Title: Double modulation - optical scanning and mechanical chopping - in atomic absorption spectrometry using a continuum source
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 Material Information
Title: Double modulation - optical scanning and mechanical chopping - in atomic absorption spectrometry using a continuum source
Physical Description: xiii, 91 leaves. : illus. ; 28 cm.
Language: English
Creator: Elser, Robert Cooper, 1941-
Publication Date: 1971
Copyright Date: 1971
 Subjects
Subject: Spectrometer   ( lcsh )
Absorption spectra   ( lcsh )
Atomic spectra   ( lcsh )
Chemistry thesis Ph. D
Dissertations, Academic -- Chemistry -- UF
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
 Notes
Thesis: Thesis--University of Florida, 1971.
Bibliography: Bibliography: leaves 88-89.
General Note: Manuscript copy.
General Note: Vita.
 Record Information
Bibliographic ID: UF00098391
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: alephbibnum - 000958613
oclc - 17063952
notis - AES1424

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ii' ,'.t.c Jic .:\b :. ) ti. t n .7: rl. :. ^ r v i a Conri"i rl 'LUn 3.,.ir 3



























!*'i I _i -t7 '.- I ..-T-: UA IN PARTIAL
UIL I .!.ii-:. ,. : r:, .I? .: 2POR THE D):GR3E OF
D. .:'.'. -'IL H 'PHY


I :II'mR.?IQV *.j? I.' RIPA
1.-c-,'







































3 1262 06552 4816








3 1262 08552 4816

















DEDICATION


The work contained in this dissertation represents

the attainment of a goal which would have been exceedingly

difficult without the love and encouragement of my wife,

Kay. It is to her and to her understanding that I

dedicate this dissertation.

















Any author has many debts to colleagues and teachers

who have aided and guided him along the way. In this

regard, I must express my gratitude to Dr. John Savory,

who believed in me when it counted, to Drs. Eugene Sander,

Gerhard Schmid and Roger Bates for their guidance as

teachers and especially to Dr. James D. Vinefordner for

his direction and encouragement of my work. To

Mr. Theodore Booher I owe a debt which can never be repaid,

that of his friendship, encouragement and advice ,when it

was needed most.












TABLE OF CONTENTS


ACK O EDG ENTS . . . . . . .

LIST OF TABLES . . . . . . .

LIST OF FIGURES . . . . . . .

KEY TO SYMBOLS . . . . . . .

ABSTRACT . . . . . . . .

Chapter

I. INTRODUCTION . . . . .

II. THEORETICAL CONSIDERATIONS ..

Mechanical Chopper Modulation.

Refjac or Plate IIodulation .

Intensity Expressions . . .

Limits of Detection, . . .

Signal-to-IToise Ratio. . . .

III. EXPERIMENTAL SYSTEM AID PROCEDURES.


Description of Sysbem. .

Source . . . . .

Burner and Nebulizer .

Monochromator and Optics .

Electronic Components. .

Solutions. . . . .

Experimental Procedure .


. . "


Page

. iii

S vi

Svii

S ix

. xii



1

* 7

* 7

* 9



33

S 3?

S 38

* 38

* 38

Z 8

49

S 55

. 57

. 58


. . .











i.;'lT 0" 'L A P.ELFS


.... 1 :I I J. f '

".'.",r':aI.: ,',..'n *.f I -it.; :ii ,..t '-. y:-", T; .'ty | 92

2. Optic oi: Components ............. 41

3. Electrical Components. . . . . ..

4. Verification of Theory . . . . . . 61

5. Limits of Detection. . . . . . . 84










IV. RESULTS AND DISCUSSION . . . . .

Verification of Theory ....... . 60

Analytical Curves and. Limits of Detection 66

Conclusions . . . . . . ... 85

LIST OF REFERENCES . . . . . . . ... 88

BIOGRAPHICAL SKETCH. . . . . . . . . 90











1.1T U -.LS,

Figure Fa:.

la. Refraction of an axial beam inciden:ui I.1..
refractor plate at an angle, a . . 11
lb. Refraction of a non-axial beam incident to
the refractor plate at an anglo, a . . .. 11

2. Schematic diagram of the optical system. .16

3a. First derivative of Ca resonance line profile
at 4-227 A at a concentration of 25 ug ml-I 29
3b. Second derivative of Ca resonance line profile
0 -1
at 4227 A at a concentration of 25 ug ml 29

'l-. Theoretical curve of growth for Ca at 4227 A
by first derivative analysis . . . .. 32

5. Block diagram of experimental system . . 40

6. Relative spectral radiance of xenon arc . 46

7. Electrode holder for piezoelectric transducer. 51

8. Spectral modulation amplitude (slit image
displacement) versus voltage supplied to the
binorph. . . . . . . . . . 53

9. Circuit for chopper reference signal' . .. 54

10. First derivative signal intensity versus
spectral modulation amplitude (slit image
disnlacerient) at constant; spectral bandwidth
of 0.40 . . . . . . . . . 63

11. Analytical curve for silver taken at 320 A. 68

12. Analytical curro for calciumi taken at 4227 A 70
0
13. Analytical, curve for cadniun taken at 2288 A 72

14. Analytical curve for chromium taken at 3579 A. 74










Figure Page
0
15. Analytical curve for copper taken at 3217 A 76

16, Analytical curve for iron taken at 3719 A 78

17. Analytical curve for magnesium taken at
2852 A. .. . . . . . . . . 80

18. Analytical curve for nickel taken at 3414 A 82


viii













i '7C" TO ?"-Iirl .3


0
a Lateral displacement of refracted bcam, A.

A = Atomic w-eight, amu.

B = Factor accounting for noise contribution from dynodes,
no units.

B = Unmodulated source spectral radiance, watts cm-2
Xo -1 -1

c -2
Sr 11m

Bc = Modulated source spectral radiance, watts cm2
Xo 0 -1 -1
sr nm
c -2
B c = Radiance transmitted through flame, watts c-2
-1 -1
sr 1m .

BT(c,, ) = Modulated spectrum viewed by phototube, watts.
J--I
c Speed of light, cm sec-.

C = HIinimim detectable solution concentration, pg ml-1

d = Lