)

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77 Determination of the Detector Spectral Efficiency The efficiency of the grating and the spectral response of th e detector must be known over the whole spectral range of interest since their re sponse is usually not flat with wavelength. The spectral efficiency of the detection system was determined using deuterium and halogen calibrated light sources (DH-2000; Ocean Optics) The experiment was performed by placing the fiber optic approximately at the plasma position. For experi ments which require the use of a vacuum cell, the fiber optic was placed behind th e sample chamber in order to correct for the effect of the quartz window on plasma emissi on. The theoretical response curves of the deuterium and halogen lamps are shown in Fig. 4-11a and the experimental response curves of the detection system is shown in Fig. 4-11b. The relative response curv e shown in Fig. 4-11c was obtained by dividing the experimental resp onse by the theoretical response. Due to the difference in the optical power be tween the two sources, it can be observed that the outputs from the deuterium and the halogen sources do not overlap. However, a simple multiplication of a constant factor to the halogen response curve corrects for this difference. All experimental spectra are corrected for the detector spectral effi ciency using the merged spectral efficiency data shown in Fig. 4-11d. For experiments that requ ire the use of a vacuum sample chamber, the spectra were corrected using the spectra l efficiency shown in Fig. 4-11e. Determination of the Effect of CCD Pixel Binning Another parameter that was evaluated in this re search is the number of CCD vertical pixels to be included in the binning process. Binning is a clocking scheme that allows charges from adjacent pixels on a CCD array to be combined or summed. It is also a consequence of carrying out measurements in spectroscopy mode rather than imaging mode. This can offer advantages of faster readout speeds and improved signal to noise ratios at the expense of reduced spatial resolution. In spectroscopic CCD systems, a spectra l line is typically an image of the slit formed

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78 on the CCD. The image of the slit typically has a high aspect ratio, i.e., very long and thin, and is orientated perpendicular to the readout register of the CCD. The signal from a single spectral line can be binned to achieve the best signal to noise ratio (S/N) without any deterioration in spectral resolution [115]. Shown in Fig. 4-12a is the zero order image of a soil plasma taken at a delay time of 1 s and 0.5 s integration time, as well as the differen t number of pixels included in each binning process. The effect of binning was determined using a Mg I line at 285.3 nm shown in Fig. 412b. The integrated intensities at different binni ng sets is shown on the first panel of Fig. 4-12c and it can be observed that the intensity increases as more pixels are summed which is to be expected. The background signal was also calculat ed and it also increased, almost linearly with the number of pixels binned. The corresponding relative standard deviation or RSD was also determined and it improved as more pixels are bi nned. It can be concl uded that binning more pixels is better in terms of si gnal, RSD and S/N but only up to a certain limit. In this case, the limit is set by the constant S/N and RSD observe d for binning sets 5 and 6. From the results obtained, the limit to the number of pixels included in the binning for all succeeding measurements was the height of the plasma, sin ce binning more than the height of the plasma increased the background more th an the signal. Therefore, the emission measurements are spatially-integrated over the full height of the plasma and as a consequence, the succeeding values obtained for electron number density and temperature determinations are spatiallyintegrated as well. Optimization of the Number of Accumula ted Laser Shots and Sampling Procedure Castle et al. [43] comprehensively investig ated the effect of several controllable variables on the precision of LIBS measurements. In this research, a similar experiment was

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79 undertaken in order optimize the experimental op erating conditions in terms of the number of accumulated laser shots for a single spectral acquisition by comparing the relative standard deviation (RSD) obtained for inter-measurements. Inter-measurements, based on the definition given in Ref. [43], are measurements consisting of the summation of spectra from several laser shots. An investigation of the ef fect of sampling a fresh spot (set A) or the same spot (set B) on LIBS inter-measurement precision was carried out as well. Set A was carried out by recording the spectra of 80 individual laser shots while the sample was being translated every shot in order to sample a fresh surface. Set B, on the othe r hand, was taken by reco rding the spectra of 80 individual laser shots while the sa mple was translated every 20 shots. In this manner, 5, 10 and 20 shots can be accumulated which results to 8, 8, and 4 inter-measurements, respectively, for both sets considered. The LIBS measurements were performed on an aluminum alloy standard S-11 using a delay of 1.0 s and a gate width of 1.0 s. The components of the alloy are summarized in Table E-1 in Appendix E. The analytical line investigat ed in this study is the singl y-ionized Al line at 281.619 nm and the corresponding spectra for the two sets ca rried out in conjunction with the different number of laser shots accumulated are shown in Fig. 4-13a and 4-13b. The signal intensities shown are the average of inter-measurements and the error bars correspond to the standard deviation calculated. The resul ting spectrally integrated line in tensity is plotted against the number of shots accumulated in each set and is sh own in Fig. 4-13c. The intensities increased with the number of laser shot s and are generally much higher for set A when translational sampling is carried out similar to the results obtained by Castle et al [43]. The corresponding RSD calculated by using the accumulated signal in tensities from sequential measurements was plotted against the number of laser shots accumu lated for sets A and B and the precision was

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80 highest when 10 shots were accumulated as shown in Fig. 4-13. Also, comparing translational sampling from stationary sampling at 10 accumulate d shots, the precision is highest when a new surface is sampled per shot, however, the differen ce between the RSDs are not very significant. Hence, in all measurements that followed, accumulation of 10 laser shots on the same spot was carried out. Such an accumulation allows averag ing of the shot-to-shot fluctuations in the plasma and improves the signal-to-noise ratio. This also gives the simple advantage of conserving the amount of target surface samp led for each spectral window acquired since multiple narrow spectral windows from 220 to 700 nm were recorded for a LIBS quantitative analysis.

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81 Figure 4-1. Experimental LI BS set-up for experiments under atmospheric conditions.

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82 Figure 4-2. Schematic diagram of (a) cable connections and the co rresponding (b) timing sequence used in the experimental system. Th e pulse widths depicted in (b) are not to scale.

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83 Figure 4-3. Experimental LIBS set-up for experiments under vacuum conditions.

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84 Figure 4-4. Ray diagram for Fraunhofer diffraction by a sing le slit and the corresponding intensity distribution and image of the diffrac tion pattern. In (a) parallel source rays illuminate the slit where diffraction o ccurs. The diffraction minimum at P1 is seen to arise in (b) from the superposition of rays diffracted at angle that are at a distance w/2 apart. (Adapted from Ref. [106])

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85 Figure 4-5. Experimental set-up used in th e calibration of the micrometer slit dial. Figure 4-6. Experimental set-up used in the optimization of the slit width and measurement of the instrumental function.

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86 020406080100120 0.03 0.04 0.05 0.06 0.07 0.08 265.3 nm Hg I 289.3 nm Hg I 294.2 nm Hg I 507.3 nm Hg I 576.9 nm Hg IFWHM (nm)Slit Width (m)294.1 294.2 294.3 294.4 0.0 0.2 0.4 0.6 0.8 1.0 Normalized IntensityWavelength (nm) 15 m 25 m 35 m 45 m 55 m 65 m 75 m 85 m 95 m 105 m 294.263 nm Hg I020406080100120 0.00 0.02 0.04 0.06 0.08 Experimental FWHM of 294.263 nm Hg I Calculated Spectral Bandpass (s = Rd x w)FWHM (nm)Slit Width (m) c c b b a a020406080100120 0.03 0.04 0.05 0.06 0.07 0.08 265.3 nm Hg I 289.3 nm Hg I 294.2 nm Hg I 507.3 nm Hg I 576.9 nm Hg IFWHM (nm)Slit Width (m)294.1 294.2 294.3 294.4 0.0 0.2 0.4 0.6 0.8 1.0 Normalized IntensityWavelength (nm) 15 m 25 m 35 m 45 m 55 m 65 m 75 m 85 m 95 m 105 m 294.263 nm Hg I020406080100120 0.00 0.02 0.04 0.06 0.08 Experimental FWHM of 294.263 nm Hg I Calculated Spectral Bandpass (s = Rd x w)FWHM (nm)Slit Width (m) c c b b a a Figure 4-7. Effect of slit width on the (a) normali zed intensity distribution and (b) full width at half maximum of 294.263 nm Hg I line, and (c ) full width at half maxima of other Hg I lines.

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87 200 300 400 500 600 700 0.0 4.0x1068.0x1061.2x1071.6x107 Intensity (counts)Wavelength (nm)350 360 370 380 390 0 2000000 4000000 6000000 Intensity (counts)Wavelength (nm) 200 300 400 500 600 700 0.0 4.0x1068.0x1061.2x1071.6x107 Intensity (counts)Wavelength (nm)350 360 370 380 390 0 2000000 4000000 6000000 Intensity (counts)Wavelength (nm) Figure 4-8. Example of a merged spectrum. The di fferent colors depict th e 67 individual spectral windows optimally spliced together using an in-house merging software written in QBasic. Figure 4-9. A schematic diagram of the componen ts of a Czerny-Turner-based spectrometer and the respective rays and angles form ed when light enters the slit.

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88 200300400500600700 0.01 0.02 0.03 0.04 0.05 0.06 0.07 Experimental FWHM (PseudoVoigt) 2nd Order Polynomial FitFWHM (nm)Wavelength (nm)200300400500600700 0.01 0.02 0.03 0.04 0.05 0.06 0.07 Experimental FWHM (PseudoVoigt) 2nd Order Polynomial FitFWHM (nm)Wavelength (nm)200300400500600700 0.01 0.02 0.03 0.04 0.05 0.06 0.07 Experimental FWHM (PseudoVoigt) 2nd Order Polynomial FitFWHM (nm)Wavelength (nm) 200300400500600700 0.01 0.02 0.03 0.04 0.05 0.06 0.07 FWHM (nm)Wavelength (nm) Calculated Spectral Bandpass (wslit = 35 m) Experimental Fit 1 Experimental Fit 2 Experimental Fit 3 Average300 400 500 600 0 50 100 150 200 250 300 Intensity (a.u.)Wavelength (nm)300 400 500 600 0 50 100 150 200 250 300 Intensity (a.u.)Wavelength (nm)300 400 500 600 0 50 100 150 200 250 300 Intensity (a.u.)Wavelength (nm)a a b b c c200300400500600700 0.4 0.8 1.2 1.6 Theoretical ExperimentalReciprocal Linear Dispersion (nm mm-1)Wavelength (nm)d d 200300400500600700 0.01 0.02 0.03 0.04 0.05 0.06 0.07 Experimental FWHM (PseudoVoigt) 2nd Order Polynomial FitFWHM (nm)Wavelength (nm)200300400500600700 0.01 0.02 0.03 0.04 0.05 0.06 0.07 Experimental FWHM (PseudoVoigt) 2nd Order Polynomial FitFWHM (nm)Wavelength (nm)200300400500600700 0.01 0.02 0.03 0.04 0.05 0.06 0.07 Experimental FWHM (PseudoVoigt) 2nd Order Polynomial FitFWHM (nm)Wavelength (nm) 200300400500600700 0.01 0.02 0.03 0.04 0.05 0.06 0.07 FWHM (nm)Wavelength (nm) Calculated Spectral Bandpass (wslit = 35 m) Experimental Fit 1 Experimental Fit 2 Experimental Fit 3 Average300 400 500 600 0 50 100 150 200 250 300 Intensity (a.u.)Wavelength (nm)300 400 500 600 0 50 100 150 200 250 300 Intensity (a.u.)Wavelength (nm)300 400 500 600 0 50 100 150 200 250 300 Intensity (a.u.)Wavelength (nm)a a b b c c200300400500600700 0.4 0.8 1.2 1.6 Theoretical ExperimentalReciprocal Linear Dispersion (nm mm-1)Wavelength (nm)d d Figure 4-10. Determination of the instrumental function. (a) Spectra taken using a Hg hollow cathode lamp in Ar buffer gas. (b) The lin e widths calculated from the fitting of spectral lines are plotted as a function of wavelength. (c) The instrumental function was fitted with a second order polynomial and the average of the three trials is shown in yellow. The corresponding theoretical spectral bandpass is also shown on the same plot (black solid line). (d) Comparison between theoretical (red) and experimental reciprocal linear disp ersion function (blue).

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89 200300400500600700 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 Intensity (W cm-2 nm-1)Wavelength (nm) Deuterium Lamp Tungsten Halogen Lamp 200300400500600700 0 2000 4000 6000 8000 10000 12000 Deuterium Lamp Tungsten Halogen LampIntensity (counts)Wavelength (nm) 200300400500600700 0 2000 4000 6000 8000 Relative Response (counts/W cm-2 nm-1)Wavelength (nm) Deuterium Lamp Tungsten Halogen Lamp 200300400500600700 0 2000 4000 6000 8000 10000 Corrected Relative Response (counts/W cm-2 nm-1)Wavelength (nm) Deuterium Lamp Tungsten Halogen Lampa a b b c c d d200300400500600700 0 5000 10000 15000 20000 Corrected Relative Response (counts/W cm-2 nm-1)Wavelength (nm) Deuterium Lamp Tungsten Halogen Lampe e 200300400500600700 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 Intensity (W cm-2 nm-1)Wavelength (nm) Deuterium Lamp Tungsten Halogen Lamp 200300400500600700 0 2000 4000 6000 8000 10000 12000 Deuterium Lamp Tungsten Halogen LampIntensity (counts)Wavelength (nm) 200300400500600700 0 2000 4000 6000 8000 Relative Response (counts/W cm-2 nm-1)Wavelength (nm) Deuterium Lamp Tungsten Halogen Lamp 200300400500600700 0 2000 4000 6000 8000 10000 Corrected Relative Response (counts/W cm-2 nm-1)Wavelength (nm) Deuterium Lamp Tungsten Halogen Lampa a b b c c d d 200300400500600700 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 Intensity (W cm-2 nm-1)Wavelength (nm) Deuterium Lamp Tungsten Halogen Lamp 200300400500600700 0 2000 4000 6000 8000 10000 12000 Deuterium Lamp Tungsten Halogen LampIntensity (counts)Wavelength (nm) 200300400500600700 0 2000 4000 6000 8000 Relative Response (counts/W cm-2 nm-1)Wavelength (nm) Deuterium Lamp Tungsten Halogen Lamp 200300400500600700 0 2000 4000 6000 8000 10000 Corrected Relative Response (counts/W cm-2 nm-1)Wavelength (nm) Deuterium Lamp Tungsten Halogen Lampa a b b c c d d200300400500600700 0 5000 10000 15000 20000 Corrected Relative Response (counts/W cm-2 nm-1)Wavelength (nm) Deuterium Lamp Tungsten Halogen Lampe e Figure 4-11. Determination of the detector spectral effici ency. (a) Theoretical response curves of deuterium (black) and halogen (red) lamps. (b) Experimental response curves of the detection system. (c) Relative spectral efficiency of the detection system. (d) Corrected relative detector sp ectral efficiency. (e) Corrected relative detector spectral efficiency for experiments using a vacuum chamber.

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90 284.8285.0285.2285.4285.6 0 100000 200000 300000 400000 500000 600000 6 5 4 3 2 1 Wavelength (nm)Intensity (counts) 123456 2000 2250 2500 2750 NoiseBinning Set6 8 10 12 S/N7.5 10.0 12.5 15.0 %RSD6000 12000 18000 24000 Background12000 18000 24000 30000 Signal 6 5 4 3 2 11: 350 1: 350 395 = 45 pixels 395 = 45 pixels 2: 320 2: 320 410 = 90 pixels 410 = 90 pixels 3: 315 3: 315 420 = 105 pixels 420 = 105 pixels 4: 290 4: 290 450 = 160 pixels 450 = 160 pixels 5: 260 5: 260 460 = 200 pixels 460 = 200 pixels 6: 230 6: 230 480 = 250 pixels 480 = 250 pixelsa a b b c c 284.8285.0285.2285.4285.6 0 100000 200000 300000 400000 500000 600000 6 5 4 3 2 1 Wavelength (nm)Intensity (counts) 123456 2000 2250 2500 2750 NoiseBinning Set6 8 10 12 S/N7.5 10.0 12.5 15.0 %RSD6000 12000 18000 24000 Background12000 18000 24000 30000 Signal 6 5 4 3 2 11: 350 1: 350 395 = 45 pixels 395 = 45 pixels 2: 320 2: 320 410 = 90 pixels 410 = 90 pixels 3: 315 3: 315 420 = 105 pixels 420 = 105 pixels 4: 290 4: 290 450 = 160 pixels 450 = 160 pixels 5: 260 5: 260 460 = 200 pixels 460 = 200 pixels 6: 230 6: 230 480 = 250 pixels 480 = 250 pixels 6 5 4 3 2 11: 350 1: 350 395 = 45 pixels 395 = 45 pixels 2: 320 2: 320 410 = 90 pixels 410 = 90 pixels 3: 315 3: 315 420 = 105 pixels 420 = 105 pixels 4: 290 4: 290 450 = 160 pixels 450 = 160 pixels 5: 260 5: 260 460 = 200 pixels 460 = 200 pixels 6: 230 6: 230 480 = 250 pixels 480 = 250 pixels 6 5 4 3 2 11: 350 1: 350 395 = 45 pixels 395 = 45 pixels 2: 320 2: 320 410 = 90 pixels 410 = 90 pixels 3: 315 3: 315 420 = 105 pixels 420 = 105 pixels 4: 290 4: 290 450 = 160 pixels 450 = 160 pixels 5: 260 5: 260 460 = 200 pixels 460 = 200 pixels 6: 230 6: 230 480 = 250 pixels 480 = 250 pixelsa a b b c c Figure 4-12. Effect of binning. (a) Image of the laser-induced plasma obtained from a soil sample and the corresponding binning set parameters. (b) The effect of binning was monitored using a Mg I line at 285.3 nm. (c) The signal, background, RSD, S/N and noise as a function of binning set.

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91 A5A10A20B5B10B20 0 5000 10000 15000 20000 25000 30000 35000 Integrated Intensity (a.u.)Number of Laser Shots AccumulatedA5A10A20B5B10B20 8 10 12 14 16 18 20 22 24 26 28 %RSDNumber of Laser Shots Accumulated281.4 281.7 282.0 20000 40000 60000 Intensity (a.u.)Wavelength (nm) Al II281.4 281.6 281.8 40000 60000 80000 Intensity (a.u.)Wavelength (nm) Al II281.4 281.6 281.8 282.0 80000 100000 120000 Intensity (a.u.)Wavelength (nm) Al I281.4 281.7 282.0 30000 60000 90000 Intensity (a.u.)Wavelength (nm) Al II281.4 281.6 281.8 282.0 50000 100000 150000 Intensity (a.u.)Wavelength (nm) Al II281.4 281.6 281.8 282.0 100000 200000 300000 Intensity (a.u.)Wavelength (nm) Al IA5 A10 A20 B5 B10 B20a a b b c c d dA5A10A20B5B10B20 0 5000 10000 15000 20000 25000 30000 35000 Integrated Intensity (a.u.)Number of Laser Shots AccumulatedA5A10A20B5B10B20 8 10 12 14 16 18 20 22 24 26 28 %RSDNumber of Laser Shots Accumulated281.4 281.7 282.0 20000 40000 60000 Intensity (a.u.)Wavelength (nm) Al II281.4 281.6 281.8 40000 60000 80000 Intensity (a.u.)Wavelength (nm) Al II281.4 281.6 281.8 282.0 80000 100000 120000 Intensity (a.u.)Wavelength (nm) Al I281.4 281.7 282.0 30000 60000 90000 Intensity (a.u.)Wavelength (nm) Al II281.4 281.6 281.8 282.0 50000 100000 150000 Intensity (a.u.)Wavelength (nm) Al II281.4 281.6 281.8 282.0 100000 200000 300000 Intensity (a.u.)Wavelength (nm) Al IA5 A10 A20 B5 B10 B20a a b b c c d d Figure 4-13. Effect of laser shot accumulation on the spectra of singly-ionized aluminum line at 281.619 nm taken with (a) tran slational sampling and (b) st ationary sampling and its corresponding influence on (c) integrated line intensity and (d) precision.

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92 Table 4-1. Results of the calibra tion of the micrometer slit dial. Nominal slit width ( m) Diffraction order, m Distance, x( m) Calculated slit width, w ( m) Calculated offset ( m) +1 29.50 15.6115.61 0 -1 29.50 15.6115.61 +1 18.25 25.2315.23 -1 18.25 25.2315.23 10 -2 31.25 24.5614.56 +1 13.00 35.4215.42 -1 13.00 35.4215.42 20 -2 23.00 33.3713.37 +2 17.00 45.1515.15 -3 23.50 45.7215.72 30 -4 30.50 45.3015.30 +2 13.50 56.8516.85 40 -3 19.50 55.1015.10

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93 Table 4-2. Calculated central wavelengths for spectral data acquisition. Central wavelength (nm) Central wavelength (nm) 225.0 514.7 234.6 521.8 244.2 528.8 253.7 535.8 263.2 542.7 272.6 549.5 281.9 556.2 291.2 562.8 300.4 569.3 309.6 575.7 318.7 582.0 327.7 588.2 336.7 594.4 345.6 600.5 354.4 606.5 363.1 612.4 371.8 618.2 380.4 623.9 388.9 629.5 397.4 635.1 405.8 640.5 414.1 645.8 422.3 651.0 430.5 656.1 438.6 661.1 446.6 666.0 454.5 670.8 462.3 675.6 470.0 680.3 477.7 684.9 485.3 689.4 492.8 693.8 500.2 698.1 507.5

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94 CHAPTER 5 QUANTITATIVE STANDARD-FREE ALGORITHMS IN LASER-INDUCED BREAKDOW N SPECTROSCOPY Introduction Quantitative analysis in laser-induced breakdown spectroscopy (LIBS) is commonly achieved by construction of calibration curves using proper refe rence standards [30, 116-121]. This is of course limited by the availability of standards which are matrix-matched and in the case of highly variable or fully unknown matrices, the calibrati on curve approach limits the analysis usually to semi-quantitative only. In order to alleviate the limitation presented by the requirement of reference standard s, standard-free techniques su ch as the calibration-free LIBS (CF-LIBS) and the Monte Carlo simulated ann ealing optimization for LIBS (MC-LIBS) were developed independently by two different research groups. The principles of the techniques are described comprehensively in this chapter. Calibration-Free Laser-Induced Breakdown Spectroscopy (CF-LIBS) The CF-LIBS approach was developed and pate nted in 1999 by the Istituto per i Processi Chimico-Fisici (IPCF) of the Consiglio Nazionale delle Richerche (CNR) in Pisa, Italy [57, 122]. The main points which initiated its development were the problems posed by matrix effects and the difficulty in obtaining matrix-matched refe rence standards, particularly for quantitative multi-elemental LIBS analysis in highly comple x or unknown matrices. Detailed description of the algorithm is presented herein and can be found in Refs. [55-57, 122-125]. Working Hypotheses The CF-LIBS measurement protocol applied in this research is based on three supporting assumptions regarding the experimental method of operation and the theore tical representation of the conditions of the plasma.

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95 Stoichiometric ablation. The assumption of stoichiometric ablation forms the very foundation of the LIBS method [56]. During abla tion, the plasma compos ition is representative of the actual sample composition when the laser irradiance at the sample surface is in the range of 109 W cm-2 or greater, a value which is usually achieved in LIBS experiments [124, 126]. According to Russo et al. [127], it is expected that even at moderately high laser intensities ( 1 GW cm-2) using picosecond or femtosecond lasers, the energy focused onto the sample surface exceeds the latent heat of vaporization of a ll the sample components and that the thermal properties of each constituent will not have a significant effect on the mass removal, which implies that all sample constituents can be vapor ized and subsequently removed. Reduction of fractionation may be an outcome of this non-ther mal ablation mechanism due to the increase in the amount of sample mass removed regardless of the thermal properties of the components of the sample [127]. In addition, at much higher laser intensities ( 20 GW cm-2), the phase transition involved is from solid to liquid to vapor even before th e thermodynamic critical te mperature is achieved. The amount of energy required to convert the sample mass from solid to vapor includes a large fraction of absorbed laser energy to satisfy th e latent heat of melting and vaporization. Furthermore, when the temperature of the samp le surface approaches the thermodynamic critical point, which is several times higher than the vapo rization temperature, a similar amount of laser energy absorbed by the material can significantly transport more mass into the vapor phase. As a consequence, fractionation is reduced even further at this regime due to the rapid transition from a superheated liquid to a mixture of vapor and li quid droplets which are explosively ejected from the sample surface in micrometer-siz e droplets or particles [127].

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96 Stoichiometric ablation still remains a big challenge in quantitative LIBS measurements due mainly to matrix effects. Several studies on laser-material interacti on have been performed over the years in order to further understand th e different processes and mechanisms involved, which is a step towards overcoming the matrix effect problem, thus, achieving a representative ablation of the sample. Bleiner et al. [128] investigated the effect s of melting and vaporization of different metal targets during ICP-MS and LIBS analysis by modeling the laser-material interactions which included processes such as heating, melting and vaporization of the metal target, vapor plume expansion, plasma formation, and laserplasma intera ction. The variables incorporated in their complex algorithm were th e optical absorption coefficients, reflectivities, and thermal diffusivity of the target surface. They concluded that the optical and thermal properties of metal targets have a significant effect on the target te mperature under identical irradiation conditions. For example, Al exhibi ted the lowest surface temperature and its ablation was dominated by the formation of a melt phase which enhanced the development of a high crater aspect ratio (depth /diameter). In the case of other metal targets, e.g., Fe, they found out that the vapor phase played a more important ro le in the surface recession mechanism. They stated that the practicality of their simulations and experiments was based on an understanding of the melting and vaporization mechanisms of ablation, as these are considered to be potentially responsible for the non-stoichiometric sampling of aerosols used for elemental and trace analysis. Mao et al. [129] have also investigated laser ablation mechanisms using picosecond and nanosecond lasers. In their study, it was evident that there were different distinct mechanisms which dominated the ablation process depending on the pulse duration, wavelength and energy of the laser used while maintaining all the othe r experimental parameters constant. In their

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97 study, they used a 266 nm Nd:YAG laser with a pulse width of 30 ns and a 248 nm KrF excimer laser with a pulse width of 35 ps. They showed that in the ablation of a brass sample, the nslaser ablation approached the stoichiometric ratio of Cu and Zn only at 0.3 GW cm-2 and deviated from the stoichiometric value at higher irradiances. However, with ps-laser ablation, representative sampling was achieved at increasing irradiances. The authors indicated that thermal vaporization predominated at lower ir radiances for the ns-l aser ablation and a nonthermal mechanism which involved an interactio n between space charges and ionized species at the sample surface appeared to account for the beha vior for ps-laser ablation. They also pointed out that from an analytical point of view, the ps -laser was more appropriate for chemical analysis since it could provide a higher emission intens ity and a wider irradiance range over which accurate stoichiometric analysis could be accomplished. An investigation regarding el emental fractionation of aerosols was also undertaken by Chen et al. [14] using double pulse LIBS in an ort hogonal configuration. They studied the temporal and spatial distributions of the aeroso ls generated by ablating a brass target with a Zn/Cu molar ratio of 0.81. The results indicated that the particulate material close to the surface of the target was enriched with Cu compared to the bulk at most times, except at early delay times ( 200 s). They attributed this effect to the lower vapori zation temperature of Zn compared to Cu, hence, leaving behind a molten pool of Cu. However, at the very beginning ( 200 s delay) the molar ratio was closer to that of the bulk since the vaporization process took time and its effect on the molar ratio was minimal. In other words, the ablation at this stage was stoichiometric. They also reported that for aer osols analyzed at a longer distance from the surface and at much later times, th e Zn/Cu molar ratio was higher than that of the bulk material. The authors rationalized that this was because sp uttered particles reached the cold regions at

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98 longer distances from the surface where they act as nucleation centers for vapor condensation. In addition, the composition of the vapor at this distance was enriched in the more volatile component, which was Zn in this case, hence, th e Zn/Cu molar ratio was higher than that in the bulk. Although it was not directly stated in the study, it was evident from the results the importance of choosing the correct experimental conditions, specifically the temporal and spatial parameters, to ascertain that sampling would be representative of the bulk solid. Therefore, under careful choice of experi mental conditions the assumpti on of stoichiometric ablation necessary for CF-LIBS may hold. Local thermodynamic equilibrium. Another important as sumption of the CF-LIBS approach is the existence of local thermodynami c equilibrium (LTE) in the actual temporal and spatial observation gate [54-56]. In this stat e, a common temperature describes the Boltzmann distribution of species in energy levels, the Saha distribution of population of ionization stages and the Maxwell distribution of kinetic energy of electrons, atoms and ions [25]. Accordingly, the excitation temperature in the Boltzmann re lationship (Eq. 5-1), which determines the population of atomic and ionic energy levels, must be equal to the ionization temperature in the Saha equation (Eq. 5-2), which controls the distri bution of atoms of the same element in different ionization stages [124]. All the parameters in Eqs. 5-1 and 5-2 are defined in pp. 19-23. )( e/TU g nns TkE k s tot s kexcBk (5-1) ionB I II ionBe I II eTk TU TU h Tkm n n n exp 2 23 2/3 (5-2) The criterion for LTE is that electron collisi on rates must dominate over radiative ones so that the radiation distribution can be allowed to deviate from the Planck function. This is why the observed plasma radiation, which is often comp letely transparent or optically thin over very

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99 wide range of wavelengths, is not a blackbody source [130] In other words, an excited state must have a higher probability of undergoing de-excitation by inelas tic collision with an electron than by spontaneous radiative decay. This is analogous to setting a minimum value for the electron number density, ne. In physical terms, the criterion in order to satisfy the LTE condition as given by Thorne [25] is: 3 3 12 ,cm 106.1 ET nK LTEe (5-3) where TK is the temperature (K) and E is the largest energy transition considered (eV). This is also oftentimes referred to as the McWhirte r criterion. A complete treatment on local thermodynamic equilibrium is described in Refs. [25, 130, 131]. An investigation of the state of local ther modynamic equilibrium in laser-induced plasmas was recently undertaken by Barthlemy et al. [132]. In their study, they used an aluminum target and measured the excitation temperature at di fferent delay times by the Boltzmann plot method using several neutral iron lines over the range of 3.21-6.56 eV. They obtained excellent linear Boltzmann plots at all delay times considered which implies that the Boltzmann equilibrium condition is met. However, the excitation temperatures calculat ed at delay times less than 1 s were lower than the ionization temperatures calc ulated using the Saha relations. Error bars on the excitation and ionization temperatures calculated, which included uncer tainties in transition probabilities and electron number density as well as statistical errors, onl y began to overlap after about 0.8 s. To further explore the existence or non-existence of LTE, they compared the temporal evolution of experimental and calculate d line intensities of Mg I at 285.21 nm, Mg II at 279.55 nm and Al II at 281.62 nm. They re ported a remarkable ag reement between the experimental and calculated time-dependent intensities for the Mg I line with a slight underpopulation of the neutral states with respect to LTE conditions at delay times lower than 1 s,

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100 but still falling within the experimental errors. From these results, together with the Boltzmann equilibrium observed for the neutral states, they concluded that the neutral species were in thermal equilibrium with electrons even at earl y times, and hence, the electron temperature can be approximated by the excitation temperature. On the other hand, there was no convergence between experimental and theoretical curves for ionic lines except at delay times longer than 2 s and significant overpopulation occurred at early times which implied that Saha equilibrium was not met. The authors asserted that this was because the plasma could be considered as stationary for the higher energy states. Capitelli et al. [133] published an excellent treatise on equilibrium and non-equilibrium problems which occurred during th e expansion of laser-induced plasmas. They discussed nonequilibrium plasmas in terms of the characteri stic times of plasma expansion using fluid dynamics, deviation from Boltzmann distributio n of excited state population using collisional radiative models and non-Maxwell behavior of the electron energy dist ribution function using the kinetic Boltzmann equation. On the other hand, equilibrium plasmas we re discussed in terms of the challenges associated with partition f unction calculation, equi librium composition and thermodynamic and transport properties of thermal pl asmas. In brief, they have described the existence of a quasi-equilibrium state in which the Boltzmann relation was satisfied while the ionization equilibrium was violated either by predominance of the ionization process over recombination one or vice-versa. They also asse rted that non-equilibrium conditions in a plasma near the surface was caused by the decrease in plasma temperature due to expansion and occurred whenever the follo wing condition is satisfied: exp iontt (5-4)

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101 where tion is the characteristic ionization time and texp is the characteristic time of plasma expansion. For typi cal plasma conditions, tion is in the range of 1-10 s and is given by: 1ionI ionknt (5-5) where nI is the number density of neutral atoms in cm-3 and kion is the ionization rate coefficient with typical values of 10-11-10-14 cm3 s-1. texp on the other hand, is given by: d texp (5-6) where d is the laser spot diameter in cm and is the plasma expansion velocity with values in the range of 105-106 cm s-1. Verification of the validity of local thermodynamic equilibriu m in laser-induced plasmas using the line-to-continuum approach has also been recently proposed by Moon et al. [134]. The method is based on a similar research done by Sola et al. [135] in which the line-to-continuum intensity ratio method was used to determine the electron temperatur e in a high-pressure microwave discharge. The equation can be written as: Be Be eB excB k e kki ck hc T G k hc T Tk Tk E TTU gA I 1 exp 1 exp1 exp exp 10005.25 (5-7) where I is the wavelength-integrated intensity of emitted light (W cm-3), c, is the nonintegrated continuum radiation intensity (W cm-3 nm-1), is the free-bound continuum correction factor, G is the free-free Gaunt factor and the other variables are defined in pp. 19-23. The main premise of this method is to compare the electron temperature, Te, calculated using Eq. 5-7 with the excitation temperature, Texc, determined using the Boltmann plot method at several delay times.

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102 An excellent overview of the literature regarding the evaluation of local thermodynamic equilibrium in laser-induced plasmas is given in Ref. [124]. Tognoni et al. [124] concluded that it is evident from the results published in the literat ure that LTE is a good approximation in describing the plasma conditions us ually at delays longer than 1 s but that the reliability of the hypothesis is heavily dependent on various experimental parameters such as laser pulse energy, pulse width, ambient gas, temporal parameters, etc. The authors in Ref. [124] advise that it is necessary that all these parameters be reported as accurately as possible in order to determine the extent of the validity of the LTE condition and reproduce the exact experi mental conditions, if necessary. Optically thin plasma. In the CF-LIBS protocol, it is recommended that the spectral lines chosen for quantitative analysis do not suffer from self-absorption. In other words, the plasma must be optically thin. The measured intensit ies of lines which are possibly self-absorbed are lower than expected and have br oader line widths, hen ce, resulting in an underestimation of the concentration of a sample component [54]. The radiation source is considered optically thin if all the emitted radiation reaches the detection system without re-a bsorption or if the product nifikl approaches zero, where ni is the number density (cm-3) at lower level i fik is the absorption oscillator strength (dimensionless) and l is the path length (cm) [106]. Although atoms at lower energy levels have a higher probability to re-absorb the radiation emitted by other atoms of the same elements in the plasma, it is less problematic in relatively small laser-induced pl asmas where path lengths are short and for trace elements where there is only a small am ount of analyte present in the plume. The most recent version of the CF-LIBS approach does not have the exacting requirement of having an optically thin ra diation source since the modified algorithm includes a method for

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103 the correction of self-absorpti on as described in Refs. [54, 1 23, 125, 136]. However, it should be noted that this part of the algorithm underw ent major revisions and improvements at the beginning of this research and a new method of correction was developed almost every year. For these reasons alone and for some limitations intrinsic to the methods of self-absorption correction, the CF-LIBS version that was used in the spectral data analysis does not include any form of self-absorption correction, hence, the n ecessity for optically thin spectral lines remains critical. Measurement of Integrated Line Intensity In the CF-LIBS routine, after the raw sp ectrum has been corrected for background and detector spectral efficiency, the peaks are manua lly labeled and identified by comparison of the approximate central wavelength with the NIST at omic spectra database [137]. Only the lines emitted by neutral (I) and singly-ionized species (II) are detected based on the experimental conditions of typical LIBS measur ements [56]. The assigned peaks are fitted with an analytical approximation of the Voigt function which gives the measured central wavelengths, net line widths and the integrated line in tensities as outp uts [55, 56]. Under the assumption of local thermodynamic equilibrium, the integrated line intensity, kiI, in photons cm-3 s-1, corresponding to the transition between upper energy level Ek and lower energy level Ei of an atomic species s can be expressed as [54, 56]: TU g AnAnIs TkE k ki s totki s kkiBk/e (5-8) where is the transition wavelength (nm), s kn is the number density (cm-3) of species s at level k s totn is the total number density (cm-3) of emitting atoms for each species, Aki is the line transition probability for spontaneous emission (s-1), gk is the upper level degeneracy, kB is the Boltzmanns

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104 constant (J K-1), T is the plasma temperature (K), and Us( T ) is the partition function for the emitting species at the plasma temperature (dimensionless). Spectral efficiency correction of the raw spect rum is not required at the beginning of the CF-LIBS analysis since it can be executed within the software as long the detector efficiency correction file is loaded into the program. This step is important because the measured integral line intensities, Iki,meas, are affected by the optical efficiency of the collection system, Fdet() which acts as a scale factor, as given in Eq. 5-9 and can be expresse d as the product of the wavelength-dependent re lative efficiency, Frel(), and the wavelength-independent absolute efficiency, Fabs, so that [138]: kiabs relki det measkiIFFIFI (5-9) Rearrangement of Eq. 5-9 yields: kiabs rel measki kiIF F I I (5-10) where kiI is the measured integrated line intensity corrected for relative spectral efficiency. Also, in order to take into account the to tal particle number density of the plasma, ntot, an overall experimental factor F is introduced: s s totabs s totabsFCCnFnF (5-11) where Cs refers to the relative number density of the species s in the sample. Combining Eqs. 58 to 5-11 yields the final expression for the measured integrated line intensity: TU g AFCIs TkE k ki s kiBk/e (5-12)

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105 Determination of Electron Number Density Knowledge of the electron number density is essential in de scribing the conditions of the plasma. In the CF-LIBS algorithm, there are thre e different approaches in determining electron number density and each method is desc ribed in detail in this section. Saha-Boltzmann method. In this approach, the Boltzma nn and Saha equations, given in Eqs. 5-1 and 5-2, respectively, are combined in order to describe the population ratio of two excited levels k and m of successive ionization stages of the same element, neutral and singlyionized, respectively [124]. The resulti ng equation is given in Eq. 5-13: Tk EE g g h Tkm n n nB I k II m I k II m Be I k II m e exp 23 2/3 (5-13) where is the ionizatio n potential (eV), is the lowering of the i onization potential (eV) and the rest of the parameters are defined in pp. 19-23. Substitution of Eq. 5-8 into Eq. 5-13 and simplification of variables yi elds the final expression: eV I k II m eV I ml I k II ki II m II ml I ki eT EE T Ag Ag I I nexp 100.62/3 21 (5-14) This approach requires that the plasma must be sufficiently close to LTE conditions, otherwise, Eqs. 5-13 and 5-14 will not hold. Also, the use of Eq. 5-14 necessitates, in advance, the knowledge of the plasma temperature which us ually presents a problem since methods of determining plasma temperature usually requires th at electron number density is known as well. Stark broadening method. As mentioned in Chapter 3, spectr al line profiles are affected by different broadening effects and under typical experimental conditions employed in LIBS measurements, the main contribution to the spectral line width comes from Stark broadening. This type of broadening results fr om the interactions of the emitting atom with the electric field produced by the surrounding charged particles.

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106 There are two computational methods based on the Stark effect which are incorporated into the CF-LIBS algorithm, one is based on the quadr atic Stark effect of non-hydrogenic elements and the other is based on the Stark broa dening of the Balmer hydrogen-alpha line, H at 656.27 nm, which follows a linear Stark effect. Both methods have an advantage over the SahaBoltzmann approach since they do not require the plasma to be in local thermodynamic equilibrium. However, knowledge of Stark broade ning coefficients is requi red and most of them are scattered in the literature and some are not available. Quadratic Stark effect The electron number density calculation based on the quadratic Stark broadening of a line expressed as the FWHM in nanometers is given by [124]: 16 3/1 4/1 16 1610 1 10 5.3 10 2e D e e Starkn wn n n w (5-15) 2/1 2/3 910x72.1e eV Dn T n (5-16) where w is the electron-impact half-width in nm, is the ion-broadening parameter, is a coefficient equal to 0.75 or 1.2 for ne utral and ionic lines, respectively, ne is the electron number density in cm-3 and nD is the number of particles in the Debye sphere in cm-3 (Eq. 5-16). Several Stark broadening parameters for different neutral and singly-charged ionic lines are tabulated in Refs. [131, 139] and excellent critical reviews of more recent calculated Stark coefficients are found in Refs. [140-143]. Furthermore, the second term in Eq. 5-15 is normally neglected due to the negligible contribution of ion-broadening under typical LIBS conditions, hence: 1610 2e Starkn w (5-17) The Stark width, Stark, which is Lorentzian in nature, can be estimated from the net line width, V, of the resulting fit of the line which fo llows a Voigt function. Assuming that other

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107 broadening mechanisms (e.g. natural, van der Waals, etc.) have negligible contribution to the line width, the Stark width can be calculated using Eq. 5-18: V G V Stark 2 2 (5-18) where G is the Gaussian line width determined from contribution of Doppler and instrumental broadening [54, 106]. In addition, it is crucial that lines chosen do not suffer from selfabsorption since self-absorbed lines result in much broader line widths and an over-estimation of the electron number density. Linear Stark Effect The Stark broadening of hydrogen and hydrogenic ions is symmetric and is a linear function of the elect ric field strength. The use of hydrogen lines for electron number density determin ation, particularly, the lines in the Balmer series, is a wellestablished plasma diagnostic method. In brief, th e Balmer series involves transitions with n = 2 as the lowest level, where n is the principal quan tum number. The different lines in a particular series are ordered according to a change in n ( n). Transition involving a n = 1 is called an transition, a n = 2 is a transition, and so on. The Stark broadening of hydrogen lines have been effectively used in the past for diagnostics of several different kinds of plasmas. Escarguel et al. [144] observed and analyzed for the first time the emission fr om hydrogen lines in a plasma cr eated with a si ngle-pulse laser in bulk water. Ashkenazy et al. [145] measured the electron number density of plasma jets generated by a high-pressure cap illary discharge capillary based on the Stark broadening of H and H lines at various capillary currents and spa tial positions. In astronomy, Hanaoka et al. [146] used high-cadence imaging, linear polarization and velocity field of H line to study the high energy aspect of the solar flares.

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108 One of the very first studies that reported the use of H line at 656.272 nm for the determination of electron number density in lase r-induced plasmas from solid targets in humid air was by El Sherbini et al [147]. The H approach is based on the premise that plasmas produced in the presence of a very small concen tration of water in the ambient atmosphere is optically thin and is, therefore, ideal for dete rmining electron number density. Fig. 5-1 shows the temporal evolution of the H line and it can be observed th at it is characterized by a relatively large signal-to-noise ra tio and a broad line width. Expe riments have also shown that the H line persists a long time af ter the termination of the laser pulse, up to about 10 s [147]. In addition, any uncertainties on the spectral line fitting and on the estimation of instrumental broadening as well as Doppler br oadening contributions can be c onsidered less significant due to the relatively large line widths of the H lines, which are typically in the range of 0.5 to 3.0 nm [145]. The electron number density can be determined by using Eq. 5-19 [145, 147]: 2/3 2/1 12 31002.8)(cm H en (5-19) where His the line width of the H line in nm and 1/2 is the FWHM of the reduced Stark profiles in nm per cgs field strength unit, whic h is weak function of temperature and electron number density through the ion-ion correlation an d Debye shielding correction and the velocity dependence of the impact broadeni ng [147]. A partial list of 1/2 values at selected temperatures and electron number densities are f ound in Table 5-1. More calculated 1/2 values can be found in Refs. [131, 139].

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109 Determination of Laser-Induced Plasma Temperature As discussed previously, under the assump tion of local thermodynamic equilibrium, a single temperature describes th e distribution of species in energy levels, the population of ionization states and kinetic energy of electrons, atoms and ions. Several techniques have been described in the literature for determining the plasma temperature and these include the line-pair ratio, line-to-continuum ratio, Boltzmann plot and Saha-Boltzmann plot. In the CF-LIBS algorithm, only the Boltzmann and the Saha-Boltzmann plots are included. Boltzmann plot method. Evaluation of the laser-induced plasma temperature using the Boltzmann plot approach requires the measurement of intensities of a series of optically thin spectral lines from different excitation states of the same species on condition that transition probabilities, statistical weights and excitation energies are ava ilable. Linearization of the expression given in Eq. 5-12 yields the Boltzmann plot equation [55, 56]: )( ln 1 ln TU FC E TkAg Is s k B kik ki (5-20) Plotting the left-hand side of Eq. 5-20 against the upper energy level Ek in eV yields a slope equal to -1/ kBT The Boltzmann plot method allows plasma temperature to be determined through a simple linear regression without knowledge of the concentration (or number densities) and the partition function, which is also a function of temperature. Although, it is important that the spectral lines chosen have excitation energi es which are widely distributed in order to increase the accuracy of the determination. In addition, compared to the line-pair ratio method which is also based on the Boltzmann equati on, the Boltzmann plot method leads to better precision in the plasma temperature calculation si nce a series of lines are used simultaneously, which in effect averages out any uncertainties inherent to the transition pr obabilities available in atomic spectra databases [124]. An example of a Boltzmann plot generated for neutral iron lines

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110 in aluminum alloy sample is illustrated in Fig. 52. The calculated temperature from the slope is 10677 K. Saha-Boltzmann plot method. The calculation of laser-induced plasma temperature based on the Saha-Boltzmann plot approach was first reported by Yalcin et al [103]. The main difference between this method and the Boltzmann pl ot approach is that both neutral and singlyionized species are placed on the same plot. Th is presents a huge advantage for this method since it provides a larger energy spread using the transitions from different ionization stages. In brief, the x and y -coordinates of neutral lines are exactly the same as those of the Boltzmann plot method. However, in the case of lines from singly-ionized species, adjustment of the x and y -coordinates is required in order to place the ions on the same plot as the neutrals. The corrected x and y -coordinate for the ionic li nes can be obtained by li nearization of Eq. 5-13 after substitution of Eq. 5-8, as shown in Eq. 5-21: Tk E Tk E Ag I n T h km Ag IB I k B II m I ki I k I ki e Be II ml II m II ml ln )2(2 ln ln2/3 3 2/3 (5-21) For clarity on the transitions involved (and subscrip ts used), a schematic of the energy levels are illustrated in Fig. 5-3. The adjusted abscissa an d ordinate points for the singly-ionized lines are shown in Eqs. 5-22 and 5-23, respectively. II m IIEx (5-22) e Be II ml II m II ml IIn T h km Ag I y2/3 3 2/3)2(2 ln ln (5-23) Similar to the Boltzmann plot, this method allows for the determination of temperature from the slope of the line (-1/ kBT ). However, several iterations of yII must be performed due to the T3/2 term in the ordinate ion points and the Saha-B oltzmann plot method requir es the electron number

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111 density to be determined independently [103]. Examples of Saha-Boltz mann plots using neutral and singly-ionized lines of differe nt elements are depicted in Fi g. 5-4. The average temperature calculated from the slopes of the line is 11141 600 K. Determination of Relative Concentration and Experimental Factor The final aspect of the CF-LIB S routine is the calculation of the elemental concentration using the Boltzmann plot equation given by Eq. 5-20, where each spectral line is represented as a point and the points from different species lie on several paralle l lines under LTE condition [56]. The concentration parameter FCs can be solved from the y-intercept, bs, of the different lines in the Boltzmann plane (Eq. 5-24), but in order to determine the overall experimental factor F it is essential to normalize to unity the sum of the sp ecies concentrations (E q. 5-25) [56]. It is because of this simplification th at only relative percentages of sample components are possible with CF-LIBS. Absolute measurement is possible only if the total particle number density, ntot, which appears in Eq. 5-11 can be determined independently. )( ln TU FC bs s s (5-24) 1e 1 sb s s s sTU F C (5-25) Rearrangement of Eq. 5-25 gives the expr ession for the experimental factor F: sb s sTUF e (5-26) Therefore, the elemental species concentration can be determined by combining Eqs. 5-24 and 526, so that: F TU TU TU Cs s sbs b s s bs se e e (5-27)

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112 After obtaining all the relative species concentrations, addition of values corresponding to neutral and singly-ionized sp ecies for a given element M is required in order to determine the total elemental composition, as given by [55, 56]: II M I M TOT MCCC (5-28) Monte Carlo Simulated Annealing Optimization Method for Laser-Induced Breakdown Spectroscopy (MC-LIBS) The other key part of this research is the a pplication of the semi-empirical radiative model developed by Gornushkin et al. [61-64]. Th e initial purpose of its formulation was the development of a radiation dynamic model for pos t-breakdown laser-induced plasma expansion in vacuum as applied to practical spectroscopy [61] However, a distinct aspect of this modeling algorithm is that it is also possible to find a solu tion to the inverse problem of determining initial plasma conditions by a direct comparison of e xperimental with calculated spectra using an algorithm called the Monte Carlo simulated annea ling optimization [62]. Complete theoretical information on the evolution and derivation of th e model can be found in Refs. [61-64] and only the aspects analogous to the CF-LIBS algorithm will be described in detail. Working Hypotheses and General Theoretical Considerations The semi-empirical model, describes the expansion of a non-viscous and non-conducting plasma into vacuum at the end of the laser pulse when the laser-matter interaction has terminated (post-breakdown) and the plasma has thermalized (LTE is established). This time is taken as the starting point ( t = 0) of the model. The algorithm is written in MATLAB 7.3.0 (R2006b) and the first version of the model assumes that th e plasma acquires a spherical symmetry during expansion [61-63]. It is also assumed that the plasma composition remains constant in time (stoichiometric ablation) and that the species distribution is collision-dominated [61, 62].

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113 In the model, the plasma is effectively described by a system of gas dynamic equations, in addition to the radiative transfer and state equations. There is also no limitation set on the character of atomic transitions; in other words, resonance or non-resonance lines can be used as long as the required spectroscopic parameters are av ailable in atomic spectra databases [61]. In contrast with the CF-LIBS approach, higher io nization states can also be included in the simulations. The combination of al l these factors yields an analyt ical expression for the radiation dynamics of the plasma and the structur e of the plasma emission spectra. A non-isothermal asymmetric laser-induced plasma expansion model was recently formulated by Gornushkin et al. [64] as a modi fication to the original version in order to eliminate the restrictive spherical symmetry assumption and to formally extend the plasma model to more realistic plasma shapes, specifically an ellipsoidal one [64]. The mathematical treatment of the asymmetric expansion of th e radiative, thermally anisotropi c plasma into vacuum has been extensively described in Ref. [64] and will not be discussed in this chapter due to the complexity of the equations and theories i nvolved which are beyond the scope of this research. However, in order to understand the basic prin ciples of the semi-empirical plasma radiative model as applied to analytical spectroscopy, the modeling of the expansion of spherically symmetrical laserinduced plasmas into vacuum will be described in detail in the succeeding sections. All variables used in the next sections are defined in pp. 19-23. Calculation of Total Number Density, Temperature and Their Initial Distributions The total number density of the j th constituent, trnj,, is a function of the radial coordinate r of particle in the plasma and time t and can be expressed as: tR R rg tR R trnj j0 0 ,3 (5-29)

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114 wheretR is the radius of the outer boundary of the plasma at a particular time t and rgjis the initial distribution of the number density of j th constituent at t = 0 or 0, rnj. In the model, trnj, is calculated from the gas dynamic equation of conservation of mass which is given by: 0 12 2 j junr r r t n (5-30) The details of the derivation of E q. 5-29 are given in Appendix B. Solution of Eq. 5-30 requires knowledge of the radial expansion velocity, tru,: r tR tV rttru (5-31) where tV is the velocity of the plasma boundary (cm s-1), a measurable parameter initially introduced into the model. In the model it is assumed that the collectiv e velocity of particles inside the plasma only has a radi al component and depends linear ly on the radial position of a particle where tRr 0. The plasma expansion speed, tru,, can be determined once the proportionality coefficient between collec tive velocity of particles and radius,t is solved from the momentum conservation equation (Eq. 5-32): r p nur r r nu tj jj j jj 22 21 (5-32) where j is the mass of j th constituen t (g) and p is the gas pressure (dyne cm-2). The proportionality coefficient at t = 0, 0 can be determined by: R j jjrdrrn p0 20, 0 0 (5-33) where0 p is the pressure at the plasma center. The values of the moving plasma boundary velocity, initial plasma radius, and gas pre ssure are essential input parameters in the

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115 aforementioned calculations [61]. Typical values for these parameters are 105-106 cm s-1, 0.1-0.5 cm and 0.01-0.1 Torr, respectively. The deriva tion of Eq. 5-33 can be found in Appendix A. The laser-induced plasma temperature, T can be determined using the energy conservation equation (Eq. 5-34) which considers only the cont ribution of plasma thermal energy and plasma expansion energy since the energy supplied by the photons is considered negligible: q u pu u ttotal 2 22 2 (5-34) where is the gas density (cm-3) and is the internal ener gy per unit mass (erg g-1) of the gas species. The energy balance equation also includes a radiation loss term q, in erg cm-3 s-1, which is particularly significant during the early hot stage of plasma evolution. Moreover, the plasma expansion energy, calculated from the plasma expansion speed, tru ,, is included as well because this energy is comparable to the therma l motion energy [61]. Ta king into consideration all of the above points, the time derivative of temperature, give n by Eq. 5-35, can be obtained by solving the energy balance equation [61] j jj B j jj j j j jj R j j j jj j jj j jj j jnk q s n nT r r r T r trnrdr tntT n nr n n T t T ,0,0 2 5 30 2 (5-35) where j is ratio of specific heat cap acities. The complete details of the derivation of the time derivative of plasma temperature T are found Appendix C. Another important aspect included in the m odel is the parabolic initial distribution functions for both temperature (Eq. 5-36) and number density (Eq. 5-37):

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116 2 1 010,rkTrT (5-36) 2 2 010,rknrnj j (5-37) where T0 and n0 j are the initial temperature and the ini tial number density, re spectively, of the j th constituent at the plasma center, and k1 and k2 are numerical coefficien ts which are dependent on the gradient desired. It is also important to indicate the boundary conditions used to solve the system of equations de scribed above [61]: the radius R(t) of the plasma after LTE has established (t = 0) is between 0.1 and 0.5 cm, the plasma expansion speed at the pl asma center (r = 0) is zero, and the pressure as the radius of the plasma approaches the outer boundary R is equal to zero. Calculation of Number Density of Atoms, Ions and Electrons In the model, calculation of the number dens ities of electrons (Eq. 5-38), atoms (Eq. 5-39), and ions (Eq. 5-40) within the plasma are obtained by the use of the Saha ionization equation, the total mass conservation equation an d the charge equilibrium equation, which are given by Eqs. 541, 5-42 and 5-43, respectively. j e j jj enTs Tsn n (5-38) e j e j j anTs nn n (5-39) e j jj j inTs Tsn n (5-40) Tk h Tkm U U Tsn n nB j Be j a j i j e j a j i exp 2 22/3 2 (5-41) jj i j annn (5-42) e j j inn (5-43)

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117 Here, subscripts a, i, and e denote atoms, ions, and electrons, and all the other parameters are defined in pp. 19-23. Details of the derivation of Eqs. 5-38 through 5-40 are found in Appendix D. Calculation of Emission Spect ral Radiance and Line Profile The radiative transfer equation, which describes the effect of radiation on the plasma, is given by the following equation, in spherical coordinates: rKII I rr Ib '' 12 (5-44) where trII ,,, is the emission spectral radiance (erg s-1 cm-2 Hz-1 sr-1), tr ,,'' is the total absorption coefficient including stimulated emission (cm-1) at any given point in the plasma, TIIbb is the spectral radiance of blackbody radiation at temperaturetrT (erg s-1 cm-2 Hz-1 sr-1), is the angular factor cos and is the angle formed by the radius-vector r from the plasma center to an arbitrary point inside the plasma. An illustration of the spherical coordinate system used in the model is given in Fig. 5-5. In addition, it is assumed in the model that the rates of gas dynamic processes are much sl ower than the rates of radiative processes that only the stationary radiative tran sfer equation can be considered. The spectral radiance can be solved from Eq. 5-44 for any boundary conditi on in two ways in order to execute two computational routines. Rough approximation. This approximation is used to calculate the radiation loss term in the energy equation. The spectral radiance inside the plasma sphe re is calculated under the assumption that no radiation enters the plasma. Th e first order partial differential of Eq. 5-44 can be solved explicitly for any boundary conditions and can be expressed as:

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118 r z r rRrsds rzdzK rI222 1 2221 exp1 ,222 (5-45) The calculations are carried out in a wide frequency range and requi re the use of the approximate expression for absorption coefficient given by the Planck mean absorption coefficient, mean, as given by: N j j i e e B meann T n ch Gez m k1 2/73 62 2/3 2/127 128 (5-46) which considers only the free-fr ee and free-bound transitions. G in Eq. 5-46 is the dimensionless free-free Gaunt factor which is a weak function of temperature and elect ron number density and improves the theoretical descrip tion of the free-free continuum. However, precise quantummechanical calculation of Gaunt factors exist mo stly for hydrogenic species and in most cases, the numerical value of G is approximately unity [148, 149]. The rest of the variables in Eq. 5-46 are defined in pp. 19-23. The use of th e Planck mean absorption coefficient, mean, also implies that that the line structure of the spectrum is not included since bound-bound transitions were neglected. The spectral radiance given by Eq. 5-45 and the Planck mean absorption coefficient mean are then used in the calculat ion of the radiation loss term q (Eq. 5-47) in the energy balance equation. d d' 0II qb (5-47) The use of mean as an approximate expression for in the calculation of the radiation loss term q is valid and rationalizes the assumption of negligible bound-bound transitions since for the total energy emitted by the plasma, the radia tion due to bound-bound transitions is a small

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119 fraction of the total radiation en ergy. In other words, the line structure of the spectrum does not significantly affect the energy balance and is, therefore, omitted [61]. Also, as the plasma cools down and emits at frequencies of discrete atomic and ionic lines at late r times, the radiation energy loss q becomes less significant [61]. Detailed approximation. The second solution to the radia tive transfer equation allows the calculation of radiation emitted by the exterior of the plasma in a narrow frequency range in the vicinity of atomic or ionic transitions. The detailed approximation describes in detail the radiation emitted by the plasma. For th e point on the sphere boundary where r = R the spectral radiance can be written as: R z R RRsds RzdzK RI2 22 2 221 exp1 (5-48) The calculation requires the use of the exact absorption coefficient,', which now includes the contribution of a ll three dominant transitions, i.e., free-free, free-bound, and boundbound, and can be expressed as: bbfbff' (5-49) Expressions for the free-free ff, free-bound fb and bound-bound bbabsorption coefficients are given in Eqs. 5-50, 5-51, and 5-52, respectively, N j j i Tkh e N j j i Tkh e Be e ffn e G z T n cgs n e G z T n kmhcm eB B1 1/ 3 2 2/1 8 1 1/ 3 2 2/12/1 6107.3 63 8 (5-50)

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120 N j j i Tkh Tkh ze N j j i Tkh Tkh ze Be e fbn eez T n cgs n eez T n kmhcm eB B B B1 2 / / 3 2 2/1 8 1 2 / / 3 2 2/1 2/1 61 107.3 1 63 8 (5-51) Tkh N j j lu j s ul j lu bbBetrPnB c h/ 1,1,, (5-52) where is the dimensionless free-bound continuum corr ection factor that ta kes into account the electron structure of the atom and usually assumes a value of unity, j luBis the Einstein coefficient for absorption transition l to u (in cm3 erg-1 s-1 Hz), j snis the number density of atoms or ions of constituent j which undergoes the transition from l to u (cm-3) and j luP is the normalized line profile expressed by the Voigt function. Spectral line profile. The contribution of the line shape function,j luP, in the bound-bound absorption coefficient, bb, determines the appearance of the line spectrum. In the model, the line profile is described by a Voigt function under the assumption that the dominant line broadening mechanism is Stark broadening which competes with Doppler broadening as the plasma evolves in time. The Stark-shifted Vo igt function in frequency terms is given by: dy trayt e tra Py 2 2, ,2 (5-53) where y is the integration parameter, tra is radial and time dependent damping parameter, t is the line shift normalized by Doppler width, D (Eq. 5-55). tr tr tD StarkShift, 2 ,0 (5-54)

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121 tr tr traD Stark, 2ln, (5-55) The calculation of the Voigt f unction was performed using a modified Humlicek algorithm as proposed by Schreier [150]. Solution to the Inverse Problem In order to extend the analytical applicability of the theoretica l radiative model of the laserinduced plasma expansion in vacuum, an additi onal computational routine based on the Monte Carlo simulated annealing optimizati on was developed by Gornushkin et al [62]. This method allows the determination of initial plasma parameters, such as temperature and particle number densities, by a direct compar ison of an experimentally measured LIBS spectrum with a calculated synthetic emission spec trum obtained from the model [62]. In its simplest form, a simulated annealing algorithm can be generally used to search for the optimum solution to a variety of mathematical problems. It is anal ogous to the thermodynamic pr ocess involved in the cooling of glass where the atoms are initially heat ed to a very high temper ature and then slowly cooled until the most stable system configur ation is achieved. The simulated annealing algorithm is usually a part of a standard Monte Carlo (MC) simulation procedure which statistically samples all the possi ble states of a system by arbitr ary selection of new parameters; in effect, the MC simulation represents a larg e number of random trials. However, not all changes are accepted since each MC step or atte mpt has to follow a certain probability criterion, known as the Metropolis criterion [151], defined by a particular cost function [152]. In the MC-LIBS approach, the necessary input parameters ar e the initial te mperature and the initial number densities of plasma constitu ents. When the simulate d annealing optimization method is applied to this initial set of data, th e parameters are randomly varied within a given

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122 range of values until the global maximum of the cost function is reached. In this case, the cost function is the linear correlation coeffi cient function given by Eq. 5-56: i i i i i i iyyxx yyxx R2 2 (5-56) where xi and yi are the intensities of the experimental and theoretical spectra at the same wavelength i, respectively, and x and yare the mean of the xis and yis, respectively [153]. The linear correlation provides a measure of the a ssociation between variables and, in this case, the value of the correlation coefficient R determines the similarity between the experimental and synthetic spectrum [62, 154]. Fig. 5-6 shows an example of the corr elation between an experimental and a simulated spectrum of an Al alloy after multiple iterations. The R value obtained is 0.9913. Ideally, the optimization undergoes several iter ations of the initial parameters until the extreme maximum of the correlation coefficient is reached. However, realistically, a fixed value for the number of iterations is used to minimize the computer run time. In general, a shortfall of the maximization (or minimization in other cases) of a function is that the extremum point can be either global, which is truly the highest or lowest function value, or local, which is the highest or lowest in a finite neighborhood. These are illustrated in Fig. 5-7. Simulate d annealing alleviates this difficulty, in most cases. A more extensiv e discussion of the Monte Carlo algorithm, as well as the simulated annealing proce ss is found in Ref. [153].

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123 Figure 5-1. Temporal evolution of the H line at 656.272 nm. LIBS measurements were performed on an aluminum alloy sample us ing 5 different delay times and gate width of 500 ns at a pressure of 100 mbar in air. Figure 5-2. Boltzmann plot obtaine d using Fe I lines in an aluminum alloy sample. LIBS measurement was performed using a delay of 2.0 s and a gate width of 0.5 s under atmospheric conditions. The temperature cal culated from the slope of the line is 10677 K.

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124 Figure 5-3. Energy levels of atom ic (I) and ionic (II) species. Ek I and Em II are the excitation energies of the atom and ion, respectively, is the ionization energy and ni I, nk I, nl II and nm II are the number densities for different levels and for different species. (Adapted from Ref. [25])

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125 Figure 5-4. Saha-Boltzmann plots of different elements using neutral (points in yellow background) and singly-ionized (points in blue background) lines. LIBS measurements were performed using a delay of 2.0 s and a gate width of 0.5 s at atmospheric conditions. The average temperature calculated from the slopes of the line is 11141 600 K.

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126 Figure 5-5. Illustration of the c oordinate system used in the semi-empirical vacuum plasma expansion model. (a) Circular plasma projection viewed by an observer in the z direction where P is a spatially-resolved observati on point. (b) Ci rcular plasma projection viewed by an observed in the y -direction; OP is the line of sight, I ( r ,) is the spectral radiance emitted along the line of sight and is the polar angle of the spherical coordinate system. (Adapted from Ref. [61]) Figure 5-6. Correlation between the experimental (blue line) and si mulated (red dots) spectrum. The correlation coefficient calculated from the MC-LIBS analysis is 0.9913. LIBS measurements were performed using a delay of 50 ns and a gate width of 100 ns at a pressure of 0.1 mbar.

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127 Figure 5-7. Extrema of a function in an interval. Points A, C and E are local but not global maxima. Points B and F are local but not global mimina. The global maximum occurs at G and the global minimum is at D. (Adapted from Ref. [153])

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128 Table 5-1. Calculated FWHM of reduced Star k profiles in nm per cg s field strength unit. Temperature (K) Electron number density (cm-3) 1/2 (nm) 10000 1 1015 7.77 10-4 1 1016 1.34 10-3 1 1017 1.86 10-3 1 1018 2.15 10-320000 1 1015 6.01 10-4 1 1016 1.14 10-3 1 1017 1.75 10-3 1 1018 2.26 10-3 1 1019 2.35 10-3

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129 CHAPTER 6 COMPARATIVE STUDY OF TWO STAN DARD-FREE APPROACHES IN LASERINDUCE D BREAKDOWN SPECTROSCOPY Introduction In laser-induced breakdown spectroscopy (LIBS), quantitative information regarding the sample composition can be usually obtained by constructing several calib ration curves for each component in the sample. This generally involve s the requirement of ma trix-matched standards which are very difficult to acquire, particularly in cases of highly variable or fully unknown matrices. The main challenge that has to be overcome in LIBS quantit ative analysis is the occurrence of matrix effects wh ich is characterized by the str ong dependence of atomic emission spectra on relatively small variations in samp le composition. Several studies on the various types of matrix effects [45, 46, 48, 49] have been carried out in order to fully develop the potential of LIBS for quantitati ve measurements. Matrix effects have been found to have a dependence on several factors which include par ticle size [45, 49], chemical speciation [46], amount of energy coupled to the plasma [48] and latent heat of vaporization [49]. Furthermore, numerous solutions to the matr ix effects problem have been proposed in recent years [50, 51, 53]. The most common corr ection methods involve normalization of the analyte signal with a particular physical parameter, e.g. plasma temperature [50], ablated mass [50], sample surface density [53], and background signal [51]. Alternative analytical procedures based on chemometric methods have also been recently associated with LIBS in order to improve its analytical performan ce with respect to standard calibration curves. Among these are multivariate analysis [155-158], principal compon ent analysis (PCA) [158-161], partial least squares (PLS) regression [158, 159, 162-164] and neural networks [161, 163, 165]. However, the aforementioned methods still require the use of standards followed by a certain type of correction or data treatment algorithm in order to extract useful quantitative

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130 information from LIBS measurements. Several re search groups have found an alternative route from sample to element composition which elimin ates the use of matrix-matched standards for calibration purposes. Ciucci et al. [55, 56] pion eered the work on calibration-free LIBS analysis which is based on the Boltzmann plot approach and operates on the basic assumptions of stoichiometric ablation and lo cal thermodynamic equilibrium. Gornushkin et al. [61, 62] modeled the expansion of laser-induced plasmas into vacuum which also solves the initial plasma conditions through a step-wise Monte Carl o optimization of calculated synthetic spectra in order to obtain a close correlation with experimentally measured ones. Yaroshchyk et al. [166] developed a fully automatic analytical soft ware which uses a database of atomic emission lines to calculate a th eoretical emission spectrum for selected elements using defined plasma parameters. The plasma temperature, which is th e most important parameter in their model, is optimized using the Golden Search in One Dime nsion routine until the best least squares fit between theoretical and experime ntal spectrum is obtained. They obtained a 25% agreement between calculated and certified values for the ma jor elements present in bauxites, brass, mineral samples and laboratory air. De Giacomo et al. [167] similarly proposed a self-calibrated LIBS (SC-LIBS) approach in which the analyte emissi on signals are normalized with respect to the blackbody emission. In their model, it is assumed that a partial LTE condition exists within the excitation energy range in terval of 30,000 to 50,000 cm-1 included in the Boltzmann plot and that there is no appreciable ionizat ion in the acquisition delay ti mes used. The SC-LIBS was demonstrated to be applicable in the analysis of the minor components of copper-based alloys using fs and ns lasers. The aim of this research is to evaluate the ap plicability of two standa rd-free approaches for LIBS quantitative analysis of different alum inum alloy samples: the calibration-free LIBS

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131 approach and the Monte Carlo simulated anne aling optimization method for LIBS. The two methods were applied to two type s of measurements, spatially-inte grated and spatially-resolved LIBS measurements, in order to characterize th e laser-induced plasma and to determine the elemental composition of the samples under investig ation without the use of calibration curves. The parameters determined in this study include temperature and electron number density of the plasma, the relative elemental composition of the sample and the percentage errors associated with the measurement. Experimental The LIBS experimental system and spectral data acquisition used in the measurements have already been described in detail in Chapte r 4. All measurements in this study were carried out under vacuum conditions at a pressure of 0.1 mbar using a delay time of 50 ns and a gate width of 100 ns. The schematic of the set-up is illustrated in Fig. 4-3. The samples used were aluminum alloy standard disks (B8, D33, S4, SM10, V14 and Z8) from APEX Smelter Co. in South Africa. The elemental compositions are given in Table E-1 in Appendix E. No other sample pre-treatment, other than cleaning the sa mple surface with pure methanol prior to LIBS measurements, was necessary. Two operational modes were used in this st udy: spectroscopy mode and imaging mode. In spectroscopy mode, the laser-i nduced breakdown spectra from 10 laser shots were summed up using the built-in accumulation function in th e WinSpec32 software (Version 2.5.18.2; Princeton Instruments). In imaging mode, the spatial resolution was conserved since two-dimensional images of the spectral lines were recorded which were later on converted to spatially-resolved spectra using the binning and skipping function of the WinSpec32 program. In both modes, ~10 nm wide spectra l windows between 220 and 700 nm were consecutively recorded and the spectra in each re gion were measured in 3 successive runs. The

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132 set of spectra obtained in each run were spliced together using a simple in-house program written in Q-Basic and the merged spectra were subseq uently averaged. All merged spectra were corrected for background and relative detector spectral effici ency using in-house programs written in MATLAB before any standard-f ree spectral analyses were carried out. Results and Discussion Standard-Free Analysis of Aluminum Alloys General a ssessment of procedure. The relatively high quality (in terms of the resolution and signal-to-noise ratio) of the laser-induced breakdown spectra measured in the current study is evident from the data shown in Fig. 6-1. CF-LIBS analysis required identification of several neutral and singly-ionized lines from the constituents present in the sample. The lines used for each sample are listed in Tables 6-1 to 6-6. It can be inferred from the tables that there are differences in the number of spectral lines used for each sample; this is a consequence of the variation in elemental composition. More lines can be identified and approximated with a fitting function if the concentration of the element is hi gh and fewer lines if the concentration is low. Resonance lines of major elements in the alloy sample are usually not included in the calibrationfree analysis as they are often self-absorbe d. Use of resonance lines can lead to an underestimation of the relative concentration si nce there is no correction for self-absorption applied in the current study. However, it has to be remarked that the identification of lines in a wide spectral range data is not a trivial task especially wh en analyzing samples of unknown origin and composition. The pro cess involves a great deal of d ecision-making and requires much knowledge and experience. Identif ication of the lines and the de termination of integrated line intensities constitute the bulk of the work involved in the calib ration-free procedure since both steps are user-dependent.

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133 In the Monte Carlo LIBS simulated anneali ng optimizations, only 22 spectral lines from 6 different elements (Al, Cu, Fe, Mg, Mn and Si ) found between the range of 270 and 335 nm were used in the simulated annealing optimization of Al alloys B8, D33, V14 and Z8. Two additional lines from Zn were used for Al alloys S4 and SM10. Table 6-7 lists the lines used in the Monte Carlo LIBS simulations. Both resonance and non -resonance emission lines were included in the simulation procedure since there is no limitation se t on the character of atomic transitions as long as the required spectroscopic parameters are availa ble in atomic spectra databases. Resonance lines of major sample components do not present any difficulty in this case since the modeling algorithm takes into account the occu rrence of self-absorp tion or self-reversal of lines. Ideally, lines from both neutral and singlyionized species must be used to improve the accuracy of the optimization procedure but the limitation was set on the spectral range to decrease computation time. The chosen range allowed the use of only ne utral lines for Cu, Si and Zn. In general, the selection and number of lines in cluded and the spectral range used in the optimization procedure is mainly limited by the computation time and the availability of atomic transition probabilities [137, 168], Stark broadening parameters [131, 13 9], and partition functions [130, 169, 170]. Other minor sample components such as Cr, Ni and Ti were excluded in the calculations for reasons described above. Also, the MC-LIBS algorithm requires an initial guess for the temperature and number densities of sample constituents. In this study, the initial values used for the temperature and number densities were usually based on the values obtained with CF-LIBS. However, in cases where no references are availa ble, typical plasma temperat ure values between 10000 and 20000 K and total number densities between 1016 and 1017 cm-3 can be used. The accuracy of the initial guess values is not essential because they are only used as starting parameters of the optimization

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134 which are subsequently iterated in the algorithm. The only inc onvenience of using values which are far from the true values is that the calculati on will take longer before the values converge to optimal ones. The latter correspond to high co rrelation between the simulated spectra and the experimental spectra. The computation time depe nds on the number of parameters that need to be iterated, which includes the temperature and the number density of each sample component. The computation time also depends on the numbe r of lines included in the simulations, the number of iterations and computer CPU speed. The symmetry of the plasma is also a required input parameter (although not iterat ed) and can be easily determined from images of the plasma (Fig. 6-2a). The axis x perpendicular to the image plane corr esponds to the optical axis (line-ofsight direction) and the vertical axis z parallel to the image plane corresponds to the direction of the laser beam (axial direction), as illustrated in Fig. 6-2b. The dimensions of the laser-induced plasma in the x and y directions were the same and approximately equal to 0.24 cm and the height of the plasma in the axial direction was 0.29 cm. As mentioned previously, the num ber of iterations is one of the factors which affects the computation time. It is a user-settable parame ter which was initially optimized in order to determine the minimum number of iterations requ ired to obtain a high co rrelation between the experimental spectrum and the synthetic spectrum calculated from the plasma expansion model. The optimization of the number of iterations per parameter, Niteration, was performed using the experimental spectrum of Al alloy D33 and Niteration was varied as follows: 20, 35, 50, 75, 100, and 150. From the results of the simulations shown in Fig. 6-3, it can be observed that the correlation coefficient R, which determines the similarity between the experimental and synthetic spectrum, did not improve any further even after 150 Niteration. In fact, R reaches a constant value at about 0.95 after 35 Niteration which is a huge advantage since the computer run time increases

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135 linearly with the number of iterations. It s hould be noted that the number of iterations, Niteration, is applied to each parameter to be optimized. In th is case, there are seven parameters that need to be iterated; hence, the tota l number of iterations is 7 Niteration. The total number of iterations corresponds to the maximal abscissa s of the correlation coefficient plots in Fig. 6-3. It is also evident from the correlation coefficient plots in Fi g. 6-3 that at the beginn ing of the Monte Carlo simulated annealing procedure, the R values are highly dispersed. This is typical of Monte Carlo annealing simulations where extreme conditions are initially applie d to the system and subsequently allowed to stabilize as signified by the almost constant correlation coefficient obtained after the 300th iteration. Hence, for all the simu lations carried out using Monte Carlo LIBS, the number of iterations was kept at 35 for each iterated parameter. Determination of electron number density and temperature. In the CF-LIBS approach, the electron number density can be calculated in a number of ways, in this study, the electron number density was determined using the Stark width of the H line at 656.272 nm which was still very prominent under the experimental conditi ons applied (Fig. 6-4). The equation used in the calculations is given in E q. 5-19. The electron number densities obtained are on the order of 1016 cm-3 (Table 6-8). The plasma temperatures were calculated by constructing several SahaBoltzmann plots using lines from di fferent elements present in the metallic alloy sample and the results were on the order of 9800 to 11000 K, sim ilar to previously repo rted values in the literature [171, 172]. The Saha-Boltzmann plots of selected elements for each alloy sample are shown in Fig. 6-5. The parallelity exhibited by the Saha-Boltzmann plots of different sample constituents is a satisfactory i ndication of the existence of loca l thermodynamic equilibrium in the plasma. Furthermore, the parallel slopes obt ained in the Saha-Boltzmann plots also verify that the effect of the shot-to-shot variability of the laser pulse is not very significant in this case

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136 regardless of the sequential acquisitions that had to be performed to obtain spectral data from 220 to 700 nm for a single measurement. The negligible effect of laser fluctuations can be attributed to the statistical av eraging of three measurements ta ken at different positions on the sample and due to the attention paid to mainta in the optimum target surface conditions. The minimum electron number density required to further validate the existence of local thermodynamic equilibrium was also calculated us ing Eq. 5-19 and the results indicated that LTE condition was indeed satisfied in th is particular analysis (Fig. 6-8). In the Monte Carlo LIBS approach, the tempor al evolution of temperature and electron number density at different spatial positions in the laser-induced plasma can be obtained and the three-dimensional plots are show n in Fig. 6-6 for the six alloy samples. The temporal window begins at the end of the laser pulse when the laser-matter interaction has terminated (postbreakdown) and local thermodynamic equilibrium is established. This time is taken as the starting point ( t = 0) of the model. The spatial window, on the other hand, is related to the number of equipotential surfaces or subshells assigned to the plasma where each subshell is characterized by a single value for temperature, number density and pre ssure. Spatial position zero in Fig. 6-6 indicates the center of the plasma and the last sp atial position indicates the outer plasma boundary [173]. During the onset of expansion ( t = 0), the temperatures at the core ranged from 28000 to 33000 K and the electron number densities were between 4 1017 to 1 1018 cm-3 for the six samples analyzed. However, for the actual temporal window of observation used in the experiment, the spatial distribution of temperature and electron number density are shown in Fig. 6-7, where the values at each sp atial position correspond to tempor ally-integrated measurements between 50 ns and 100 ns of plasma evolution. From the plots obtained (Figs. 6-6 and 6-7), it is

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137 evident that both temperature and electron numbe r density have a maximum at the center and decreases towards the plasma edge. A similar trend was experimentally obtained by Aguilera and Aragon [174] by deconvolution of spatially resolved spectra of laser-induced plasmas formed on an iron-nickel alloy under atmospheric conditions. Furthermore, the temperature and electron num ber density values calculated using the CFLIBS technique were spatially-int egrated along the direction of lin e-of-sight and the full height of the plasma, in other words, the emission from the whole plasma was taken into consideration. In order to compare the values obtained with CF -LIBS with that of MC-LIBS, the average of the spatially resolved temperature and electron number density values in Fig. 6-7 was obtained for each alloy sample and the results are plotted in Fig. 6-8 and summarized in Table 6-8. The averaging resulted in large standa rd deviations for the MC-LIBS values (Table 6-8) due to the wide spatial distribution of electron number densities and temperatures over the whole plasma volume and over the whole duration of data acquisition (100 ns) as de picted in Figs. 6-6 and 6-7. Comparing the calculated temperature and electr on number density values obtained using the two standard-free approaches, it can be conclude d that spatially and temporally-integrated MCLIBS temperatures are in close agreement w ith the temperatures obtained using the SahaBoltzmann plot approach (CF-LIBS) for all six a lloys investigated. The range of temperature values are between 9000 and 11000 K. However, the spatially and temporally-integrated electron number densities calcula ted using the Monte Carlo appro ach are about 3-8 times higher than the those determined usi ng the linear Stark broadening of the hydrogen alpha line at 656.272 nm but the differences are within experiment al and statistical errors of the measurement considering the widely distributed electron number density values in both spatial and temporal windows of observation obtained in the plasma modeling routine. However, it should be

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138 emphasized that, theoretically, the average te mperature and electron number density values reported for MC-LIBS do not exist since the mode l was principally built on the concept of nonuniform distribution in laser-induced plasmas [173]. The concept of inhomogeneity in temperature and number density distribution in laser-induced plasmas has been extensively studied and confirmed by nearly all experiment al works [63, 172, 175-186]. The errors reported in Table 6-8 for temperature and electron number density values do not necessarily reflect uncertainties of the model but rather demonstrat es the large spatial non-uniformity of plasma parameters which is particularly evident when spatially-integrated measurements are used to characterize laser-induced plasmas. Determination of relative composition. In the CF-LIBS measurement protocol, several Boltzmann plots were constructed using the different species identified in the aluminum alloy sample in order to determine the relative elemen tal composition. The results of the calibrationfree analysis are shown in Fig. 6-9 and summarized in Tables 6-9 to 6-11. There is close agreement between the CF-LIBS re sults and certified values only for the most abundant element present in the sample (Al). The analysis resulted in relative errors below 3% for Al. However, in the case of the other components of the metallic alloy sample, the analysis can be considered semi-quantitative only due to the large magnitude of errors that were calculated which ranged from 2-98% as illustrated in Fig. 6-10. The relatively large errors calculate d can be attributed to the shot-to-shot intensity fluctuations, uncertain ties related to the determination of temperature and non-uniformity of the temperature within the plasma. According to the numerical investigation carried out by Tognoni et al. [138] on the expected CF-LIBS precision and accuracy, the relative elemental compositions of sample components other than the most abundant element varied within 150-200% under a simulation of broad temperature dispersion

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139 and large intensity fluctuations which is similar to the results obtained in this study for most of the components present in the sample. On the other hand, in their simulations involving the most abundant element, the concentration only varied within 1% even under the extreme conditions applied which is in agreement with the relative c oncentration values calculated for Al in this case. In the MC-LIBS method, quantitative inform ation was obtained through an extensive Monte Carlo simulated annealing optimization of the composite theoretical spectra to match them with experimental spectra. The process was carried out by varying seven parameters, the number densities of Al, Cu, Fe, Mg, Mn, Si and th e initial plasma temperature, for Al alloys B8, D33, V14 and Z8. The number density of Zn was also iterated in the case of Al alloys S4 and SM10. The results of the optimization procedure are shown in Fig. 6-11 where the experimental spectra and the best-fit simulated spectra are shown in blue and red, respectively. Excellent correlation between the experimental and synthe tic spectra was obtaine d after the simulated annealing optimization procedure, with correlation coefficients in the range of 0.93-0.96. Since only 35 iterations were used in the procedure, the optimization of a maximum of 8 parameters and 24 lines took about ~4 hours using well-tuned initial input parameters and a 3.1 GHz PC. The optimized number densities calc ulated for the elements that were iterated are listed in Table 6-12. The orders of magnitude obtained for the sa mple constituents are co mparable to the results obtained by Gornushkin et al. [62] using a similar set of Al alloy standards for the initial verification of the plasma expansion model. In order to compare the number densities obtained from the Monte Carlo optimizations alongside the relative elemental c oncentrations obtained with CF-LIBS and relative certified

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140 values, the number densities were converted to relative mass c oncentrations using the simple equation given by: 100 %1 N j jj jj jMn Mn C (6-1) where Cj is the relative mass concentr ation of sample constituent j in %, nj is the number density of j in cm-3, M j is the atomic mass of j in g mol-1 and N is the number of sample constituents iterated. The relative concentration values obta ined using CF-LIBS and MC-LIBS are plotted in Fig. 6-12 are and tabulated in Tables 6-13 to 6-18. In all six alloys analyzed, the relative concentrations obtained for Al using the calib ration-free technique were in much closer agreement with the certified values than t hose values obtained using the Monte Carlo optimization. CF-LIBS resulted in relative er rors below 4% while MC-LIBS resulted in errors better than 20% for the major component in the sa mple (Fig. 6-13). However, for most of the other elements present in the sample, the uncerta inties obtained using the MC-LIBS approach is usually below 50% except in the case of Si where relativel y large errors (>100%) were determined for all six alloy samples as shown in Fig. 6-13. The poor accuracy obtained for Si can be attributed to the fact th at only one Si line was used in th e Monte Carlo optimizations. It could also explain the observed overestimation of the Si cont ent in all six alloys under investigation as clearly depicted in Fig. 6-12. In a few cases, 200% relative errors were obtained for elements such as Fe in alloy sample S4, Cu in alloy sample SM10 and Mg in alloy samples SM10 and Z8 using the MC optimization procedure. On the other hand, relative concentration values calculated using the CF-LIBS method for el ements besides Al exhibited errors better than 90%. From the determined relative errors in this particular study, the results from both approaches fall into the semi-quantitative category (30-200% error) as defined in Ref. [65]. A

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141 plausible explanation regarding the semi-quantitative results obt ained with the standard-free analysis of Al alloy samples is that the vapor composition of the plasma does not necessarily reflect the composition in the sample due to vari ous thermal optical processes involved in laser ablation which may induce fractional vaporization [62] It can be concluded that stoichiometric ablation, which is one of the main assumptions in the CF-LIBS measurement protocol, is not properly justified in this study a nd therefore requires further inde pendent investigation which is beyond the scope of this research. It should also be noted that in the radiative model of plasma expansion into vacuum, the laser-m aterial interaction is not taken into acc ount since the model simulates the plasma expansion at the onset of the post-breakdown proces s after the laser pulse has terminated. Spatially-Resolved Standard-Free Analysis of Aluminum Alloy Spatially-resolved emission spectra. In this part of the study, spatially-resolved LIBS measurements were obtained by recording the pl asma emission in imaging mode and binning the resulting image into 11 different spatial positions (A through K) along the axial direction as depicted in Fig. 6-14. Each binne d region consisted of 11 vertical pixels which is equivalent to 0.02475 cm of the vertical plasma partition. Ho wever, it should be noted that the spectrum obtained for each spatial position was still spatially-integrated along the line-of-sight. The spatially-resolved spectra of Al alloy D33 at various spectral windows are shown in Fig. 6-15. The spatially-resolved analysis was carried out under the assumption that the laser-induced plasma is imaged with 1:1 magnification at the fo cal plane and that the de tection system does not suffer from any significant optical aberrations such as astigma tism, coma, spherical aberration, etc. A distinct trend in the intensi ties of neutral and singly-ionized lines can be observed in the spatially-resolved data shown in Fig. 6-15. The difference is clearly demonstrated in Fig. 6-16

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142 where the spatial evolution of spectrally-integra ted intensities of different neutral and singlyionized lines of Al, Fe, Mg a nd Mn are plotted. It can be easily deduced from the spatial evolution plot of neutral line in tensities (black bars) that a maximum value for the intensity is approached at approximately the same position, i.e., at positions cl ose to the plasma center for all the neutral lines considered. A similar maxi mum along the axial and ra dial directions was observed by Aragon and Aguilera [177] in the spatia l profiling of Fe I emission from a stainless steel plasma produced in air at atmospheric pr essure using different laser irradiances (80-900 GW cm-2). However, a slightly different behavior was observed for singly-ionized lines (gray bars) of different elements. The intensities slowly increase as the plasma center is approached from the top portion of the plasma (spatial position A) unlike that of neutral lines where the increase is much sharper and the maximum intensity is very well-pronounced. It is also evident from the spatial profiles in Fig. 6-16 that the distribution of intensities along the axial direction is not symmetric with respect to the plasma center, pa rticularly for the singly-ionized lines whose maximal intensities are reached at high axial distances from the surface of the sample. The position of the maximum intensity also varied depending on the emitting species. This implies that it is possible to minimize spectral interference s, if present, for certain elements by finding an optimum distance from the sample surface [5]. In the CF-LIBS approach, the number of lines identified for each sample component in the Al alloy sample vary as a function of the spa tial position as illustrated in Fig. 6-17 and it is evident for elements such as Cu, Fe, Mn, and Ni that more neutral lines (blue squares) can be identified at distances closer to the surface of the sample. For ionic lines (red circles), on the other hand, the number of lines identified is usua lly constant, except in the case of Cr and Ti

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143 where a certain maximum was reached at spatia l position F, which corres ponded to the center of the plasma. It should be emphasized that the number of lines chosen for the CF-LIBS algorithm at each point in space does not necessarily indicate that the line is not present at a particular spatial position due to the limited information available. The main reason a certain emission wavelength was omitted in the analysis is that th e signal-to-noise ratio was too low which made it difficult to differentiate the line from the b ackground and impossible to fit with an analytical function with high certainties. Sp atial positions J and K were not included in Fig. 6-17 and in the calibration-free LIBS analys is for the same reason. The aforementioned observations made on the sp atially-resolved data can be related to a mass-dependent spatial dispersion of different species during th e plasma expansion which was reported by Corsi et al. [187] in their study of the temporal and sp atial evolution of laser-induced plasma from a steel target and by Di Palma et al [188] in their investigation of the composition and gas dynamics of laser ablated AlN plumes fo r pulsed-laser deposition applications. At high laser irradiances (2.3 1011 W cm-2), Corsi et al. [187] observed th at all species in the plasma exhibited a maximum intensity at approximately the same time at a given distance from the sample and showed similar spatial evolution profile of line emissions. The authors explained this by the fact that the flow of all atomic speci es is characterized by a single streaming velocity which only occurs when collisions are significant during the plum e expansion so that different species move as a single system. Howe ver, at lower laser irradiances (1.5 109 W cm-2) used in their study, they observed that the maximum intensity of Cr I occurred at a much earlier time than Fe I which they attributed to a much sl ower plume expansion and lower mass ablated which means less frequent collisions and possibly a non -stoichiometric plasma. The authors further

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144 rationalized that the particles which are subjecte d to a lower collision rate move almost freely, this means that the heavier atoms (Fe I) move slower than lighter ones (Cr I). Based on the above argument, it is a possibility that the apparent higher intensities of Cu I, Fe I, Ni I, and Mn I lines found at lower axial di stances (close to the sample surface) are due to the relatively heavier masses of these atoms comp ared to the masses of Al, Cr, Mg, Si and Ti (Table 6-19). This implies that the species in the plasma do not move with a single streaming velocity as the plasma expands in the z -direction which results in more of the heavier neutrals close to the sample surface where the temperature is also lower as will be described in the next section. Determination of electron number density and temperature. Similar to the CF-LIBS analysis of Al alloys previously discussed, th e electron number density at each spatial position was estimated using the Stark width of the H line at 656.272 nm (Fig. 6-18a). The calculated values are plotted in the upper pa nel of Fig. 6-18b and the results show that the plasma electron number density has an approxi mately constant value of 1.9 1016 cm-3 from spatial positions B through G and decreases to about 1.1 1016 cm-3 towards the edges of the plasma (spatial positions A and I). The same behavior along the axial direction was reported by Aguilera and Aragon [174] in their characterizat ion of a laser-induced plasma formed on an iron-nickel alloy in air at atmospheric pressure. The laser-induced plasma temperature at each spatial posi tion was calculated by constructing several Saha-Boltzmann plots using lin es from different elements present in the alloys sample. Saha-Boltzmann plots of selected lines are shown in Fig. 6-19 and the averaged temperatures are summarized in Table 620. Fr om the results obtained, it is evident that there are no significant differences in the calculated temperature values from spatial positions A

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145 through G which varied between 11000 and 12000 K but temperature values decrease as the sample surface is approached. A similar trend in plasma temperatures was reported in Ref. [174] along the axial direction, except that a decrease in temperatur e was also observed at higher axial distances. The Monte Carlo simulated annealing optim ization method was also applied to the different spatially-resolved spectra. The actual position of the recorded plasma emission was taken into account in the algor ithm to simulate the correct experimental conditions and to minimize the errors of the calculations. However, it should be noted that the model still simulates and calculates the evolution of the whol e plasma expansion at different space and time points and the corresponding spatia l and temporal evolutions of the temperature and electron number density obtained using different spatial input parameters (denoted by letters A through K) are shown in Fig. 6-20. Ideally, all three-dime nsional plots in Fig. 6-20 must be similar since the same expanding plasma is being simulated in each case and the only difference is the portion of the plasma where emission is being collected. The temperatures of the plasma at the core at the end of the laser pulse ranged from 20000 to 40000 K and the corresponding electron number densities calculated were between 8.0 1017 cm-3 and 2.3 1018 cm-3. Since LIBS measurements are usually temporally-integrated, the three-dimensional plots can be transformed into a two-dimensional plot of the spatial evolution of temper ature and electron number density at a delay time of 50 ns and gate width of 100 ns as shown in Fig. 6-21. The abscissa in this case are still in relative term s but directly proportional to the radius Spatial position zero pertains to the center of the plasma and the last spatial pos ition refers to the last subshell and the distance from the center to the outermost subshell is equal to the radius of the plasma.

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146 In order to obtain local information regard ing temperature and el ectron number density using the results of the optimization procedure, the curves in Fig. 6-21 were fitted with a sigmoidal function given by: dx xx AA Ay0 21 2exp1 (6-2) The fitting parameters for the temperature and electron number density curves are given in Tables 6-21 and 6-22, respectively. The temp erature and electron number density values at specific spatial positions corres ponding to the experimentally-obtained spatially-re solved spectra were calculated by simple interpolation using Eq. 6-2. The interpolated temperature and electron number density values at the highlighted portion of Fig. 6-21 were averaged and summarized in Table 6-20 and Fig. 6-18c. From the results obt ained, it is evident that the electron number density and temperature attain maximum values close to the center of the plasma and then decrease towards the edge, simila r to the experimental results re ported in Refs. [174, 177, 179]. Furthermore, it can be observed from Fig. 618c that the minimum electron number density for LTE is only slightly below the el ectron number density value found at the edges of the plasma (spatial points A and K), hence, measurements at these two extremes must be carried out with caution in order for the LTE assumption to remain valid. The temperature and electron number density va lues obtained using th e two standard-free approaches, although not equal in magnitude, demons trated similar trends especially at lower axial distances which agree reasonably well with previous studies [174, 177, 179]. It is also quite interesting to note that the trend observe d in the local temperature and electron number density values predicted by the plasma modeling algorithm and those obtained by the SahaBoltzmann plot approach is reflected on the spat ial evolution profiles of integrated emission

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147 intensities of neutral and singly-ionized lines depi cted in Fig. 6-16. The intensities of spectral lines also decrease as the edges of the plasma is approached. The lower temperatures obtained at distances closer to the sample surface may also explain the evident broadening due possible selfabsorption of the four resonance lines of Al at 308.215 nm, 309.271 nm, 394.401 nm and 396.152 nm shown in Fig. 6-15a. The temperatures obtained using the two standard-free approaches are clearly not comparable except at spatial positions close to the plasma center where the temperatures are between 11000 and 12000 K and it cannot be concl uded with a high degree of certainty which temperature values are more accurate for each sp atial position since the methods used in the determination are very much different in and of itself. In the Saha-B oltzmann plot approach, several lines from different elements contribute in the determination of the temperature and from previous discussion it is quite evident that some species are di stributed unevenly in the axial direction. The apparent axial inhomogeneity of the plasma might be the cause of the slightly unparallel slopes of the Saha-Boltzmann plots c onstructed at spatial po sitions H and I where more neutral lines from heavier elements are mo re easily resolved which contributes to a much higher slope, hence, resulting in a fairly lower temperature compared to those predicted by the plasma model (Table 6-20). On the other ha nd, although the behavior of temperature and electron number density values determined using MC-LIBS at different spatial points is similar to those reported in the litera ture, their accuracy cannot be fully ascertained since only a relatively small spectral window was used compared to the much wider window with more spectral lines used in CF-LIBS method. Determination of relative composition. The final step in the CF-LIBS measurement protocol is, of course, the dete rmination of the relative elemental composition. The results are

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148 summarized in Fig. 6-22 and Table 6-23. A notic eable trend in the concentration values can be deduced from Fig. 6-22 where the relative concentr ations calculated for each sample constituent are shown as a function of spatial position. Fo r Cr, Mg, Mn, Si, and Ti sample components, the relative concentration values calculated genera lly decrease towards the edges of the plasma (spatial positions A and K) and to some extent a maximum value is attained around the center of the plasma. However, since Al is the predom inant element in the alloy sample, no noticeable trend is observed and relatively satisfactory accuracy is obtained at any spatial position with errors better than 9% (Table 6-24). On the other hand, for Cu, Fe and Ni, there is an apparent decrease in the calculated concentration values towards spatial pos ition I. However, it should be emphasized that the values obtained with CF -LIBS are only relative, which implies that overestimation of one component will lead to an underestimation of another. Hence, it is difficult to attach any physical m eaning to the trend observed. The experimentally obtained sp atially-resolved spectra were also optimized using the Monte Carlo simulated annealing procedure and results of the simulations yield correlation coefficients in the range of 0.81-0.98 between the simulated and experimental spectra as illustrated in Fig. 6-23. The elemental number de nsities obtained in the optimization procedure are plotted in Fig. 6-24 as a func tion of spatial position and it is interesting to note that along the axial direction, the predicted num ber densities for most of the elements considered exhibited an almost Gaussian-like distribution around the center, particularly fo r Mg, Mn and Si. This also confirms the observed trend in the calculated relative elemental concentrations obtained with CFLIBS as previously described since the values obtained in this case are absolute (in cm-3). Several studies [174, 179-181] have already been carried out on the spatial distri bution of the number densities of neutrals and ions along the axial direction but the values reported, which

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149 were calculated through the Saha eq uation (Eq. 5-2), were only in re lative terms. However, for comparative purposes, the total relative number dens ities also show a reduction in value towards the plasma edges [174]. Similar to the previous analysis of spatially-integrated measurements of different aluminum alloy samples, the total number dens ities obtained with MC-L IBS were converted to relative weight concentrations using Eq. 6-1 so that a compar ison can be made between the calculated results and certified concentration values. The results are summarized in Fig. 6-25 and tabulated in Tables 6-25 to 6-35. The highest accuracies were obtained for the major component in the sample, which is Al, with re lative errors of 20% or better for MC-LIBSobtained values and 10% or better for CF-LIB S-obtained values at all spatial positions considered. Comparable errors we re obtained for the other elements in the sample with errors as low as 20% and as high as 100%, except for Si where relatively hi gher errors were obtained for MC-LIBS-obtained concentration values (60-250%), similar to the results of previous measurements on different aluminum alloys. With respect to spatial positions, it can be observed that lower errors were obtained for most elem ents in both methods at positions closer to the center of the plasma (spatial position E, F and G). This can be attributed to the relatively higher temperatures and electron number densities at this region of the plasma, as predicted by the plasma modeling routine, which ensures the ex istence of local thermodynamic equilibrium, an assumption which is particularly significant in both standard-free approaches. Conclusion In this study, two techniques for quantitative LIBS analysis which do not require the use calibration curves, were evaluate d: the calibration-free LIBS (CFLIBS) approach and the Monte Carlo simulated annealing optimization method for LIBS (MC-LIBS). Both methods were applied to LIBS measurements performed under vacuum condition (0.1 mbar pressure). The

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150 spectral data acquisition method de veloped in this research proved to be suitable for both approaches, CF-LIBS in particular, for it allo wed spectral data to be acquired over a wide wavelength range (200-700 nm). CF-LIBS required full characterization of the spectrum so that numerous lines from most, if not all, elements can be included in the analysis. This certainly improved the reliability of the method as a quantitative technique. However, the CF-LIBS approach is not a fully-automated algorithm, i.e ., it is a highly user-dep endent technique from start to finish, which also required proficiency in spectral line identification. The analysis may take from a few hours to a day depending on the sample and the number of lines included in the analysis. The MC-LIBS approach, on the other hand, although more complex in its formulation since it simulates the expansion of a laser-indu ced plasma into vacuum using several gas and fluid dynamic and radiative transf er equations, is relatively less user-involved compared to CFLIBS. The only initial requirements are input fi les which contain releva nt spectroscopic and physical parameters, partition functions and Star k broadening parameters of all the species included in the simulations. The Monte Carlo op timization procedure may take from a few hours to several days depending on the computer CPU speed, the number of iterations, the number of lines and the number of element numb er densities to be iterated. The results of the analysis of the spatiallyintegrated spectra of six different aluminum alloy samples demonstrated that both methods are satisfactory semi-quantitative techniques for LIBS analysis of elements other than the most abundant component in the sample. Comparatively, concentration va lues obtained with CF-LIBS for the matrix element Al were much closer to the certified values than those obta ined with MC-LIBS. This may be attributed to the larger amount of information used in CF-L IBS compared to the limited number of lines and elements as well as spectral wi ndow size used in the MC-LIBS anal ysis. However, regardless of

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151 the limitations imposed on MC-LIBS, the relative concentration obtained for the remainder of the sample components resulted in lower relative errors compared to those determined with CFLIBS. Plasma temperatures calculated usi ng both approaches were between 9800-11000 K and electron number densities were on the order of 1016 cm-3, comparable to results reported in the literature for vacuum LIBS measurements [171, 172]. Also, in this study, CF-LIBS and MC-LIBS appr oaches were applied for the first time to the analysis of spatially-resolved measurements taken at different points along the laser beam axis (axial direction). Plasma temperature and electron number density values obtained from both methods, although not equal magnitude, show similarities in behavior along the axial direction. The electron number density values ca lculated at different sp atial positions using both approaches indicated a maximum around the center of the plasma, similar to the trend observed for the plasma temperatures calculated using the MC optimization routine. Temperatures calculated from the Saha-Boltzmann plot method only demonstrated a reduction in temperature towards the sample surface. Furthermore, elemen t number densities obtained from the extensive MC optimization and relative con centration values obtained from the calibration-free analysis exhibited higher values around the plasma center which could be attributed to the higher temperatures and electron number densities in this region. Lower relative errors were also obtained for the calculated concen tration values using either met hod at spatial positions close to the plasma center. However, regardless of the type of meas urement, spatially-integrated over the whole plasma emission or spatially-resolved at a specific position along the axial direction, it should be remarked that the plasma emission is still spat ially-integrated along th e line of sight (pathintegrated) and could have contributed to the errors obtained with standard-free LIBS analysis.

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152 Previous studies have already s hown that radial inhomogeneity in the plasma is evident [174, 179-181] and should be taken into ac count. The contributions arisi ng from regions with different electron number density and temperature values could be avoide d by obtaining radially-resolved spectra using Abel inversion [103, 179, 184, 187].

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153 250 300 350 400 0 100 200 300 400B8 D33 S4 SM10 V14 Z8 Wavelength (nm)Intensity (a.u.) 279 280 281 282 0 100 200 300 400B8 D33 S4 SM10 V14 Z8 Mg II Mg II Mg II Mg II Al II Wavelength (nm)Intensity (a.u.) 250 300 350 400 0 100 200 300 400B8 D33 S4 SM10 V14 Z8 Wavelength (nm)Intensity (a.u.) 279 280 281 282 0 100 200 300 400B8 D33 S4 SM10 V14 Z8 Mg II Mg II Mg II Mg II Al II Wavelength (nm)Intensity (a.u.) Figure 6-1. Section of laser-indu ced breakdown spectra of different aluminum alloys. The inset shows spectrally-resolved lines from singly-ionized Mg and Al. Figure 6-2. Images of laser-induced plasmas obt ained from different aluminum alloy samples using a delay time of 50 ns and gate widt h of 100 ns. The images in (a) are the projections of the plasma on the yz -plane as defined in (b); the z -axis corresponds to the direction of the laser beam and the x -axis corresponds to the direction of line-ofsight.

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154 Figure 6-3. Effect of the number of iterations per parameter, Niteration, (a) 20, (b) 35, (c) 50, (d) 75, (e) 100 and (f) 150, on the correlation coefficient R and computer run time of a 3.1 GHz PC. The upper panel shows the overl ap of the experimental spectrum (blue) with the calculated synthetic spectrum (re d). The lower panel shows plot of the correlation coefficient versus the iteration number. The total number of iterations is 7 Niteration, where 7 is the number of parameters iterated.

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155 Figure 6-4. The Stark broadene d hydrogen alpha line at 656.272 nm in the aluminum alloy spectra used for electron number density determination in CF-LIBS.

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156 3691215182124 -20 -16 -12 -8 -4 0 4 8 Al Cu Ni Siln(I/gkAki)*Ek + (eV)Al alloy B83691215182124 -20 -16 -12 -8 -4 0 4 8 Al Cu Ni Siln(I/gkAki)*Ek + (eV)Al alloy D333691215182124 -20 -16 -12 -8 -4 0 4 8 Al Cu Mg Si Znln(I/gkAki)*Ek + (eV)Al alloy S43691215182124 -20 -16 -12 -8 -4 0 4 8 Al Cu Ni Siln(I/gkAki)*Ek + (eV)Al alloy SM103691215182124 -20 -16 -12 -8 -4 0 4 8 Al Cu Niln(I/gkAki)*Ek + (eV)Al alloy V143691215182124 -20 -16 -12 -8 -4 0 4 8 Al Cu Ni Siln(I/gkAki)*Ek + (eV)Al alloy Z8a a c c e e b b d d f f10885 625 K 10881 691 K 9901 658 K 9799 405 K 10964 539 K 10622 673 K 3691215182124 -20 -16 -12 -8 -4 0 4 8 Al Cu Ni Siln(I/gkAki)*Ek + (eV)Al alloy B83691215182124 -20 -16 -12 -8 -4 0 4 8 Al Cu Ni Siln(I/gkAki)*Ek + (eV)Al alloy D333691215182124 -20 -16 -12 -8 -4 0 4 8 Al Cu Mg Si Znln(I/gkAki)*Ek + (eV)Al alloy S43691215182124 -20 -16 -12 -8 -4 0 4 8 Al Cu Ni Siln(I/gkAki)*Ek + (eV)Al alloy SM103691215182124 -20 -16 -12 -8 -4 0 4 8 Al Cu Niln(I/gkAki)*Ek + (eV)Al alloy V143691215182124 -20 -16 -12 -8 -4 0 4 8 Al Cu Ni Siln(I/gkAki)*Ek + (eV)Al alloy Z8a a c c e e b b d d f f3691215182124 -20 -16 -12 -8 -4 0 4 8 Al Cu Ni Siln(I/gkAki)*Ek + (eV)Al alloy B83691215182124 -20 -16 -12 -8 -4 0 4 8 Al Cu Ni Siln(I/gkAki)*Ek + (eV)Al alloy D333691215182124 -20 -16 -12 -8 -4 0 4 8 Al Cu Mg Si Znln(I/gkAki)*Ek + (eV)Al alloy S43691215182124 -20 -16 -12 -8 -4 0 4 8 Al Cu Ni Siln(I/gkAki)*Ek + (eV)Al alloy SM103691215182124 -20 -16 -12 -8 -4 0 4 8 Al Cu Niln(I/gkAki)*Ek + (eV)Al alloy V143691215182124 -20 -16 -12 -8 -4 0 4 8 Al Cu Ni Siln(I/gkAki)*Ek + (eV)Al alloy Z8a a c c e e b b d d f f10885 625 K 10881 691 K 9901 658 K 9799 405 K 10964 539 K 10622 673 K Figure 6-5. Saha-Boltzmann plots of selected elements in aluminum alloy sample (a) B8, (b) D33, (c) S4, (d) SM10, (e) V14 and (f) Z8.

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157 0.0 0.2 0.4 0.6 0.8 1.0 0 8000 16000 24000 32000 20 40 60 80 100 120 140 T e m p e r a t u r e ( K )T i m e ( n s )S p a t i a l P o s i t i o n ( a u )B8 0.0 0.2 0.4 0.6 0.8 1.0 0.0 2.0x10174.0x10176.0x10178.0x1017 20 40 60 80 100 120 140 S p a t i a l P o s i t i o n ( a u )E l e c t r o n N u mb e r D e n s i t y ( c m3)T i m e ( n s )B8 0.0 0.2 0.4 0.6 0.8 1.0 0 8000 16000 24000 32000 20 40 60 80 100 120 140 S p a t i a l P o s i t i o n ( a u )T e m p e r a t u r e ( K )T i m e ( n s )D33 0.0 0.2 0.4 0.6 0.8 1.0 0.0 2.0x10174.0x10176.0x10178.0x1017 20 40 60 80 100 120 140 S p a t i a l P o s i t i o n ( a u )E l e c t ro n N u m b e r D e n s i t y (c m3)T i m e ( n s )D33 0.0 0.2 0.4 0.6 0.8 1.0 0 8000 16000 24000 32000 20 40 60 80 100 120 140 S p a t i a l P o s i t i o n ( a u )T e m p e r a t u r e ( K )T i m e ( n s )S4 0.0 0.2 0.4 0.6 0.8 1.0 0.0 2.0x10174.0x10176.0x10178.0x10171.0x1018 20 40 60 80 100 120 140 S p a t i a l P o s i t i o n ( a u )E l e c t ro n N u m b e r D e n s i t y (c m3)T i m e ( n s )S4 0.0 0.2 0.4 0.6 0.8 1.0 0 8000 16000 24000 32000 20 40 60 80 100 120 140 T e m p e r a t u r e ( K )T i m e ( n s )S p a t i a l P o s i t i o n ( a u )B8 0.0 0.2 0.4 0.6 0.8 1.0 0.0 2.0x10174.0x10176.0x10178.0x1017 20 40 60 80 100 120 140 S p a t i a l P o s i t i o n ( a u )E l e c t r o n N u mb e r D e n s i t y ( c m3)T i m e ( n s )B8 0.0 0.2 0.4 0.6 0.8 1.0 0 8000 16000 24000 32000 20 40 60 80 100 120 140 S p a t i a l P o s i t i o n ( a u )T e m p e r a t u r e ( K )T i m e ( n s )D33 0.0 0.2 0.4 0.6 0.8 1.0 0.0 2.0x10174.0x10176.0x10178.0x1017 20 40 60 80 100 120 140 S p a t i a l P o s i t i o n ( a u )E l e c t ro n N u m b e r D e n s i t y (c m3)T i m e ( n s )D33 0.0 0.2 0.4 0.6 0.8 1.0 0 8000 16000 24000 32000 20 40 60 80 100 120 140 S p a t i a l P o s i t i o n ( a u )T e m p e r a t u r e ( K )T i m e ( n s )S4 0.0 0.2 0.4 0.6 0.8 1.0 0.0 2.0x10174.0x10176.0x10178.0x10171.0x1018 20 40 60 80 100 120 140 S p a t i a l P o s i t i o n ( a u )E l e c t ro n N u m b e r D e n s i t y (c m3)T i m e ( n s )S4 Figure 6-6. Spatial and temporal evolution of temperature (left) and electron number density (right) obtained using the MC-LIBS approach for aluminum alloy samples.

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158 0.0 0.2 0.4 0.6 0.8 1.0 0 8000 16000 24000 32000 20 40 60 80 100 120 140 S p a t i a l P o s i t i o n ( a u )T e m p e r a t u r e ( K )T i m e ( n s )SM10 0.0 0.2 0.4 0.6 0.8 1.0 0 1x10172x10173x10174x10175x1017 20 40 60 80 100 120 140 S p a t i a l P o s i t i o n ( a u )E l e c t r o n N u mb e r D e n s i t y ( c m3)T i m e ( n s )SM10 0.0 0.2 0.4 0.6 0.8 1.0 0 8000 16000 24000 32000 20 40 60 80 100 120 140 S p a t i a l P o s i t i o n ( a u )T e m p e r a t u r e ( K )T i m e ( n s )V14 0.0 0.2 0.4 0.6 0.8 1.0 0.0 2.0x10174.0x10176.0x10178.0x1017 20 40 60 80 100 120 140 S p a t i a l P o s i t i o n ( a u )E l e c t ro n N u m b e r D e n s i t y (c m3)T i m e ( n s )V14 0.0 0.2 0.4 0.6 0.8 1.0 0 8000 16000 24000 32000 20 40 60 80 100 120 140 S p a t i a l P o s i t i o n ( a u )T e m p e r a t u r e ( K )T i m e ( n s )Z8 0.0 0.2 0.4 0.6 0.8 1.0 0 1x10172x10173x10174x10175x1017 20 40 60 80 100 120 140 S p a t i a l P o s i t i o n ( a u )E l e c t r o n N u mb e r D e n s i t y ( c m3)T i m e ( n s )Z8 0.0 0.2 0.4 0.6 0.8 1.0 0 8000 16000 24000 32000 20 40 60 80 100 120 140 S p a t i a l P o s i t i o n ( a u )T e m p e r a t u r e ( K )T i m e ( n s )SM10 0.0 0.2 0.4 0.6 0.8 1.0 0 1x10172x10173x10174x10175x1017 20 40 60 80 100 120 140 S p a t i a l P o s i t i o n ( a u )E l e c t r o n N u mb e r D e n s i t y ( c m3)T i m e ( n s )SM10 0.0 0.2 0.4 0.6 0.8 1.0 0 8000 16000 24000 32000 20 40 60 80 100 120 140 S p a t i a l P o s i t i o n ( a u )T e m p e r a t u r e ( K )T i m e ( n s )V14 0.0 0.2 0.4 0.6 0.8 1.0 0.0 2.0x10174.0x10176.0x10178.0x1017 20 40 60 80 100 120 140 S p a t i a l P o s i t i o n ( a u )E l e c t ro n N u m b e r D e n s i t y (c m3)T i m e ( n s )V14 0.0 0.2 0.4 0.6 0.8 1.0 0 8000 16000 24000 32000 20 40 60 80 100 120 140 S p a t i a l P o s i t i o n ( a u )T e m p e r a t u r e ( K )T i m e ( n s )Z8 0.0 0.2 0.4 0.6 0.8 1.0 0 1x10172x10173x10174x10175x1017 20 40 60 80 100 120 140 S p a t i a l P o s i t i o n ( a u )E l e c t r o n N u mb e r D e n s i t y ( c m3)T i m e ( n s )Z8 Figure 6-6. Continued.

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159 0.00.10.20.30.40.50.60.70.80.91.0 0 5000 10000 15000 20000 0.0 3.0x10166.0x10169.0x10161.2x10171.5x1017 Spatial Position (a.u.)Temperature (K)Electron Number Density (cm-3)Sample: Al alloy Z80.00.10.20.30.40.50.60.70.80.91.0 0 5000 10000 15000 20000 0.0 5.0x10161.0x10171.5x10172.0x1017 Spatial Position (a.u.)Temperature (K)Electron Number Density (cm-3)Sample: Al alloy V140.00.10.20.30.40.50.60.70.80.91.0 0 5000 10000 15000 20000 0.0 5.0x10161.0x10171.5x10172.0x10172.5x1017 Spatial Position (a.u.)Temperature (K)Electron Number Density (cm-3)Sample: Al alloy D330.00.10.20.30.40.50.60.70.80.91.0 0 5000 10000 15000 20000 0.0 5.0x10161.0x10171.5x10172.0x10172.5x1017 Temperature (K)Spatial Position (a.u.)Electron Number Density (cm-3)Sample: Al alloy B80.00.10.20.30.40.50.60.70.80.91.0 0 5000 10000 15000 20000 0.0 5.0x10161.0x10171.5x10172.0x10172.5x10173.0x1017 Spatial Position (a.u.)Temperature (K)Electron Number Density (cm-3)Sample: Al alloy S40.00.10.20.30.40.50.60.70.80.91.0 0 5000 10000 15000 20000 0.0 3.0x10166.0x10169.0x10161.2x10171.5x1017 Spatial Position (a.u.)Temperature (K)Electron Number Density (cm-3)Sample: Al alloy SM10a a c c e e b b d d f f0.00.10.20.30.40.50.60.70.80.91.0 0 5000 10000 15000 20000 0.0 3.0x10166.0x10169.0x10161.2x10171.5x1017 Spatial Position (a.u.)Temperature (K)Electron Number Density (cm-3)Sample: Al alloy Z80.00.10.20.30.40.50.60.70.80.91.0 0 5000 10000 15000 20000 0.0 5.0x10161.0x10171.5x10172.0x1017 Spatial Position (a.u.)Temperature (K)Electron Number Density (cm-3)Sample: Al alloy V140.00.10.20.30.40.50.60.70.80.91.0 0 5000 10000 15000 20000 0.0 5.0x10161.0x10171.5x10172.0x10172.5x1017 Spatial Position (a.u.)Temperature (K)Electron Number Density (cm-3)Sample: Al alloy D330.00.10.20.30.40.50.60.70.80.91.0 0 5000 10000 15000 20000 0.0 5.0x10161.0x10171.5x10172.0x10172.5x1017 Temperature (K)Spatial Position (a.u.)Electron Number Density (cm-3)Sample: Al alloy B80.00.10.20.30.40.50.60.70.80.91.0 0 5000 10000 15000 20000 0.0 5.0x10161.0x10171.5x10172.0x10172.5x10173.0x1017 Spatial Position (a.u.)Temperature (K)Electron Number Density (cm-3)Sample: Al alloy S40.00.10.20.30.40.50.60.70.80.91.0 0 5000 10000 15000 20000 0.0 3.0x10166.0x10169.0x10161.2x10171.5x1017 Spatial Position (a.u.)Temperature (K)Electron Number Density (cm-3)Sample: Al alloy SM10a a c c e e b b d d f f Figure 6-7. Spatial evolution of temporally-int egrated temperature (black) and electron number density (blue) obtained using the MC-LIBS approach for aluminum alloy sample (a) B8, (b) D33, (c) S4, (d) SM10, (e) V14 and (f) Z8. The abscissa indicates relative spatial positions where spatial position zero indicates the first equipotential layer at the center of the plasma and the last spatial position indicates the outer layer of the plasma. There are no expected differences in the 6 plots since the samples are compositionally close.

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160 B8D33S4SM10V14Z80 2000 4000 6000 8000 10000 12000 Temperature (K) MC-LIBS CF-LIBS B8D33S4SM10V14Z80 2 4 6 8 10 Electron Number Density (x 1016 cm-3) MC-LIBS CF-LIBS Minimum ne for LTEa a b b B8D33S4SM10V14Z80 2000 4000 6000 8000 10000 12000 Temperature (K) MC-LIBS CF-LIBS B8D33S4SM10V14Z80 2 4 6 8 10 Electron Number Density (x 1016 cm-3) MC-LIBS CF-LIBS Minimum ne for LTEa a b b Figure 6-8. Comparison of (a) el ectron number densities and (b) plasma temperatures calculated using MC-LIBS (blue bars) and CF-LIBS approaches (red bars). The minimum electron number density values for LTE ar e shown as black bars in (a).

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161 AlCrCuFeMgMnNiSiTi1E-3 0.01 0.1 1 10 80 90 %Relative Composition of Al alloy B8 Certified CF-LIBS AlCrCuFeMgMnNiSiTiZn1E-3 0.01 0.1 1 10 80 90 %Relative Composition of Al alloy SM10 Certified CF-LIBS AlCrCuFeMgMnNiSiTi1E-3 0.01 0.1 1 10 80 90 %Relative Composition of Al alloy D33 Certified CF-LIBS AlCrCuFeMgMnNiSiTiZn1E-3 0.01 0.1 1 10 75 80 85 %Relative Composition of Al alloy S4 Certified CF-LIBS AlCrCuFeMgMnNiSiTi1E-3 0.01 0.1 1 10 80 90 %Relative Composition of Al alloy V14 Certified CF-LIBS AlCrCuFeMgMnNiSiTi1E-3 0.01 0.1 1 10 75 78 81 %Relative Composition of Al alloy Z8 Certified CF-LIBSa a b b c c d d e e f f AlCrCuFeMgMnNiSiTi1E-3 0.01 0.1 1 10 80 90 %Relative Composition of Al alloy B8 Certified CF-LIBS AlCrCuFeMgMnNiSiTiZn1E-3 0.01 0.1 1 10 80 90 %Relative Composition of Al alloy SM10 Certified CF-LIBS AlCrCuFeMgMnNiSiTi1E-3 0.01 0.1 1 10 80 90 %Relative Composition of Al alloy D33 Certified CF-LIBS AlCrCuFeMgMnNiSiTiZn1E-3 0.01 0.1 1 10 75 80 85 %Relative Composition of Al alloy S4 Certified CF-LIBS AlCrCuFeMgMnNiSiTi1E-3 0.01 0.1 1 10 80 90 %Relative Composition of Al alloy V14 Certified CF-LIBS AlCrCuFeMgMnNiSiTi1E-3 0.01 0.1 1 10 75 78 81 %Relative Composition of Al alloy Z8 Certified CF-LIBSa a b b c c d d e e f f Figure 6-9. Relative elemental compositions of al uminum alloy samples (a) B8, (b) D33, (c) S4, (d) SM10, (e) V14 and (c) Z8 obtained with CF-LIBS compared with certified values (black bars).

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162 AlCrCuFeMgMnNiSiTiZn20 40 60 80 100 Relative Error (%) B8 D33 S4 SM10 V14 Z8 Figure 6-10. Relative percentage errors of the elemental composition calculated using CF-LIBS.

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163 270280290300310320330 0.0 0.2 0.4 0.6 0.8 1.0 D33 Simulated R = 0.94976Normalized IntensityWavelength (nm)270280290300310320330 0.0 0.2 0.4 0.6 0.8 1.0 D33 ExperimentalNormalized Intensity 270280290300310320330 0.0 0.2 0.4 0.6 0.8 1.0 V14 Simulated R = 0.94009Normalized IntensityWavelength (nm)270280290300310320330 0.0 0.2 0.4 0.6 0.8 1.0 V14 ExperimentalNormalized Intensity 270280290300310320330 0.0 0.2 0.4 0.6 0.8 1.0 Z8 Simulated R = 0.9611Normalized IntensityWavelength (nm)270280290300310320330 0.0 0.2 0.4 0.6 0.8 1.0 Z8 ExperimentalNormalized Intensity 270280290300310320330 0.0 0.2 0.4 0.6 0.8 1.0 B8 Simulated R = 0.93523Normalized IntensityWavelength (nm)270280290300310320330 0.0 0.2 0.4 0.6 0.8 1.0 B8 ExperimentalNormalized Intensity 270280290300310320330 0.0 0.2 0.4 0.6 0.8 1.0 S4 Simulated R = 0.94402Normalized IntensityWavelength (nm)270280290300310320330 0.0 0.2 0.4 0.6 0.8 1.0 S4 ExperimentalNormalized Intensity 270280290300310320330 0.0 0.2 0.4 0.6 0.8 1.0 SM10 Simulated R = 0.96376Normalized IntensityWavelength (nm)270280290300310320330 0.0 0.2 0.4 0.6 0.8 1.0 SM10 ExperimentalNormalized Intensitya a c c e e b b d d f f 270280290300310320330 0.0 0.2 0.4 0.6 0.8 1.0 D33 Simulated R = 0.94976Normalized IntensityWavelength (nm)270280290300310320330 0.0 0.2 0.4 0.6 0.8 1.0 D33 ExperimentalNormalized Intensity 270280290300310320330 0.0 0.2 0.4 0.6 0.8 1.0 V14 Simulated R = 0.94009Normalized IntensityWavelength (nm)270280290300310320330 0.0 0.2 0.4 0.6 0.8 1.0 V14 ExperimentalNormalized Intensity 270280290300310320330 0.0 0.2 0.4 0.6 0.8 1.0 Z8 Simulated R = 0.9611Normalized IntensityWavelength (nm)270280290300310320330 0.0 0.2 0.4 0.6 0.8 1.0 Z8 ExperimentalNormalized Intensity 270280290300310320330 0.0 0.2 0.4 0.6 0.8 1.0 B8 Simulated R = 0.93523Normalized IntensityWavelength (nm)270280290300310320330 0.0 0.2 0.4 0.6 0.8 1.0 B8 ExperimentalNormalized Intensity 270280290300310320330 0.0 0.2 0.4 0.6 0.8 1.0 S4 Simulated R = 0.94402Normalized IntensityWavelength (nm)270280290300310320330 0.0 0.2 0.4 0.6 0.8 1.0 S4 ExperimentalNormalized Intensity 270280290300310320330 0.0 0.2 0.4 0.6 0.8 1.0 SM10 Simulated R = 0.96376Normalized IntensityWavelength (nm)270280290300310320330 0.0 0.2 0.4 0.6 0.8 1.0 SM10 ExperimentalNormalized Intensitya a c c e e b b d d f f Figure 6-11. Comparison of experimental spectra of aluminum a lloys (blue) and the best-fit simulated spectra (red) calculated with MC -LIBS. Maximized values of the cost function (correlation coefficient R ) are also shown for each sample.

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164 AlCuFeMgMnSi1E-3 0.01 0.1 1 10 80 100 %Relative Composition for Z8 Certified MC-LIBS CF-LIBS AlCuFeMgMnSi1E-3 0.01 0.1 1 10 80 100 %Relative Composition for V14 Certified MC-LIBS CF-LIBS AlCuFeMgMnSi1E-3 0.01 0.1 1 10 80 100 %Relative Composition for D33 Certified MC-LIBS CF-LIBS AlCuFeMgMnSi1E-3 0.01 0.1 1 10 80 100 %Relative Composition for B8 Certified MC-LIBS CF-LIBS AlCuFeMgMnSiZn1E-3 0.01 0.1 1 10 80 100 %Relative Composition for S4 Certified MC-LIBS CF-LIBS AlCuFeMgMnSiZn1E-3 0.01 0.1 1 10 80 100 %Relative Composition for SM10 Certified MC-LIBS CF-LIBSa a c c e e b b d d f f AlCuFeMgMnSi1E-3 0.01 0.1 1 10 80 100 %Relative Composition for Z8 Certified MC-LIBS CF-LIBS AlCuFeMgMnSi1E-3 0.01 0.1 1 10 80 100 %Relative Composition for V14 Certified MC-LIBS CF-LIBS AlCuFeMgMnSi1E-3 0.01 0.1 1 10 80 100 %Relative Composition for D33 Certified MC-LIBS CF-LIBS AlCuFeMgMnSi1E-3 0.01 0.1 1 10 80 100 %Relative Composition for B8 Certified MC-LIBS CF-LIBS AlCuFeMgMnSiZn1E-3 0.01 0.1 1 10 80 100 %Relative Composition for S4 Certified MC-LIBS CF-LIBS AlCuFeMgMnSiZn1E-3 0.01 0.1 1 10 80 100 %Relative Composition for SM10 Certified MC-LIBS CF-LIBS AlCuFeMgMnSi1E-3 0.01 0.1 1 10 80 100 %Relative Composition for Z8 Certified MC-LIBS CF-LIBS AlCuFeMgMnSi1E-3 0.01 0.1 1 10 80 100 %Relative Composition for V14 Certified MC-LIBS CF-LIBS AlCuFeMgMnSi1E-3 0.01 0.1 1 10 80 100 %Relative Composition for D33 Certified MC-LIBS CF-LIBS AlCuFeMgMnSi1E-3 0.01 0.1 1 10 80 100 %Relative Composition for B8 Certified MC-LIBS CF-LIBS AlCuFeMgMnSiZn1E-3 0.01 0.1 1 10 80 100 %Relative Composition for S4 Certified MC-LIBS CF-LIBS AlCuFeMgMnSiZn1E-3 0.01 0.1 1 10 80 100 %Relative Composition for SM10 Certified MC-LIBS CF-LIBSa a c c e e b b d d f f Figure 6-12. Relative concentra tion values obtained using MC-LIBS (blue bars) and CF-LIBS (red bars) compared with certified values (black bars).

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165 AlCuFeMgMnSi0 20 40 60 80 400 Relative Error for Al Alloy B8 (%) MCLIBS CFLIBS AlCuFeMgMnSi0 20 40 60 80 200 240 Relative Error for Al Alloy D33(%) MCLIBS CFLIBS AlCuFeMgMnSiZn0 20 40 60 80 200 300 Relative Error for Al Alloy S4 (%) MCLIBS CFLIBS AlCuFeMgMnSiZn0 20 40 60 80 150 200 Relative Error for Al Alloy SM10 (%) MCLIBS CFLIBS AlCuFeMgMnSi0 20 40 60 80 150 200 Relative Error for Al Alloy V14 (%) MCLIBS CFLIBS AlCuFeMgMnSi0 20 40 60 80 150 200 Relative Error for Al Alloy Z8 (%) MCLIBS CFLIBSa a b b c c d d e e f f AlCuFeMgMnSi0 20 40 60 80 400 Relative Error for Al Alloy B8 (%) MCLIBS CFLIBS AlCuFeMgMnSi0 20 40 60 80 200 240 Relative Error for Al Alloy D33(%) MCLIBS CFLIBS AlCuFeMgMnSiZn0 20 40 60 80 200 300 Relative Error for Al Alloy S4 (%) MCLIBS CFLIBS AlCuFeMgMnSiZn0 20 40 60 80 150 200 Relative Error for Al Alloy SM10 (%) MCLIBS CFLIBS AlCuFeMgMnSi0 20 40 60 80 150 200 Relative Error for Al Alloy V14 (%) MCLIBS CFLIBS AlCuFeMgMnSi0 20 40 60 80 150 200 Relative Error for Al Alloy Z8 (%) MCLIBS CFLIBS AlCuFeMgMnSi0 20 40 60 80 400 Relative Error for Al Alloy B8 (%) MCLIBS CFLIBS AlCuFeMgMnSi0 20 40 60 80 200 240 Relative Error for Al Alloy D33(%) MCLIBS CFLIBS AlCuFeMgMnSiZn0 20 40 60 80 200 300 Relative Error for Al Alloy S4 (%) MCLIBS CFLIBS AlCuFeMgMnSiZn0 20 40 60 80 150 200 Relative Error for Al Alloy SM10 (%) MCLIBS CFLIBS AlCuFeMgMnSi0 20 40 60 80 150 200 Relative Error for Al Alloy V14 (%) MCLIBS CFLIBS AlCuFeMgMnSi0 20 40 60 80 150 200 Relative Error for Al Alloy Z8 (%) MCLIBS CFLIBSa a b b c c d d e e f f Figure 6-13. Relative errors of calculated conc entration values obtained using MC-LIBS (blue bars) and CF-LIBS (red bars).

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166 Figure 6-14. Image of the laser-i nduced plasma obtained from an Al alloy D33 us ing a delay time of 50 ns and gate width of 100 ns under 0.1 mbar pressure. Spatially-resolved measurements were obtained by binning the spectral emission images into 11 different spatial positions designated by letters A through K. The pixel numbers included in the binning process are shown on the left. Each binned region consists of 11 ve rtical pixels which is equal to 0.02475 cm.

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167 Figure 6-15. Spatially-resolved spectra of differe nt (a) neutral and (b) singly-ionized lines.

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168 ABCDEFGHIJK0 5 10 15 20 25 274.932 nm Fe IISpectrally Integrated Intensity (a.u.)Spatial Position ABCDEFGHIJK0.0 0.2 0.4 0.6 0.8 1.0 1.2 278.810 nm Fe I ABCDEFGHIJK0 5 10 15 20 25 280.270 nm Mg IIIntegrated Intensity (a.u.)Spatial Position ABCDEFGHIJK0 3 6 9 12 15 285.213 nm Mg I ABCDEFGHIJK0 2 4 6 8 10 385.602 nm Si IIIntegrated Intensity (a.u.)Spatial Position ABCDEFGHIJK0 20 40 60 80 288.158 nm Si I ABCDEFGHIJK0 3 6 9 12 15 18 Integrated Intensity (a.u.) 294.920 nm Mn II Spatial Position ABCDEFGHIJK0 1 2 3 4 5 6 280.106 nm Mn Ic c d d e e f f ABCDEFGHIJK0 5 10 15 20 25 274.932 nm Fe IISpectrally Integrated Intensity (a.u.)Spatial Position ABCDEFGHIJK0.0 0.2 0.4 0.6 0.8 1.0 1.2 278.810 nm Fe I ABCDEFGHIJK0 5 10 15 20 25 280.270 nm Mg IIIntegrated Intensity (a.u.)Spatial Position ABCDEFGHIJK0 3 6 9 12 15 285.213 nm Mg I ABCDEFGHIJK0 2 4 6 8 10 385.602 nm Si IIIntegrated Intensity (a.u.)Spatial Position ABCDEFGHIJK0 20 40 60 80 288.158 nm Si I ABCDEFGHIJK0 3 6 9 12 15 18 Integrated Intensity (a.u.) 294.920 nm Mn II Spatial Position ABCDEFGHIJK0 1 2 3 4 5 6 280.106 nm Mn Ic c d d e e f f ABCDEFGHIJK0 50 100 150 200 250 Integrated Intensity (a.u.) 281.619 nm Al II Spatial Position ABCDEFGHIJK0 30 60 90 120 150 308.215 nm Al I a a ABCDEFGHIJK0 50 100 150 200 250 Integrated Intensity (a.u.) 281.619 nm Al II Spatial Position ABCDEFGHIJK0 30 60 90 120 150 308.215 nm Al I a a b b c c d d e e ABCDEFGHIJK0 5 10 15 20 25 274.932 nm Fe IISpectrally Integrated Intensity (a.u.)Spatial Position ABCDEFGHIJK0.0 0.2 0.4 0.6 0.8 1.0 1.2 278.810 nm Fe I ABCDEFGHIJK0 5 10 15 20 25 280.270 nm Mg IIIntegrated Intensity (a.u.)Spatial Position ABCDEFGHIJK0 3 6 9 12 15 285.213 nm Mg I ABCDEFGHIJK0 2 4 6 8 10 385.602 nm Si IIIntegrated Intensity (a.u.)Spatial Position ABCDEFGHIJK0 20 40 60 80 288.158 nm Si I ABCDEFGHIJK0 3 6 9 12 15 18 Integrated Intensity (a.u.) 294.920 nm Mn II Spatial Position ABCDEFGHIJK0 1 2 3 4 5 6 280.106 nm Mn Ic c d d e e f f ABCDEFGHIJK0 5 10 15 20 25 274.932 nm Fe IISpectrally Integrated Intensity (a.u.)Spatial Position ABCDEFGHIJK0.0 0.2 0.4 0.6 0.8 1.0 1.2 278.810 nm Fe I ABCDEFGHIJK0 5 10 15 20 25 280.270 nm Mg IIIntegrated Intensity (a.u.)Spatial Position ABCDEFGHIJK0 3 6 9 12 15 285.213 nm Mg I ABCDEFGHIJK0 2 4 6 8 10 385.602 nm Si IIIntegrated Intensity (a.u.)Spatial Position ABCDEFGHIJK0 20 40 60 80 288.158 nm Si I ABCDEFGHIJK0 3 6 9 12 15 18 Integrated Intensity (a.u.) 294.920 nm Mn II Spatial Position ABCDEFGHIJK0 1 2 3 4 5 6 280.106 nm Mn Ic c d d e e f f ABCDEFGHIJK0 50 100 150 200 250 Integrated Intensity (a.u.) 281.619 nm Al II Spatial Position ABCDEFGHIJK0 30 60 90 120 150 308.215 nm Al I a a ABCDEFGHIJK0 50 100 150 200 250 Integrated Intensity (a.u.) 281.619 nm Al II Spatial Position ABCDEFGHIJK0 30 60 90 120 150 308.215 nm Al I a a b b c c d d e e Figure 6-16. Spectrally-integ rated intensities of different neut ral (black bars) and singly-ionized (gray bars) lines of (a) Al, (b) Fe, (c) Mg, (d) Mn and (e) Si at various spatial positions.

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169 ABCDEFGHI0 5 10 15 20 25 Neutrals IonsNumber of Identified LinesSpatial PositionAl alloy D33AlABCDEFGHI0 3 6 9 12 Neutrals IonsNumber of Identified LinesSpatial PositionAl alloy D33CrABCDEFGHI2 4 6 8 10 Neutrals IonsNumber of Identified LinesSpatial PositionAl alloy D33CuABCDEFGHI0 20 40 60 80 Neutrals IonsNumber of Identified LinesSpatial PositionAl alloy D33FeABCDEFGHI0 1 2 3 4 5 Neutrals IonsNumber of Identified LinesSpatial PositionAl alloy D33MgABCDEFGHI0 4 8 12 16 20 Neutrals IonsNumber of Identified LinesSpatial PositionAl alloy D33MnABCDEFGHI0 6 12 18 24 30 36 Neutrals IonsNumber of Identified LinesSpatial PositionAl alloy D33NiABCDEFGHI4 6 8 10 12 Neutrals IonsNumber of Identified LinesSpatial PositionAl alloy D33SiABCDEFGHI0 5 10 15 20 Neutrals IonsNumber of Identified LinesSpatial PositionAl alloy D33TiABCDEFGHI60 90 120 150 180 Neutrals IonsNumber of Identified LinesSpatial Position Al alloy D33TotalABCDEFGHI0 5 10 15 20 25 Neutrals IonsNumber of Identified LinesSpatial PositionAl alloy D33AlABCDEFGHI0 3 6 9 12 Neutrals IonsNumber of Identified LinesSpatial PositionAl alloy D33CrABCDEFGHI2 4 6 8 10 Neutrals IonsNumber of Identified LinesSpatial PositionAl alloy D33CuABCDEFGHI0 20 40 60 80 Neutrals IonsNumber of Identified LinesSpatial PositionAl alloy D33FeABCDEFGHI0 1 2 3 4 5 Neutrals IonsNumber of Identified LinesSpatial PositionAl alloy D33MgABCDEFGHI0 4 8 12 16 20 Neutrals IonsNumber of Identified LinesSpatial PositionAl alloy D33MnABCDEFGHI0 6 12 18 24 30 36 Neutrals IonsNumber of Identified LinesSpatial PositionAl alloy D33NiABCDEFGHI4 6 8 10 12 Neutrals IonsNumber of Identified LinesSpatial PositionAl alloy D33SiABCDEFGHI0 5 10 15 20 Neutrals IonsNumber of Identified LinesSpatial PositionAl alloy D33TiABCDEFGHI0 5 10 15 20 25 Neutrals IonsNumber of Identified LinesSpatial PositionAl alloy D33AlABCDEFGHI0 3 6 9 12 Neutrals IonsNumber of Identified LinesSpatial PositionAl alloy D33CrABCDEFGHI2 4 6 8 10 Neutrals IonsNumber of Identified LinesSpatial PositionAl alloy D33CuABCDEFGHI0 20 40 60 80 Neutrals IonsNumber of Identified LinesSpatial PositionAl alloy D33FeABCDEFGHI0 1 2 3 4 5 Neutrals IonsNumber of Identified LinesSpatial PositionAl alloy D33MgABCDEFGHI0 4 8 12 16 20 Neutrals IonsNumber of Identified LinesSpatial PositionAl alloy D33MnABCDEFGHI0 6 12 18 24 30 36 Neutrals IonsNumber of Identified LinesSpatial PositionAl alloy D33NiABCDEFGHI4 6 8 10 12 Neutrals IonsNumber of Identified LinesSpatial PositionAl alloy D33SiABCDEFGHI0 5 10 15 20 Neutrals IonsNumber of Identified LinesSpatial PositionAl alloy D33TiABCDEFGHI60 90 120 150 180 Neutrals IonsNumber of Identified LinesSpatial Position Al alloy D33TotalABCDEFGHI60 90 120 150 180 Neutrals IonsNumber of Identified LinesSpatial Position Al alloy D33Total Figure 6-17. Spatial frequency di stribution profile of different species in the aluminum alloy plasma.

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170 655.5656.0656.5657.0657.5 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 A B C D E F G H I Wavelength (nm)Intensity (a.u.) H 11908 11605 11298 11558 11768 11118 11137 9271 8655 1.09 1.891.89 1.98 1.96 1.89 2.10 1.65 1.12 ABCDEFGHI6000 8000 10000 12000 14000 Temperature (K)Spatial Position ABCDEFGHI0.0 0.5 1.0 1.5 Minimum ne for LTEElectron Density (x1016 cm-3) 4507 9498 13286 12855 14301 12685 10862 9638 9056 8101 4567 0.8 4.7 12.0 9.5 25.9 23.8 24.1 16.9 9.8 8.8 2.5 ABCDEFGHIJK0 6000 12000 18000 Temperature (K)Spatial Position ABCDEFGHIJK0.01 0.1 1 10 100 1000 Minimum ne for LTEElectron Density (x1016 cm-3)a bc 655.5656.0656.5657.0657.5 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 A B C D E F G H I Wavelength (nm)Intensity (a.u.) H 11908 11605 11298 11558 11768 11118 11137 9271 8655 1.09 1.891.89 1.98 1.96 1.89 2.10 1.65 1.12 ABCDEFGHI6000 8000 10000 12000 14000 Temperature (K)Spatial Position ABCDEFGHI0.0 0.5 1.0 1.5 Minimum ne for LTEElectron Density (x1016 cm-3) 4507 9498 13286 12855 14301 12685 10862 9638 9056 8101 4567 0.8 4.7 12.0 9.5 25.9 23.8 24.1 16.9 9.8 8.8 2.5 ABCDEFGHIJK0 6000 12000 18000 Temperature (K)Spatial Position ABCDEFGHIJK0.01 0.1 1 10 100 1000 Minimum ne for LTEElectron Density (x1016 cm-3)a bc Figure 6-18. Electron number density and temperature values calculated at different spatial positions using (b) CF-LIBS and (c) MC-LIB S. The spectra in (a) shows the H line used to calculate the electr on number density in CF-LIBS.

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171 3691215182124 -20 -16 -12 -8 -4 0 4 8 Al Fe Mg Siln(I/gkAki)*Ek + (eV)Spatial Point A3691215182124 -20 -16 -12 -8 -4 0 4 8 Al Fe Mg Siln(I/gkAki)*Ek + (eV)Spatial Point B3691215182124 -20 -16 -12 -8 -4 0 4 8 Al Fe Ni Siln(I/gkAki)*Ek + (eV)Spatial Point C3691215182124 -20 -16 -12 -8 -4 0 4 8 Al Mg Siln(I/gkAki)*Ek + (eV)Spatial Point D3691215182124-20 -16 -12 -8 -4 0 4 8 Al Cu Fe Mn Ni Siln(I/gkAki)*Ek + (eV)Spatial Point E3691215182124 -20 -16 -12 -8 -4 0 4 8 Al Cu Fe Mn Ni Siln(I/gkAki)*Ek + (eV)Spatial Position F3691215182124 -20 -16 -12 -8 -4 0 4 8 Al Cu Ni Siln(I/gkAki)*Ek + (eV)Spatial Position G3691215182124 -20 -16 -12 -8 -4 0 4 8 Cr Cu Fe Mg Mn Niln(I/gkAki)*Ek + (eV)Spatial Point H3691215182124 -20 -16 -12 -8 -4 0 4 8 Cr Cu Fe Mg Mn Niln(I/gkAki)*Ek + (eV)Spatial Position I3691215182124 -20 -16 -12 -8 -4 0 4 8 Al Fe Mg Siln(I/gkAki)*Ek + (eV)Spatial Point A3691215182124 -20 -16 -12 -8 -4 0 4 8 Al Fe Mg Siln(I/gkAki)*Ek + (eV)Spatial Point B3691215182124 -20 -16 -12 -8 -4 0 4 8 Al Fe Ni Siln(I/gkAki)*Ek + (eV)Spatial Point C3691215182124 -20 -16 -12 -8 -4 0 4 8 Al Mg Siln(I/gkAki)*Ek + (eV)Spatial Point D3691215182124-20 -16 -12 -8 -4 0 4 8 Al Cu Fe Mn Ni Siln(I/gkAki)*Ek + (eV)Spatial Point E3691215182124 -20 -16 -12 -8 -4 0 4 8 Al Cu Fe Mn Ni Siln(I/gkAki)*Ek + (eV)Spatial Position F3691215182124 -20 -16 -12 -8 -4 0 4 8 Al Cu Ni Siln(I/gkAki)*Ek + (eV)Spatial Position G3691215182124 -20 -16 -12 -8 -4 0 4 8 Cr Cu Fe Mg Mn Niln(I/gkAki)*Ek + (eV)Spatial Point H3691215182124 -20 -16 -12 -8 -4 0 4 8 Cr Cu Fe Mg Mn Niln(I/gkAki)*Ek + (eV)Spatial Position I Figure 6-19. Saha-Boltzmann plots of selected elements in aluminum alloy sample D33 at different spatial positions (Left to right, top to bottom: spatial positions A through I).

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172 0.0 0.2 0.4 0.6 0.8 1.0 0 10000 20000 30000 40000 20 40 60 80 100 120 140 T e m p e r a t u r e ( K )S p a t i a l P o s i t i o n ( a u )T i m e ( n s )C 0.0 0.2 0.4 0.6 0.8 1.0 0.0 3.0x10176.0x10179.0x10171.2x1018 20 40 60 80 100 120 140 S p a t i a l P o s i t i o n ( a u )E l e c t ro n N u m b e r D e n s i t y (c m3)T i m e ( n s )C 0.0 0.2 0.4 0.6 0.8 1.0 0 10000 20000 30000 40000 20 40 60 80 100 120 140 T e m p e r a t u r e ( K )S p a t i a l P o s i t i o n ( a u )T i m e ( n s )B 0.0 0.2 0.4 0.6 0.8 1.0 0.0 2.0x10174.0x10176.0x10178.0x10171.0x1018 20 40 60 80 100 120 140 S p a t i a l P o s i t i o n ( a u )E l e c t ro n N u m b e r D e n s i t y (c m3)T i m e ( n s )B 0.0 0.2 0.4 0.6 0.8 1.0 0 10000 20000 30000 40000 20 40 60 80 100 120 140 T e m p e r a t u r e ( K )T i m e ( n s )S p a t i a l P o s i t i o n ( a u )A 0.0 0.2 0.4 0.6 0.8 1.0 0.0 2.0x10174.0x10176.0x10178.0x10171.0x1018 20 40 60 80 100 120 140 S p a t i a l P o s i t i o n ( a u )E l e c t ro n N u m b e r D e n s i t y (c m3)T i m e ( n s )A 0.0 0.2 0.4 0.6 0.8 1.0 0 10000 20000 30000 40000 20 40 60 80 100 120 140 T e m p e r a t u r e ( K )S p a t i a l P o s i t i o n ( a u )T i m e ( n s )C 0.0 0.2 0.4 0.6 0.8 1.0 0.0 3.0x10176.0x10179.0x10171.2x1018 20 40 60 80 100 120 140 S p a t i a l P o s i t i o n ( a u )E l e c t ro n N u m b e r D e n s i t y (c m3)T i m e ( n s )C 0.0 0.2 0.4 0.6 0.8 1.0 0 10000 20000 30000 40000 20 40 60 80 100 120 140 T e m p e r a t u r e ( K )S p a t i a l P o s i t i o n ( a u )T i m e ( n s )B 0.0 0.2 0.4 0.6 0.8 1.0 0.0 2.0x10174.0x10176.0x10178.0x10171.0x1018 20 40 60 80 100 120 140 S p a t i a l P o s i t i o n ( a u )E l e c t ro n N u m b e r D e n s i t y (c m3)T i m e ( n s )B 0.0 0.2 0.4 0.6 0.8 1.0 0 10000 20000 30000 40000 20 40 60 80 100 120 140 T e m p e r a t u r e ( K )T i m e ( n s )S p a t i a l P o s i t i o n ( a u )A 0.0 0.2 0.4 0.6 0.8 1.0 0.0 2.0x10174.0x10176.0x10178.0x10171.0x1018 20 40 60 80 100 120 140 S p a t i a l P o s i t i o n ( a u )E l e c t ro n N u m b e r D e n s i t y (c m3)T i m e ( n s )A Figure 6-20. Spatial and temporal evolution of temperature (left) and electron number density (right) obtained using the MC -LIBS approach for aluminum alloy sample D33. The optimizations were carried out on spatia lly-resolved spectra denoted by letters A through K.

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173 0.0 0.2 0.4 0.6 0.8 1.0 0 5000 10000 15000 20000 25000 20 40 60 80 100 120 140 T e m p e r a t u r e ( K )S p a t i a l P o s i t i o n ( a u )T i m e ( n s )F 0.0 0.2 0.4 0.6 0.8 1.0 0.0 5.0x10171.0x10181.5x10182.0x1018 20 40 60 80 100 120 140 S p a t i a l P o s i t i o n ( a u )E l e c t ro n N u m b e r D e n s i t y (c m3)T i m e ( n s )F 0.0 0.2 0.4 0.6 0.8 1.0 0 5000 10000 15000 20000 25000 30000 20 40 60 80 100 120 140 T e m p e r a t u r e ( K )S p a t i a l P o s i t i o n ( a u )T i m e ( n s )E 0.0 0.2 0.4 0.6 0.8 1.0 0.0 5.0x10171.0x10181.5x10182.0x1018 20 40 60 80 100 120 140 S p a t i a l P o s i t i o n ( a u )E l e c t r o n N u mb e r D e n s i t y ( c m3)T i m e ( n s )E 0.0 0.2 0.4 0.6 0.8 1.0 0 5000 10000 15000 20000 25000 30000 20 40 60 80 100 120 140 T e m p e r a t u r e ( K )S p a t i a l P o s i t i o n ( a u )T i m e ( n s )D 0.0 0.2 0.4 0.6 0.8 1.0 0.0 2.0x10174.0x10176.0x10178.0x10171.0x1018 20 40 60 80 100 120 140 S p a t i a l P o s i t i o n ( a u )E l e c t ro n N u m b e r D e n s i t y (c m3)T i m e ( n s )D 0.0 0.2 0.4 0.6 0.8 1.0 0 5000 10000 15000 20000 25000 20 40 60 80 100 120 140 T e m p e r a t u r e ( K )S p a t i a l P o s i t i o n ( a u )T i m e ( n s )F 0.0 0.2 0.4 0.6 0.8 1.0 0.0 5.0x10171.0x10181.5x10182.0x1018 20 40 60 80 100 120 140 S p a t i a l P o s i t i o n ( a u )E l e c t ro n N u m b e r D e n s i t y (c m3)T i m e ( n s )F 0.0 0.2 0.4 0.6 0.8 1.0 0 5000 10000 15000 20000 25000 30000 20 40 60 80 100 120 140 T e m p e r a t u r e ( K )S p a t i a l P o s i t i o n ( a u )T i m e ( n s )E 0.0 0.2 0.4 0.6 0.8 1.0 0.0 5.0x10171.0x10181.5x10182.0x1018 20 40 60 80 100 120 140 S p a t i a l P o s i t i o n ( a u )E l e c t r o n N u mb e r D e n s i t y ( c m3)T i m e ( n s )E 0.0 0.2 0.4 0.6 0.8 1.0 0 5000 10000 15000 20000 25000 30000 20 40 60 80 100 120 140 T e m p e r a t u r e ( K )S p a t i a l P o s i t i o n ( a u )T i m e ( n s )D 0.0 0.2 0.4 0.6 0.8 1.0 0.0 2.0x10174.0x10176.0x10178.0x10171.0x1018 20 40 60 80 100 120 140 S p a t i a l P o s i t i o n ( a u )E l e c t ro n N u m b e r D e n s i t y (c m3)T i m e ( n s )D Figure 6-20. Continued.

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174 0.0 0.2 0.4 0.6 0.8 1.0 0 5000 10000 15000 20000 25000 20 40 60 80 100 120 140 T e m p e r a t u r e ( K )S p a t i a l P o s i t i o n ( a u )T i m e ( n s )I 0.0 0.2 0.4 0.6 0.8 1.0 0.0 3.0x10176.0x10179.0x10171.2x10181.5x1018 20 40 60 80 100 120 140 S p a t i a l P o s i t i o n ( a u )E l e c t ro n N u m b e r D e n s i t y (c m3)T i m e ( n s )I 0.0 0.2 0.4 0.6 0.8 1.0 0 5000 10000 15000 20000 25000 20 40 60 80 100 120 140 T e m p e r a t u r e ( K )S p a t i a l P o s i t i o n ( a u )T i m e ( n s )H 0.0 0.2 0.4 0.6 0.8 1.0 0.0 3.0x10176.0x10179.0x10171.2x10181.5x1018 20 40 60 80 100 120 140 S p a t i a l P o s i t i o n ( a u )E l e c t ro n N u m b e r D e n s i t y (c m3)T i m e ( n s )H 0.0 0.2 0.4 0.6 0.8 1.0 0 5000 10000 15000 20000 25000 20 40 60 80 100 120 140 T e m p e r a t u r e ( K )S p a t i a l P o s i t i o n ( a u )T i m e ( n s )G 0.0 0.2 0.4 0.6 0.8 1.0 0.0 3.0x10176.0x10179.0x10171.2x10181.5x1018 20 40 60 80 100 120 140 S p a t i a l P o s i t i o n ( a u )E l e c t ro n N u m b e r D e n s i t y (c m3)T i m e ( n s )G 0.0 0.2 0.4 0.6 0.8 1.0 0 5000 10000 15000 20000 25000 20 40 60 80 100 120 140 T e m p e r a t u r e ( K )S p a t i a l P o s i t i o n ( a u )T i m e ( n s )I 0.0 0.2 0.4 0.6 0.8 1.0 0.0 3.0x10176.0x10179.0x10171.2x10181.5x1018 20 40 60 80 100 120 140 S p a t i a l P o s i t i o n ( a u )E l e c t ro n N u m b e r D e n s i t y (c m3)T i m e ( n s )I 0.0 0.2 0.4 0.6 0.8 1.0 0 5000 10000 15000 20000 25000 20 40 60 80 100 120 140 T e m p e r a t u r e ( K )S p a t i a l P o s i t i o n ( a u )T i m e ( n s )H 0.0 0.2 0.4 0.6 0.8 1.0 0.0 3.0x10176.0x10179.0x10171.2x10181.5x1018 20 40 60 80 100 120 140 S p a t i a l P o s i t i o n ( a u )E l e c t ro n N u m b e r D e n s i t y (c m3)T i m e ( n s )H 0.0 0.2 0.4 0.6 0.8 1.0 0 5000 10000 15000 20000 25000 20 40 60 80 100 120 140 T e m p e r a t u r e ( K )S p a t i a l P o s i t i o n ( a u )T i m e ( n s )G 0.0 0.2 0.4 0.6 0.8 1.0 0.0 3.0x10176.0x10179.0x10171.2x10181.5x1018 20 40 60 80 100 120 140 S p a t i a l P o s i t i o n ( a u )E l e c t ro n N u m b e r D e n s i t y (c m3)T i m e ( n s )G Figure 6-20. Continued.

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175 0.0 0.2 0.4 0.6 0.8 1.0 0.0 5.0x10171.0x10181.5x10182.0x10182.5x1018 20 40 60 80 100 120 140 S p a t i a l P o s i t i o n ( a u )E l e c t r o n N u mb e r D e n s i t y ( c m3)T i m e ( n s )J 0.0 0.2 0.4 0.6 0.8 1.0 0 10000 20000 30000 40000 20 40 60 80 100 120 140 T e m p e r a t u r e ( K )S p a t i a l P o s i t i o n ( a u )T i m e ( n s )J 0.0 0.2 0.4 0.6 0.8 1.0 0 10000 20000 30000 40000 20 40 60 80 100 120 140 T e m p e r a t u r e ( K )S p a t i a l P o s i t i o n ( a u )T i m e ( n s )K 0.0 0.2 0.4 0.6 0.8 1.0 0.0 5.0x10171.0x10181.5x10182.0x10182.5x10183.0x1018 20 40 60 80 100 120 140 S p a t i a l P o s i t i o n ( a u )E l e c t r o n N u m b e r D e n s i t y ( c m3)T i m e ( n s )K 0.0 0.2 0.4 0.6 0.8 1.0 0.0 5.0x10171.0x10181.5x10182.0x10182.5x1018 20 40 60 80 100 120 140 S p a t i a l P o s i t i o n ( a u )E l e c t r o n N u mb e r D e n s i t y ( c m3)T i m e ( n s )J 0.0 0.2 0.4 0.6 0.8 1.0 0 10000 20000 30000 40000 20 40 60 80 100 120 140 T e m p e r a t u r e ( K )S p a t i a l P o s i t i o n ( a u )T i m e ( n s )J 0.0 0.2 0.4 0.6 0.8 1.0 0 10000 20000 30000 40000 20 40 60 80 100 120 140 T e m p e r a t u r e ( K )S p a t i a l P o s i t i o n ( a u )T i m e ( n s )K 0.0 0.2 0.4 0.6 0.8 1.0 0.0 5.0x10171.0x10181.5x10182.0x10182.5x10183.0x1018 20 40 60 80 100 120 140 S p a t i a l P o s i t i o n ( a u )E l e c t r o n N u m b e r D e n s i t y ( c m3)T i m e ( n s )K Figure 6-20. Continued.

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176 0.00.10.20.30.40.50.60.70.80.91.0 0 5000 10000 15000 20000 0.0 5.0x10161.0x10171.5x10172.0x10172.5x1017 Spatial Position (a.u.)Temperature (K)Electron Number Density (cm-3)BSigmoidal fit Sigmoidal fit0.00.10.20.30.40.50.60.70.80.91.0 0 3000 6000 9000 12000 15000 18000 0.0 4.0x10168.0x10161.2x10171.6x1017 Spatial Position (a.u.)Temperature (K)Electron Number Density (cm-3)DSigmoidal fit Sigmoidal fit0.00.10.20.30.40.50.60.70.80.91.0 0 3000 6000 9000 12000 15000 0.0 7.0x10161.4x10172.1x10172.8x1017 Spatial Position (a.u.)Temperature (K)Electron Number Density (cm-3)FSigmoidal fit Sigmoidal fit0.00.10.20.30.40.50.60.70.80.91.0 0 3000 6000 9000 12000 0.0 7.0x10161.4x10172.1x10172.8x1017 Spatial Position (a.u.)Temperature (K)Electron Number Density (cm-3)GSigmoidal fit Sigmoidal fit0.00.10.20.30.40.50.60.70.80.91.0 0 3000 6000 9000 12000 0.0 5.0x10161.0x10171.5x10172.0x10172.5x1017 Spatial Position (a.u.)Temperature (K)Electron Number Density (cm-3)HSigmoidal fit Sigmoidal fit0.00.10.20.30.40.50.60.70.80.91.0 0 3000 6000 9000 12000 15000 0.0 5.0x10161.0x10171.5x10172.0x10172.5x1017 Spatial Position (a.u.)Temperature (K)Electron Number Density (cm-3)ISigmoidal fit Sigmoidal fit0.00.10.20.30.40.50.60.70.80.91.0 0 4000 8000 12000 16000 0 1x10172x10173x10174x1017 Spatial Position (a.u.)Temperature (K)Electron Number Density (cm-3)JSigmoidal fit Sigmoidal fit0.00.10.20.30.40.50.60.70.80.91.0 0 5000 10000 15000 20000 0.00 1.20x10172.40x10173.60x10174.80x10176.00x1017 Spatial Position (a.u.)Temperature (K)Electron Number Density (cm-3)KSigmoidal fit Exponential growth fit0.00.10.20.30.40.50.60.70.80.91.0 0 4000 8000 12000 16000 0.0 7.0x10161.4x10172.1x10172.8x1017 Spatial Position (a.u.)Temperature (K)Electron Number Density (cm-3)ESigmoidal fit Sigmoidal fit0.00.10.20.30.40.50.60.70.80.91.0 0 5000 10000 15000 20000 0.0 5.0x10161.0x10171.5x10172.0x10172.5x10173.0x1017 Spatial Position (a.u.)Temperature (K)Electron Number Density (cm-3)CSigmoidal fit Sigmoidal fit0.00.10.20.30.40.50.60.70.80.91.0 0 5000 10000 15000 20000 0.0 5.0x10161.0x10171.5x10172.0x1017 Temperature (K)Spatial Position (a.u.)Sigmoidal fit Sigmoidal fit Electron Number Density (cm-3)A 0.00.10.20.30.40.50.60.70.80.91.0 0 5000 10000 15000 20000 0.0 5.0x10161.0x10171.5x10172.0x10172.5x1017 Spatial Position (a.u.)Temperature (K)Electron Number Density (cm-3)BSigmoidal fit Sigmoidal fit0.00.10.20.30.40.50.60.70.80.91.0 0 3000 6000 9000 12000 15000 18000 0.0 4.0x10168.0x10161.2x10171.6x1017 Spatial Position (a.u.)Temperature (K)Electron Number Density (cm-3)DSigmoidal fit Sigmoidal fit0.00.10.20.30.40.50.60.70.80.91.0 0 3000 6000 9000 12000 15000 0.0 7.0x10161.4x10172.1x10172.8x1017 Spatial Position (a.u.)Temperature (K)Electron Number Density (cm-3)FSigmoidal fit Sigmoidal fit0.00.10.20.30.40.50.60.70.80.91.0 0 3000 6000 9000 12000 0.0 7.0x10161.4x10172.1x10172.8x1017 Spatial Position (a.u.)Temperature (K)Electron Number Density (cm-3)GSigmoidal fit Sigmoidal fit0.00.10.20.30.40.50.60.70.80.91.0 0 3000 6000 9000 12000 0.0 5.0x10161.0x10171.5x10172.0x10172.5x1017 Spatial Position (a.u.)Temperature (K)Electron Number Density (cm-3)HSigmoidal fit Sigmoidal fit0.00.10.20.30.40.50.60.70.80.91.0 0 3000 6000 9000 12000 15000 0.0 5.0x10161.0x10171.5x10172.0x10172.5x1017 Spatial Position (a.u.)Temperature (K)Electron Number Density (cm-3)ISigmoidal fit Sigmoidal fit0.00.10.20.30.40.50.60.70.80.91.0 0 4000 8000 12000 16000 0 1x10172x10173x10174x1017 Spatial Position (a.u.)Temperature (K)Electron Number Density (cm-3)JSigmoidal fit Sigmoidal fit0.00.10.20.30.40.50.60.70.80.91.0 0 5000 10000 15000 20000 0.00 1.20x10172.40x10173.60x10174.80x10176.00x1017 Spatial Position (a.u.)Temperature (K)Electron Number Density (cm-3)KSigmoidal fit Exponential growth fit0.00.10.20.30.40.50.60.70.80.91.0 0 4000 8000 12000 16000 0.0 7.0x10161.4x10172.1x10172.8x1017 Spatial Position (a.u.)Temperature (K)Electron Number Density (cm-3)ESigmoidal fit Sigmoidal fit0.00.10.20.30.40.50.60.70.80.91.0 0 5000 10000 15000 20000 0.0 5.0x10161.0x10171.5x10172.0x10172.5x10173.0x1017 Spatial Position (a.u.)Temperature (K)Electron Number Density (cm-3)CSigmoidal fit Sigmoidal fit0.00.10.20.30.40.50.60.70.80.91.0 0 5000 10000 15000 20000 0.0 5.0x10161.0x10171.5x10172.0x1017 Temperature (K)Spatial Position (a.u.)Sigmoidal fit Sigmoidal fit Electron Number Density (cm-3)A Figure 6-21. Spatial evolution of temporally-integrated temperature (black) and electron number density (blue) obtained using the MC-LIBS approach for aluminum alloy sample D33. The abscissa indicates relative spatial positions where spatial point zero indicates the first equipotential layer at the center of the plasma and the last spatial position indicates the outer layer of the plas ma. The highlighted portion indicates the spatially-integrated portion of the plasma used to calculate the local temperatures at specific spatial positi ons (A through K). The solid and dotted red lines are the result of the curve fitting using a sigmoidal function.

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177 0.01 0.02 0.03 0.03 0.04 0.02 0.02 0.0003 0.0005ABCDEFGHI 0.00 0.01 0.02 0.03 0.04 0.05 %Chromium 2.1 1.9 1.3 3.3 1.8 1.1 0.7 0.1 0.06ABCDEFGHI 0 1 2 3 4 %Copper 1.0 1.0 0.7 0.8 0.5 0.2 0.1 0.009 0.004ABCDEFGHI 0.0 0.2 0.4 0.6 0.8 1.0 1.2 %Iron 0.02 0.03 0.03 0.04 0.04 0.04 0.02 0.004 0.001ABCDEFGHI 0.00 0.01 0.02 0.03 0.04 0.05 %Magnesium 0.07 0.10 0.08 0.09 0.09 0.07 0.06 0.004 0.002ABCDEFGHI 0.0 0.1 0.2 0.3 0.4 %Manganese 1.4 1.4 1.6 1.0 0.6 0.2 0.2 0.01 0.007ABCDEFGHI 0.0 0.3 0.6 0.9 1.2 1.5 1.8 %Nickel 5.7 8.9 9.0 9.9 11.3 12.1 12.3 6.0 6.6ABCDEFGHI 0 2 4 6 8 10 12 14 %Silicon 0.004 0.005 0.004 0.007 0.009 0.007 0.006 0.0008 0.0007ABCDEFGHI 0.00 0.01 0.02 0.03 0.04 0.05 0.06 %Titanium 89.6 86.6 87.2 84.7 85.7 86.3 86.6 93.8 93.3ABCDEFGHI 50 60 70 80 90 100 %Aluminum 0.01 0.02 0.03 0.03 0.04 0.02 0.02 0.0003 0.0005ABCDEFGHI 0.00 0.01 0.02 0.03 0.04 0.05 %Chromium 2.1 1.9 1.3 3.3 1.8 1.1 0.7 0.1 0.06ABCDEFGHI 0 1 2 3 4 %Copper 1.0 1.0 0.7 0.8 0.5 0.2 0.1 0.009 0.004ABCDEFGHI 0.0 0.2 0.4 0.6 0.8 1.0 1.2 %Iron 0.02 0.03 0.03 0.04 0.04 0.04 0.02 0.004 0.001ABCDEFGHI 0.00 0.01 0.02 0.03 0.04 0.05 %Magnesium 0.07 0.10 0.08 0.09 0.09 0.07 0.06 0.004 0.002ABCDEFGHI 0.0 0.1 0.2 0.3 0.4 %Manganese 1.4 1.4 1.6 1.0 0.6 0.2 0.2 0.01 0.007ABCDEFGHI 0.0 0.3 0.6 0.9 1.2 1.5 1.8 %Nickel 5.7 8.9 9.0 9.9 11.3 12.1 12.3 6.0 6.6ABCDEFGHI 0 2 4 6 8 10 12 14 %Silicon 0.004 0.005 0.004 0.007 0.009 0.007 0.006 0.0008 0.0007ABCDEFGHI 0.00 0.01 0.02 0.03 0.04 0.05 0.06 %Titanium 89.6 86.6 87.2 84.7 85.7 86.3 86.6 93.8 93.3ABCDEFGHI 50 60 70 80 90 100 %Aluminum Figure 6-22. Relative concen tration values at different spatial pos itions calculated with CF-LIBS. The dashed lines indicate the certified values.

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178 270280290300310320330 0.0 0.2 0.4 0.6 0.8 1.0 A Simulated R = 0.81156Normalized IntensityWavelength (nm)270280290300310320330 0.0 0.2 0.4 0.6 0.8 1.0 A ExperimentalNormalized Intensity 270280290300310320330 0.0 0.2 0.4 0.6 0.8 1.0 C Simulated R = 0.97548Normalized IntensityWavelength (nm)270280290300310320330 0.0 0.2 0.4 0.6 0.8 1.0 C ExperimentalNormalized Intensity 270 280 290 325330 0.0 0.2 0.4 0.6 0.8 1.0 E Simulated R = 0.98102Normalized IntensityWavelength (nm)270 280 290 325330 0.0 0.2 0.4 0.6 0.8 1.0 E ExperimentalNormalized Intensity 270 280 290 325330 0.0 0.2 0.4 0.6 0.8 1.0 G Simulated R = 0.96166Normalized IntensityWavelength (nm)270 280 290 325330 0.0 0.2 0.4 0.6 0.8 1.0 G ExperimentalNormalized Intensity 270 280 290 325330 0.0 0.2 0.4 0.6 0.8 1.0 I Simulated R = 0.94276Normalized IntensityWavelength (nm)270 280 290 325330 0.0 0.2 0.4 0.6 0.8 1.0 I ExperimentalNormalized Intensity 270 280 290 325330 0.0 0.2 0.4 0.6 0.8 1.0 K Simulated R = 0.97773Normalized IntensityWavelength (nm)270 280 290 325330 0.0 0.2 0.4 0.6 0.8 1.0 K ExperimentalNormalized Intensity 270280290300310320330 0.0 0.2 0.4 0.6 0.8 1.0 B Simulated R = 0.95667Normalized IntensityWavelength (nm)270280290300310320330 0.0 0.2 0.4 0.6 0.8 1.0 B ExperimentalNormalized Intensity 270280290300310320330 0.0 0.2 0.4 0.6 0.8 1.0 D Simulated R = 0.95103Normalized IntensityWavelength (nm)270280290300310320330 0.0 0.2 0.4 0.6 0.8 1.0 D ExperimentalNormalized Intensity 270 280 290 325330 0.0 0.2 0.4 0.6 0.8 1.0 F Simulated R = 0.96766Normalized IntensityWavelength (nm)270 280 290 325330 0.0 0.2 0.4 0.6 0.8 1.0 F ExperimentalNormalized Intensity 270 280 290 325330 0.0 0.2 0.4 0.6 0.8 1.0 H Simulated R = 0.95235Normalized IntensityWavelength (nm)270 280 290 325330 0.0 0.2 0.4 0.6 0.8 1.0 H ExperimentalNormalized Intensity 270 280 290 325330 0.0 0.2 0.4 0.6 0.8 1.0 J Simulated R = 0.9475Normalized IntensityWavelength (nm)270 280 290 325330 0.0 0.2 0.4 0.6 0.8 1.0 J ExperimentalNormalized Intensity 270280290300310320330 0.0 0.2 0.4 0.6 0.8 1.0 A Simulated R = 0.81156Normalized IntensityWavelength (nm)270280290300310320330 0.0 0.2 0.4 0.6 0.8 1.0 A ExperimentalNormalized Intensity 270280290300310320330 0.0 0.2 0.4 0.6 0.8 1.0 C Simulated R = 0.97548Normalized IntensityWavelength (nm)270280290300310320330 0.0 0.2 0.4 0.6 0.8 1.0 C ExperimentalNormalized Intensity 270 280 290 325330 0.0 0.2 0.4 0.6 0.8 1.0 E Simulated R = 0.98102Normalized IntensityWavelength (nm)270 280 290 325330 0.0 0.2 0.4 0.6 0.8 1.0 E ExperimentalNormalized Intensity 270 280 290 325330 0.0 0.2 0.4 0.6 0.8 1.0 G Simulated R = 0.96166Normalized IntensityWavelength (nm)270 280 290 325330 0.0 0.2 0.4 0.6 0.8 1.0 G ExperimentalNormalized Intensity 270 280 290 325330 0.0 0.2 0.4 0.6 0.8 1.0 I Simulated R = 0.94276Normalized IntensityWavelength (nm)270 280 290 325330 0.0 0.2 0.4 0.6 0.8 1.0 I ExperimentalNormalized Intensity 270 280 290 325330 0.0 0.2 0.4 0.6 0.8 1.0 K Simulated R = 0.97773Normalized IntensityWavelength (nm)270 280 290 325330 0.0 0.2 0.4 0.6 0.8 1.0 K ExperimentalNormalized Intensity 270280290300310320330 0.0 0.2 0.4 0.6 0.8 1.0 B Simulated R = 0.95667Normalized IntensityWavelength (nm)270280290300310320330 0.0 0.2 0.4 0.6 0.8 1.0 B ExperimentalNormalized Intensity 270280290300310320330 0.0 0.2 0.4 0.6 0.8 1.0 D Simulated R = 0.95103Normalized IntensityWavelength (nm)270280290300310320330 0.0 0.2 0.4 0.6 0.8 1.0 D ExperimentalNormalized Intensity 270 280 290 325330 0.0 0.2 0.4 0.6 0.8 1.0 F Simulated R = 0.96766Normalized IntensityWavelength (nm)270 280 290 325330 0.0 0.2 0.4 0.6 0.8 1.0 F ExperimentalNormalized Intensity 270 280 290 325330 0.0 0.2 0.4 0.6 0.8 1.0 H Simulated R = 0.95235Normalized IntensityWavelength (nm)270 280 290 325330 0.0 0.2 0.4 0.6 0.8 1.0 H ExperimentalNormalized Intensity 270 280 290 325330 0.0 0.2 0.4 0.6 0.8 1.0 J Simulated R = 0.9475Normalized IntensityWavelength (nm)270 280 290 325330 0.0 0.2 0.4 0.6 0.8 1.0 J ExperimentalNormalized Intensity Figure 6-23. Comparison of experime ntal spectra of aluminum all oy D33 (blue) and the best-fit simulated spectra (red) calculated with MC-LIBS at different spatial positions (A through K). Maximized values of the cost function (correlation coefficient R ) are also shown for each case.

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179 ABCDEFGHIJK0.0 2.0x10174.0x10176.0x10178.0x10171.0x1018 Number Density (cm-3)Al ABCDEFGHIJK0 1x10162x10163x10164x10165x10166x1016 Number Density (cm-3)Cu ABCDEFGHIJK0 1x10152x10153x10154x10155x1015 Number Density (cm-3)Fe ABCDEFGHIJK0 1x10142x10143x10144x10145x1014 Number Density (cm-3)Mg ABCDEFGHIJK0 1x10152x10153x10154x10155x1015 Number Density (cm-3)Mn ABCDEFGHIJK0.0 5.0x10161.0x10171.5x10172.0x1017 Number Density (cm-3)Si ABCDEFGHIJK0.0 2.0x10174.0x10176.0x10178.0x10171.0x1018 Number Density (cm-3)Al ABCDEFGHIJK0 1x10162x10163x10164x10165x10166x1016 Number Density (cm-3)Cu ABCDEFGHIJK0 1x10152x10153x10154x10155x1015 Number Density (cm-3)Fe ABCDEFGHIJK0 1x10142x10143x10144x10145x1014 Number Density (cm-3)Mg ABCDEFGHIJK0 1x10152x10153x10154x10155x1015 Number Density (cm-3)Mn ABCDEFGHIJK0.0 5.0x10161.0x10171.5x10172.0x1017 Number Density (cm-3)Si Figure 6-24. Number densities (cm-3) of different elements in the alloy sample calculated at different spatial positions using MC-LIBS.

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180 AlCuFeMgMnSi1E-3 0.01 0.1 1 10 80 100 %Relative Composition for A Certified MC-LIBS CF-LIBS AlCuFeMgMnSi1E-3 0.01 0.1 1 10 80 100 %Relative Composition for B Certified MC-LIBS CF-LIBS AlCuFeMgMnSi1E-3 0.01 0.1 1 60 80 100 %Relative Composition for C Certified MC-LIBS CF-LIBS AlCuFeMgMnSi1E-3 0.01 0.1 1 10 60 80 100 %Relative Composition for D Certified MC-LIBS CF-LIBS AlCuFeMgMnSi1E-3 0.01 0.1 1 10 60 80 100 %Relative Composition for E Certified MC-LIBS CF-LIBS AlCuFeMgMnSi1E-3 0.01 0.1 1 10 80 100 %Relative Composition for F Certified MC-LIBS CF-LIBS AlCuFeMgMnSi1E-3 0.01 0.1 1 10 80 100 %Relative Composition for G Certified MC-LIBS CF-LIBS AlCuFeMgMnSi1E-3 0.01 0.1 1 10 60 80 100 %Relative Composition for H Certified MC-LIBS CF-LIBS AlCuFeMgMnSi1E-4 1E-3 0.01 0.1 1 10 80 100 %Relative Composition for I Certified MC-LIBS CF-LIBS AlCuFeMgMnSi1E-3 0.01 0.1 1 10 100 %Relative Composition for J Certified MC-LIBS CF-LIBS AlCuFeMgMnSi1E-3 0.01 0.1 1 10 80 90 100 %Relative Composition for K Certified MC-LIBS CF-LIBS AlCuFeMgMnSi1E-3 0.01 0.1 1 10 80 100 %Relative Composition for A Certified MC-LIBS CF-LIBS AlCuFeMgMnSi1E-3 0.01 0.1 1 10 80 100 %Relative Composition for B Certified MC-LIBS CF-LIBS AlCuFeMgMnSi1E-3 0.01 0.1 1 60 80 100 %Relative Composition for C Certified MC-LIBS CF-LIBS AlCuFeMgMnSi1E-3 0.01 0.1 1 10 60 80 100 %Relative Composition for D Certified MC-LIBS CF-LIBS AlCuFeMgMnSi1E-3 0.01 0.1 1 10 60 80 100 %Relative Composition for E Certified MC-LIBS CF-LIBS AlCuFeMgMnSi1E-3 0.01 0.1 1 10 80 100 %Relative Composition for F Certified MC-LIBS CF-LIBS AlCuFeMgMnSi1E-3 0.01 0.1 1 10 80 100 %Relative Composition for G Certified MC-LIBS CF-LIBS AlCuFeMgMnSi1E-3 0.01 0.1 1 10 60 80 100 %Relative Composition for H Certified MC-LIBS CF-LIBS AlCuFeMgMnSi1E-4 1E-3 0.01 0.1 1 10 80 100 %Relative Composition for I Certified MC-LIBS CF-LIBS AlCuFeMgMnSi1E-3 0.01 0.1 1 10 100 %Relative Composition for J Certified MC-LIBS CF-LIBS AlCuFeMgMnSi1E-3 0.01 0.1 1 10 80 90 100 %Relative Composition for K Certified MC-LIBS CF-LIBS Figure 6-25. Relative concentration values calculat ed at different spatial positions (A through K) using MC-LIBS (blue bars) and CF-LIBS (red bars) compared with certified values (black bars).

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181 AlCuFeMgMnSi0 20 40 60 80 100 Relative Error at Spatial Position A (%) MC-LIBS CF-LIBS AlCuFeMgMnSi0 20 40 60 80 100 Relative Error at Spatial Position B (%) MC-LIBS CF-LIBS AlCuFeMgMnSi0 20 40 60 80 100 Relative Error at Spatial Position C (%) MC-LIBS CF-LIBS AlCuFeMgMnSi0 30 60 90 120 150 Relative Error at Spatial Position D (%) MC-LIBS CF-LIBS AlCuFeMgMnSi0 50 100 150 200 250 Relative Error at Spatial Position E (%) MC-LIBS CF-LIBS AlCuFeMgMnSi0 50 100 150 200 Relative Error at Spatial Position F (%) MC-LIBS CF-LIBS AlCuFeMgMnSi0 50 100 150 200 Relative Error at Spatial Position G (%) MC-LIBS CF-LIBS AlCuFeMgMnSi0 50 100 150 200 Relative Error at Spatial Position H (%) MC-LIBS CF-LIBS AlCuFeMgMnSi0 20 40 60 80 100 500 600 Relative Error at Spatial Position I (%) MC-LIBS CF-LIBS AlCuFeMgMnSi0 20 40 60 80 100 Relative Error at Spatial Position A (%) MC-LIBS CF-LIBS AlCuFeMgMnSi0 20 40 60 80 100 Relative Error at Spatial Position B (%) MC-LIBS CF-LIBS AlCuFeMgMnSi0 20 40 60 80 100 Relative Error at Spatial Position C (%) MC-LIBS CF-LIBS AlCuFeMgMnSi0 30 60 90 120 150 Relative Error at Spatial Position D (%) MC-LIBS CF-LIBS AlCuFeMgMnSi0 50 100 150 200 250 Relative Error at Spatial Position E (%) MC-LIBS CF-LIBS AlCuFeMgMnSi0 50 100 150 200 Relative Error at Spatial Position F (%) MC-LIBS CF-LIBS AlCuFeMgMnSi0 50 100 150 200 Relative Error at Spatial Position G (%) MC-LIBS CF-LIBS AlCuFeMgMnSi0 50 100 150 200 Relative Error at Spatial Position H (%) MC-LIBS CF-LIBS AlCuFeMgMnSi0 20 40 60 80 100 500 600 Relative Error at Spatial Position I (%) MC-LIBS CF-LIBS Figure 6-26. Relative errors of calculated concentration values at different spatial positions calculated using MC-LIBS (blue bars) and CF-LIBS (red bars).

PAGE 182

182 Table 6-1. List of spectral lines used in the CF-LIBS analysis of Al alloy B8. Al I 236.705 Fe II 262.567 Mn I 405.893 Al I 256.798 Fe II 273.955 Ni II 230.300 Al I 265.248 Fe II 274.320 Ni II 239.452 Al I 266.039 Fe II 274.648 Ni I 300.249 Al II 281.619 Fe II 275.329 Ni I 341.476 Al I 305.468 Fe II 275.573 Ni I 343.356 Al I 305.714 Fe I 296.689 Ni I 345.847 Al I 306.429 Fe I 298.357 Ni I 346.165 Al I 306.614 Fe I 364.784 Ni I 351.505 Al II 466.305 Fe I 371.993 Ni I 352.454 Al II 622.618 Fe I 373.486 Ni I 361.939 Al II 623.178 Fe I 373.713 Si I 250.690 Al II 624.336 Fe I 374.556 Si I 251.432 Cr II 283.563 Fe I 374.948 Si I 251.611 Cr II 284.325 Fe I 375.823 Si I 251.920 Cr II 284.984 Fe I 376.378 Si I 252.411 Cr II 297.191 Fe I 376.719 Si I 252.851 Cr II 297.974 Fe I 382.042 Si I 288.158 Cr I 357.869 Fe I 385.991 Si II 385.602 Cr I 359.349 Fe I 404.581 Si II 386.259 Cr I 360.533 Fe I 406.359 Si I 390.552 Cr I 520.604 Fe I 407.173 Si II 412.807 Cr I 520.844 Fe I 432.576 Si II 505.598 Cu II 221.027 Fe I 438.354 Ti II 323.452 Cu II 221.810 Mg II 279.078 Ti II 332.294 Cu II 222.886 Mg II 279.800 Ti II 332.946 Cu II 224.261 Mg I 285.213 Ti II 333.520 Cu II 224.700 Mn II 259.373 Ti II 334.034 Cu II 227.625 Mn II 260.569 Ti II 334.941 Cu II 229.436 Mn II 261.020 Ti I 335.464 Cu II 240.012 Mn II 293.306 Ti II 336.121 Cu I 261.837 Mn II 293.930 Ti II 337.280 Cu I 427.511 Mn II 294.920 Ti I 363.546 Cu I 510.554 Mn II 344.199 Ti I 365.350 Fe II 238.204 Mn II 348.291 Ti II 375.930 Fe II 256.253 Mn I 356.949 Ti II 376.132 Fe II 258.588 Mn I 380.672 Ti I 498.173 Fe II 259.837 Mn I 403.076 Ti I 499.107 Fe II 259.940 Mn I 403.307 Ti I 499.951 Fe II 260.709 Mn I 403.449 Ti I 500.721 Fe II 261.187 Mn I 403.573 Ti I 501.424 Fe II 261.382 Mn I 404.136

PAGE 183

183 Table 6-2. List of spectral lines used in the CF-LIBS analysis of Al alloy D33. Al I 232.156 Fe II 261.187 Fe I 404.581 Ni I 300.249 Al I 256.798 Fe II 261.382 Fe I 406.359 Ni I 300.363 Al I 265.248 Fe II 261.762 Fe I 407.173 Ni I 301.200 Al I 266.039 Fe II 262.167 Fe I 427.175 Ni I 313.411 Al II 281.619 Fe II 262.567 Fe I 430.790 Ni I 339.105 Al I 305.007 Fe II 262.829 Fe I 432.576 Ni I 339.299 Al I 305.468 Fe II 272.754 Fe I 438.354 Ni I 341.476 Al I 305.714 Fe II 273.697 Fe I 440.475 Ni I 342.371 Al I 306.429 Fe II 273.955 Mg II 279.078 Ni I 343.356 Al I 306.614 Fe I 274.240 Mg II 279.553 Ni I 343.728 Al II 466.305 Fe II 274.320 Mg II 279.800 Ni I 344.626 Al II 622.621 Fe II 274.648 Mg II 280.270 Ni I 345.289 Al II 623.175 Fe II 274.932 Mg I 285.213 Ni I 345.847 Al II 624.337 Fe II 275.329 Mn II 259.373 Ni I 346.165 Cr II 297.974 Fe II 275.573 Mn II 260.569 Ni I 349.296 Cr II 342.273 Fe I 296.689 Mn II 261.814 Ni I 351.505 Cr I 427.480 Fe I 297.313 Mn I 280.106 Ni I 352.454 Cu II 224.261 Fe I 298.357 Mn II 293.305 Ni I 356.637 Cu II 224.700 Fe II 298.482 Mn II 293.931 Si I 250.690 Cu II 227.625 Fe I 299.442 Mn II 294.921 Si I 251.432 Cu I 296.116 Fe I 300.094 Mn II 344.199 Si I 251.611 Cu I 301.084 Fe I 300.814 Mn II 346.032 Si I 251.920 Cu I 510.554 Fe I 300.956 Mn I 403.076 Si I 252.411 Fe II 233.131 Fe I 302.063 Mn I 403.307 Si I 252.851 Fe II 233.280 Fe I 346.586 Mn I 403.449 Si I 288.158 Fe II 233.801 Fe I 349.057 Mn I 403.573 Si I 298.764 Fe II 234.349 Fe I 351.381 Mn I 404.136 Si II 385.367 Fe II 234.428 Fe I 356.537 Mn I 404.876 Si II 385.602 Fe II 234.830 Fe I 357.009 Mn I 405.554 Si II 386.259 Fe II 238.204 Fe I 358.119 Ni II 220.672 Si I 390.552 Fe II 238.863 Fe I 361.876 Ni II 221.648 Si II 412.807 Fe II 239.563 Fe I 363.146 Ni II 222.296 Ti II 323.452 Fe II 239.924 Fe I 364.784 Ni II 225.385 Ti II 323.658 Fe II 240.489 Fe I 368.745 Ni II 226.446 Ti II 323.904 Fe II 240.666 Fe I 371.993 Ni II 227.021 Ti II 323.966 Fe II 241.052 Fe I 373.486 Ni II 227.877 Ti II 334.941 Fe II 241.107 Fe I 373.713 Ni II 229.655 Ti II 336.122 Fe II 241.331 Fe I 374.556 Ni II 229.714 Ti II 338.376 Fe II 243.930 Fe I 374.826 Ni II 230.300 Ti II 338.785 Fe II 256.253 Fe I 374.948 Ni II 231.604 Ti II 339.458 Fe II 256.348 Fe I 375.823 Ni I 232.003 Ti II 350.490 Fe II 258.588 Fe I 376.378 Ni II 233.458 Ti I 363.546 Fe II 259.154 Fe I 382.042 Ni II 239.452 Ti I 364.268 Fe II 259.837 Fe I 382.588 Ni II 241.613 Ti II 368.520 Fe II 259.940 Fe I 382.782 Ni II 243.789 Ti II 376.132 Fe II 260.709 Fe I 385.991 Ni I 298.165

PAGE 184

184 Table 6-3. List of spectral lines used in the CF-LIBS analysis of Al alloy S4. Al I 226.910 Fe II 239.562 Fe I 374.826 Mn I 405.554 Al I 236.705 Fe II 239.924 Fe I 374.948 Ni I 300.249 Al I 237.312 Fe II 240.488 Fe I 375.823 Ni I 336.957 Al I 237.840 Fe II 240.666 Fe I 376.378 Ni I 338.057 Al I 256.798 Fe II 241.052 Fe I 376.554 Ni I 339.299 Al I 257.510 Fe II 241.331 Fe I 376.719 Ni I 341.476 Al I 265.248 Fe II 249.326 Fe I 382.042 Ni I 344.626 Al I 266.039 Fe II 256.253 Fe I 385.991 Ni I 345.847 Al I 305.007 Fe II 256.348 Fe I 388.628 Ni I 346.165 Al I 305.468 Fe II 258.588 Fe I 404.581 Ni I 351.505 Al I 305.714 Fe II 259.837 Fe I 406.359 Ni I 352.454 Al I 306.429 Fe II 259.940 Fe I 407.173 Si I 250.690 Al I 306.614 Fe II 260.709 Fe I 427.175 Si I 251.432 Al II 466.305 Fe II 261.187 Fe I 430.790 Si I 251.611 Al II 622.621 Fe II 261.382 Fe I 432.576 Si I 251.920 Al II 623.175 Fe II 261.762 Fe I 438.354 Si I 252.411 Al II 624.337 Fe II 262.567 Fe I 440.475 Si I 252.851 Cr II 283.563 Fe II 262.829 Fe I 441.512 Si I 288.158 Cr II 284.325 Fe II 271.441 Mg I 277.669 Si II 385.602 Cr II 284.984 Fe I 271.902 Mg I 277.827 Si I 390.552 Cr II 285.568 Fe II 272.754 Mg I 278.142 Si II 412.807 Cr I 300.089 Fe II 273.697 Mg I 278.297 Ti II 323.452 Cr II 313.206 Fe II 273.955 Mg II 279.078 Ti II 323.657 Cr I 360.533 Fe II 274.320 Mg II 279.553 Ti II 323.904 Cr I 425.433 Fe II 274.648 Mg II 279.800 Ti II 324.199 Cr I 427.480 Fe II 275.329 Mg II 280.270 Ti II 332.294 Cr I 428.972 Fe II 275.574 Mg I 285.213 Ti II 334.941 Cu II 221.027 Fe II 278.369 Mg II 292.863 Ti II 336.121 Cu II 221.810 Fe I 296.689 Mg II 293.651 Ti II 337.280 Cu II 222.886 Fe I 297.313 Mn II 257.610 Ti II 338.376 Cu II 224.261 Fe I 298.357 Mn II 259.373 Ti II 338.784 Cu II 224.700 Fe I 299.442 Mn II 260.569 Ti II 339.458 Cu II 227.625 Fe I 302.063 Mn II 261.020 Ti I 363.546 Cu II 229.436 Fe I 344.060 Mn I 280.106 Ti I 364.268 Cu II 240.333 Fe I 346.586 Mn II 293.306 Ti I 365.350 Cu I 276.637 Fe I 356.537 Mn II 293.930 Ti II 368.520 Cu I 296.116 Fe I 357.009 Mn II 294.920 Ti II 375.930 Cu I 327.396 Fe I 360.885 Mn II 344.199 Zn II 250.199 Cu I 510.554 Fe I 361.876 Mn II 346.033 Zn II 255.795 Fe II 233.131 Fe I 363.146 Mn I 380.672 Zn I 328.233 Fe II 233.280 Fe I 364.784 Mn I 403.076 Zn I 330.258 Fe II 233.801 Fe I 371.993 Mn I 403.307 Zn I 334.502 Fe II 234.349 Fe I 372.761 Mn I 403.449 Zn I 468.014 Fe II 234.830 Fe I 373.486 Mn I 403.573 Zn I 472.215 Fe II 238.204 Fe I 373.713 Mn I 404.136 Zn I 481.053 Fe II 238.863 Fe I 374.556 Mn I 404.876 Zn II 491.162

PAGE 185

185 Table 6-4. List of spectral lines used in the CF-LIBS analysis of Al alloy SM10. Al I 226.910 Fe II 233.801 Fe I 346.586 Mn II 294.920 Al I 236.705 Fe II 234.349 Fe I 356.537 Mn II 344.199 Al I 237.207 Fe II 234.428 Fe I 357.009 Mn II 346.033 Al I 237.312 Fe II 234.830 Fe I 358.119 Mn I 380.672 Al I 265.248 Fe II 238.204 Fe I 360.668 Mn I 403.076 Al I 266.039 Fe II 238.863 Fe I 360.885 Mn I 403.307 Al II 281.619 Fe II 239.562 Fe I 361.876 Mn I 403.449 Al I 305.007 Fe II 239.924 Fe I 363.146 Mn I 403.573 Al I 305.468 Fe II 240.488 Fe I 364.784 Mn I 404.136 Al I 305.714 Fe II 240.666 Fe I 371.993 Mn I 404.876 Al I 306.429 Fe II 241.052 Fe I 372.761 Mn I 405.554 Al I 306.614 Fe II 241.107 Fe I 373.486 Ni II 221.648 Al II 466.305 Fe II 241.331 Fe I 373.713 Ni I 300.249 Al II 622.621 Fe I 252.284 Fe I 374.556 Ni I 344.626 Al II 623.175 Fe II 256.253 Fe I 374.826 Si I 250.690 Al II 624.337 Fe II 256.348 Fe I 374.948 Si I 251.432 Cr II 283.563 Fe II 258.588 Fe I 375.823 Si I 251.611 Cr II 284.325 Fe II 259.154 Fe I 376.378 Si I 251.920 Cr II 284.984 Fe II 259.837 Fe I 376.554 Si I 252.411 Cr II 285.568 Fe II 259.940 Fe I 376.719 Si I 252.851 Cr II 297.974 Fe II 260.709 Fe I 381.584 Si I 288.158 Cr I 300.089 Fe II 261.187 Fe I 382.042 Si II 385.602 Cr II 313.206 Fe II 261.382 Fe I 385.991 Si II 386.259 Cr I 357.869 Fe II 261.762 Fe I 404.581 Si I 390.552 Cr I 359.349 Fe II 262.567 Fe I 406.359 Si II 412.807 Cr I 360.533 Fe II 262.829 Fe I 407.173 Ti II 323.452 Cr I 425.433 Fe II 271.441 Fe I 427.175 Ti II 323.657 Cr I 427.480 Fe I 271.902 Fe I 430.790 Ti II 323.904 Cr I 428.972 Fe II 272.754 Fe I 432.576 Ti II 324.199 Cu II 221.027 Fe II 273.697 Fe I 438.354 Ti II 336.121 Cu II 221.810 Fe II 273.955 Fe I 440.475 Ti II 337.280 Cu II 222.886 Fe II 274.320 Fe I 441.512 Ti II 338.376 Cu II 224.261 Fe II 274.648 Mg I 277.669 Ti II 368.520 Cu II 224.700 Fe II 275.329 Mg I 277.827 Ti II 375.930 Cu II 227.625 Fe II 275.574 Mg I 278.142 Ti II 376.132 Cu II 229.436 Fe II 278.369 Mg I 278.297 Zn II 250.199 Cu II 240.012 Fe I 294.787 Mg II 448.116 Zn II 255.795 Cu I 330.795 Fe I 298.357 Mn II 259.373 Zn I 328.233 Cu I 465.112 Fe I 299.442 Mn II 260.569 Zn I 334.502 Cu I 510.554 Fe I 302.063 Mn II 261.020 Zn I 472.215 Fe II 233.131 Fe I 305.908 Mn II 293.306 Zn I 481.053 Fe II 233.280 Fe I 344.060 Mn II 293.930

PAGE 186

186 Table 6-5. List of spectral lines used in the CF-LIBS analysis of Al alloy V14. Al I 231.249 Fe II 241.052 Fe I 382.043 Ni I 349.296 Al I 232.156 Fe II 241.107 Fe I 382.588 Ni I 351.505 Al I 236.705 Fe II 241.331 Fe I 382.782 Ni I 352.454 Al I 237.312 Fe II 242.836 Fe I 383.422 Ni I 356.637 Al I 256.798 Fe II 243.930 Fe I 385.991 Ni I 361.939 Al I 265.248 Fe I 247.977 Fe I 407.173 Si I 221.089 Al I 266.039 Fe I 248.814 Fe I 427.175 Si I 243.515 Al II 281.619 Fe II 249.326 Fe I 430.790 Si I 250.690 Al I 305.007 Fe I 251.083 Fe I 432.576 Si I 251.432 Al I 305.468 Fe I 252.743 Fe I 438.354 Si I 251.611 Al I 305.714 Fe II 256.253 Fe I 440.475 Si I 251.920 Al I 306.429 Fe II 256.348 Mg II 279.078 Si I 252.411 Al I 306.614 Fe II 258.588 Mg II 279.553 Si I 252.851 Al II 466.305 Fe II 259.837 Mg II 279.800 Si I 288.158 Cr II 266.602 Fe II 259.940 Mg II 280.270 Si II 385.367 Cr II 267.181 Fe II 260.709 Mg I 285.213 Si II 385.602 Cr II 283.563 Fe II 261.187 Mn II 257.610 Si II 386.260 Cr II 284.325 Fe II 261.382 Mn II 259.373 Si I 390.552 Cr II 284.984 Fe II 261.762 Mn II 260.569 Si II 412.805 Cr II 285.568 Fe II 262.567 Mn II 261.020 Ti II 323.452 Cr II 297.974 Fe II 262.829 Mn II 261.814 Ti II 323.658 Cr II 313.206 Fe II 266.466 Mn I 280.106 Ti II 323.904 Cr I 357.869 Fe II 272.754 Mn II 293.306 Ti II 324.199 Cr I 359.349 Fe II 273.697 Mn II 293.931 Ti II 328.766 Cr I 360.533 Fe II 273.955 Mn II 294.921 Ti II 332.294 Cr I 425.433 Fe II 274.320 Mn II 344.199 Ti II 333.520 Cr I 427.480 Fe II 274.648 Mn II 346.032 Ti II 334.036 Cr I 428.972 Fe II 274.932 Mn II 347.413 Ti II 334.941 Cu II 221.027 Fe II 275.329 Mn II 348.868 Ti II 336.122 Cu II 221.810 Fe II 275.573 Mn II 349.584 Ti II 337.280 Cu II 222.886 Fe I 295.394 Mn II 349.753 Ti II 338.377 Cu II 224.261 Fe I 298.357 Mn I 403.076 Ti II 338.785 Cu II 224.700 Fe II 298.482 Mn I 403.307 Ti II 339.458 Cu II 227.625 Fe II 298.554 Mn I 403.449 Ti II 344.431 Cu II 229.436 Fe I 356.537 Mn I 403.573 Ti II 350.490 Cu I 296.116 Fe I 357.009 Mn I 404.136 Ti I 363.546 Cu I 510.554 Fe I 358.119 Ni II 220.672 Ti I 364.268 Cu I 578.213 Fe I 360.885 Ni II 221.648 Ti I 365.350 Fe II 233.131 Fe I 361.876 Ni II 227.877 Ti II 368.520 Fe II 233.280 Fe I 363.146 Ni II 230.300 Ti II 374.164 Fe II 233.801 Fe I 364.784 Ni II 231.604 Ti II 375.930 Fe II 234.349 Fe I 371.993 Ni II 239.452 Ti II 376.132 Fe II 234.428 Fe I 373.486 Ni II 241.613 Ti II 454.962 Fe II 234.830 Fe I 373.713 Ni I 313.411 Ti II 457.198 Fe II 236.483 Fe I 374.556 Ni I 338.057 Ti I 498.173 Fe II 238.204 Fe I 374.826 Ni I 339.299 Ti I 499.107 Fe II 238.863 Fe I 374.948 Ni I 341.476 Ti I 499.951 Fe II 239.563 Fe I 375.823 Ni I 343.356 Ti I 500.721 Fe II 239.924 Fe I 376.378 Ni I 344.626 Fe II 240.489 Fe I 376.719 Ni I 345.847 Fe II 240.666 Fe I 381.584 Ni I 346.165

PAGE 187

187 Table 6-6. List of spectral lines used in the CF-LIBS analysis of Al alloy Z8. Al I 231.906 Cu I 296.116 Fe II 261.187 Al I 232.156 Cu I 301.084 Fe II 261.382 Al I 256.798 Cu I 319.410 Fe II 261.762 Al I 265.248 Cu I 328.271 Fe II 262.167 Al I 266.039 Cu I 329.054 Fe II 262.567 Al II 281.619 Cu I 333.784 Fe II 262.829 Al I 305.007 Cu I 465.112 Fe II 266.466 Al I 305.468 Cu I 510.554 Fe II 271.441 Al I 305.714 Cu I 529.252 Fe I 272.090 Al I 306.429 Cu I 578.213 Fe II 272.754 Al I 306.614 Fe II 233.131 Fe II 273.697 Al II 622.621 Fe II 233.280 Fe II 273.955 Al II 623.175 Fe II 233.801 Fe II 274.320 Al II 624.337 Fe II 234.349 Fe II 274.648 Cr II 276.259 Fe II 234.428 Fe II 274.932 Cr II 282.238 Fe II 234.830 Fe II 275.329 Cr II 283.563 Fe II 238.204 Fe II 275.573 Cr II 284.001 Fe II 238.863 Fe II 278.369 Cr II 284.325 Fe II 239.563 Fe I 294.787 Cr II 284.984 Fe II 239.924 Fe I 296.689 Cr II 285.568 Fe II 240.489 Fe I 297.313 Cr II 285.890 Fe II 240.666 Fe I 299.442 Cr II 286.257 Fe II 241.052 Fe I 299.951 Cr II 297.190 Fe II 241.107 Fe I 300.094 Cr II 311.865 Fe II 241.331 Fe I 300.814 Cr II 312.036 Fe II 243.930 Fe I 341.313 Cr II 312.869 Fe I 247.977 Fe I 356.537 Cr II 313.206 Fe I 248.327 Fe I 358.119 Cr II 313.668 Fe I 248.814 Fe I 360.885 Cr I 357.869 Fe II 249.326 Fe I 361.876 Cr I 359.349 Fe I 251.083 Fe I 363.146 Cr I 360.533 Fe I 252.284 Fe I 364.784 Cr I 425.433 Fe I 252.743 Fe I 375.823 Cr I 427.480 Fe II 253.363 Fe I 376.378 Cr I 428.972 Fe II 253.442 Fe I 376.719 Cu II 221.027 Fe I 253.560 Fe I 381.584 Cu II 221.810 Fe II 253.820 Fe I 382.042 Cu II 222.886 Fe II 253.899 Fe I 385.991 Cu II 224.261 Fe II 256.253 Fe I 404.581 Cu II 224.700 Fe II 256.348 Fe I 406.359 Cu II 227.625 Fe II 258.588 Fe I 407.173 Cu II 229.436 Fe II 259.154 Fe I 427.175 Cu II 260.027 Fe II 259.837 Fe I 430.790 Cu I 282.437 Fe II 260.709 Fe I 432.576

PAGE 188

188 Table 6-6. Continued. Fe I 438.354 Ni II 231.604 Ti II 322.860 Fe I 440.475 Ni I 232.003 Ti II 322.860 Mg I 277.669 Ni II 233.458 Ti II 323.452 Mg I 277.827 Ni II 239.452 Ti II 323.658 Mg I 278.142 Ni II 241.613 Ti II 323.904 Mg I 278.297 Ni II 243.789 Ti II 323.966 Mg II 279.078 Ni I 300.249 Ti II 333.520 Mg II 279.800 Ni I 300.363 Ti II 334.036 Mg I 285.213 Ni I 301.200 Ti I 334.188 Mg II 292.863 Ni I 313.411 Ti II 334.941 Mg II 293.651 Ni I 338.057 Ti II 336.122 Mg I 382.930 Ni I 339.105 Ti II 337.280 Mg I 383.230 Ni I 339.299 Ti II 338.377 Mg I 383.829 Ni I 341.476 Ti II 338.785 Mg I 516.733 Ni I 343.356 Ti II 344.431 Mg I 517.268 Ni I 344.626 Ti II 350.490 Mg I 518.361 Ni I 345.847 Ti II 362.482 Mn II 257.610 Ni I 346.165 Ti I 363.546 Mn II 259.373 Ni I 349.296 Ti II 364.133 Mn II 260.569 Ni I 351.505 Ti I 364.268 Mn II 261.020 Ni I 352.454 Ti I 365.350 Mn II 261.814 Ni I 356.637 Ti II 368.520 Mn II 293.305 Ni I 361.939 Ti II 374.164 Mn II 293.931 Si I 250.690 Ti II 375.930 Mn II 294.921 Si I 251.432 Ti II 376.132 Mn I 322.809 Si I 251.611 Ti II 390.055 Mn II 344.199 Si I 251.920 Ti II 391.347 Mn II 346.032 Si I 252.411 Ti I 398.176 Mn II 349.584 Si I 252.851 Ti I 398.976 Mn II 349.753 Si I 288.158 Ti I 399.864 Mn I 380.672 Si II 385.602 Ti II 429.410 Mn I 403.076 Si I 390.552 Ti II 430.005 Mn I 403.307 Si II 412.805 Ti II 439.503 Mn I 403.449 Ti II 315.226 Ti II 444.379 Mn I 403.573 Ti II 315.421 Ti II 446.850 Mn I 404.136 Ti II 315.568 Ti II 450.127 Mn I 404.876 Ti II 316.122 Ti II 454.962 Ni II 220.672 Ti II 316.177 Ti II 457.198 Ni II 221.648 Ti II 316.257 Ti I 498.173 Ni II 222.296 Ti II 316.853 Ti I 499.107 Ni II 226.446 Ti II 319.088 Ti I 499.951 Ni II 227.021 Ti II 320.254 Ti I 500.721 Ni II 227.877 Ti II 321.706 Ni II 230.300 Ti II 322.284

PAGE 189

189 Table 6-7. List of spectral lines used in the Monte Carlo LIBS simulations. Wavelength (nm) Lower energy level (cm-1) Upper energy level (cm-1) Absorption oscillator strength, f gi gk Al I 308.2151 032435 0.18 24 Al I 309.2708 11232437 0.16 46 Al II 281.6185 5985295351 0.15 31 Cu I 324.7540 030784 0.439 24 Cu I 327.3960 030535 0.22 22 Fe I 278.8105 692842784 0.087 1113 Fe II 273.9548 795544447 0.217 88 Fe II 274.3197 884745290 0.406 24 Fe II 274.6484 868045080 0.33 46 Fe II 274.9321 839244754 0.318 68 Fe II 275.3288 2635362662 0.162 1012 Fe II 275.5737 795544233 0.3 810 Mg I 285.2126 035051 1.81 13 Mg II 279.0777 3566971491 0.92 24 Mg II 279.5528 035761 0.627 24 Mg II 279.7998 3576171490 0.828 46 Mg II 280.2705 035669 0.313 22 Mn I 280.1081 035690 0.29 64 Mn II 293.3055 947343557 0.15 53 Mn II 293.9308 947343485 0.25 55 Mn II 294.9200 947343371 0.35 57 Si I 288.1577 629940992 0.14 53 Zn I* 328.2328 3231162769 0.44 13 Zn I* 330.2584 3250162772 0.33 35 *Only used for Al alloys S4 and SM10.

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190 Table 6-8. Electron number density (in cm-3) and temperature (in K) values calculated using MC-LIBS and CF-LIBS for 6 Al alloy standards. Electron number density, ne ( 1016 cm-3) Temperature, T ( 104 K) Al alloy sample MC-LIBS* CF-LIBS MC-LIBS* CF-LIBS B8 7.58 7.56 1.22 0.02 1.0 0.6 1.09 0.06 D33 6.52 6.55 1.33 0.02 1.0 0.5 1.09 0.07 S4 8.46 8.49 1.35 0.02 1.0 0.6 0.99 0.07 SM10 4.40 4.41 1.40 0.02 1.0 0.5 0.98 0.04 V14 6.01 5.98 1.47 0.02 1.0 0.5 1.10 0.05 Z8 4.06 4.02 1.20 0.02 0.9 0.5 1.06 0.07 *The temperature and electron number density reported is the average of temperatures at different spatial points. Table 6-9. Relative concentration values and re lative errors (in %) calculated from CF-LIBS analysis of aluminum alloys B8 and D33. Table 6-10. Relative concentration values and re lative errors (in %) calculated from CF-LIBS analysis of aluminum alloys S4 and SM10. Element Al alloy B8 Al alloy D33 Certified CF-LIBS Relative error Certified CF-LIBS Relative error Al 88.8095 89.7 1.086.178286.1 0.1 Cr 0.1716 0.02 86.20.047700.005 89.5 Cu 7.0155 6.8 2.42.93282.4 19.7 Fe 0.8075 0.1 84.11.16700.2 80.0 Mg 0.0767 0.009 88.50.03860.006 83.4 Mn 0.4038 0.03 92.30.40590.03 93.3 Ni 0.2019 0.2 1.70.50740.7 29.2 Si 2.3520 3.0 29.68.666510.6 22.4 Ti 0.1615 0.01 92.90.05580.004 92.1 Element Al alloy S4 Al alloy SM10 Certified CF-LIBS Relative error Certified CF-LIBS Relative error Al 84.0937 84.2 0.285.099887.0 2.2 Cr 0.1305 0.005 96.20.20100.01 95.3 Cu 2.6495 1.7 36.12.81422.4 13.7 Fe 0.1194 0.05 54.91.97000.1 95.1 Mg 0.3513 0.03 93.01.08550.2 77.8 Mn 0.3814 0.009 97.60.29650.006 97.9 Ni 0.1807 0.01 92.10.06530.04 33.1 Si 1.0337 1.0 3.42.93482.5 16.5 Ti 0.1204 0.003 97.90.05530.001 97.8 Zn 10.9394 13.0 18.45.47777.8 41.9

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191 Table 6-11. Relative concentration values and re lative errors (in %) calculated from CF-LIBS analysis of aluminum alloys V14 and Z8. Table 6-12. Number densities (in cm-3) calculated from MC-LIBS analysis of six different aluminum alloys. Element Alloy B8 Alloy D33 Alloy S4 Alloy SM10 Alloy V14 Alloy Z8 Al 2.35 1017 1.73 10172.53 10171.23 10171.83 1017 1.35 1017 Cu 4.28 1015 1.46 10152.57 10154.45 10151.84 1015 3.82 1015Fe 5.83 1014 7.67 10146.39 10146.42 10148.62 1014 6.10 1014Mg 8.98 1013 4.26 10131.26 10155.8 10151.42 1013 6.37 1015Mn 2.82 1014 2.89 10144.84 10147.29 10133.94 1014 1.24 1014Si 3.42 1016 6.83 10161.16 10167.55 10154.46 1016 2.83 1015Zn 5.01 10161.52 1016 Table 6-13. Relative concentration values and re lative errors (in %) calculated from MC-LIBS and CF-LIBS analysis of Al alloy B8. Element Relative concentration Relative error Certified MC-LIBS CF-LIBS MC-LIBS CF-LIBS Al 89.2872 83.189.46.90.2 Cu 7.0533 3.67.349.03.1 Fe 0.8119 0.40.150.782.8 Mg 0.0771 0.030.00961.187.8 Mn 0.4060 0.20.0350.791.5 Si 2.3646 12.63.1432.931.4 Element Al alloy V14 Al alloy Z8 Certified CF-LIBS Relative error Certified CF-LIBS Relative error Al 87.4618 87.6 0.179.466981.6 2.6 Cr 0.1815 0.02 88.00.15130.02 87.1 Cu 4.0836 5.2 26.416.186516.4 1.4 Fe 0.9075 0.2 73.21.09930.2 82.0 Mg 0.0252 0.003 87.71.28080.3 79.5 Mn 0.5848 0.06 89.80.26220.03 88.3 Ni 0.3327 0.3 3.40.53450.3 41.6 Si 6.2514 6.6 5.40.84711.2 41.4 Ti 0.1714 0.01 91.70.17140.01 93.8

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192 Table 6-14. Relative concentration values and re lative errors (in %) calculated from MC-LIBS and CF-LIBS analysis of Al alloy D33. Element Relative concentration Relative error Certified MC-LIBS CF-LIBS MC-LIBS CF-LIBS Al 86.7080 69.385.020.12.0 Cu 2.9508 1.43.153.15.3 Fe 1.1742 0.60.445.969.7 Mg 0.0388 0.020.00960.377.6 Mn 0.4084 0.20.0442.489.4 Si 8.7198 28.411.5226.231.7 Table 6-15. Relative concentration values and re lative errors (in %) calculated from MC-LIBS and CF-LIBS analysis of Al alloy S4. Element Relative concentration Relative error Certified MC-LIBS CF-LIBS MC-LIBS CF-LIBS Al 84.4582 88.281.14.44.0 Cu 2.6610 2.12.720.31.7 Fe 0.1200 0.50.1285.17.4 Mg 0.3528 0.40.0412.288.3 Mn 0.3830 0.30.0210.194.8 Si 1.0382 4.21.2305.816.9 Zn 10.9868 4.314.861.335.0 Table 6-16. Relative concentration values and re lative errors (in %) calculated from MC-LIBS and CF-LIBS analysis of Al alloy SM10. Element Relative concentration Relative error Certified MC-LIBS CF-LIBS MC-LIBS CF-LIBS Al 85.3743 81.084.65.10.9 Cu 2.8233 7.03.3146.415.9 Fe 1.9763 0.90.255.691.9 Mg 1.0890 3.50.2217.182.6 Mn 0.2975 0.10.0167.096.4 Si 2.9443 5.22.576.314.3 Zn 5.4953 2.49.355.668.4 Table 6-17. Relative concentration values and re lative errors (in %) calculated from MC-LIBS and CF-LIBS analysis of Al alloy V14. Element Relative concentration Relative error Certified MC-LIBS CF-LIBS MC-LIBS CF-LIBS Al 88.0656 77.587.212.01.0 Cu 4.1118 1.85.755.338.0 Fe 0.9137 0.80.317.669.4 Mg 0.0254 0.0050.00378.786.6 Mn 0.5889 0.30.0742.588.1 Si 6.2946 19.66.8211.27.4

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193 Table 6-18. Relative concentration values and re lative errors (in %) calculated from MC-LIBS and CF-LIBS analysis of Al alloy Z8. Element Relative concentration Relative error Certified MC-LIBS CF-LIBS MC-LIBS CF-LIBS Al 80.1540 87.580.59.20.5 Cu 16.3264 5.917.764.08.7 Fe 1.1088 0.80.226.079.8 Mg 1.2919 3.70.3188.878.6 Mn 0.2645 0.20.0938.066.7 Si 0.8545 1.91.1123.934.2 Table 6-19. Atomic masses (in g) of differe nt elements in the aluminum alloy sample. Element Mass ( 10-23 g) Mg 4.04 Al 4.48 Si 4.66 Ti 7.95 Cr 8.64 Mn 9.12 Fe 9.27 Ni 9.75 Cu 10.55 Table 6-20. Electron number density (in cm-3) and temperature (in K) values calculated using MC-LIBS and CF-LIBS for Al alloy standa rd D33 at different spatial positions. Electron number density, ne ( 1016 cm-3) Temperature, T ( 104 K) Spatial position MC-LIBS CF-LIBS MC-LIBS CF-LIBS A 0.8 0.6 1.090.5 0.2 1.2 B 4.7 1.4 1.891.0 0.1 1.2 C 12.0 2.0 1.891.33 0.09 1.1 D 9.5 0.8 1.981.29 0.05 1.2 E 25.9 1.0 1.961.43 0.03 1.2 F 23.8 0.1 1.891.27 0.01 1.1 G 24.1 0.6 2.101.09 0.02 1.1 H 16.9 1.6 1.650.96 0.03 0.9 I 9.8 1.9 1.120.91 0.06 0.9 J 8.8 2.7 0.8 0.1 K 2.5 2.0 0.5 0.2

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194 Table 6-21. Sigmoidal fitting parameters for the spatial evolution of temperature. (Equation: y = A2 + ( A1 A2) / (1 + exp(( x x0)/d x )). Spatial position A1 (K) A2 (K) x0 dx A 18894.10 -13896.93 0.93 0.26 B 19196.56 -14126.06 0.93 0.27 C 19163.45 -14101.23 0.93 0.27 D 15590.02 -11471.51 0.93 0.27 E 15821.39 -11640.55 0.93 0.27 F 13490.44 -9926.33 0.93 0.27 G 12017.23 -8842.37 0.93 0.27 H 11688.34 -8599.35 0.93 0.27 I 13061.62 -9610.13 0.93 0.27 J 16371.27 -12047.07 0.93 0.27 K 19147.64 -14088.17 0.93 0.27 Table 6-22. Sigmoidal fitting parameters for th e spatial evolution of electron number density. (Equation: y = A2 + ( A1 A2) / (1 + exp(( x x0)/d x )). Spatial position A1 ( 1017 cm-3) A2 ( 1016 cm-3) x0 dx A 1.92 -1.93 0.52 0.18 B 2.25 -2.230.520.18 C 2.67 -2.670.520.18 D 1.40 -2.180.540.20 E 2.98 -3.990.540.18 F 2.45 -2.010.540.14 G 2.57 -1.340.510.12 H 2.18 -1.040.500.12 I 1.87 -1.460.550.13 J 4.06 -5.860.500.20 K 6.00 -7.050.520.19

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195 Table 6-23. Relative concentration values (in %) calculated from CF-LIBS analysis of aluminum alloys D33 at di fferent spatial positions. Al Cr Cu Fe Mg Mn Ni Si Ti Certified 86.1782 0.0477 2.9328 1.167 0.0386 0.4059 0.5074 8.6665 0.0558 A 89.6 0.01 2.11.00.020.071.4 5.70.004 B 86.6 0.03 1.91.00.030.11.4 8.90.005 C 87.2 0.03 1.30.70.030.081.6 9.00.004 D 84.7 0.03 3.30.80.040.091.0 9.90.007 E 85.7 0.04 1.80.50.040.090.6 11.30.009 F 86.3 0.02 1.10.20.040.070.2 12.10.007 G 86.6 0.02 0.70.10.020.060.2 12.30.006 H 93.8 0.0003 0.10.0090.0040.0040.01 6.00.0008 I 93.3 0.0005 0.060.0040.0010.0020.007 6.620.0007 Table 6-24. Relative errors (in %) of calcula ted CF-LIBS concentration values at different spatial positions. Al Cr Cu Fe Mg Mn Ni Si Ti A 4.0 74.4 27.010.241.282.3182.3 34.592.8 B 0.5 48.4 35.313.212.776.2181.2 2.491.4 C 1.2 40.9 54.839.615.580.4218.8 4.293.2 D 1.7 42.3 12.428.62.677.7103.2 14.688.2 E 0.5 9.2 40.259.71.377.216.8 30.384.8 F 0.1 52.4 61.183.91.082.166.9 39.487.5 G 0.5 62.7 77.390.750.084.963.1 42.090.0 H 8.9 99.4 95.299.289.999.097.2 30.698.6 I 8.2 99.0 97.999.796.499.698.6 23.498.7

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196 Table 6-25. Relative concentration values, rela tive errors (in %) and number densities (in cm-3) calculated from MC-LIBS and CF-LIBS analysis of Al alloy D33 at spatial position A. Relative concentration Relative error Number density (cm-3) Certified MC-LIBS CF-LIB S MC-LIBS CF-LIBS MC-LIBS Al 86.7080 93.2 90.97.54.8 2.76 1017 Cu 2.9508 2.1 2.229.926.4 2.59 1015Fe 1.1742 1.8 1.157.19.4 2.64 1015Mg 0.0388 0.03 0.0219.340.6 1.03 1014Mn 0.4084 0.3 0.0721.782.2 4.65 1014Si 8.7198 2.5 5.871.433.9 7.08 1015 Table 6-26. Relative concentration values, rela tive errors (in %) and number densities (in cm-3) calculated from MC-LIBS and CF-LIBS analysis of Al alloy D33 at spatial position B. Relative concentration Relative error Number density (cm-3) Certified MC-LIBS CF-LIB S MC-LIBS CF-LIBS MC-LIBS Al 86.7080 89.7 87.9 3.41.4 3.16 1017 Cu 2.9508 4.8 1.9 61.134.7 7.08 1015Fe 1.1742 1.6 1.03 32.912.4 2.66 1015Mg 0.0388 0.04 0.03 1.811.9 1.54 1014Mn 0.4084 0.4 0.1 5.876.0 7.48 1014Si 8.7198 3.5 9.0 59.33.3 1.20 1016 Table 6-27. Relative concentration values, rela tive errors (in %) and number densities (in cm-3) calculated from MC-LIBS and CF-LIBS analysis of Al alloy D33 at spatial position C. Relative concentration Relative error Number density (cm-3) Certified MC-LIBS CF-LIB S MC-LIBS CF-LIBS MC-LIBS Al 86.7080 81.0 88.6 6.62.2 3.46 1017 Cu 2.9508 1.6 1.3 47.254.3 2.81 1015Fe 1.1742 1.8 0.7 49.339.0 3.62 1015Mg 0.0388 0.04 0.03 6.214.7 1.95 1014Mn 0.4084 0.8 0.08 89.480.2 1.62 1015Si 8.7198 14.8 9.2 70.25.3 6.10 1016

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197 Table 6-28. Relative concentration values, rela tive errors (in %) and number densities (in cm-3) calculated from MC-LIBS and CF-LIBS analysis of Al alloy D33 at spatial position D. Relative concentration Relative error Number density (cm-3) Certified MC-LIBS CF-LIB S MC-LIBS CF-LIBS MC-LIBS Al 86.7080 75.4 85.7 13.11.2 2.10 1017 Cu 2.9508 0.9 3.3 67.912.9 1.11 1015Fe 1.1742 0.9 0.8 20.128.3 1.26 1015Mg 0.0388 0.04 0.04 7.53.1 1.11 1014Mn 0.4084 0.5 0.09 20.777.6 6.74 1014Si 8.7198 22.2 10.0 154.615.2 5.94 1016 Table 6-29. Relative concentration values, rela tive errors (in %) and number densities (in cm-3) calculated from MC-LIBS and CF-LIBS analysis of Al alloy D33 at spatial position E. Relative concentration Relative error Number density (cm-3) Certified MC-LIBS CF-LIB S MC-LIBS CF-LIBS MC-LIBS Al 86.7080 66.9 86.3 22.80.5 4.55 1017 Cu 2.9508 2.0 1.8 30.940.2 5.87 1015Fe 1.1742 1.2 0.5 3.159.7 3.98 1015Mg 0.0388 0.05 0.04 34.51.5 3.94 1014Mn 0.4084 0.7 0.09 66.877.2 2.28 1015Si 8.7198 29.1 11.4 233.730.3 1.90 1017 Table 6-30. Relative concentration values, rela tive errors (in %) and number densities (in cm-3) calculated from MC-LIBS and CF-LIBS analysis of Al alloy D33 at spatial position F. Relative concentration Relative error Number density (cm-3) Certified MC-LIBS CF-LIB S MC-LIBS CF-LIBS MC-LIBS Al 86.7080 73.3 86.5 15.40.3 5.24 1017 Cu 2.9508 1.4 1.1 53.961.2 4.11 1015Fe 1.1742 1.0 0.2 11.983.9 3.57 1015Mg 0.0388 0.04 0.04 11.90.8 3.44 1014Mn 0.4084 0.7 0.07 79.882.2 2.58 1015Si 8.7198 23.5 12.1 169.338.8 1.61 1017

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198 Table 6-31. Relative concentration values, rela tive errors (in %) and number densities (in cm-3) calculated from MC-LIBS and CF-LIBS analysis of Al alloy D33 at spatial position G. Relative concentration Relative error Number density (cm-3) Certified MC-LIBS CF-LIB S MC-LIBS CF-LIBS MC-LIBS Al 86.7080 74.4 86.8 14.20.1 6.32 1017 Cu 2.9508 2.3 0.7 23.777.4 8.08 1015Fe 1.1742 0.8 0.1 30.490.8 3.35 1015Mg 0.0388 0.03 0.02 11.650.3 3.23 1014Mn 0.4084 0.7 0.06 64.584.9 2.80 1015Si 8.7198 21.8 12.3 150.241.4 1.78 1017 Table 6-32. Relative concentration values, rela tive errors (in %) and number densities (in cm-3) calculated from MC-LIBS and CF-LIBS analysis of Al alloy D33 at spatial position H. Relative concentration Relative error Number density (cm-3) Certified MC-LIBS CF-LIB S MC-LIBS CF-LIBS MC-LIBS Al 86.7080 67.3 93.822.48.2 5.00 1017 Cu 2.9508 5.8 0.197.795.2 1.83 1016Fe 1.1742 0.4 0.00965.099.2 1.48 1015Mg 0.0388 0.02 0.00442.389.9 1.85 1014Mn 0.4084 0.6 0.00443.099.0 2.13 1015Si 8.7198 25.9 6.0196.831.0 1.85 1017 Table 6-33. Relative concentration values, rela tive errors (in %) and number densities (in cm-3) calculated from MC-LIBS and CF-LIBS analysis of Al alloy D33 at spatial position I. Relative concentration Relative error Number density (cm-3) Certified MC-LIBS CF-LIB S MC-LIBS CF-LIBS MC-LIBS Al 86.7080 74.1 93.314.67.6 4.34 1017 Cu 2.9508 17.9 0.06506.397.9 4.43 1016Fe 1.1742 0.3 0.00474.499.7 8.49 1014Mg 0.0388 0.01 0.00171.196.4 7.26 1013Mn 0.4084 0.3 0.00230.999.6 8.12 1014Si 8.7198 7.5 6.614.523.8 4.20 1016 Table 6-34. Relative concentration values, rela tive errors (in %) and number densities (in cm-3) calculated from MC-LIBS and CF-LIBS analysis of Al alloy D33 at spatial position J. Certified Relative concentration Relative error Number density (cm-3) Al 86.7080 59.4 31.5 2.69 1017 Cu 2.9508 29.2 890.8 5.60 1016Fe 1.1742 1.2 0.1 2.57 1015Mg 0.0388 0.04 9.6 1.76 1014Mn 0.4084 0.4 9.6 9.96 1014Si 8.7198 9.7 11.0 4.21 1016

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199 Table 6-35. Relative concentration values, rela tive errors (in %) and number densities (in cm-3) calculated from MC-LIBS analysis of Al alloy D33 at spatial position K. Certified Relative concentration Relative error Number density (cm-3) Al 86.7080 91.6 5.6 9.75 1017 Cu 2.9508 4.5 52.6 2.03 1016Fe 1.1742 0.3 71.9 1.69 1015Mg 0.0388 0.02 51.5 2.21 1014Mn 0.4084 0.2 58.8 8.81 1014Si 8.7198 3.4 61.1 3.47 1016

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200 CHAPTER 7 SEMI-QUANTITATIVE ANALYSIS OF DIFF ERENT SAMPLES BY CALIBR ATION-FREE LASER-INDUCED BREAKDOWN SPECTROSCOPY Introduction Since its inception, the calibration-free la ser-induced breakdown spectroscopy (CF-LIBS) approach has been applied by several research groups to the analysis of different types of samples of varying degrees of complexities. One of the first applications of the CF-LIBS technique was on the analysis of aluminum alloys and ambient air [55, 56]. Ciucci et al. [55, 56] reported excellent agreement between the nominal composition of the untreated metallic alloy and CF-LIBS results. Moreover, all the elements in the alloy were detected and quantitatively determined in a wide dynamic range from 250 ppm Cu up to 96% Al. In the CF-LIBS analysis of ambient air, the results repor ted for Ar, C, N, O and H were also in good agreement with standard atmospheric composition data. CF-LIBS has also been applied in the field of cultural heritage conservation where the samples are very precious, irreplaceable and have to be analyzed in situ and in a non-destructive manner. Borgia et al. [189] obt ained quantitative stratigraphic resu lts in the analysis of ancient Roman fresco samples. Two iron-based fresco fra gments were analyzed and results showed that although the spectra are similar qualit atively, the pigments can be differentiated quantitatively. Stratigraphic analysis also shows the variation in elemental composition fo r each layer of sample probed by a single laser shot. The CF-LIBS approach demonstrated, in this case, the feasibility of its use in real-time for in situ stratigraphic analysis of pi gment composition without substrate contamination or destruction. Corsi et al. [190] demonstrat ed the applicability of CF-LIBS in the determination of caratage of precious ternary and quaternary alloys The errors reported on the concentration values calculated with CF-LIBS were below 1%. Four hypothetical calibration curves were also

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201 constructed using neutral Au lines at 267.5 nm, 274.8 nm, 312.2 nm and 627.8 nm but the experimental data were highly sc attered which led the authors to conclude that CF-LIBS in this case is evidently superior compared to conventio nal calibration methods since large dispersion in calibration points greatly affects the precision an d accuracy of calculated elemental composition. In addition, the LIBS signal corresponding to th e same gold caratage for ternary and quaternary alloys did not coincide at all in the calibra tion plots constructed which demonstrates that calibration curves for gold caratage determinatio n are highly affected by matrix effects. The CF-LIBS protocol has also been applied to continuous in situ monitoring of metal smoke emissions from industrial plants [191]. A micro-plasma was generated in a flue duct of a 150 MW oil-fired power plant and the spectra take n showed elemental emissions from Ni, V, Ti, Mg, Fe, etc. The results obtained with CF-L IBS were confirmed by analyzing a sample of combustion products with ICP-MS. Corsi et al. [192] also studie d the feasibility of the CF-L IBS technique for hair tissue mineral analysis (HTMA) which is a useful medical diagnostic tool for detecting mineral deficiencies or imbalances in patients. CF -LIBS allowed for the measurement of relative concentrations of Mg, K, Ca, Na, and Al at the level of few milligrams per 100 grams of sample and the determination of their ra tios. Although the potential of CF-LIBS for hair analysis was not fully exploited in this work, the authors concluded that the adva ntage provided by CF-LIBS in alleviating the requirement for reference standa rds and calibration curves is the most crucial part due to the high variability of different hair types. Colao et al. [193] attempted to quantitativ ely determine the elemental composition of ancient Roman bronze coins. However, because of the intrinsic difficu lties related to the quantitative analysis of Cu based alloys due to large differences in the physical properties of

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202 metal constituents, the authors proposed two data reduction algorithms, one was based on the calibration-free approach and the other on calibrati on curves. The authors modified the CF-LIBS approach by considering that the plasma was a super-position of two nonor weakly interacting plumes described by two temperatures to account for inhomogeneity. Two normalization procedures were also used in the calibration method to minimize st atistical fluctuations in both background level and spectrum intensity. The au thors reported that there was only a partial agreement between the CF-LIBS and calibration results for the bronze coins due to possible inhomogeneity in the coin alloy, surface oxi dation and preferential evaporation. Burakov and Raikov [194] carried out a quantitativ e determination of different samples of bronze, brass and gold alloys, and glass samples using the calibration-free technique. A close agreement between CF-LIBS results and referen ce data was demonstrated for most of the constituents in the analyzed samples. The authors also reported that absolute errors in the determined concentration values were generally larger for the glass samples compared to the metal alloys which they attributed to the highe r transparency and melting temperatures of glass targets, as well as the lower efficiency of the lase r-to-sample interaction. They also investigated the effect of uncertainties in temperature de terminations on CF-LIBS quantitative results and found out that in order to achieve accuracy be tter than 1% for elemen tal concentration, the precision of temperature measurements must also be better than 1%. The main objective of this study is the further evaluation of CF-LIBS under various experimental working conditions using the spectr al acquisition method described in Chapter 4. The capabilities and limitations of laser-indu ced breakdown spectroscopy as a calibration-free approach are investigated by analyzing different samples of metallic alloys (Al, Ti, Cu, Zn, Ni) and soil samples.

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203 Experimental The experimental system and spectral data acquisition used in all measurements have already been described in detail in Chapter 4. The schematic of the set-up is illustrated in Fig. 41 for experiments under atmospheric conditions and in Fig. 4-3 for vacuum measurements. The samples used in this study were aluminum all oy standard disks (B8, D33, S4, SM10, V14 and Z8) from APEX Smelter Co. in South Africa, sta ndard reference materials of Zn alloy (SRM 627 and 629), Cu-Ni alloy (SRM 1276a), Ti alloy (S RM 654b), Ni alloy powder (SRM 882), Cu-Zn alloy (SRM 1107, 1108, 1110 to 1117) and soil (SRM 1646, 2704, 2710 and 2711) from NIST, Ti alloy powder (SRM 88395) from Alfa Aesar and soil standards (CAN SO-2 and SO-3) from Canadian Certified Reference Materials Project The elemental compositions are given in Appendix E. The alloys in powder form were mixed in a 1:4 ratio with Licowax C micropowder amide binder (Clariant). The mixing was accomplished by ball milling each sample for 20 minutes in a mixer (8000M; SPEX SamplePrep) to ensure that the samples are homogeneously mixed. All samples in powder form were placed in aluminum sample discs (Spec-Cap 3619; SPEX SamplePrep) and pressed into pe llets using a manual hydraulic steel pump (P-39, Enerpac) under a pressure of 5000 psi. The size of the resu lting pellet was 31 mm in diameter and 5 mm in thickness. The pellets that were prepared we re stored in a desiccator to prevent surface contamination and minimize moisture absorption. Spectra from 10 laser shots were summed up using the accumulation mode that is incorporated in the WinSpec32 software (Version 2.5.18.2; Princeton Instruments). A total of 67 spectral windows between 220 and 700 nm were recorded and each region was measured in 3 consecutive runs. Each set of recorded laserinduced breakdown spectra were merged together using an in-house program written in Q-Basic. Th e set of 3 merged spectra were subsequently

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204 averaged and the resulting spect rum was corrected for background and relative detector spectral efficiency using in-house programs written in MATLAB. Imaging of the laser-induced plasmas were also carried out prior to LIBS measurements to determine the size of the plasma in the axial direc tion (laser beam axis) since it is the full plasma height that dictates the number of vertical pixe ls to be included in the binning process. The plasma image was recorded by setting the diffracti on grating to zero order (mirror reflection) and opening the entrance slit of the spectrometer close to its maximum width (3 mm). Results and Discussion Temporally-Resolved Analys is of Aluminum Alloys The wide wavelength range spectra from 220 to 700 nm of two aluminum alloy samples, B8 and SM10, were recorded at diffe rent delay times starting from 0.5 s until 3.0 s at a gate width of 0.5 s. The experiments were carried out under a pressure of 100 mbar. A small section of the wide spectral range data for each de lay time are shown in Fig. 7-1a and 7-1b for Al alloy B8 and SM10, respectively, which contai ns singly-ionized lines of Mg and Al. As expected, the continuum radiati on and line intensities decrease as the plasma evolves. In addition, the number of neutral and singlyionized lines for every element identified in Al alloy B8 and Al alloy SM10 are plotted against delay time as well as the total number of neutral and ionic lines (Figs. 7-2a and 7-2b). It can be observed that the number of neutral lines (blue squares) increase at longer delays while the number of si ngly-ionized lines (red circles) generally decrease as the delay time is increased. This is, of course, due to electron-ion radiative recombination which occurs when an ion captures an electron and causes a radiative transition to a bound state, a so-called free-bound transition, as the plasma expa nds and evolves in time.

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205 The corresponding images of the laser-induced plasma obtained at different delay times were recorded for the two samples analyzed and are shown in Fig. 7-3. The plasma size is about 2.5 cm in diameter and the symmetry is approxim ately spherical at all c onditions considered. By vertically binning the pixels over the full height of the plasma, approximately 120 pixels, the values calculated for electron number density and temperature are regarded as spatially-averaged since spatial information is lost when applyi ng the CCD pixel binning clocking scheme. It can also be observed from Fig. 7-3 that the plasma moves away from the sample surface as the plasma expands and evolves with time. According to Wen et al. [95], this phenomenon is due to the vortex ring which is formed immediately afte r the internal shockwave reaches the sample surface which then causes the vapor plume to be propelled away from the target. The electron number density was determined using the Stark widt h of the hydrogen-alpha (H ) line at 656.272 nm. The equation used in th e calculation is given in Eq. 5-19. The temporal evolution of the H line and the calculated electron numb er densities for the alloys B8 and SM10 are shown in Figs. 7-4a and 7-4b, resp ectively. For Al alloy B8, the electron number density values ranged from 3.6 0.1 1017 cm-3 to 0.37 0.02 1017 cm-3 and for Al alloy SM10, the electron number densities are between 2.7 0.2 1017 cm-3 and 0.32 0.02 1017 cm-3. The minimum value for electr on number density in order to satisfy local thermodynamic equilibrium (LTE) conditions were also calculated using Eq. 5-3 a nd are plotted against the delay time (blue squares). It is apparent that at delays longer than 2.0 s, the minimum criterion is not reached in both samples. The calculated temp erature and electron number density values for alloys B8 and SM10 are also summarized in Tables 7-1 and 7-2, respectively. The precision of the calculated electron numb er densities using the H approach is 8% or better depending on the

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206 delay time, which is within the typical uncertainties (~10%) associated with the use of the H line for electron number density measurements [138]. The temperature of the plasma was determined using the Saha-Boltzmann plot approach described in Chapter 5 and the plots for selected elements in samples B8 and SM10 at different delay times are shown in Figs. 7-5a and 7-5b, resp ectively. The parallelity of the slopes obtained for different elements at the delay times considered in this study is a satisfactory demonstration of the existence of local thermodynamic equilib rium. The goodness of the agreement between temperature values obtained for the different sample constituents also verifies, to some extent, the gross effect of any shot-to-s hot variability of the laser pulse which in this case is not as severe regardless of the fact that multiple acquisitions have to be carried out in order to obtain spectral information from 220 to 700 nm for a singl e measurement. The temperature values (in eV) calculated from the slope of the Saha-Boltz mann plots for each constituent of the sample are also plotted against the delay time and are shown in Figs. 7-6a and 7-6b for alloys B8 and SM10, respectively. For all elements considered, the temperature decreases as the plasma expands and evolves in time. The temporal evolution of the averaged temperatures (in K) with the corresponding error bars are shown in Figs. 7-7a and 7-7b. The error bars were obtained by averaging the temperature values calculated from the atomic constituents of the target. The highest RSD calculated from the measurements is 12%. The precision obtained for the temperatures calculated at diffe rent delay times are summarized in Tables 7-1 and 7-2. The results of the calibration-free analysis of Al alloys B8 and SM10 at different delays are reported in Tables 7-3 and 7-4, respectively. The relative concentration values for each element identified in the two Al alloys are plotted agains t delay time and are illustrated in Figs. 7-8a and 7-8b. The certified concentration va lue in each case is depicted as a dashed line. In general, the

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207 results obtained from CF-LIBS agree well with the certified value for the major component in the sample only, in this case, Al of which the accuracy of the determination is in the range of 16% for sample B8 and 0.3-2% for sample SM10. For the other constituents present in the sample, the calculated relative errors at different delays, which are listed in Tables 7-5 and 7-6 and plotted in Figs. 7-9a and 7-9b, are within th e accuracy range for a semi-quantitative analysis only (30-200% error) as defined in Ref. [65]. The relatively large errors calculated can be attributed to the uncertainties associated with temperature determination as well as intensity fluctuations. This conclusion is based on the results of the numerical study carried out by Tognoni et al. [138] regarding the expected precision and accuracy in CF-LIBS, wherein under a simulation of broad temperature dispersion and large intensity fluctuations, the relative concentrations of the elements other than the most abundant element varied within 150-200%, similar to the results obtained in the CF-LIBS anal ysis of the two Al alloy samples carried out in this study. In the case of the most abundant el ement, even under the extreme conditions applied in their simulations, the concentration only varied within 1%, which agrees to some extent with the relative concentration values calculated for Al. In addition, for moderate intensity fluctuations and temperature di spersion simulations carried out in Ref. [138], the calculated concentration of minor elements varied within 20%. However, their simulations on the effect of a 10% variation in electron num ber density values resulted in about 1-2% uncertainty in the concentrations of the most abundant element and about 10% in the concentration of minor components. Therefore, based on the aforementione d discussion, it can be concluded that for the most abundant element present in the samples used in this study, quantitat ive analysis is possible within 5% accuracy, with relative er rors due to the contributions from electron number density and temperature determinations and intensity fluctu ations. On the other hand, the relatively large

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208 errors calculated for the other sample constituen ts can be attributed to moderate to extreme fluctuation in intensities and dispersion in temperatures for which the composition of most elements in the sample can be determined to within a factor of 2 to 3. Quantitative Analysis of Brass Calibration-free LIBS. For the CF-LIBS analysis of brass, 10 NIST standards were used and the measurements were carried out using a delay time of 2.0 s and a gate width of 0.5 s. The elemental composition is summarized in Table E-2 in Appendix E. All of the Cu-Zn alloys used in this study were consid ered as binary compounds since the concentra tions of the constituents other than Cu and Zn are well below 0.1%. A narrow region of the wide spectral range da ta obtained for each brass sample are shown in Fig. 7-10a. The spectra are arranged in orde r of decreasing Zn concentration (or increasing Cu concentration) starting from sample 1107 (black fi ll). The narrow spectral region shown in Fig. 7-10a contains six resonance lines of Cu and Zn a nd it is evident that the intensities of Zn I at 328.23 nm and 330.26 nm decrease w ith concentration. However, it can be observed that the intensities of the 4 Cu I lines do not increase with concentration due to the possible occurrence of self-absorption in the plasma. The correspondi ng images of the laserinduced plasma obtained from brass samples are depicted in Fig. 7-10b an d the images clearly indicate the spherically symmetrical shape of the plasmas formed wh ich were about 2.5 cm in diameter. The application of CF-LIBS algorithm to different lines of Cu and Zn identified in the brass standards resulted in a ve ry good agreement between calculated and certified values for both elements. The results are summarized in Tabl e 7-7 and are plotted in Figs. 7-11a and 7-11b. The corresponding relative erro rs calculated are also listed in Table 7-7 and are plotted in Fig. 711d. The highest relative error obtained is 1.25% for Cu and 12. 78% for Zn. The results in this

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209 case can be considered quantitative, particularly for the major element which is Cu due to the relatively low relative errors calculated. Howeve r, in 9 out of 10 brass standards analyzed, the concentration of Zn is always much higher than the nominal Zn concentration (Fig. 7-11b) which means that the vapor plume from the ablated bras s contains increased amounts of Zn. Baldwin [195] attributed the Zn enrichment in the abla ted mass to the lower vaporization temperature of Zn, which is 906C as compared to the 2595 C vaporization temperature of Cu. The goodness of the agreement between CF-LIB S and the certified values are quite unexpected due to the nature of the samples used Several works have shown that brass samples suffer significantly from fractionation and numerous studies have already been carried out to understand the mechanisms behind the fractional ab lation using a variety of laser and sample conditions [129, 195-199]. The main factors which influence fractionation in brass are the laser wavelength, pulse duration and irra diance. Mao et al. [196] indicated that at low irradiances (<0.3 GW cm-2) and long pulse durations (>30 ns), the mechanism involved is thermal vaporization and at higher irradiances (>1 GW cm-2) and shorter pulse durations (~3 ns), the mechanism is governed by both thermal and non-thermal processes and the Zn/Cu ratio approaches stoichiometry but the ablated mass always remains enriched in Zn. On the other hand, use of lasers with short pulse durations (35 ps) appears to shift the mechanism to a nonthermal nature and the vapor plume is more enrich ed with Cu [129]. Hence, the choice of the appropriate laser parameters is cr itical in obtaining accurate and stoichiometric ratios. In this case, the experimental parameters used seem suitabl e in the analysis of brass since stoichiometric ablation is apparent from the re sults obtained with CF-LIBS. The calculated plasma temperatures and elec tron number densities are summarized and plotted in Table 7-8 and Fig. 7-11c. The plasma temperatur e was calculated by constructing

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210 Saha-Boltzmann plots for Cu and Zn lines. There is no significant difference in the temperatures obtained for the different brass standards used an d the average temperature for all 10 samples is 13900 200 K. The electron number density was estimated using the Stark broadening of 510.554 nm Cu I line instead of the 656.272 nm H line since the latter has a spectral interference with the second or der wavelength of 328.233 nm Zn I line. There is also no significant difference in the elec tron number densities calculated which averages to about 1.4 0.1 1017 cm-3. In addition, the calculated electron number densities are all well above the minimum electron number density values requir ed for local thermodynamic equilibrium. CF-LIBS versus conventional LIBS. In order to extend the e xperimental evaluation of the CF-LIBS approach, the results for selected brass standards were compared to those obtained by using the conventional analyt ical calibration procedure. Three calibration curves were constructed using the lines listed in Table 7-9. Plots of integrated intensity against certified Zn concentration are shown in Fig. 7-12. Excellent linear calibration curves were obtained using the three Zn lines with correlation coefficients greate r than 0.99 in all cases (Table 7-10). For each set of calibration plots constructed, several bras s standards were chosen to serve as unknown samples for comparison with CF-LIBS and the spectra of these selected standards are shown with white fill background in Fig. 7-12. In Fig. 7-12a, a singly-ionized Zn line at 255.795 nm was used in the calibration and two neutral Zn li nes at 328. 233 nm and 330.258 nm were used to construct the plots in Fig. 7-12b and 7-12c, resp ectively. The calibratio n graphs exhibited a relatively wide dynamic range particularly the calibration plot constructed using the 255.795 nm Zn II line (Fig. 7-12a). Comparison of the Zn concentration values calculated via the CF-LIBS and calibration curve approach are tabulated in Table 7-11 and th e corresponding relative errors of the analysis

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211 are listed in Table 7-12. In general, the resu lts of the CF-LIBS and ca libration techniques agree well with certified values. In addition, the CF-L IBS technique resulted in lower relative errors (5-8%) compared to the calibration curve me thod (10-27%), except in the case of brass 1112 where the calibration plot using the 330.258 nm Zn I yield a relative erro r of ~2% and CF-LIBS yield a higher relative error of ~12%. The corresponding limit s of detection, cL, of the Zn content were also calculated using the expression [106]: m s cblank L3 (7-1) where sblank is the standard deviation of blank measurements and m is the slope of the calibration curve. The calculated limits of detection for each calibration plot and the resulting parameters of the linear regression are summarized in Table 7-10. The best detection limit obtained based the three calibration curv es constructed for Zn was 0.084%. Quantitative Analysis of Aluminum Alloys Calibration-free LIBS. The analysis of metallic samp les has very important industrial applications which include production process and quality assurance monitoring. In this study, six different aluminum alloy standards from South Africa were used. The elemental composition is summarized in Table E-1 in Appendix E. Anal ysis of Al alloys B8 and SM10 were carried out at three different ambient pressures: 1000, 100 and 0.1 mbar and analysis of Al alloys D33, S4, V14 and Z8 were carried out at two different pressures: 1000 and 0. 1 mbar. LIBS experiments at pressures of 1000 and 100 mbar were pe rformed using a de lay time of 2.0 s and a gate width of 0.5 s and experiments at a pressure of 0.1 mbar were performed using a delay time of 50 ns and gate width of 100 ns. The delay times and gate widths were selected by considering the significantly different evolution dyn amics of the plasma at different ambient pressures. In fact,

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212 under atmospheric conditions, the acquisition dela y time must be long enough to allow the decay of continuum emission due to bremsstrahlung radiation and free-bound electronic radiative recombination, which is very intense at higher pressures; then again, under vacuum conditions, the rapid evolution of the laserinduced plasma requires that the delay time is not too long in order that the emission signal coming from both ne utral and singly-ionized species still reaches the detector. The rapid expansion of the plasma as the pressure is decreased can be observed from the images of the laser-induced plasmas shown in Fig. 7-13. The plasma sizes at 1000 mbar and 0.1 mbar pressures are not exactly comparable due to the difference in the delay times and gate widths used in the measurements. However, it can be clearly observed that under similar gating conditions, the plasmas formed at 1000 mbar have a smaller diameter (~2.0 cm) than the plasma formed at 100 mbar (~2.5 cm) and that in both ca ses, the plasmas are approximately spherical in shape. Furthermore, it is evident that at early delays, the plasmas formed under vacuum conditions are not spherically symmetrical but acquires an ellipsoidal shape which agrees with the initial growth of the plasma emission in the direction of the laser beam. Aragon and Aguilera [172] reported a similar observati on regarding the shape of the laser-induced plasmas generated with an iron sample at different gas pressures. The line intensities also decrease as the pressure is reduced as can be observed in Fig. 7-14 where a narrow portion of the Al alloy spectra un der different ambient conditions are shown. This observation is contrary to the results repor ted in previous studies [171, 200, 201] where the intensities increase significantly when the pressu re is reduced to an optimum value, usually between 50 and 350 Torr depending on the experimental conditions, and then decreases when the pressure is further reduced. However, there were only 2-3 pressure conditions that were used in

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213 this particular study, hence the ap parent increase in intensity wa s not observed when the pressure approached low vacuum conditions. The observed behavior of emi ssion intensities at various air pressures, as shown and explained in previ ous studies [171, 200, 201], can be attributed primarily to the plasma shielding effect which is particularly crucial when using infrared lasers because the absorption of the laser energy is ca used by the inverse bremsstrahlung processes in the plasma whose absorption cro ss-section is proportional to 3 [171]. Under atmospheric conditions, the laser energy absorbed by the plasma is rapidly converted into kinetic energy and causes ionization which translates into high temper atures and high electron number densities in the plasma. This is confirmed by the electron nu mber density and temperature values calculated at 1000 mbar air pressure. In this study, the electron numb er densities at different pressures were determined using the H line at 656.272 nm and the results are plotted a nd tabulated in Fig. 7-15a and Table 7-13. The calculated values agree well with electron number densitie s reported in the literature under similar ambient conditions [171, 172]. There is an order of magnitude difference between the electron number densities calculated at 1000 mbar (1017 cm-3) and at 0.1 mbar (1016 cm-3). The temperatures were calculated using the Saha-Bol tzmann plot approach an d the results are shown in Fig. 7-15b and summarized in Table 7-14. The temperatures obtained under atmospheric conditions are about 12000 K which is ~1000 K hi gher than the temperatures obtained under low pressure conditions. Furthermore, under vac uum conditions, despite the increase in mass removal due to the reduction in plasma shieldi ng [202], lower emission is still generated by the plasma due to its lower temperature [171]. Ii da [200] also indicated that besides plasma shielding, the confinement of th e plasma under different ambient pressures plays a major role as well. Under atmospheric conditions, the plasma expansion is signifi cantly confined by the

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214 surrounding background gas and the resultant plas ma usually produces an intense background continuum instead of a strong analytical emission lines. On the other hand, at reduced pressures, the rapidly expanding plasma causes a decrease in emission intensity due to the rapid escape of emissive species from the temporal and spatial window of observation. The results of the CF-LIBS analys is of the Al alloys at diffe rent pressures are summarized in Figs. 7-16 and 7-17 and are tabulated in Tables 7-15 to 7-20. In general, it can be observed that the calculated concentrati on values for Al, which is the most predominant element in the sample, agree very well with certified values and therefore, resulted in very low relative errors (0.08-6%). However, for the remainder of the el ements present in the alloy samples, the results are semi-quantitative only due to the relatively hi gh relative errors obtained in the calculations for which the sample components can be determined within a factor of 2 except for Fe which can be determined within a factor of 3. CF-LIBS versus conventional LIBS. Similar to the analysis of brass, calibration curves were constructed for a few elements in the Al alloy samples for comparison with CF-LIBS results. Only the measurements under atmospheri c conditions (1000 mbar) were used in this part of the study. The lines used to generate the calibration graphs are: 229.436 nm Cu II, 327.396 nm Cu I and 288.158 nm Si I. The pertinent spec troscopic parameters are listed in Table 7-21. Linear calibration curves with correlation coe fficients greater than 0.99 were obtained using some of the Al alloy standards while the rest serve as unknown samples for comparison with CF-LIBS. The resulting calibrati on plots and the spectra of the lin es used are shown in Fig, 718. The Cu and Si content in the unknown samp les were calculated usin g the linear regression parameters tabulated in Table 7-22 and the resu lts are summarized in Tables 7-23 and 7-25 for Cu and Si concentration values, respectively. The limits of detection were also calculated using

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215 Eq. 7-1 and the results are shown in Fig. 7-18. The lowest detection limit obtained was 0.0084% using the 229.436 nm Cu II line. Sabsabi and Ci elo [24] reported detection limits of 10 ppm for Cu and 14 ppm for Si using the lines at 327.393 nm Cu I and 251.611 nm Si I, respectively. Although, the detection limits cal culated in this study are about two orders of magnitude higher than those reported in the liter ature, a wider dynamic range was obtained for Cu and Si despite the limited number of standards used in th e construction of the calibration curves. The calibration curve reported in Ref. [24] for Cu start to deviate from linearity at about 1%. The accuracy of the two techniques used in this study was evaluated by determining the relative errors of the me asurement. Although, in general, the CF-LIBS results were closer to the certified values than those calculated using the calibration curve approach, the relative errors were still in the semi-quantitative category ( 30%) specifically the errors obtained for Cu which are better than 50% (Table 7-24). On the other hand, the accuracy of the calculated Si content using the CF-LIBS method is better than that for Cu since the errors are in the range of 2-20% (Table 7-25). Quantitative Analysis of Soils Application of laser-induced breakdown spectroscopy to quantitative analysis of soils has been demonstrated to have a significant potential for remote and in situ terrestrial and extraterrestrial applications [ 28-30, 119, 203-207]. In this part of the study, the calibration-free LIBS approach was applied to six different type s of soil standards from NIST [208] and Natural Resources Canada [209]. The elemental composition of the standards used is listed in Table E-3 in Appendix E. The soil samples were made into pressed pellets as previously described in the experimental section. LIBS measurements were carried out using a delay time of 1.2 s and a gate width of 0.1 s. A small portion of the soil spectra ar e shown in Fig. 7-19a and the images

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216 of the laser-induced plasmas obtained from the soil samples are illustrated in Fig. 7-19b. The plasmas formed were approximately 2.0 cm diameter in size. Due to the complexity of the soil matrix, only major and minor elements have been identified and used in the analysis. The CF-LIBS results for each soil standard analyzed are shown in Fig. 7-20 and tabulated in Tables 7-26 to 7-28. The result s are in relative terms and are dependent on the number of species included in the CF-LIBS analysis. Approximately 50-60% of the soil composition remained undetermined in this case which includes organic compounds and other minor constituents, e.g. barium, phos phorus, potassium, sodium, sulfur, etc. From the CF-LIBS results, the highest accuracy ( 2%) was obtained for Si which is the most abundant element in the soil standards (Fig 7-21a). However, a 13-14% relative error was obtained for the same element in the Canadian soil standards. The s light difference obtained between the two soil types may be attributed to factors such as provenance, sample preparation, texture and particle size. More over, several works have alrea dy shown that soil samples are strongly affected by matrix effects and different approaches have been used in order to correct or overcome these effects [26, 160, 210-212]. Chemom etric methods such as principal components analysis (PCA) [160] and multivaria te analysis [212] are the most recent techniques applied to soil analysis. For the remainder of the elements determined with CF-LIBS, the relative errors were randomly distributed with in the range of 20-120% which makes the analysis of soil matrices semi-quantitative. Corsi et al. [213] recently applied double-pulse LIBS in the analysis of soils and sediment and found enhancements on the LIBS signal of the order of 5-10 times depending on the upper energy level of the transiti on which may be particularly advantageous to standard-free techniques such as CF-LIBS.

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217 The electron number density of the laser-induced plasma was calculated using the Stark width of the H line and the temperature was determin ed by generating Saha-Boltzmann plots using lines from different elements identified from the soil spectrum. The plasmas formed are in local thermodynamic equilibrium since the calculat ed electron number densities are all above the minimum value required for LTE (Fig. 7-21b and Table 7-29). The measured plasma temperatures for different samples were between 11000 and 12500 K, while the estimated electron number density was on the order of 1017 cm-3. Quantitative Analysis of Different Types of Alloys The calibration-free LIBS approach was also app lied to Ti alloys, Zn alloys, Ni alloy and Cu-Ni alloy. The elemental composition of the sa mples used is listed in Table E-4 in Appendix E. Some of the samples were in powder form and were made into pressed pellets before analysis as described previously in the experimental sect ion. The LIBS measurements of metal alloys were carried out in atmospheric c onditions using a delay time of 2.0 s and a gate width of 0.5 s while the pelletized samples were measured using a delay time of 1.2 s and a gate width of 0.1 s. A section of the wide spectral range data for each alloy sample analyzed are shown in Fig. 7-22a. The images of the laser-induced plas mas obtained from different alloy samples show a distinct difference in the plasma symmetry (F ig. 7-22b). The plasmas formed on the Ni alloy pellet and Ti alloy samples in both metal and pelle t forms were flattened in the radial direction while the plasmas formed on the Zn and Cu-Ni all oys were elongated in the direction of the laser beam. The difference can be attributed generally to the samples used and not to the form of samples, i.e., pellet or metal form, since the plasmas formed on two different forms of Ti alloys acquired a similar shape.

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218 The results of the CF-LIBS an alysis of the six alloys are shown Fig. 7-23 and the corresponding accuracy of the measurement are summ arized in Fig. 7-24a-d. The Ti content of the ternary Ti alloy sample in both pellet and metal forms agree well with certified values and the relative errors obtained are below 7% (Table 7-30). The Al and V content, on the other hand, resulted in relative errors between 14-120%. The Zn concentration of the NIST Zn alloys calculated with CF-LIBS gave the highest accuracy with relative percentage errors which are below 1% (Table 7-31). Also, for the remainder of the elements present in the Zn alloy sample (Al, Cu and Fe) semi-quantitative results were obtained with errors in the range of 2-60%. Excellent results were obtained for both Ni and Cu in the Ni alloy pellet and the Cu alloy metal with errors below 4% (Table 7-32). On the other hand, 30-120% errors were obtained for the other elements present in the alloy standards. The electron number density of the laser-induced plasma wa s determined using the Stark widths of different lines: the H line for the Ti and Ni alloy, th e Ni I line at 361.939 nm for the Cu-Ni alloy and the Al I line at 394.401 nm for the Zn alloys. The Ni I line was used to determine the electron number density of the Cu-Ni alloy plasma instead of the H line since the latter was very weak and cannot be fitted with re latively high accuracy. Conversely, the Al I line was used for electron number density determinat ion since one of the s econd order wavelengths of Zn interferes with the H line. The electron number density values calculated for the six alloys analyzed are within the range of 2.2 1017 to 3.7 1017 cm-3 (Table 7-33). Furthermore, the plasma temperature was determined using th e Saha-Boltzmann plot approach and the results are plotted in Fig. 7-24e and ta bulated in Table 7-33. The measured plasma temperatures for different alloy samples were of the order of 12500 to 14600 K.

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219 Conclusion In this study, calibration-free LIBS was applie d to the analysis of different samples of varying degrees of complexities. Temporally-res olved measurements of Al alloy samples have demonstrated the importance of optimization of gating parameters to ascertain that the minimum value of electron number density for local thermodynamic equilibrium condition is achieved. As far as the experiments carried out under different ambient pre ssures, no significant effect has been observed on the calculated accuracy of th e relative elemental composition of the alloy samples analyzed. Also, in the analysis of Al alloy and brass samples, the results obtained with CF-LIBS are generally in closer agreement with nominal values compared to those obtained with conventional analytical calibration methods. In general, quantitative results with accuracy better than 5% were obtained for the most abundant constituent in the sample. However, for the remainder of the components of the sample, the results are semi-quantitative, with relative errors between 30 and 200% in most of the samples that were analyzed. The relatively la rge errors obtained particularly for minor and trace elements can be attributed to uncertainties associated mainly with the determination of temperature, as well as uncertainties in the fittin g of spectral lines and th e transition probabilities used in the calculations. There are other minor contributing factors that affect the accuracy of the final elemental concentration values calcula ted with CF-LIBS and numerical simulations of the effect of each parameter on CF-LIBS results have already been undertaken and described succinctly in Ref. [138]. Ther e is no correction for self-absorp tion considered in this study but resonance lines of major elements were not used in the CF-LIBS analysis, whenever possible, in order to avoid underestimation of the element composition. Analysis of samples in the form of presse d pellets also did no t show any significant influence on the accuracy of the results obtaine d, positive or otherwise. However, CF-LIBS

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220 analysis of soil matrices proved to be more co mplicated than alloy matrices and only about 4050% of the total sample composition was determined which excludes organic compounds and other minor constituents such as barium, phosphorus, potassium, sodium, sulfur, etc. The spectral acquisition method developed in th is research proved effective for CF-LIBS analysis due to the large spect ral window it offered along with the moderately high-resolution provided by the detection system. Hundreds of emission lines were resolved within the spectral range from 220 to 700 nm which were certai nly necessary in improving the accuracy and precision of the Boltzmann and Saha-Boltzmann plot s generated, which are the framework of the CF-LIBS protocol.

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221 Figure 7-1. Section of the wide spectral range data of aluminum alloy sample (a) B8 and (b) SM10 at different delay times.

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222 0.51.01.52.02.53.0 3 6 9 12 15 18 21 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy B8Al0.51.01.52.02.53.0 0 3 6 9 12 15 18 21 24 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy B8Cr0.51.01.52.02.53.0 0 3 6 9 12 15 18 21 24 27 30 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy B8Cu0.51.01.52.02.53.0 10 15 20 25 30 35 40 45 50 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy B8Fe0.51.01.52.02.53.0 0 1 2 3 4 5 6 7 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy B8Mg0.51.01.52.02.53.0 6 8 10 12 14 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy B8Mn0.51.01.52.02.53.0 0 2 4 6 8 10 12 14 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy B8Ni0.51.01.52.02.53.0 3 4 5 6 7 8 9 10 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy B8Si0.51.01.52.02.53.0 0 10 20 30 40 50 60 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy B8Ti0.51.01.52.02.53.0 60 70 80 90 100 110 120 130 140 150 160 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy B8Totala a0.51.01.52.02.53.0 3 6 9 12 15 18 21 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy B8Al0.51.01.52.02.53.0 0 3 6 9 12 15 18 21 24 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy B8Cr0.51.01.52.02.53.0 0 3 6 9 12 15 18 21 24 27 30 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy B8Cu0.51.01.52.02.53.0 10 15 20 25 30 35 40 45 50 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy B8Fe0.51.01.52.02.53.0 0 1 2 3 4 5 6 7 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy B8Mg0.51.01.52.02.53.0 6 8 10 12 14 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy B8Mn0.51.01.52.02.53.0 0 2 4 6 8 10 12 14 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy B8Ni0.51.01.52.02.53.0 3 4 5 6 7 8 9 10 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy B8Si0.51.01.52.02.53.0 0 10 20 30 40 50 60 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy B8Ti0.51.01.52.02.53.0 60 70 80 90 100 110 120 130 140 150 160 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy B8Total0.51.01.52.02.53.0 3 6 9 12 15 18 21 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy B8Al0.51.01.52.02.53.0 0 3 6 9 12 15 18 21 24 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy B8Cr0.51.01.52.02.53.0 0 3 6 9 12 15 18 21 24 27 30 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy B8Cu0.51.01.52.02.53.0 10 15 20 25 30 35 40 45 50 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy B8Fe0.51.01.52.02.53.0 0 1 2 3 4 5 6 7 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy B8Mg0.51.01.52.02.53.0 6 8 10 12 14 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy B8Mn0.51.01.52.02.53.0 0 2 4 6 8 10 12 14 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy B8Ni0.51.01.52.02.53.0 3 4 5 6 7 8 9 10 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy B8Si0.51.01.52.02.53.0 0 10 20 30 40 50 60 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy B8Ti0.51.01.52.02.53.0 3 6 9 12 15 18 21 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy B8Al0.51.01.52.02.53.0 0 3 6 9 12 15 18 21 24 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy B8Cr0.51.01.52.02.53.0 0 3 6 9 12 15 18 21 24 27 30 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy B8Cu0.51.01.52.02.53.0 10 15 20 25 30 35 40 45 50 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy B8Fe0.51.01.52.02.53.0 0 1 2 3 4 5 6 7 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy B8Mg0.51.01.52.02.53.0 6 8 10 12 14 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy B8Mn0.51.01.52.02.53.0 0 2 4 6 8 10 12 14 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy B8Ni0.51.01.52.02.53.0 3 4 5 6 7 8 9 10 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy B8Si0.51.01.52.02.53.0 0 10 20 30 40 50 60 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy B8Ti0.51.01.52.02.53.0 60 70 80 90 100 110 120 130 140 150 160 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy B8Totala a Figure 7-2. Temporal evolution of the number of identified neutral lin es (blue squares) and singly-ionized lines (red circles) for the diffe rent elements present in (a) Al alloy B8 and (b) Al alloy SM10. The number of neut ral lines increases with delay time while the number of singly-ionized lines decrease s with delay time due to electron-ion radiative recombination. (Left to right, t op to bottom: (a) Al, Cr, Cu, Fe, Mg, Mn, Ni, Si, Ti and total and (b) Al, Cr, Cu, Fe Mg, Mn, Ni, Si, Ti, Zn and total)

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223 0.51.01.52.02.53.0 0 2 4 6 8 10 12 14 16 18 20 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy SM10Al0.51.01.52.02.53.0 0 5 10 15 20 25 30 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy SM10Cr0.51.01.52.02.53.0 6 8 10 12 14 16 18 20 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy SM10Cu0.51.01.52.02.53.0 40 50 60 70 80 90 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy SM10Fe0.51.01.52.02.53.0 4 6 8 10 12 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy SM10Mg0.51.01.52.02.53.0 6 8 10 12 14 16 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy SM10Mn0.51.01.52.02.53.0 0 2 4 6 8 10 12 14 16 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy SM10Ni0.51.01.52.02.53.0 0 2 4 6 8 10 12 14 16 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy SM10Si0.51.01.52.02.53.0 0 10 20 30 40 50 60 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy SM10Ti0.51.01.52.02.53.0 0 2 4 6 8 10 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy SM10Zn0.51.01.52.02.53.0 100 120 140 160 180 200 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy SM10Totalb b0.51.01.52.02.53.0 0 2 4 6 8 10 12 14 16 18 20 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy SM10Al0.51.01.52.02.53.0 0 5 10 15 20 25 30 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy SM10Cr0.51.01.52.02.53.0 6 8 10 12 14 16 18 20 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy SM10Cu0.51.01.52.02.53.0 40 50 60 70 80 90 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy SM10Fe0.51.01.52.02.53.0 4 6 8 10 12 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy SM10Mg0.51.01.52.02.53.0 6 8 10 12 14 16 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy SM10Mn0.51.01.52.02.53.0 0 2 4 6 8 10 12 14 16 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy SM10Ni0.51.01.52.02.53.0 0 2 4 6 8 10 12 14 16 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy SM10Si0.51.01.52.02.53.0 0 10 20 30 40 50 60 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy SM10Ti0.51.01.52.02.53.0 0 2 4 6 8 10 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy SM10Zn0.51.01.52.02.53.0 100 120 140 160 180 200 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy SM10Total0.51.01.52.02.53.0 0 2 4 6 8 10 12 14 16 18 20 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy SM10Al0.51.01.52.02.53.0 0 5 10 15 20 25 30 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy SM10Cr0.51.01.52.02.53.0 6 8 10 12 14 16 18 20 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy SM10Cu0.51.01.52.02.53.0 40 50 60 70 80 90 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy SM10Fe0.51.01.52.02.53.0 4 6 8 10 12 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy SM10Mg0.51.01.52.02.53.0 6 8 10 12 14 16 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy SM10Mn0.51.01.52.02.53.0 0 2 4 6 8 10 12 14 16 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy SM10Ni0.51.01.52.02.53.0 0 2 4 6 8 10 12 14 16 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy SM10Si0.51.01.52.02.53.0 0 10 20 30 40 50 60 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy SM10Ti0.51.01.52.02.53.0 0 2 4 6 8 10 12 14 16 18 20 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy SM10Al0.51.01.52.02.53.0 0 5 10 15 20 25 30 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy SM10Cr0.51.01.52.02.53.0 6 8 10 12 14 16 18 20 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy SM10Cu0.51.01.52.02.53.0 40 50 60 70 80 90 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy SM10Fe0.51.01.52.02.53.0 4 6 8 10 12 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy SM10Mg0.51.01.52.02.53.0 6 8 10 12 14 16 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy SM10Mn0.51.01.52.02.53.0 0 2 4 6 8 10 12 14 16 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy SM10Ni0.51.01.52.02.53.0 0 2 4 6 8 10 12 14 16 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy SM10Si0.51.01.52.02.53.0 0 10 20 30 40 50 60 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy SM10Ti0.51.01.52.02.53.0 0 2 4 6 8 10 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy SM10Zn0.51.01.52.02.53.0 100 120 140 160 180 200 Neutrals IonsNumber of Identified LinesDelay Time (s) Al alloy SM10Totalb b Figure 7-2. Continued.

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224 Figure 7-3. Temporal evolution of laser-i nduced plasmas obtained from (a ) Al alloy B8 and (b) Al a lloy SM10. The plasma is propelled away from the target surface indicated by the dash ed yellow line. This is due to the vortex ring formed immediately after the internal shockwave reaches the sample surface which then causes the vapor plume to be propelled away from the target.

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225 652654656658660662 0 5 10 15 20 25 0500 1000 1500 2000 2500 3000 Wavelength (nm)Intensity (a.u.)D e l a y T i m e ( n s )0.51.01.52.02.53.03.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 2.733 1.250 0.990 0.560 0.473 0.320Al alloy SM10 Electron density calculated using H Minimum electron density for LTEElectron Number Density (x 1017 cm-3)Delay Time (s) 652654656658660662 0 5 10 15 20 25 30 0500 1000 1500 2000 3000 Wavelength (nm)Intensity (a.u.)D e l a y T i m e ( n s )0.51.01.52.02.53.03.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 3.573 1.647 1.027 0.667 0.367 Electron density calculated using H Minimum electron density for LTEElectron Number Density (x 1017 cm-3)Delay Time (s)Al alloy B8a a b b 652654656658660662 0 5 10 15 20 25 0500 1000 1500 2000 2500 3000 Wavelength (nm)Intensity (a.u.)D e l a y T i m e ( n s )0.51.01.52.02.53.03.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 2.733 1.250 0.990 0.560 0.473 0.320Al alloy SM10 Electron density calculated using H Minimum electron density for LTEElectron Number Density (x 1017 cm-3)Delay Time (s) 652654656658660662 0 5 10 15 20 25 30 0500 1000 1500 2000 3000 Wavelength (nm)Intensity (a.u.)D e l a y T i m e ( n s )0.51.01.52.02.53.03.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 3.573 1.647 1.027 0.667 0.367 Electron density calculated using H Minimum electron density for LTEElectron Number Density (x 1017 cm-3)Delay Time (s)Al alloy B8a a b b Figure 7-4. Temporal evolution of the elec tron number density calculated using the H line at 656.272 nm (shown on the left) for (a) Al all oy B8 and (b) Al alloy SM10. The blue squares indicate the minimum electron number density for the plasma to be in LTE at different delay times.

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226 0 510152025 -10 -5 0 5 10 Al T = 1.22 eV Cu T = 1.30 eV Fe T = 1.23 eV Mg T = 1.24 eV Ni T = 1.29 eV Si T = 1.19 eVln (I/gkAki)*Ek+(eV) Delay = 0.5 s0 510152025 -15 -10 -5 0 5 10 Al T = 1.13 eV Fe T = 1.06 eV Mg T = 1.11 eV Mn T = 1.04 eV Ni T = 1.09 eV Si T = 1.04 eV Ti T = 1.00 eVln (I/gkAki)*Ek+(eV) Delay = 1.0 s0 510152025 -15 -10 -5 0 5 10 Al T = 1.09 eV Cr T = 0.93 eV Cu T = 1.05 eV Fe T = 0.97 eV Mg T = 1.04 eV Mn T = 0.95 eV Ni T = 0.98 eV Si T = 0.98 eV Ti T = 0.93 eVln (I/gkAki)*Ek+(eV) Delay = 1.5 s0 510152025 -15 -10 -5 0 5 10 Al T = 0.95 eV Cr T = 0.87 eV Cu T = 0.97 eV Fe T = 0.91 eV Mg T = 1.01 eV Mn T = 0.90 eV Ni T = 0.92 eV Si T = 0.92 eV Ti T = 0.88 eVln (I/gkAki)*Ek+(eV) Delay = 2.0 s0 5 10 15 20 25 -15 -10 -5 0 5 10 Delay = 3.0 s Al T = 0.89 eV Cr T = 0.79 eV Cu T = 0.93 eV Fe T = 0.81 eV Mg T = 0.88 eV Mn T = 0.82 eV Ni T = 0.90 eV Si T = 0.87 eV Ti T = 0.78 eVln(I/gkAki)*Ek+ (eV)a a0 510152025 -10 -5 0 5 10 Al T = 1.22 eV Cu T = 1.30 eV Fe T = 1.23 eV Mg T = 1.24 eV Ni T = 1.29 eV Si T = 1.19 eVln (I/gkAki)*Ek+(eV) Delay = 0.5 s0 510152025 -15 -10 -5 0 5 10 Al T = 1.13 eV Fe T = 1.06 eV Mg T = 1.11 eV Mn T = 1.04 eV Ni T = 1.09 eV Si T = 1.04 eV Ti T = 1.00 eVln (I/gkAki)*Ek+(eV) Delay = 1.0 s0 510152025 -15 -10 -5 0 5 10 Al T = 1.09 eV Cr T = 0.93 eV Cu T = 1.05 eV Fe T = 0.97 eV Mg T = 1.04 eV Mn T = 0.95 eV Ni T = 0.98 eV Si T = 0.98 eV Ti T = 0.93 eVln (I/gkAki)*Ek+(eV) Delay = 1.5 s0 510152025 -15 -10 -5 0 5 10 Al T = 0.95 eV Cr T = 0.87 eV Cu T = 0.97 eV Fe T = 0.91 eV Mg T = 1.01 eV Mn T = 0.90 eV Ni T = 0.92 eV Si T = 0.92 eV Ti T = 0.88 eVln (I/gkAki)*Ek+(eV) Delay = 2.0 s0 5 10 15 20 25 -15 -10 -5 0 5 10 Delay = 3.0 s Al T = 0.89 eV Cr T = 0.79 eV Cu T = 0.93 eV Fe T = 0.81 eV Mg T = 0.88 eV Mn T = 0.82 eV Ni T = 0.90 eV Si T = 0.87 eV Ti T = 0.78 eVln(I/gkAki)*Ek+ (eV)0 510152025 -10 -5 0 5 10 Al T = 1.22 eV Cu T = 1.30 eV Fe T = 1.23 eV Mg T = 1.24 eV Ni T = 1.29 eV Si T = 1.19 eVln (I/gkAki)*Ek+(eV) Delay = 0.5 s0 510152025 -15 -10 -5 0 5 10 Al T = 1.13 eV Fe T = 1.06 eV Mg T = 1.11 eV Mn T = 1.04 eV Ni T = 1.09 eV Si T = 1.04 eV Ti T = 1.00 eVln (I/gkAki)*Ek+(eV) Delay = 1.0 s0 510152025 -15 -10 -5 0 5 10 Al T = 1.09 eV Cr T = 0.93 eV Cu T = 1.05 eV Fe T = 0.97 eV Mg T = 1.04 eV Mn T = 0.95 eV Ni T = 0.98 eV Si T = 0.98 eV Ti T = 0.93 eVln (I/gkAki)*Ek+(eV) Delay = 1.5 s0 510152025 -15 -10 -5 0 5 10 Al T = 0.95 eV Cr T = 0.87 eV Cu T = 0.97 eV Fe T = 0.91 eV Mg T = 1.01 eV Mn T = 0.90 eV Ni T = 0.92 eV Si T = 0.92 eV Ti T = 0.88 eVln (I/gkAki)*Ek+(eV) Delay = 2.0 s0 5 10 15 20 25 -15 -10 -5 0 5 10 Delay = 3.0 s Al T = 0.89 eV Cr T = 0.79 eV Cu T = 0.93 eV Fe T = 0.81 eV Mg T = 0.88 eV Mn T = 0.82 eV Ni T = 0.90 eV Si T = 0.87 eV Ti T = 0.78 eVln(I/gkAki)*Ek+ (eV)a a Figure 7-5. Saha-Boltzmann plots of selected lines at different delay times. The temperature values obtained are given in eV where 1 eV is equivalent to 11605 K. (Left to right, top to bottom: (a) 0.5, 1.0, 1.5, 2.0 and 3.0 s and (b) 0.5, 1.0, 1.5, 2.0, 2.5 and 3.0 s).

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227 0 510152025 -15 -10 -5 0 5 10 Al T = 1.25 eV Cr T = 1.03 eV Cu T = 1.14 eV Fe T = 1.08 eV Mg T = 1.21 eV Mn T = 1.10 eV Ni T = 1.13 eV Si T = 1.19 eV Zn T = 1.19 eVln (I/gkAki)*Ek+(eV) Delay = 0.5 s0 510152025 -15 -10 -5 0 5 10 Al T = 1.13 eV Cr T = 0.92 eV Cu T =1.18 eV Fe T = 0.98 eV Mg T = 1.07 eV Mn T = 0.92 eV Si T = 1.07 eV Zn T = 1.13 eVln (I/gkAki)*Ek+(eV) Delay = 1.0 s051015202530 -15 -10 -5 0 5 10 Al T = 1.09 eV Cr T = 0.87 eV Fe T = 0.96 eV Mg T = 1.00 eV Mn T = 0.88 eV Si T = 1.05 eV Ti T = 0.80 eV Zn T = 1.08 eVln (I/gkAki)*Ek+(eV) Delay = 1.5 s051015202530 -15 -10 -5 0 5 10 Al T = 0.91 eV Cr T = 0.87 eV Cu T =0.99 eV Fe T = 0.90 eV Mg T = 0.94 eV Mn T = 0.87 eV Ni T = 0.95 eV Si T = 0.96 eV Ti T = 0.81 eVln (I/gkAki)*Ek+(eV) Delay = 2.0 s051015202530 -15 -10 -5 0 5 10 Al T = 0.95 eV Cr T = 0.81 eV Fe T = 0.84 eV Mg T = 0.91 eV Mn T = 0.87 eV Si T = 0.92 eV Ti T = 0.79 eVln (I/gkAki)*Ek+(eV) Delay = 2.5 s051015202530 -15 -10 -5 0 5 10 Al T = 0.87 eV Cr T = 0.78 eV Cu T = 0.89 eV Fe T = 0.80 eV Mg T = 0.86 eV Mn T = 0.78 eV Si T = 0.88 eV Ti T = 0.81 eV Zn T = 0.87 eVln (I/gkAki)*Ek+(eV) Delay = 3.0 sb b0 510152025 -15 -10 -5 0 5 10 Al T = 1.25 eV Cr T = 1.03 eV Cu T = 1.14 eV Fe T = 1.08 eV Mg T = 1.21 eV Mn T = 1.10 eV Ni T = 1.13 eV Si T = 1.19 eV Zn T = 1.19 eVln (I/gkAki)*Ek+(eV) Delay = 0.5 s0 510152025 -15 -10 -5 0 5 10 Al T = 1.13 eV Cr T = 0.92 eV Cu T =1.18 eV Fe T = 0.98 eV Mg T = 1.07 eV Mn T = 0.92 eV Si T = 1.07 eV Zn T = 1.13 eVln (I/gkAki)*Ek+(eV) Delay = 1.0 s051015202530 -15 -10 -5 0 5 10 Al T = 1.09 eV Cr T = 0.87 eV Fe T = 0.96 eV Mg T = 1.00 eV Mn T = 0.88 eV Si T = 1.05 eV Ti T = 0.80 eV Zn T = 1.08 eVln (I/gkAki)*Ek+(eV) Delay = 1.5 s051015202530 -15 -10 -5 0 5 10 Al T = 0.91 eV Cr T = 0.87 eV Cu T =0.99 eV Fe T = 0.90 eV Mg T = 0.94 eV Mn T = 0.87 eV Ni T = 0.95 eV Si T = 0.96 eV Ti T = 0.81 eVln (I/gkAki)*Ek+(eV) Delay = 2.0 s051015202530 -15 -10 -5 0 5 10 Al T = 0.95 eV Cr T = 0.81 eV Fe T = 0.84 eV Mg T = 0.91 eV Mn T = 0.87 eV Si T = 0.92 eV Ti T = 0.79 eVln (I/gkAki)*Ek+(eV) Delay = 2.5 s051015202530 -15 -10 -5 0 5 10 Al T = 0.87 eV Cr T = 0.78 eV Cu T = 0.89 eV Fe T = 0.80 eV Mg T = 0.86 eV Mn T = 0.78 eV Si T = 0.88 eV Ti T = 0.81 eV Zn T = 0.87 eVln (I/gkAki)*Ek+(eV) Delay = 3.0 s0 510152025 -15 -10 -5 0 5 10 Al T = 1.25 eV Cr T = 1.03 eV Cu T = 1.14 eV Fe T = 1.08 eV Mg T = 1.21 eV Mn T = 1.10 eV Ni T = 1.13 eV Si T = 1.19 eV Zn T = 1.19 eVln (I/gkAki)*Ek+(eV) Delay = 0.5 s0 510152025 -15 -10 -5 0 5 10 Al T = 1.13 eV Cr T = 0.92 eV Cu T =1.18 eV Fe T = 0.98 eV Mg T = 1.07 eV Mn T = 0.92 eV Si T = 1.07 eV Zn T = 1.13 eVln (I/gkAki)*Ek+(eV) Delay = 1.0 s051015202530 -15 -10 -5 0 5 10 Al T = 1.09 eV Cr T = 0.87 eV Fe T = 0.96 eV Mg T = 1.00 eV Mn T = 0.88 eV Si T = 1.05 eV Ti T = 0.80 eV Zn T = 1.08 eVln (I/gkAki)*Ek+(eV) Delay = 1.5 s051015202530 -15 -10 -5 0 5 10 Al T = 0.91 eV Cr T = 0.87 eV Cu T =0.99 eV Fe T = 0.90 eV Mg T = 0.94 eV Mn T = 0.87 eV Ni T = 0.95 eV Si T = 0.96 eV Ti T = 0.81 eVln (I/gkAki)*Ek+(eV) Delay = 2.0 s051015202530 -15 -10 -5 0 5 10 Al T = 0.95 eV Cr T = 0.81 eV Fe T = 0.84 eV Mg T = 0.91 eV Mn T = 0.87 eV Si T = 0.92 eV Ti T = 0.79 eVln (I/gkAki)*Ek+(eV) Delay = 2.5 s051015202530 -15 -10 -5 0 5 10 Al T = 0.87 eV Cr T = 0.78 eV Cu T = 0.89 eV Fe T = 0.80 eV Mg T = 0.86 eV Mn T = 0.78 eV Si T = 0.88 eV Ti T = 0.81 eV Zn T = 0.87 eVln (I/gkAki)*Ek+(eV) Delay = 3.0 sb b Figure 7-5. Continued.

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228 0123 0.8 1.0 1.2 1.4 Cr0123 0.8 1.0 1.2 1.4 Cu0123 0.8 1.0 1.2 1.4 FeTemperature (eV)0123 0.8 1.0 1.2 1.4 Mg0123 0.8 1.0 1.2 1.4 Mn0123 0.8 1.0 1.2 1.4 NiTemperature (eV)Delay Time (s)0123 0.8 1.0 1.2 1.4 Si Delay Time (s)0123 0.8 1.0 1.2 1.4 Ti Delay Time (s)0123 0.8 1.0 1.2 1.4 AlTemperature (eV) 0123 0.8 1.0 1.2 1.4 Cr0123 0.8 1.0 1.2 1.4 Cu0123 0.8 1.0 1.2 1.4 FeTemperature (eV)0123 0.8 1.0 1.2 1.4 Mg0123 0.8 1.0 1.2 1.4 Mn0123 0.8 1.0 1.2 1.4 NiTemperature (eV)Delay Time (s)0123 0.8 1.0 1.2 1.4 Si Delay Time (s)0123 0.8 1.0 1.2 1.4 Ti Delay Time (s)0123 0.8 1.0 1.2 1.4 AlTemperature (eV)a a b b 0123 0.8 1.0 1.2 1.4 Cr0123 0.8 1.0 1.2 1.4 Cu0123 0.8 1.0 1.2 1.4 FeTemperature (eV)0123 0.8 1.0 1.2 1.4 Mg0123 0.8 1.0 1.2 1.4 Mn0123 0.8 1.0 1.2 1.4 NiTemperature (eV)Delay Time (s)0123 0.8 1.0 1.2 1.4 Si Delay Time (s)0123 0.8 1.0 1.2 1.4 Ti Delay Time (s)0123 0.8 1.0 1.2 1.4 AlTemperature (eV) 0123 0.8 1.0 1.2 1.4 Cr0123 0.8 1.0 1.2 1.4 Cu0123 0.8 1.0 1.2 1.4 FeTemperature (eV)0123 0.8 1.0 1.2 1.4 Mg0123 0.8 1.0 1.2 1.4 Mn0123 0.8 1.0 1.2 1.4 NiTemperature (eV)Delay Time (s)0123 0.8 1.0 1.2 1.4 Si Delay Time (s)0123 0.8 1.0 1.2 1.4 Ti Delay Time (s)0123 0.8 1.0 1.2 1.4 AlTemperature (eV)a a b b Figure 7-6. Temporal evolution of temperature calculated for sele cted elements in (a) Al alloy B8 and (b) Al alloy SM10.

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229 0.51.01.52.02.53.03.5 9000 10000 11000 12000 13000 14000 15000 13314 12151 11632 10732 10423 9910Temperature (K)Delay Time (s)0.51.01.52.02.53.03.5 9000 10000 11000 12000 13000 14000 15000 13475 12422 11508 10744 9889Temperature (K)Delay Time (s)a a b b0.51.01.52.02.53.03.5 9000 10000 11000 12000 13000 14000 15000 13314 12151 11632 10732 10423 9910Temperature (K)Delay Time (s)0.51.01.52.02.53.03.5 9000 10000 11000 12000 13000 14000 15000 13475 12422 11508 10744 9889Temperature (K)Delay Time (s)a a b b Figure 7-7. Temporal evolution of averaged plasma temperature of (a) Al alloy B8 and (b) Al alloy SM10.

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230 0.1 0.06 0.09 0.09 0.060.511.523 0.00 0.03 0.06 0.09 0.12 0.15 0.18 %ChromiumDelay Time (s) 8.0 9 9 3.3 3.3 5.70.511.523 0 2 4 6 8 10 %CopperDelay Time (s) 0.9 0.5 0.5 0.5 0.40.511.523 0.0 0.2 0.4 0.6 0.8 1.0 %IronDelay Time (s) 0.09 0.05 0.07 0.08 0.050.511.523 0.00 0.02 0.04 0.06 0.08 0.10 %MagnesiumDelay Time (s) 0.3 0.2 0.2 0.2 0.20.511.523 0.0 0.1 0.2 0.3 0.4 %ManganeseDelay Time (s) 0.5 0.2 0.2 0.2 0.20.511.523 0.0 0.1 0.2 0.3 0.4 0.5 %NickelDelay Time (s) 2.7 1.3 1.1 1.2 2.30.511.523 0.0 0.5 1.0 1.5 2.0 2.5 3.0 %SiliconDelay Time (s) 0.10 0.05 0.080.08 0.060.511.523 0.00 0.04 0.08 0.12 0.16 %TitaniumDelay Time (s) 87.3 87.7 94.5 94.3 91.10.511.523 50 60 70 80 90 100 %AluminumDelay Time (s) a a 0.1 0.06 0.09 0.09 0.060.511.523 0.00 0.03 0.06 0.09 0.12 0.15 0.18 %ChromiumDelay Time (s) 8.0 9 9 3.3 3.3 5.70.511.523 0 2 4 6 8 10 %CopperDelay Time (s) 0.9 0.5 0.5 0.5 0.40.511.523 0.0 0.2 0.4 0.6 0.8 1.0 %IronDelay Time (s) 0.09 0.05 0.07 0.08 0.050.511.523 0.00 0.02 0.04 0.06 0.08 0.10 %MagnesiumDelay Time (s) 0.3 0.2 0.2 0.2 0.20.511.523 0.0 0.1 0.2 0.3 0.4 %ManganeseDelay Time (s) 0.5 0.2 0.2 0.2 0.20.511.523 0.0 0.1 0.2 0.3 0.4 0.5 %NickelDelay Time (s) 2.7 1.3 1.1 1.2 2.30.511.523 0.0 0.5 1.0 1.5 2.0 2.5 3.0 %SiliconDelay Time (s) 0.10 0.05 0.080.08 0.060.511.523 0.00 0.04 0.08 0.12 0.16 %TitaniumDelay Time (s) 87.3 87.7 94.5 94.3 91.10.511.523 50 60 70 80 90 100 %AluminumDelay Time (s) 0.1 0.06 0.09 0.09 0.060.511.523 0.00 0.03 0.06 0.09 0.12 0.15 0.18 %ChromiumDelay Time (s) 8.0 9 9 3.3 3.3 5.70.511.523 0 2 4 6 8 10 %CopperDelay Time (s) 0.9 0.5 0.5 0.5 0.40.511.523 0.0 0.2 0.4 0.6 0.8 1.0 %IronDelay Time (s) 0.09 0.05 0.07 0.08 0.050.511.523 0.00 0.02 0.04 0.06 0.08 0.10 %MagnesiumDelay Time (s) 0.3 0.2 0.2 0.2 0.20.511.523 0.0 0.1 0.2 0.3 0.4 %ManganeseDelay Time (s) 0.5 0.2 0.2 0.2 0.20.511.523 0.0 0.1 0.2 0.3 0.4 0.5 %NickelDelay Time (s) 2.7 1.3 1.1 1.2 2.30.511.523 0.0 0.5 1.0 1.5 2.0 2.5 3.0 %SiliconDelay Time (s) 0.10 0.05 0.080.08 0.060.511.523 0.00 0.04 0.08 0.12 0.16 %TitaniumDelay Time (s) 87.3 87.7 94.5 94.3 91.10.511.523 50 60 70 80 90 100 %AluminumDelay Time (s) a a Figure 7-8. Elemental concentrations of (a ) Al alloy B8 and (b) Al alloy SM10 calcula ted from CF-LIBS at different delay times. The dashed lines indicate the nominal concentr ation value. (Left to right, top to botto m: (a) Al, Cr, Cu, Fe, Mg, Mn, Ni, Si, and Ti and (b) Al, Cr, Cu, Fe, Mg, Mn, Ni, Si, Ti and Zn).

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231 0.2 0.1 0.1 0.1 0.1 0.20.511.522.53 0.00 0.04 0.08 0.12 0.16 0.20 %ChromiumDelay Time (s) 2.2 5.4 5.6 3.3 5.9 2.70.511.522.53 0 2 4 6 8 %CopperDelay Time (s) 1.3 1.0 1.0 1.3 1.1 1.20.511.522.53 0.0 0.5 1.0 1.5 2.0 %IronDelay Time (s) 1.1 0.7 0.5 0.7 0.7 0.70.511.522.53 0.0 0.3 0.6 0.9 1.2 %MagnesiumDelay Time (s) 0.2 0.1 0.1 0.2 0.1 0.20.511.522.53 0.0 0.1 0.2 0.3 %ManganeseDelay Time (s) 0.2 0.2 0.2 0.2 0.1 0.40.511.522.53 0.0 0.1 0.2 0.3 0.4 %NickelDelay Time (s) 3.0 2.5 3.2 4.8 3.7 3.90.511.522.53 0 1 2 3 4 5 6 %SiliconDelay Time (s) 0.04 0.04 0.03 0.04 0.04 0.050.511.522.53 0.00 0.01 0.02 0.03 0.04 0.05 0.06 %TitaniumDelay Time (s) 84.8 83.6 83.3 85.9 84.4 84.50.511.522.53 50 60 70 80 90 %AluminumDelay Time (s) 7.0 6.3 5.9 3.4 3.8 6.20.511.522.53 0 2 4 6 8 %ZincDelay Time (s) b b 0.2 0.1 0.1 0.1 0.1 0.20.511.522.53 0.00 0.04 0.08 0.12 0.16 0.20 %ChromiumDelay Time (s) 2.2 5.4 5.6 3.3 5.9 2.70.511.522.53 0 2 4 6 8 %CopperDelay Time (s) 1.3 1.0 1.0 1.3 1.1 1.20.511.522.53 0.0 0.5 1.0 1.5 2.0 %IronDelay Time (s) 1.1 0.7 0.5 0.7 0.7 0.70.511.522.53 0.0 0.3 0.6 0.9 1.2 %MagnesiumDelay Time (s) 0.2 0.1 0.1 0.2 0.1 0.20.511.522.53 0.0 0.1 0.2 0.3 %ManganeseDelay Time (s) 0.2 0.2 0.2 0.2 0.1 0.40.511.522.53 0.0 0.1 0.2 0.3 0.4 %NickelDelay Time (s) 3.0 2.5 3.2 4.8 3.7 3.90.511.522.53 0 1 2 3 4 5 6 %SiliconDelay Time (s) 0.04 0.04 0.03 0.04 0.04 0.050.511.522.53 0.00 0.01 0.02 0.03 0.04 0.05 0.06 %TitaniumDelay Time (s) 84.8 83.6 83.3 85.9 84.4 84.50.511.522.53 50 60 70 80 90 %AluminumDelay Time (s) 7.0 6.3 5.9 3.4 3.8 6.20.511.522.53 0 2 4 6 8 %ZincDelay Time (s) 0.2 0.1 0.1 0.1 0.1 0.20.511.522.53 0.00 0.04 0.08 0.12 0.16 0.20 %ChromiumDelay Time (s) 2.2 5.4 5.6 3.3 5.9 2.70.511.522.53 0 2 4 6 8 %CopperDelay Time (s) 1.3 1.0 1.0 1.3 1.1 1.20.511.522.53 0.0 0.5 1.0 1.5 2.0 %IronDelay Time (s) 1.1 0.7 0.5 0.7 0.7 0.70.511.522.53 0.0 0.3 0.6 0.9 1.2 %MagnesiumDelay Time (s) 0.2 0.1 0.1 0.2 0.1 0.20.511.522.53 0.0 0.1 0.2 0.3 %ManganeseDelay Time (s) 0.2 0.2 0.2 0.2 0.1 0.40.511.522.53 0.0 0.1 0.2 0.3 0.4 %NickelDelay Time (s) 3.0 2.5 3.2 4.8 3.7 3.90.511.522.53 0 1 2 3 4 5 6 %SiliconDelay Time (s) 0.04 0.04 0.03 0.04 0.04 0.050.511.522.53 0.00 0.01 0.02 0.03 0.04 0.05 0.06 %TitaniumDelay Time (s) 84.8 83.6 83.3 85.9 84.4 84.50.511.522.53 50 60 70 80 90 %AluminumDelay Time (s) 7.0 6.3 5.9 3.4 3.8 6.20.511.522.53 0 2 4 6 8 %ZincDelay Time (s) b b Figure 7-8. Continued.

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232 AlCrCuFeMgMnNiSiTi0 10 20 30 40 50 60 126 128 130 %Relative Error 0500 ns 1000 ns 1500 ns 2000 ns 3000 ns AlCrCuFeMgMnNiSiTiZn0 30 60 90 120 150 180 400 500 %Relative Error 0500 ns 1000 ns 1500 ns 2000 ns 2500 ns 3000 nsa a b b AlCrCuFeMgMnNiSiTi0 10 20 30 40 50 60 126 128 130 %Relative Error 0500 ns 1000 ns 1500 ns 2000 ns 3000 ns AlCrCuFeMgMnNiSiTiZn0 30 60 90 120 150 180 400 500 %Relative Error 0500 ns 1000 ns 1500 ns 2000 ns 2500 ns 3000 nsa a b b Figure 7-9. Relative errors calcula ted from CF-LIBS results of (a) Al alloy B8 and (b) Al alloy SM10.

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233 Figure 7-10. LIBS measurements of 10 NIST brass standards. A section of the laser-induced breakdown spectra of brass showing selected Cu I and Zn I lines are shown in (a) and the corresponding images of the laser-induced plasma obtained at 2.0 s delay time and 0.5 s gate width are illustrated in (b). 324326328330332 0 1000 2000 3000 4000 5000 6000 7000 80001107 1108 1110 1111 1115 1116 1117 1112 1113 1114 Cu I Cu I Zn I Zn I Cu I Wavelength (nm)Intensity (a.u.)B r a s s S a m p l e Cu Ia a b b 324326328330332 0 1000 2000 3000 4000 5000 6000 7000 80001107 1108 1110 1111 1115 1116 1117 1112 1113 1114 Cu I Cu I Zn I Zn I Cu I Wavelength (nm)Intensity (a.u.)B r a s s S a m p l e Cu Ia a b b

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234 11071108111011111115111611171112111311140 20 40 60 80 100 %CuNIST Standard Certified CF-LIBS 11071108111011111115111611171112111311140 5 10 15 20 25 30 35 40 %ZnNIST Standard Certified CF-LIBS 11071108111011111115111611171112111311140 3 6 9 12 15 %Relative ErrorNIST Standard Cu Zna a b b d d 13439 13502 14037 13825 1401014007 13953 13992 1399013981 1.59 1.75 1.46 1.5 1.36 1.45 1.31 1.37 1.47 1.21 11071108111011111112111511161117111311147500 10000 12500 15000 Temperature (K)NIST Brass Standard 11071108111011111112111511161117111311140.00 0.50 1.00 1.50 2.00 2.50 Minimum electron density for LTEElectron Number Density (x 1017 cm-3)c c 11071108111011111115111611171112111311140 20 40 60 80 100 %CuNIST Standard Certified CF-LIBS 11071108111011111115111611171112111311140 5 10 15 20 25 30 35 40 %ZnNIST Standard Certified CF-LIBS 11071108111011111115111611171112111311140 3 6 9 12 15 %Relative ErrorNIST Standard Cu Zna a b b d d 13439 13502 14037 13825 1401014007 13953 13992 1399013981 1.59 1.75 1.46 1.5 1.36 1.45 1.31 1.37 1.47 1.21 11071108111011111112111511161117111311147500 10000 12500 15000 Temperature (K)NIST Brass Standard 11071108111011111112111511161117111311140.00 0.50 1.00 1.50 2.00 2.50 Minimum electron density for LTEElectron Number Density (x 1017 cm-3)c c Figure 7-11. Results of the CF-LIBS analysis of 10 NIST brass standards. The relative elemental concentrations of (a) Cu and (b) Zn are show n in blue and red bars, respectively. The certified values are depicted by the black bars. The calculated electron number densities and temperatures are shown in (c) and the relative percentage errors of the CF-LIBS concentration results are summarized in (d).

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235 -5051015202530354045 0 1000 2000 3000 4000 5000 6000 1107 1108 1110 1113 1114 1115 1116 1117 Intensity of 255.795 nm Zn II (a.u.)Zn Concentration (%)-202468101214161820 -500 0 500 1000 1500 2000 2500 3000 1110 1113 1114 1115 1117 Intensity of 330.258 nm Zn I (a.u.)Zn Concentration (%)-50510152025303540 0 1000 2000 3000 4000 1108 1111 1113 1114 1115 1117 Intensity of 328.233 nm Zn I (a.u.)Zn Concentration (%) 255.60255.75255.90256.05 0 1000 2000 3000 4000 5000 60001107 1108 1110 1111 1115 1116 1117 1112 1113 1114 255.795 nm Zn II Wavelength (nm)Intensity (a.u.)B r a s s S a m p l e 327.75328.00328.25328.50328.75 0 500 1000 1500 2000 25001107 1108 1110 1111 1115 1116 1117 1112 1113 1114 328.233 nm Zn I Wavelength (nm)Intensity (a.u.)B r a s s S a m p l e 329.75330.00330.25330.50330.75 0 1000 2000 3000 40001107 1108 1110 1111 1115 1116 1117 1112 1113 1114 330.258 nm Zn I Wavelength (nm)Intensity (a.u.)B r a s s S a m p l ecL= 0.17% cL= 0.12% cL= 0.084%a a b b c c-5051015202530354045 0 1000 2000 3000 4000 5000 6000 1107 1108 1110 1113 1114 1115 1116 1117 Intensity of 255.795 nm Zn II (a.u.)Zn Concentration (%)-202468101214161820 -500 0 500 1000 1500 2000 2500 3000 1110 1113 1114 1115 1117 Intensity of 330.258 nm Zn I (a.u.)Zn Concentration (%)-50510152025303540 0 1000 2000 3000 4000 1108 1111 1113 1114 1115 1117 Intensity of 328.233 nm Zn I (a.u.)Zn Concentration (%) 255.60255.75255.90256.05 0 1000 2000 3000 4000 5000 60001107 1108 1110 1111 1115 1116 1117 1112 1113 1114 255.795 nm Zn II Wavelength (nm)Intensity (a.u.)B r a s s S a m p l e 327.75328.00328.25328.50328.75 0 500 1000 1500 2000 25001107 1108 1110 1111 1115 1116 1117 1112 1113 1114 328.233 nm Zn I Wavelength (nm)Intensity (a.u.)B r a s s S a m p l e 329.75330.00330.25330.50330.75 0 1000 2000 3000 40001107 1108 1110 1111 1115 1116 1117 1112 1113 1114 330.258 nm Zn I Wavelength (nm)Intensity (a.u.)B r a s s S a m p l ecL= 0.17% cL= 0.12% cL= 0.084%a a b b c c Figure 7-12. Calibration curves cons tructed for the quantitative anal ysis of Zn in brass samples using (a) 255.795 nm Zn II, (b) 328. 233 nm Zn I and (c) 330.258 nm Zn I lines.

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236 Figure 7-13. Images of the laser-induced plasma obtained from Al alloy (a) B8, (b) SM10, (c) D33, (d) S4, (e) V14 and (f) Z8 at different ambient pressures.

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237 278280282284286288 0 750 1500 2250 3000 3750 1000 mbarWavelength (nm)0 200 400 600 100 mbarIntensity (a.u.)0 50 100 150 200 Mg I Si I Al II 0.10 mbar Mg II Mg II Al II Mg I Si I Mg II Al II Mg I Si I 278280282284286288 0 2000 4000 6000 8000 10000 1000 mbarWavelength (nm)0 300 600 900 1200 1500 100 mbarIntensity (a.u.)0 100 200 300 400 Mg I Si I Al II 0.10 mbar Mg II Mg II Al II Mg I Si I Mg II Al II Mg I Si Ia a b b 278280282284286288 0 2000 4000 6000 8000 1000 mbarWavelength (nm)0 50 100 150 200 250 Mg I Si I Al II 0.10 mbar Mg II Mg II Al II Mg I Si IIntensity (a.u.) 278280282284286288 0 500 1000 1500 2000 2500 1000 mbarWavelength (nm)0 30 60 90 120 150 Mg I Si I Al II 0.10 mbar Mg II Mg II Al II Mg I Si IIntensity (a.u.) 278280282284286288 0 2000 4000 6000 8000 10000 1000 mbarWavelength (nm)0 100 200 300 400 500 Mg I Si I Al II 0.10 mbar Mg II Mg II Al II Mg I Si IIntensity (a.u.) 278280282284286288 0 500 1000 1500 2000 2500 1000 mbarWavelength (nm)0 25 50 75 100 125 150 Mg I Si I Al II 0.10 mbar Mg II Mg II Al II Mg I Si IIntensity (a.u.)c c d d e e f f 278280282284286288 0 750 1500 2250 3000 3750 1000 mbarWavelength (nm)0 200 400 600 100 mbarIntensity (a.u.)0 50 100 150 200 Mg I Si I Al II 0.10 mbar Mg II Mg II Al II Mg I Si I Mg II Al II Mg I Si I 278280282284286288 0 2000 4000 6000 8000 10000 1000 mbarWavelength (nm)0 300 600 900 1200 1500 100 mbarIntensity (a.u.)0 100 200 300 400 Mg I Si I Al II 0.10 mbar Mg II Mg II Al II Mg I Si I Mg II Al II Mg I Si Ia a b b 278280282284286288 0 2000 4000 6000 8000 1000 mbarWavelength (nm)0 50 100 150 200 250 Mg I Si I Al II 0.10 mbar Mg II Mg II Al II Mg I Si IIntensity (a.u.) 278280282284286288 0 500 1000 1500 2000 2500 1000 mbarWavelength (nm)0 30 60 90 120 150 Mg I Si I Al II 0.10 mbar Mg II Mg II Al II Mg I Si IIntensity (a.u.) 278280282284286288 0 2000 4000 6000 8000 10000 1000 mbarWavelength (nm)0 100 200 300 400 500 Mg I Si I Al II 0.10 mbar Mg II Mg II Al II Mg I Si IIntensity (a.u.) 278280282284286288 0 500 1000 1500 2000 2500 1000 mbarWavelength (nm)0 25 50 75 100 125 150 Mg I Si I Al II 0.10 mbar Mg II Mg II Al II Mg I Si IIntensity (a.u.)c c d d e e f f 278280282284286288 0 2000 4000 6000 8000 1000 mbarWavelength (nm)0 50 100 150 200 250 Mg I Si I Al II 0.10 mbar Mg II Mg II Al II Mg I Si IIntensity (a.u.) 278280282284286288 0 500 1000 1500 2000 2500 1000 mbarWavelength (nm)0 30 60 90 120 150 Mg I Si I Al II 0.10 mbar Mg II Mg II Al II Mg I Si IIntensity (a.u.) 278280282284286288 0 2000 4000 6000 8000 10000 1000 mbarWavelength (nm)0 100 200 300 400 500 Mg I Si I Al II 0.10 mbar Mg II Mg II Al II Mg I Si IIntensity (a.u.) 278280282284286288 0 500 1000 1500 2000 2500 1000 mbarWavelength (nm)0 25 50 75 100 125 150 Mg I Si I Al II 0.10 mbar Mg II Mg II Al II Mg I Si IIntensity (a.u.)c c d d e e f f Figure 7-14. Section of laser-i nduced breakdown spectra of Al al loy (a) B8, (b) SM10, (c) D33, (d) S4, (e) V14 and (f) Z8 at different am bient pressures (cyan: 0.1 mbar, green: 100 mbar, blue: 1000 mbar).

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238 B8D33S4SM10V14Z80 3000 6000 9000 12000 15000 Temperature (K) 1000 mbar 100 mbar 0.10 mbar 1.62 1.58 1.65 1.63 1.56 1.64 0.1216 0.1328 0.1346 0.1396 0.1471 0.1201 B8D33S4SM10V14Z80.0 0.5 1.0 1.5 2.0 2.5 1000 mbar Minimum electron density for LTEB8D33S4SM10V14Z80.00 0.05 0.10 0.15 0.20 0.10 mbar Minimum electron density for LTE Electron Number Density (x1017 cm-3)b b a a B8D33S4SM10V14Z80 3000 6000 9000 12000 15000 Temperature (K) 1000 mbar 100 mbar 0.10 mbar 1.62 1.58 1.65 1.63 1.56 1.64 0.1216 0.1328 0.1346 0.1396 0.1471 0.1201 B8D33S4SM10V14Z80.0 0.5 1.0 1.5 2.0 2.5 1000 mbar Minimum electron density for LTEB8D33S4SM10V14Z80.00 0.05 0.10 0.15 0.20 0.10 mbar Minimum electron density for LTE Electron Number Density (x1017 cm-3)b b a a Figure 7-15. Calculated (a) electr on number density and (b) temper ature values for different Al alloys under different ambient pressures.

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239 AlCrCuFeMgMnNiSiTi1E-3 0.01 0.1 1 10 80 90 %Relative Composition of Al alloy B8 Certified 1000 mbar (2.0 s delay, 0.5 s gate) 100 mbar (2.0 s delay, 0.5 s gate) 0.10 mbar (50 ns delay, 100 ns gate) AlCrCuFeMgMnNiSiTiZn1E-3 0.01 0.1 1 10 80 90 %Relative Composition of Al alloy SM10 Certified 1000 mbar (2.0 s delay, 0.5 s gate) 100 mbar (2.0 s delay, 0.5 s gate) 0.10 mbar (50 ns delay, 100 ns gate) AlCrCuFeMgMnNiSiTi1E-3 0.01 0.1 1 10 80 90 %Relative Composition of Al alloy D33 Certified 1000 mbar (2.0 s delay, 0.5 s gate) 0.10 mbar (50 ns delay, 100 ns gate) AlCrCuFeMgMnNiSiTiZn1E-3 0.01 0.1 1 10 75 80 85 %Relative Composition of Al alloy S4 Certified 1000 mbar (2.0 s delay, 0.5 s gate) 0.10 mbar (50 ns delay, 100 ns gate) AlCrCuFeMgMnNiSiTi1E-3 0.01 0.1 1 10 80 90 %Relative Composition of Al alloy V14 Certified 1000 mbar (2.0 s delay, 0.5 s gate) 0.10 mbar (50 ns delay, 100 ns gate) AlCrCuFeMgMnNiSiTi1E-3 0.01 0.1 1 10 75 78 81 %Relative Composition of Al alloy Z8 Certified 1000 mbar (2.0 s delay, 0.5 s gate) 0.10 mbar (50 ns delay, 100 ns gate) a a b b c c d d e e f f AlCrCuFeMgMnNiSiTi1E-3 0.01 0.1 1 10 80 90 %Relative Composition of Al alloy B8 Certified 1000 mbar (2.0 s delay, 0.5 s gate) 100 mbar (2.0 s delay, 0.5 s gate) 0.10 mbar (50 ns delay, 100 ns gate) AlCrCuFeMgMnNiSiTiZn1E-3 0.01 0.1 1 10 80 90 %Relative Composition of Al alloy SM10 Certified 1000 mbar (2.0 s delay, 0.5 s gate) 100 mbar (2.0 s delay, 0.5 s gate) 0.10 mbar (50 ns delay, 100 ns gate) AlCrCuFeMgMnNiSiTi1E-3 0.01 0.1 1 10 80 90 %Relative Composition of Al alloy D33 Certified 1000 mbar (2.0 s delay, 0.5 s gate) 0.10 mbar (50 ns delay, 100 ns gate) AlCrCuFeMgMnNiSiTiZn1E-3 0.01 0.1 1 10 75 80 85 %Relative Composition of Al alloy S4 Certified 1000 mbar (2.0 s delay, 0.5 s gate) 0.10 mbar (50 ns delay, 100 ns gate) AlCrCuFeMgMnNiSiTi1E-3 0.01 0.1 1 10 80 90 %Relative Composition of Al alloy V14 Certified 1000 mbar (2.0 s delay, 0.5 s gate) 0.10 mbar (50 ns delay, 100 ns gate) AlCrCuFeMgMnNiSiTi1E-3 0.01 0.1 1 10 75 78 81 %Relative Composition of Al alloy Z8 Certified 1000 mbar (2.0 s delay, 0.5 s gate) 0.10 mbar (50 ns delay, 100 ns gate) a a b b c c d d e e f f Figure 7-16. Relative elemental concentrations of Al alloy (a) B8, (b) SM10, (c) D33, (d) S4, (e) V14 and (f) Z8 at different ambient pressu res (cyan: 0.1 mbar, green: 100 mbar, blue: 1000 mbar, black: certified).

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240 AlCrCuFeMgMnNiSiTi0 20 40 60 80 100 120 %Relative Error (Al alloy B8) 1000 mbar (2.0 s delay, 0.5 s gate) 100 mbar (2.0 s delay, 0.5 s gate) 0.10 mbar (50 ns delay, 100 ns gate) AlCrCuFeMgMnNiSiTiZn0 20 40 60 80 145 150 %Relative Error (Al alloy SM10) 1000 mbar (2.0 s delay, 0.5 s gate) 100 mbar (2.0 s delay, 0.5 s gate) 0.10 mbar (50 ns delay, 100 ns gate) AlCrCuFeMgMnNiSiTi0 20 40 60 80 100 %Relative Error (Al alloy D33) 1000 mbar (2.0 s delay, 0.5 s gate) 0.10 mbar (50 ns delay, 100 ns gate) AlCrCuFeMgMnNiSiTiZn0 20 40 60 80 450 500 %Relative Error (Al alloy S4) 1000 mbar (2.0 s delay, 0.5 s gate) 0.10 mbar (50 ns delay, 100 ns gate) AlCrCuFeMgMnNiSiTi0 20 40 60 80 100 %Relative Error (Al alloy V14) 1000 mbar (2.0 s delay, 0.5 s gate) 0.10 mbar (50 ns delay, 100 ns gate) AlCrCuFeMgMnNiSiTi0 20 40 60 80 100 %Relative Error (Al alloy Z8) 1000 mbar (2.0 s delay, 0.5 s gate) 0.10 mbar (50 ns delay, 100 ns gate)a a b b c c d d e e f f AlCrCuFeMgMnNiSiTi0 20 40 60 80 100 120 %Relative Error (Al alloy B8) 1000 mbar (2.0 s delay, 0.5 s gate) 100 mbar (2.0 s delay, 0.5 s gate) 0.10 mbar (50 ns delay, 100 ns gate) AlCrCuFeMgMnNiSiTiZn0 20 40 60 80 145 150 %Relative Error (Al alloy SM10) 1000 mbar (2.0 s delay, 0.5 s gate) 100 mbar (2.0 s delay, 0.5 s gate) 0.10 mbar (50 ns delay, 100 ns gate) AlCrCuFeMgMnNiSiTi0 20 40 60 80 100 %Relative Error (Al alloy D33) 1000 mbar (2.0 s delay, 0.5 s gate) 0.10 mbar (50 ns delay, 100 ns gate) AlCrCuFeMgMnNiSiTiZn0 20 40 60 80 450 500 %Relative Error (Al alloy S4) 1000 mbar (2.0 s delay, 0.5 s gate) 0.10 mbar (50 ns delay, 100 ns gate) AlCrCuFeMgMnNiSiTi0 20 40 60 80 100 %Relative Error (Al alloy V14) 1000 mbar (2.0 s delay, 0.5 s gate) 0.10 mbar (50 ns delay, 100 ns gate) AlCrCuFeMgMnNiSiTi0 20 40 60 80 100 %Relative Error (Al alloy Z8) 1000 mbar (2.0 s delay, 0.5 s gate) 0.10 mbar (50 ns delay, 100 ns gate)a a b b c c d d e e f f Figure 7-17. Relative errors of calculated elementa l concentrations of Al alloy (a) B8, (b) SM10, (c) D33, (d) S4, (e) V14 and (f) Z8 at di fferent ambient pressures (cyan: 0.1 mbar, green: 100 mbar, blue: 1000 mbar).

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241 229.3 229.4 229.5 229.6 0 1000 2000 3000 4000 5000Z8 B8 S4 V14 SM10 D33 Wavelength (nm)Intensity (a.u. 229.436 nm Cu II 327.2327.3327.4327.5327.6 0 500 1000 1500 2000 2500 3000Z8 B8 S4 V14 SM10 D33 Wavelength (nm)Intensity (a.u. 327.396 nm Cu I 287.8287.9288.0288.1288.2288.3288.4288.5 0 200 400 600 800 1000 1200 1400 Wavelength (nm)Intensity (a.u. 288.158 nm Si I-2024681012141618 -500 0 500 1000 1500 2000 2500 3000 B8 SM10 V14 Z8 Intensity of 229.436 nm Cu IICu Concentration (%)cL= 0.0084%-2024681012141618 -500 0 500 1000 1500 2000 2500 B8 D33 Z8 Intensity of 327.396 nm Cu ICu Concentration (%)cL= 0.095%02468 0 400 800 1200 1600 2000 B8 V14 Z8 Intensity of 288.158 nm Si ISi Concentration (%)cL= 0.14%a a b b c c 229.3 229.4 229.5 229.6 0 1000 2000 3000 4000 5000Z8 B8 S4 V14 SM10 D33 Wavelength (nm)Intensity (a.u. 229.436 nm Cu II 327.2327.3327.4327.5327.6 0 500 1000 1500 2000 2500 3000Z8 B8 S4 V14 SM10 D33 Wavelength (nm)Intensity (a.u. 327.396 nm Cu I 287.8287.9288.0288.1288.2288.3288.4288.5 0 200 400 600 800 1000 1200 1400 Wavelength (nm)Intensity (a.u. 288.158 nm Si I-2024681012141618 -500 0 500 1000 1500 2000 2500 3000 B8 SM10 V14 Z8 Intensity of 229.436 nm Cu IICu Concentration (%)cL= 0.0084%-2024681012141618 -500 0 500 1000 1500 2000 2500 B8 D33 Z8 Intensity of 327.396 nm Cu ICu Concentration (%)cL= 0.095%02468 0 400 800 1200 1600 2000 B8 V14 Z8 Intensity of 288.158 nm Si ISi Concentration (%)cL= 0.14%a a b b c c Figure 7-18. Calibration curves cons tructed for the quantitative analys is of Cu and Si in the Al alloy samples using (a) 229.436 nm Cu II, (b) 327.396 nm Cu I and (c) 288.158 nm Si I.

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242 250300350400450 0 500 1000 1500 2000 2500 3000 2711 1646 2704 2710 SO2 SO3 Wavelength (nm)Intensity (a.u.)So i l S a m p l e 336337338339340 0 100 200 300 400 500 2711 1646 2704 2710 SO2 SO3 Ti II Ti II Ti II Ti II Ti II Wavelength (nm)Intensity (a.u.)S o i l S a m p l e Ti II a a b b 0 1 2 mm 250300350400450 0 500 1000 1500 2000 2500 3000 2711 1646 2704 2710 SO2 SO3 Wavelength (nm)Intensity (a.u.)So i l S a m p l e 336337338339340 0 100 200 300 400 500 2711 1646 2704 2710 SO2 SO3 Ti II Ti II Ti II Ti II Ti II Wavelength (nm)Intensity (a.u.)S o i l S a m p l e Ti II a a b b 250300350400450 0 500 1000 1500 2000 2500 3000 2711 1646 2704 2710 SO2 SO3 Wavelength (nm)Intensity (a.u.)So i l S a m p l e 336337338339340 0 100 200 300 400 500 2711 1646 2704 2710 SO2 SO3 Ti II Ti II Ti II Ti II Ti II Wavelength (nm)Intensity (a.u.)S o i l S a m p l e Ti II 250300350400450 0 500 1000 1500 2000 2500 3000 2711 1646 2704 2710 SO2 SO3 Wavelength (nm)Intensity (a.u.)So i l S a m p l e 336337338339340 0 100 200 300 400 500 2711 1646 2704 2710 SO2 SO3 Ti II Ti II Ti II Ti II Ti II Wavelength (nm)Intensity (a.u.)S o i l S a m p l e Ti II a a b b 0 1 2 mm 0 1 2 mm Figure 7-19. LIBS measurements of 6 soil sta ndards. A section of th e laser-induced breakdown spectra of soil samples showing selected Ti I lines are shown in (a) and the corresponding images of the laser-i nduced plasma obtained at 1.2 s delay time and 0.1 s gate width are illustrated in (b).

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243 AlCaFeMgSiTi0 5 10 15 66 68 70 %Relative Composition of NIST Soil 2711 Certified CF-LIBS AlCaFeMgSiTi0 5 10 70 72 74 %Relative Composition of NIST Soil 1646 Certified CF-LIBS AlCaFeMgSiTi0 5 10 15 65 66 67 %Relative Composition of NIST Soil 2704 Certified CF-LIBS AlFeMgMnSiTi0 5 10 15 68 70 %Relative Composition of NIST Soil 2710 Certified CF-LIBS AlCaFeMgSiTi0 5 10 15 50 55 60 %Relative Composition for CAN Soil SO-2 Certified CF-LIBS AlCaFeMgSiTi0 2 4 6 8 10 12 30 40 %Relative Composition for CAN Soil SO-3 Certified CF-LIBSa a c c e e b b d d f f AlCaFeMgSiTi0 5 10 15 66 68 70 %Relative Composition of NIST Soil 2711 Certified CF-LIBS AlCaFeMgSiTi0 5 10 70 72 74 %Relative Composition of NIST Soil 1646 Certified CF-LIBS AlCaFeMgSiTi0 5 10 15 65 66 67 %Relative Composition of NIST Soil 2704 Certified CF-LIBS AlFeMgMnSiTi0 5 10 15 68 70 %Relative Composition of NIST Soil 2710 Certified CF-LIBS AlCaFeMgSiTi0 5 10 15 50 55 60 %Relative Composition for CAN Soil SO-2 Certified CF-LIBS AlCaFeMgSiTi0 2 4 6 8 10 12 30 40 %Relative Composition for CAN Soil SO-3 Certified CF-LIBSa a c c e e b b d d f f Figure 7-20. Relative elemental concentrations of soil standards (a) NIST SRM 2711, (b) NIST SRM 1646, (c) NIST SRM 2704, (d) NIST SRM 2710, (e) CAN SO-2 and (f) CAN SO-3 calculated from CF-LIBS.

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244 AlCaFeMgSiTiMn0 20 40 60 80 120 130 %Error for Soil Samples NIST 2711 NIST 1646 NIST 2704 NIST 2710 CAN SO2 CAN SO3 12126 11785 11750 12056 11735 12497 3.01 2.98 2.93 2.96 2.64 2.54 NIST 2711NIST 1646NIST 2704NIST 2710CAN SO2CAN SO3 0 3000 6000 9000 12000 15000 Temperature (K)NIST 2711NIST 1646NIST 2704NIST 2710CAN SO2CAN SO3 0.00 1.00 2.00 3.00 4.00 Minimum electron density for LTEElectron Number Density (x 1017 cm-3)a a b b AlCaFeMgSiTiMn0 20 40 60 80 120 130 %Error for Soil Samples NIST 2711 NIST 1646 NIST 2704 NIST 2710 CAN SO2 CAN SO3 12126 11785 11750 12056 11735 12497 3.01 2.98 2.93 2.96 2.64 2.54 NIST 2711NIST 1646NIST 2704NIST 2710CAN SO2CAN SO3 0 3000 6000 9000 12000 15000 Temperature (K)NIST 2711NIST 1646NIST 2704NIST 2710CAN SO2CAN SO3 0.00 1.00 2.00 3.00 4.00 Minimum electron density for LTEElectron Number Density (x 1017 cm-3)a a b b Figure 7-21. The relative errors of calculated elemental concentrations of soil standards are shown in (a) while the electron number dens ity and temperature values of the laserinduced plasmas are shown in (b).

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245 0 1 2 3 mm Ti alloy pellet Ti alloy pellet Ti alloy NIST 654b Ti alloy NIST 654b Zn alloy NIST 627 Zn alloy NIST 627 Zn alloy NIST 629 Zn alloy NIST 629 Ni alloy pellet Ni alloy pellet Cu alloy NIST 1276a Cu alloy NIST 1276a 0 1 2 3 mm 0 1 2 3 mm Ti alloy pellet Ti alloy pellet Ti alloy NIST 654b Ti alloy NIST 654b Zn alloy NIST 627 Zn alloy NIST 627 Zn alloy NIST 629 Zn alloy NIST 629 Ni alloy pellet Ni alloy pellet Cu alloy NIST 1276a Cu alloy NIST 1276a 322323324325326327 0 1000 2000 3000 4000 TiPellet TiAlloy Zn627 Zn629 NiAlloy CuNiAlloy TiPellet TiAlloy Zn627 Zn629 NiAlloy CuNiAlloy Wavelength (nm)Intensity (a.u.)A l l o y S a m p l ea a b b 0 1 2 3 mm Ti alloy pellet Ti alloy pellet Ti alloy NIST 654b Ti alloy NIST 654b Zn alloy NIST 627 Zn alloy NIST 627 Zn alloy NIST 629 Zn alloy NIST 629 Ni alloy pellet Ni alloy pellet Cu alloy NIST 1276a Cu alloy NIST 1276a 0 1 2 3 mm 0 1 2 3 mm Ti alloy pellet Ti alloy pellet Ti alloy NIST 654b Ti alloy NIST 654b Zn alloy NIST 627 Zn alloy NIST 627 Zn alloy NIST 629 Zn alloy NIST 629 Ni alloy pellet Ni alloy pellet Cu alloy NIST 1276a Cu alloy NIST 1276a 322323324325326327 0 1000 2000 3000 4000 TiPellet TiAlloy Zn627 Zn629 NiAlloy CuNiAlloy TiPellet TiAlloy Zn627 Zn629 NiAlloy CuNiAlloy Wavelength (nm)Intensity (a.u.)A l l o y S a m p l ea a b b Figure 7-22. LIBS measurements of 6 different alloy standards. A section of the laser-induced breakdown spectra of alloy samples are show n in (a) and the corre sponding images of the laser-induced plasma obtained are illustrated in (b).

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246 Al Ti V0 5 10 85 90 95 %Relative Composition of Ti Alloy 88395 Pellet Certified CF-LIBS Al Ti V0 5 10 80 85 90 %Relative Composition of Ti Alloy NIST 654b Certified CF-LIBS AlCuFeZn1E-3 0.01 0.1 1 10 100 %Relative Composition for Zn Alloy NIST 627 Certified CF-LIBS AlCuFeZn1E-3 0.01 0.1 1 10 100 %Relative Composition for Zn Alloy NIST 629 Certified CF-LIBS AlCuNiTi1E-3 0.01 0.1 1 10 65 70 %Relative Composition of Ni Alloy NIST 882 Pellet Certified CF-LIBS CuFeMgMnNi1E-3 0.01 0.1 1 10 60 70 %Relative Composition of Cu Alloy NIST1276a Certified CF-LIBSa a c c e e f f b b d d Al Ti V0 5 10 85 90 95 %Relative Composition of Ti Alloy 88395 Pellet Certified CF-LIBS Al Ti V0 5 10 80 85 90 %Relative Composition of Ti Alloy NIST 654b Certified CF-LIBS AlCuFeZn1E-3 0.01 0.1 1 10 100 %Relative Composition for Zn Alloy NIST 627 Certified CF-LIBS AlCuFeZn1E-3 0.01 0.1 1 10 100 %Relative Composition for Zn Alloy NIST 629 Certified CF-LIBS AlCuNiTi1E-3 0.01 0.1 1 10 65 70 %Relative Composition of Ni Alloy NIST 882 Pellet Certified CF-LIBS CuFeMgMnNi1E-3 0.01 0.1 1 10 60 70 %Relative Composition of Cu Alloy NIST1276a Certified CF-LIBSa a c c e e f f b b d d Figure 7-23. Relative elemental concentrations of alloy standards (a) Alfa Aesar 88395 Ti alloy pellet, (b) NIST SRM 654b Ti alloy, (c) NIST SRM 627 Zn alloy, (d) NIST SRM 629 Zn alloy, (e) NIST SRM 882 Ni alloy pe llet and (f) NIST SRM 1276a Cu-Ni alloy calculated from CF-LIBS.

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247 Al Ti V0 20 40 60 80 100 120 %Relative Error for Ti Alloy Samples Ti alloy AA 88395 pellet Ti alloy NIST 654b Al Cu Fe Zn0 10 20 30 40 50 60 70 %Relative Error for Zn Alloy Samples Zn alloy NIST 627 Zn alloy NIST 629 AlCuNiTi0.0 0.5 1.0 1.5 30 40 50 %Relative Error for Ni Alloy NIST 882 Pellet CuFeMgMnNi0 5 10 15 80 100 %Relative Error for Cu Alloy NIST 1276aa a b b c c d d 12501 13266 13010 12937 14642 14516 2.96 2.21 3.17 3.28 3.71 2.96Ti alloy pelletTi alloy metalZn alloy 627Zn alloy 629Ni alloy pelletCuNi alloy metal0 5000 10000 15000 20000 Temperature (K)Ti alloy pelletTi alloy metalZn alloy 627Zn alloy 629Ni alloy pelletCuNi alloy metal0.00 1.00 2.00 3.00 4.00 Electron Number Density (x 1017 cm-3)e e Al Ti V0 20 40 60 80 100 120 %Relative Error for Ti Alloy Samples Ti alloy AA 88395 pellet Ti alloy NIST 654b Al Cu Fe Zn0 10 20 30 40 50 60 70 %Relative Error for Zn Alloy Samples Zn alloy NIST 627 Zn alloy NIST 629 AlCuNiTi0.0 0.5 1.0 1.5 30 40 50 %Relative Error for Ni Alloy NIST 882 Pellet CuFeMgMnNi0 5 10 15 80 100 %Relative Error for Cu Alloy NIST 1276aa a b b c c d d 12501 13266 13010 12937 14642 14516 2.96 2.21 3.17 3.28 3.71 2.96Ti alloy pelletTi alloy metalZn alloy 627Zn alloy 629Ni alloy pelletCuNi alloy metal0 5000 10000 15000 20000 Temperature (K)Ti alloy pelletTi alloy metalZn alloy 627Zn alloy 629Ni alloy pelletCuNi alloy metal0.00 1.00 2.00 3.00 4.00 Electron Number Density (x 1017 cm-3)e e Figure 7-24. The relative errors of calculated elemental concentrations of alloy standards are shown in (a)-(d) while the electron number density and temperature values of the laser-induced plasmas are shown in (e).

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248 Table 7-1. Electron number dens ity, temperature and relative st andard deviation calculated for aluminum alloy B8 at 5 different delay times. Delay time ( s) Electron density, ne ( 1017 cm-3) Minimum ne for LTE ( 1017 cm-3) RSD in ne (%) Temperature, T ( 104 K) RSD in T (%) 0.5 3.6 0.1 0.6962.8 1.4 0.1 7.4 1.0 1.65 0.03 0.6681.8 1.2 0.1 8.9 1.5 1.027 0.006 0.6430.6 1.15 0.07 5.7 2.0 0.67 0.02 0.6223.0 1.07 0.05 4.9 3.0 0.37 0.02 0.5965.4 0.99 0.06 6.5 Table 7-2. Electron number dens ity, temperature and relative st andard deviation calculated for aluminum alloy SM10 at 6 different delay times. Delay time ( s) Electron density, ne ( 1017 cm-3) Minimum ne for LTE ( 1017 cm-3) RSD in ne (%) Temperature, T ( 104 K) RSD in T (%) 0.5 2.7 0.2 0.6927.4 1.33 0.08 6.1 1.0 1.25 0.05 0.6614.0 1.2 0.1 9.3 1.5 0.99 0.06 0.6476.1 1.2 0.1 12.0 2.0 0.56 0.01 0.6211.8 1.07 0.05 4.8 2.5 0.47 0.01 0.6122.1 1.04 0.07 6.9 3.0 0.32 0.02 0.5976.3 0.99 0.06 6.2 Table 7-3. Relative concentration values (in %) calculated from CF-LIBS analysis of aluminum alloy B8 at 5 different delay times. Element 0.5 s 1.0 s 1.5 s 2.0 s 3.0 s Certified Al 87.3 87.7 94.594.391.188.8095 Cr 0.1 0.06 0.090.090.060.1716 Cu 8.0 9.9 3.33.35.77.0155 Fe 0.9 0.5 0.50.50.40.8075 Mg 0.09 0.1 0.070.080.050.0767 Mn 0.3 0.2 0.20.20.20.4038 Ni 0.5 0.2 0.20.20.20.2019 Si 2.7 1.3 1.11.22.32.3520 Ti 0.1 0.05 0.080.080.060.1615

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249 Table 7-4. Relative concentration values (in %) calculated from CF-LIBS analysis of aluminum alloy SM10 at 6 different delay times. Table 7-5. Relative errors (in %) calculated from CF-LIBS analysis of aluminum alloy B8 at 5 different delay times. Table 7-6. Relative errors (in %) calculated from CF-LIBS anal ysis of aluminum alloy SM10 at 6 different delay times. Element 0.5 s 1.0 s 1.5 s 2.0 s 2.5 s 3.0 s Certified Al 84.8 83.6 83.385.984.484.5 85.0998 Cr 0.2 0.08 0.060.10.080.2 0.2010 Cu 2.2 5.4 5.63.35.92.7 2.8142 Fe 1.3 1.0 1.01.31.11.2 1.9700 Mg 1.1 0.7 0.50.70.70.7 1.0855 Mn 0.2 0.1 0.090.20.10.2 0.2965 Ni 0.2 0.2 0.20.20.10.4 0.0653 Si 3.0 2.5 3.24.83.73.9 2.9348 Ti 0.04 0.04 0.030.040.040.05 0.0553 Zn 7.0 6.3 5.93.43.86.2 5.4777 Element 0.5 s 1.0 s 1.5 s 2.0 s 3.0 s Al 1.7 1.2 6.46.22.6 Cr 22.1 67.4 47.845.366.0 Cu 13.9 41.5 52.652.519.4 Fe 9.6 32.5 37.043.553.9 Mg 15.6 31.6 13.10.636.3 Mn 23.8 58.1 47.751.060.5 Ni 128.6 2.4 13.97.58.9 Si 15.7 46.9 55.148.01.4 Ti 39.3 67.3 52.052.064.8 Element 0.5 s 1.0 s 1.5 s 2.0 s 2.5 s 3.0 s Al 0.3 1.7 2.11.00.80.7 Cr 22.8 61.1 68.935.160.321.9 Cu 21.2 93.3 100.417.8108.85.1 Fe 34.8 47.4 47.131.743.341.0 Mg 0.4 33.9 52.133.131.531.4 Mn 32.6 65.7 69.943.753.239.5 Ni 191.4 170.5 148.6147.2126.7496.7 Si 1.2 14.9 9.863.725.733.3 Ti 24.4 35.7 50.122.223.113.5 Zn 28.6 15.0 7.738.631.414.0

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250 Table 7-7. Relative concentration values and re lative errors (in %) calculated from CF-LIBS analysis of 10 NIST brass standards. NIST Standard Relative Concentration of Cu (%) Relative Concentration of Zn (%) Relative Error (%) Certified CF-LIBS Certified CF-LIBS CuZn 1107 62.11162.937.88937.11.32.0 1108 65.36265.034.63835.00.61.1 1110 84.76883.915.23216.11.05.7 1111 87.18486.812.81613.70.57.2 1115 88.23487.611.76612.40.75.1 1116 90.54289.79.45810.30.98.9 1117 93.12292.26.8787.80.912.8 1112 93.68092.96.3207.00.811.1 1113 95.19294.94.8085.10.36.7 1114 96.52796.13.4733.90.411.2 Table 7-8. Temperature, elec tron number density and minimu m electron number density for LTE calculated from CF-LIBS analysis 10 NIST brass standards. NIST Standard Temperature, T ( 104 K) Electron density, ne ( 1017 cm-3) Minimum ne for LTE ( 1017 cm-3) 1107 1.34 0.06 1.59 0.02 0.275 1108 1.35 0.07 1.75 0.02 0.275 1110 1.40 0.05 1.46 0.02 0.281 1111 1.38 0.06 1.50 0.02 0.279 1115 1.40 0.07 1.36 0.02 0.280 1116 1.40 0.07 1.45 0.02 0.280 1117 1.40 0.05 1.31 0.02 0.280 1112 1.40 0.06 1.37 0.02 0.280 1113 1.40 0.05 1.47 0.02 0.280 1114 1.40 0.06 1.21 0.02 0.280

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251 Table 7-9. Spectroscopic parameters of Zn spectra l lines used in the calibration curves for brass analysis. Specie Zn II Zn I Zn I Wavelength, (nm) 255.795328.233330.258 Lower energy level, Ei (cm-1) 493553231132501 Upper energy level, Ek (cm-1) 884376276962772 Transition probability, Aki (s-1) 3.26 1080.87 1081.07 108Lower level degeneracy, gi 413 Upper level degeneracy, gk 235 Table 7-10. Zn calibration curve pa rameters and limits of detection. Specie 255. 795 nm Zn II328.233 nm Zn I 330.258 nm Zn I Slope, m 152.1 2.7107.8 5.2176.2 5.5 Intercept, b (%) -115.8 50.5113.2 77.7-75.0 47.8 Correlation coefficient, R 0.997820.994320.99612 Limit of detection, cL (%) 0.17 0.12 0.084 Table 7-11. Relative concentration of Zn (in %) calculated using CF -LIBS and conventional LIBS approaches. Sample Certified CF-LIBS Calibration curve 255.795 nm Zn II 328.233 nm Zn I 330.258 nm Zn I 1110 15.232 16.1 11.9 1.0 1111 12.816 13.7 11.3 0.5 14.0 0.9 1112 6.320 7.1 7.0 0.48.0 1.06.5 0.4 1116 9.458 10.3 7.6 1.07.8 0.4 Table 7-12. Relative errors (in %) in calculated Zn concentration. Sample CF-LIBS Calibration curve 255.795 nm Zn II 328.233 nm Zn I 330.258 nm Zn I 1110 5.7 22.0 1111 7.2 12.2 9.1 1112 12.0 10.4 26.7 2.3 1116 8.9 20.2 17.8

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252 Table 7-13. Electron number density and mini mum electron number density for LTE calculated for 6 Al alloy standards at different ambient pressures. Electron density, ne ( 1017 cm-3) Minimum ne for LTE ( 1017 cm-3) Al alloy sample 1000 mbar 100 mbar 0.10 mbar 1000 mbar 100 mbar 0.10 mbar B8 1.62 0.6670.1220.6460.622 0.0656 D33 1.58 0.1330.649 0.0656 S4 1.65 0.1350.655 0.0626 SM10 1.63 0.5600.1400.6470.621 0.0623 V14 1.56 0.1470.649 0.0659 Z8 1.64 0.1200.651 0.0648 Table 7-14. Laser-induced plasma temperatures calculated for 6 Al alloy standards at different ambient pressures. Temperature, T ( 104 K) Al alloy sample 1000 mbar 100 mbar 0.10 mbar B8 1.14 1.071.09 D33 1.17 1.09 S4 1.19 0.99 SM10 1.16 1.070.98 V14 1.17 1.10 Z8 1.18 1.06

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253 Table 7-15. Relative concentration values and re lative errors (in %) calculated from CF-LIBS analysis of aluminum alloy B8 at 3 different pressures. Table 7-16. Relative concentration values and re lative errors (in %) calculated from CF-LIBS analysis of aluminum alloy SM 10 at 3 different pressures. Table 7-17. Relative concentration values and re lative errors (in %) calculated from CF-LIBS analysis of aluminum alloy D33 at 2 different pressures. Element Certified Relative concentration Relative error 1000 mbar 100 mbar 0.1 mbar 1000 mbar 100 mbar 0.1 mbar Al 88.8095 88.0 94.389.71.06.2 1.0 Cr 0.1716 0.05 0.090.0271.645.3 86.2 Cu 7.0155 9.2 3.36.831.652.5 2.4 Fe 0.8075 0.3 0.50.159.443.5 84.1 Mg 0.0767 0.04 0.080.00949.80.6 88.5 Mn 0.4038 0.09 0.20.0377.851.0 92.3 Ni 0.2019 0.2 0.20.20.57.5 1.7 Si 2.3520 2.0 1.23.012.948.0 29.6 Ti 0.1615 0.05 0.080.0171.452.0 92.9 Element Certified Relative concentration Relative error 1000 mbar 100 mbar 0.1 mbar 1000 mbar 100 mbar 0.1 mbar Al 85.0998 84.1 85.987.01.21.0 2.2 Cr 0.2010 0.09 0.10.0154.835.1 95.3 Cu 2.8142 3.7 3.32.430.817.8 13.7 Fe 1.9700 1.1 1.30.146.731.7 95.1 Mg 1.0855 1.2 0.70.210.833.1 77.8 Mn 0.2965 0.1 0.20.00661.943.7 97.9 Ni 0.0653 0.1 0.20.0489.2147.2 33.1 Si 2.9348 2.7 4.82.59.163.7 16.5 Ti 0.0553 0.04 0.040.00125.721.0 97.8 Zn 5.4777 7.0 3.47.827.038.6 41.9 Element Certified Relative concentration Relative error 1000 mbar 0.1 mbar 1000 mbar0.1 mbar Al 86.1782 88.3 86.11.00.1 Cr 0.04770 0.02 0.00545.789.5 Cu 2.9328 3.3 2.427.619.7 Fe 1.1670 0.6 0.234.380.0 Mg 0.0386 0.03 0.0064.583.4 Mn 0.4059 0.2 0.0352.793.3 Ni 0.5074 0.6 0.747.729.2 Si 8.6665 7.0 10.614.022.4 Ti 0.0558 0.03 0.00442.192.1

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254 Table 7-18. Relative concentration values and re lative errors (in %) calculated from CF-LIBS analysis of aluminum alloy S4 at 2 different pressures. Table 7-19. Relative concentration values and re lative errors (in %) calculated from CF-LIBS analysis of aluminum alloy V14 at 2 different pressures. Table 7-20. Relative concentration values and re lative errors (in %) calculated from CF-LIBS analysis of aluminum alloy Z8 at 2 different pressures. Element Certified Relative concentration Relative error 1000 mbar 0.1 mbar 1000 mbar 0.1 mbar Al 84.0937 83.1 84.21.20.2 Cr 0.1305 0.05 0.00562.896.2 Cu 2.6495 4.2 1.757.736.1 Fe 0.1194 0.7 0.05455.654.9 Mg 0.3513 0.2 0.0344.093.0 Mn 0.3814 0.1 0.00964.297.6 Ni 0.1807 0.2 0.016.892.1 Si 1.0337 1.0 1.02.53.4 Ti 0.1204 0.04 0.00363.697.9 Zn 10.9394 10.5 13.04.418.4 Element Certified Relative concentration Relative error 1000 mbar 0.1 mbar 1000 mbar 0.1 mbar Al 87.4618 87.8 87.60.30.1 Cr 0.1815 0.08 0.0255.288.0 Cu 4.0836 6.6 5.262.726.4 Fe 0.9075 0.6 0.238.373.2 Mg 0.0252 0.02 0.0032.887.7 Mn 0.5848 0.2 0.0664.189.8 Ni 0.3327 0.5 0.357.53.4 Si 6.2514 4.1 6.633.75.4 Ti 0.1714 0.06 0.0165.891.7 Element Certified Relative concentration Relative error 1000 mbar 0.1 mbar 1000 mbar 0.1 mbar Al 79.4669 78.5 81.61.22.6 Cr 0.1513 0.06 0.0257.687.1 Cu 16.1865 17.8 16.410.11.4 Fe 1.0993 0.6 0.247.682.0 Mg 1.2808 0.9 0.333.179.5 Mn 0.2622 0.08 0.0369.688.3 Ni 0.5345 0.8 0.340.541.6 Si 0.8471 1.3 1.253.941.4 Ti 0.1714 0.04 0.0175.293.8

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255 Table 7-21. Spectroscopic parameters of spectral lines used in the calibration curves for Al alloy analysis. Table 7-22. Cu and Si calibration curve parameters and limits of detection. Specie 229.436 nm Cu II 327.396 nm Cu I 288.158 nm Si I Slope, m 175.7 2.9152.6 7.2275.8 16.9 Intercept, b (%) 6.7 24.083.6 64.228.8 56.9 Correlation coefficient, R 0.999160.995590.99627 Limit of detection, cL (%) 0.0084 0.095 0.14 Table 7-23. Relative concentration of Cu (in %) calculated using CF-LIBS and conventional LIBS approaches. Sample Certified CF-LIBS Calibration curve 229.436 nm Cu II 327.396 nm Cu I D33 2.9328 3.7 2.2 0.3 S4 2.6495 3.8 5.4 0.28.2 0.6 SM10 2.8142 3.5 7.5 0.8 V14 4.0836 6.2 5.9 0.7 Table 7-24. Relative errors (in %) in calculated Cu concentration. Sample CF-LIBS Calibration curve 229.436 nm Cu II327.396 nm Cu I D33 27.60 23.5 S4 42.02 102.6 210.5 SM10 23.15 165.3 V14 52.67 43.7 Table 7-25. Relative concentrati on of Si and relative errors (in %) calculated using CF-LIBS and conventional LIBS approaches. Sample Certified CF-LIBS Calibration curve Relative error 288.158 nm Si ICF-LIBS Calibration curve D33 8.6665 7.0 5.8 0.4 19.6 33.0 S4 1.0337 1.0 2.4 0.3 2.5 132.0 SM10 2.9348 2.7 5.2 0.4 9.1 76.2 Specie Cu II Cu I Si I Wavelength, (nm) 229.436327.396288.158 Lower energy level, Ei (cm-1) 22847 06299 Upper energy level, Ek (cm-1) 664193053540992 Transition probability, Aki (s-1) 0.25 1081.36 1081.89 108Lower level degeneracy, gi 525 Upper level degeneracy, g k 523

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256 Table 7-26. Relative concentration values and re lative errors (in %) calculated from CF-LIBS analysis of Montana soil NIST SRM 2711 and Estuarine sediment NIST SRM 1646. Table 7-27. Relative concentration values and re lative errors (in %) calculated from CF-LIBS analysis of Buffalo River sediment NIST SRM 2704 and Montana soil NIST SRM 2710. Table 7-28. Relative concentration values and re lative errors (in %) calculated from CF-LIBS analysis of Canadian soils SO-2 and SO-3. Table 7-29. Temperature, elec tron number density and minimu m electron number density for LTE calculated from CF-LIBS anal ysis of 6 soil standards. Soil Standard Temperature, T ( 104 K) Electron number density, ne ( 1017 cm-3) Minimum ne for LTE ( 1017 cm-3) NIST 2711 1.21 3.01 0.660 NIST 1646 1.18 2.98 0.651 NIST 2704 1.18 2.93 0.650 NIST 2710 1.21 2.96 0.658 CAN SO-2 1.17 2.64 0.650 CAN SO-3 1.25 2.54 0.670 Element NIST SRM 2711 NIST SRM 1646 Certified CF-LIBS Relative error Certified CF-LIBS Relative error Al 14.8086 18.0 21.414.524812.7 12.3 Ca 6.5312 3.1 52.51.92890.8 59.8 Fe 6.5539 8.2 25.37.785311.1 43.2 Mg 2.3812 2.5 4.42.53311.6 35.7 Si 69.0312 67.7 2.072.042872.9 1.2 Ti 0.6939 0.6 19.71.18520.8 30.1 Element NIST SRM 2704 NIST SRM 2710 Certified CF-LIBS Relative error Certified CF-LIBS Relative error Al 14.0276 17.5 24.515.731916.1 2.3 Ca 5.9692 1.3 77.9 Fe 9.4359 11.8 25.58.256810.4 25.8 Mg 2.7550 2.0 27.72.08371.9 10.3 Mn 2.46732.0 19.8 Si 66.7631 66.5 0.470.769069.2 2.3 Ti 1.0492 0.9 16.70.69130.5 24.3 Element CAN SO-2 CAN SO-3 Certified CF-LIBS Relative error Certified CF-LIBS Relative error Al 19.2234 26.7 38.77.58149.1 20.1 Ca 4.6689 0.3 92.636.365927.3 25.0 Fe 13.2444 19.0 43.73.75348.6 128.6 Mg 1.2863 0.8 37.812.37889.9 19.8 Si 59.5284 51.4 13.639.423344.4 12.5 Ti 2.0486 1.8 14.20.49710.8 53.3

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257 Table 7-30. Relative concentration values and re lative errors (in %) calculated from CF-LIBS analysis of Ti alloy pellet Alfa Aesar 88395 and Ti alloy metal NIST SRM 654b. Table 7-31. Relative concentration values and re lative errors (in %) calculated from CF-LIBS analysis of Zn alloys NIST SRM 627 and 629. Table 7-32. Relative concentration values and re lative errors (in %) calculated from CF-LIBS analysis of Ni alloy pellet NIST SR M 882 and Cu-Ni alloy metal NIST SRM 1276a. Table 7-33. Temperature and elec tron number density calculated from CF-LIBS analysis of 6 alloy standards. Soil Standard Temperature, T ( 104 K) Electron number density, ne ( 1017 cm-3) Ti alloy pellet 1.25 2.96 Ti alloy metal 1.33 2.21 Zn alloy 627 1.30 3.17 Zn alloy 629 1.29 3.28 Ni alloy pellet 1.46 3.71 Cu-Ni alloy 1.45 2.96 Element Alfa Aesar 88395 Ti alloy pe llet NIST SRM 654b Ti alloy metal Certified CF-LIBS Relative error Certified CF-LIBS Relative error Al 6 8.1 34.66.35467.3 14.2 Ti 90 85.0 5.589.325583.4 6.7 V 4 6.9 72.84.31999.4 116.6 Element Zn alloy NIST SRM 627 Zn alloy NIST SRM 629 Certified CF-LIBS Relative error Certified CF-LIBS Relative error Al 3.8800 4.6 19.25.15895.7 9.7 Cu 0.1320 0.2 48.91.50261.8 18.0 Fe 0.0230 0.04 63.00.01700.02 2.5 Zn 95.9650 95.1 0.993.321592.6 0.8 Element Ni alloy pellet NIST SRM 882 Cu-Ni alloy metal NIST SRM 1276a Certified CF-LIBS Relative error Certified CF-LIBS Relative error Al 2.8589 1.5 47.7 Cu 31.1165 31.2 0.267.506867.8 0.4 Fe 0.56011.1 102.3 Mg 0.12000.2 79.4 Mn 1.01011.2 19.5 Ni 65.4529 66.6 1.730.803129.6 3.8 Ti 0.5718 0.7 30.8

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258 CHAPTER 8 CONCLUSION AND FUTURE WORK Summary and Concluding Remarks An extensive experimental evaluation of tw o existing standard-free techniques for laserinduced breakdown spectroscopy (LIBS) was carried out in this research. The calibration-free LIBS (CF-LIBS) approach and th e Monte Carlo simulated annea ling optimization for LIBS both have capabilities to perform semi-quantitative analysis and provide elemental sample composition without the need for analytical cali bration curves. The two techniques have basic assumptions which are similar but the formulations of the algorithm are inherently different. CFLIBS and MC-LIBS both assume that local th ermodynamic equilibrium (LTE) exists in the spatial and temporal window of observation and that the plasma composition is representative of actual material composition prior to laser ablation. In terms of experimental flexibility and practicality, CF-LIBS prevails ove r MC-LIBS since the algorithm can be applied to any type of spectral data taken either under atmospheric or vacuum conditions. MC-LIBS, on the other hand, can only be applied to experiments perf ormed under reduced pressures since part of the algorithm is currently a model which simulates the radiative expansion of a laser-induced plasma into vacuum. However, the calibration-free me thod usually requires th e use of an echelle spectrometer because a large spectral range is requ ired in order to fully characterize the plasma and extract quantitative information. In this re search, it was demonstrated that a non-echelle, gated detection system with moderate resolution was feasible for obtaining multiple narrow spectral windows for use with CF-LIBS as long as the careful attention is paid to the spectral data acquisition and an intensive investigation of the instrumental function and detector spectral efficiency is carried out prior to LIBS measur ement. The Monte Carlo optimization procedure has the advantage in this aspect since it can still be applied even if only a few lines are present in

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259 a particular spectral window, although accuracy is guaranteed to improve significantly if more lines from all components in the sample are included. CF-LIBS is also restricted to the use of ne utral and singly-ionized lines while species of higher ionization stages can be included in MC-LIBS optimizations. Another requirement for CF-LIBS is that the plasma has to be optically thin. Resonance lines of major elements, which are usually self-absorbed, are simply excluded in the CF-LIBS analysis to avoid underestimation of the elemental concentration. On the other hand, the use of resonance lines in MC-LIBS does not present any difficulty since the modeling algorithm takes into account the occurrence of selfabsorption or self-reversal of lines. While onl y spatially-integrated temperatures and electron number densities can be calcula ted with the CF-LIBS method based on the experimental used in this research, MC-LIBS can provide spatial and temporal evolution of temperature and electron number densities. In terms of the final output, CF-LIBS can only provide relative information, i.e., all concentration values de termined are relative with resp ect to the number of elements included in the analysis, which is, of course, de pendent on the lines present within the spectral window of observation. MC-LIBS has the advant age in this regard si nce it is capable of predicting absolute number densities (in cm-3) for each element included in the optimization procedure. The CF-LIBS and MC-LIBS approaches were both applied to the analysis of certified aluminum alloy samples using spatially-integrat ed and spatially-resolved LIBS measurements carried out under vacuum conditions. The CF-LIBS technique was further evaluated under different delay times and different ambient pressure s. Different types of samples were also used, from brass to powdered soil and alloy samples. Furthermore, standard calibration curves were constructed for a few elements for comparison wi th CF-LIBS analysis. Laser-induced plasma

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260 parameters, such temperature and electron number densities, were reporte d for each sample and for every spatial position analyzed. The accur acy of the quantitative results obtained was evaluated using relative percentage errors. Generally, for the major element present in the sample, CF-LIBS resulted in errors better than 10% while MC-LIBS resulted in errors better than 20% despite the relatively high correlation be tween experimental and simulated spectra ( R > 0.9). However, in the case of the other el ements present in the sample, both methods only proved to be suitable for a semi-quantitative an alysis with relative e rrors between 30-200%. The errors can be due to the c ontributions of several factors: uncertainties in the atomic transition probabilities, uncertainties in the Star k broadening coefficients which are scattered in the literature, uncertainties in the spectral line integration for CF-LIBS and unavailability of calculated partition functions whic h takes into account all the bound quantum states of an atom or ion for some elements considered in the pr esent study, and uncertainties in the temperature and electron number density determination. Experi mental variables, e.g. laser fluctuations, crater formation, aerosol formation, etc., also affect the results of the analysis; however, these are controllable parameters which can be improved so that their effects can be minimized. In order to illustrate how these factors in fluence the calculated elemental concentration, a simple general schematic diagram is presented in Figs. 8-1a and 8-1b for CF-LIBS and MC-LIBS analysis, respectively. It is evident from Fig. 8-1 that the route to quantitative analysis, from sample to signal, is indeed a complex one [124]. Howeve r, the major factor which truly affects the calculated results and is related to most of the factors described previously is the validity of the assumptions imposed on the two algorithms, particularly, stoichiometric ablation and local thermodynamic equilibrium (LTE). If LTE condition fails, it implies that Saha, Boltzmann and Maxwell relationships cannot be used to describe the laser-induced plasma, and therefore, the

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261 calculated plasma temperature is affected and everyt hing else that is related to it. Stoichiometric ablation is also very important, perhaps even more important than LTE, since this is the basis of a standard-free quantitative analysis using LIBS. Even if the in fluences of the other variables are minimized or eliminated, if the gaseous composition of the plasma does not reflect the composition in solid phase, then the whole sche me fails. An independent investigation (see Future Research Directions) of the assumptions made in the two approaches is crucial if standard-free LIBS analysis is to compete with conventional at omic spectroscopic methods. The experimental assessment of CF-LIBS and MC-LIBS carried out in this research is a step towards the ultimate goal of absolute analys is in analytical spectroscopy. Although further investigation is still required in order to improve the accuracy of the calculated results, it can be concluded that standard-free techniques, such as CF-LIBS and MC-LIBS, have found a niche in the matrix-effect-ridden world of laser-induced breakdown spectrosc opy. This definitely opens up several avenues for the applicability of LIBS in different analytical situations. Future Research Directions As an addendum to the research carried out in this dissertation, inde pendent investigations of the assumptions imposed on both approaches are required in order to determine the ideal working conditions for an accurate standard-free quantitative LIBS analysis. The verification of the existence of local thermodynamic equilibriu m in laser-induced plasma has recently been proposed by Moon et al. [134] us ing the line-to-continuum approach which is based on a similar research done by Sola et al. [135] in which the line-to-continuum intensity ratio method was used to determine the electron temperature in a high-pre ssure microwave discharge. It is ideal if the LTE verification will involve experiments carri ed out under vacuum conditions as well. Furthermore, it is important to determine whethe r the elemental components of the sample enter the plasma in proportion to their solid phase con centrations. In close re lation is the independent

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262 determination of absolute number densities by sc anning over absorption profiles in the plasma. This may aid in improving the accuracy of calcu lated results since the value obtained in the absorption experiment can be used as an initia l estimate of the number densities in the Monte Carlo simulations, especially for unknown sample s. An extension of the radiative postbreakdown model to plasma expansion under atmosphe ric conditions also needs to be carried out so that the problems inherent to vacuum experime nts can be further eliminated. Initial work on this aspect has already been started by Kazakov et al. [214]. Use of an auxiliary technique which checks for self-absorption of emission lines is also ideal particularly for CF-LIBS so that lines can be excluded or included properly in the analysis on the basis of the presence or absence of self-absorption, respectively. This can be straightforwardly achiev ed by performing LIBS measurements with and without a concave or sphe rical mirror placed at the radius of curvature (Fig. 3-4) [110]. Moreover, with the advent of faster computers, the number of lines and elements included in the MC optimization procedur e can be increased, as well the length of the spectral range used.

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263 a a b bnplasmaCsampleAkiU ( T ) T ne Stark coefficients Spectral line fitting Experimental variables Signal ( ) I SahaStoichiometricablationBoltzmann LTE Sample LIBS nplasmaCsampleAkiU ( T ) T ne Stark coefficients Spectral line fitting Experimental variables Signal ( ) I Signal ( ) I I SahaStoichiometricablationBoltzmann LTE Sample LIBS Experimental spectrum Experimental variables Simulated spectrum AkiU ( T ) R CsampleT nplasmaneLTE Stoichiometricablation Sample LIBS Signal ( ) I Experimental spectrum Experimental variables Simulated spectrum AkiU ( T ) R CsampleT nplasmaneT nplasmaneLTE Stoichiometricablation Sample LIBS Signal ( ) I Signal ( ) I I a a b bnplasmaCsampleAkiU ( T ) T ne Stark coefficients Spectral line fitting Experimental variables Signal ( ) I SahaStoichiometricablationBoltzmann LTE Sample LIBS nplasmaCsampleAkiU ( T ) T ne Stark coefficients Spectral line fitting Experimental variables Signal ( ) I Signal ( ) I I SahaStoichiometricablationBoltzmann LTE Sample LIBS Experimental spectrum Experimental variables Simulated spectrum AkiU ( T ) R CsampleT nplasmaneLTE Stoichiometricablation Sample LIBS Signal ( ) I Experimental spectrum Experimental variables Simulated spectrum AkiU ( T ) R CsampleT nplasmaneT nplasmaneLTE Stoichiometricablation Sample LIBS Signal ( ) I Signal ( ) I I Figure 8-1. A general schematic diagram of (a) CF-LIBS and (b) MC-LIBS analysis from sample to signal. (See pp. 19-23 for the definitions of the symbols used in the scheme.)

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264 APPENDIX A CALCULATION OF RADIAL EXPANSION VELOCITY PROP ORTIONALITY CONSTANT IN MC-LIBS The conservation of momentum equation is given by: r p nur r r nu tj jj j jj 22 21 (A-1) where j is the mass of j th constituen t (g) and p is the gas pressure (dyne cm-2). Integrating Eq. A-1 along the plasma radius r from 0 to R yields: dr r p drnur r r nu tR R j jj j jj 0 0 22 21 (A-2) Simplifying the right-hand si de of Eq. A-2 yields: R j jj j jjRppdrnur r r nu t0 22 2)()0( 1 (A-3) where0 p is the pressure at the plasma center and Rp is the pressure at the outer plasma boundary which is assumed zero (vacuum). Note that the radial expansion velocity is given by: rttru (A-4) Substituting Eq. A-4 and p ( R ) = 0 into Eq. A-3 yields: R j jj j jjpdrnrtr r r nrt t0 2 2 2)0( 1 (A-5) Expanding the integral in Eq. A-5 and simplifying some of the terms yields: RR j jj j jjpdrnrt r r drnrt t00 42 2)0( 1 (A-6a) RR j jj j jjpdrnr r r tdrnrt t00 4 2 2)0( 1 (A-6b)

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265 RR j jj j jjpdrnr r tdrnrt t00 3 2 2)0( 4 1 (A-6c) RR j jj j jjpdrnrtdrnrt t00 2)0( 4 (A-6d) Further simplification of Eq. A-6d yields: R j jjprdrntt dt d0 20 4 (A-7) Note that the pressure at the plasma center, 0 p, can be calculated using the ideal gas equation: j j BnTkp00)0( (A-8) where T0 is the temperature in the plasma center ( r = 0), in K, and is also the initial guess for T provided in the simulation and n0 j is the initial guess for the total number density for the j th constituent. Recall that the in itial distribution function for temp erature and number density are given by 2 101)0,( rkTrT (A-9) and rgrknrnj j j2 201)0, (, (A-10) respectively, where k1 and k2 are numerical coefficients used for setting the boundary conditions. Substituting Eq. A-8 into Eq. A-7 yields: R j j B j jjnTkrdrntt dt d0 00 2 (A-11) Recall that the derivative of a constant is zero, therefore, the proportionality constant (t) at t = 0 or the time when the laser pulse is terminated, LTE has established and the plasma has acquired a spherical symmetry is given by:

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266 R j jjrdrrn p0 20, 0 0 (A-12)

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267 APPENDIX B CALCULATION OF THE TOTAL ELEMEN T NUMBER DENSITY I N MC-LIBS The conservation of mass or continuity equation in spherical coordinates is given by: 0 12 2 j junr r r t n (B-1) where j = 1,2,,N It is assumed that all constituent s occur as two componentsatomic and ionic so that the total number density trntrntrnj i j a j,,, where trnj a, and trnj i, are number densities of atoms and ions, respectively. Note that the radial expans ion velocity is given by: rttru (B-2) wheret is the proportionality coeffi cient between the collective ve locity of particles and the radius and r is the radial coordinate of the particle in the plasma. Substituting Eq. B-2 in Eq. B1 yields: 0 12 2 rtnr rrt nj j (B-3a) 0 13 2 j jnr r t rt n (B-3b) Multiplying both sides of Eq. B-3b by r3 yields: 03 2 3 3 j jnr r t r r nr t (B-4a) 03 3 j jnr r trnr t (B-4b) Eq. B-4b above is a first-order partial different ial equation. A partial differential equation (PDE) is an equation relating a function of two or more independent variables and its partial derivatives. Considerin g the general equation:

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268 gfu t u e x u d t u c tx u b x u a 2 2 2 2 2 (B-5) where a, b, c, d, e and f may be functions of x, t and even u. The order of the equation is given by the order of the highest derivative. Thus, if one of the functions a, b or c are non-zero, then the PDE is second order. If a = b = c = 0 but d or e are non-zero, then the PDE is first order. If the functions a, b, c, d, e and f do not depend on the dependent variable u, then Eq. B-5 is linear otherwise it is non-linear. If g = 0, then Eq. B-5 is homogeneous, otherwise it is inhomogeneous. The general solution of B-4b is given by: tR r Qtrnrj j,3 (B-6) where Qj(r/R(t)) is some function of the argument r/R(t) derived in the course of the solution of Eq. B-4b after multiple renaming of variables. No te that the initial distribution of the number density of jth constituent in the plasma is given by: rgrknrnj j j2 201)0, ( (B-7) where jn0is the initial number density of the jth constituent at the plasma center and k2 is numerical coefficient which is dependent on the spatial resolu tion and distribution gradient desired. At t = 0, Eq. B-6 becomes: 0 0,3R r Qrnrj j (B-8a) rg R r Qrj j1 03 (B-8b) After substitution of Eq. B-8b into Eq. B-6 and solving the function Qj, one can obtain the number density of constituent j as a function of th e radial coordinate r of particle in the plasma and time t:

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269 tR R rg tR R trnj j0 0 ,3 (B-9)

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270 APPENDIX C CALCULATION OF PLASMA TEMPERATURE IN MC-LIBS The conserv ation of ener gy equation is given by: q u pu u ttotal 2 22 2 (C-1) where is the gas density and is given by: j jjn (C-2) is the internal energy per unit mass of the gas species and q is the energy loss due to radiation. Note that the internal energy relation is given by: j jj BnTk (C-3) where j is ratio of specific heat capacities. Da ltons law of partial pressures is given by: j j B B j j j j totalnTkTknpp (C-4) Substituting Eqs. C-2, C-3 and C-4 into Eq. C-1 yields: qn u nTknTkun u nTk tj jj j j B j jj B j jj j jj B 2 22 2 (C-5a) qn u n Tkun u nTk tj jj j jj B j jj j jj B 2 )1( 22 2 (C-5b) Recall that the operator is given by: r r r r2 2 21 (C-6) Substituting Eq. C-6 into Eq. C-5 yields: qn u n Tkur r r n u nTk tj jj j jj B j jj j jj B 2 1 1 22 2 2 2(C-7)

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271 Distributing the partial derivativ es on the left-hand side and r2u on the right-hand side yields: qn u urn Tukr r r n u t nTk tj jj j j j B j jj j jj B 2 )1( 1 22 2 2 2 2 (C-8a) qnurn Tukr r r n u t nTk tj jj j jj B j jj j jj B 32 2 2 22 1 )1( 1 2 (C-8b) Distributing the partial derivatives on the right-hand side yields: qnur r r n Tukr r r n u t nTk tj jj j jj B j jj j jj B 32 2 2 2 22 11 )1( 1 2 (C-9) Excluding partial time derivatives of u and nj yields: qnur r r n r T uk t nu t T nkj jj j jj B j j j j jj B 32 2 22 1 )1( 2 (C-10) With the use of the conservation of mass equation: 0 12 2 j junr rrt n (C-11) and radial expansion velocity equations: rttru (C-12) Eq. C-10 becomes qnur rr n r T uknTur rr Tk nr t nu t T nkj jj j jj B j j B j jj j j j j jj B 32 2 22 2 2 22 1 )1( 2 (C-13) Dividing Eq. C-13 by Bk yields: B j jj B j jj j j j jj B j j j B j jjk q nur rrk n r T unTur rr T n k r t n k u t T n 32 2 22 2 2 22 1 )1( 2 (C-14) Solving Eq. C-14 for T / t yields:

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272 B j jj B j jj j j j jj j j j B j jjk q nur rrk n r T unTur rr T n k r t n k u t T n 32 2 22 2 2 22 1 1 2 (C-15) Dividing both sides of the equation by (jnj) yields: j jj B j jj j jj B j jj j j j j jj j j j jj j jj B j jj j j j Bnk q n nur rrk n n r T u n nTur rr T n n k r n t n k u t T 32 2 22 2 2 22 1 1 2 (C-16) Simplifying the 4th term on the right-hand side of Eq. C-16 yields: j jj B j jj j jj B j jj j j j jj j jj j j j jj j jj B j jj j j j Bnk q n nur rrk n nn r T u n nTur rr T n n k r n t n k u t T 32 2 22 2 2 22 1 2 j jj B j jj j jj B j jj j j j jj j jj j jj j j j jj j jj B j jj j j j Bnk q n nur rrk n n r T u n n r T u n nTur rr T n n k r n t n k u t T 32 2 22 2 2 22 1 2 j jj B j jj j j j jj j jj B j jj j j j jj j jj B j jj j j j Bnk q n nT r u r T u n nur rrk n nTur rr T n n k r n t n k u t T 32 2 22 2 2 22 1 2 (C-17) Substituting rttru into the 4th term of Eq. C-17 yields: j jj B j jj j j j jj j jj B j jj j j j jj j jj B j jj j j j Bnk q n nT r u r T u n rr r n rk n nTur rr T n n k r n t n k u t T 332 2 22 2 2 22 1 2 j jj B j jj j j j jj j jj B j jj j j j jj j jj B j jj j j j Bnk q n nT r u r T u n n rk r n nTur rr T n n k r n t n k u t T 2 34 22 2 2 22 5 2 j jj B j jj j j j jj j jj B j jj j j j jj j jj B j jj j j j Bnk q n nT r u r T u n n k r n nTur rr T n n k r n t n k u t T 2 5 232 22 2 2 2 (C-18)

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273 Recall that the equation for the radial expa nsion proportionality c onstant is given by: j jj R j j Btrnrdr tntTk t ,0,00 2 (C-19) Substituting Eq. C-19 into the 4th term of Eq. C-18 yields: j jj B j jj j j j jj R j j B j jj j jj B j jj j j j jj j jj B j jj j j j Bnk q n nT r u r T u trnrdr tntTk n n k r n nTur r r T n n k r n t n k u t T ,0,0 2 5 20 2 22 2 2 2 j jj B j jj j j j jj R j j j jj j jj j jj j j j jj j jj B j jj j j j Bnk q n nT r u r T u trnrdr tntT n nr n nTur r r T n n k r n t n k u t T ,0,0 2 5 20 2 22 2 2 2 (C-20) After further simplificat ion, one can obtain: j jj B j jj j j j jj R j j j jj j jj j jj j jnk q n nT r u r T u trnrdr tntT n nr n n T t T ,0,0 2 5 30 2 j jj B j jj j j j jj R j j j jj j jj j jj j jnk q n nT r r r T r trnrdr tntT n nr n n T t T ,0,0 2 5 30 2 (C-21)

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274 APPENDIX D CALCULATION OF ATOM, ION AND ELECTR ON NUMBER DE NSITIES IN MC-LIBS The Saha equation is given by: Ts Tk h Tkm U U n n nj B j Be j a j i e j a j i exp 2 22/3 2 (D-1) where j = 1,,N j an j in ,en are the number densities of atoms, ions and electrons, j aU and j iU are the atomic and ionic partition functions of the j th constituent, respectively, j is the first ionization potential of j is the defect or lowering of the ionization potential of atoms due to the electric field of surrounding electrons and the rest of the parameters are defined in pp. 19-23. The mass conservation equation for each charge state and for each plasma constituent is given by: jj a j inn n (D-2) The equation of charge equilibrium for N plasma constituents given by: e j jnni (D-3) The above algebraic system of equations dete rmines the charge di stribution for a fixed temperature and densities of elemental plasma constituents. From Eq. D-1, the ion number density is given by: e jj a j in Tsn n (D-4) Substituting Eq. D-4 into Eq. D-3 yields: e j e jj an n Tsn (D-5) Multiplying Eq. D-5 by ne yields:

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275 2 e j e e jj ann n Tsn 2e j jj anTsn (D-6) Multiplying Eq. D-2 by ne yields: e j e j ae j innnnn n (D-7) Substituting Eq. D-4 into Eq. D-7 yi elds the atom number density: e j e j ae j innnnn n e j e j ae e jj annnnn n Tsn e j e j a jj annnnTsn e j e jj annnTsn e j e j j anTs nn n (D-8) Substituting Eq. D-8 into Eq. D-6 yi elds the algebraic equation for ne which has a unique positive solution: 2 e j jj anTsn 2e j j e j e jnTs nTs nn 2e j e j e jjn nTs nTsn e j e j jjn nTs Tsn (D-9) Substituting Eq. D-8 into Eq. D-4 yi elds the ion number density:

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276 e jj a j in Tsn n e j e j e j j in Ts nTs nn n e j jj j inTs Tsn n (D-10)

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277 APPENDIX E CERTIFIED CONCENTRATION VALUES OF REFERENCE STANDARDS Table E-1. Elem ental percentage composition of South African aluminum alloy standards. B8 D33 S4 S11 SM10 V14 Z8 Al 87.980 84.920 83.79189.19784.67086.74278.797 Bi 0.099 0.680 Cr 0.170 0.047 0.1300.1150.2000.1800.150 Cu 6.950 2.890 2.6400.9802.8004.05016.050 Fe 0.800 1.150 0.1190.5701.9600.9001.090 Mg 0.076 0.038 0.3501.1101.0800.0251.270 Mn 0.400 0.400 0.3800.5000.2950.5800.260 Ni 0.200 0.500 0.1800.1000.0650.3300.530 Pb 0.165 0.140 0.130 0.245 Si 2.330 8.540 1.0300.4502.9206.2000.840 Sn 0.155 0.048 0.150 0.2600.280 Ti 0.160 0.055 0.1200.0650.0550.1700.170 Zn 0.520 0.590 10.9006.8505.4500.4200.790 Zr Table E-2. Elemental percentage co mposition of NIST brass standards. 1107 1108 1110 1111 1112 1113 1114 1115 1116 1117 Cu 61.210 64.950 84.590 87.14093.38095.03096.45087.960 90.37093.010 Fe 0.037 0.050 0.033 0.0100.0700.0430.0170.130 0.0460.014 Mn 0.025 Ni 0.098 0.033 0.053 0.0220.1000.0570.0210.074 0.0480.020 P 0.0090.0080.0090.005 0.0080.002 Pb 0.180 0.063 0.033 0.0130.0570.0260.0120.013 0.0420.069 Sn 1.040 0.390 0.051 0.0190.1200.0640.0270.100 0.0440.021 Zn 37.340 34.420 15.200 12.8106.3004.8003.47011.730 9.4406.870 Note: Certified values are obtained from the NI ST standard reference ma terials database [208].

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278 Table E-3. Elemental percentage compositi on of NIST and Canadian soil standards. NIST 1646 NIST 2704 NIST 2710 NIST 2711 CAN SO-2 CAN SO-3 Al 6.250 6.110 6.4406.5308.070 3.050 Ba 0.097 0.030 C 3.348 Ca 0.830 2.600 1.2502.8801.960 14.630 Cu 0.295 Fe 3.350 4.110 3.3802.8905.560 1.510 K 1.400 2.000 2.1102.4502.450 1.610 La Mg 1.090 1.200 0.8531.0500.540 4.980 Mn 1.010 0.072 0.052 Na 2.000 0.547 1.1401.1401.900 0.740 P 0.100 0.1060.0860.300 0.048 Pb 0.5530.116 S 0.960 0.400 0.240 Si 31.000 29.080 28.97030.44024.990 15.860 Ti 0.510 0.457 0.2830.3060.860 0.200 Zn 0.695 Note: Certified values are obtained from the NI ST standard reference ma terials database [208] and Natural Resources Canadas Canadian ce rtified reference mate rials project (CCRMP) database [209]. Table E-4. Elemental percentage com position of different alloy standards. NIST 1276a NIST 882 AA 88395* NIST 654b NIST 627 NIST 629 Cu-Ni Ni Alloy Ti-Al-V Ti Alloy Zn Alloy Zn Alloy Al 2.850 6.0006.3403.880 5.150 Co Cu 67.500 31.020 0.132 1.500 Fe 0.560 0.2300.023 0.017 Mg 0.120 0.094 Mn 1.010 Ni 30.800 65.250 Si 0.078 Ti 0.570 90.00089.120 V 4.0004.310 Zn 95.965 93.161 Note: Certified values are obtained from the NI ST standard reference ma terials database [208]. *Alfa Aesar standard.

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291 BIOGRAPHICAL SKETCH Kathleen Kate Herrera w as born on Decembe r 3, 1979 in Manila, Philippines. She attended Our Lady of Grace Academy and graduate d salutatorian of th e high school class of 1996. She pursued her Bachelors degree in Chem istry at the University of the Philippines in Diliman, Quezon City and graduated in April 200 0. In October 2000, she passed the Chemistry board licensure examination. Afterwards, Kate joined the junior faculty of the Institute of Chemistry at the University of the Philippines where she worked as a chemistry laboratory instructor for three years. In August 2003, Kate moved to Gainesville, Florida and began her graduate studies in analytical chemistry at the Un iversity of Florida. She completed her doctoral research under the supervision on Dr. Ja mes D. Winefordner in August 2008.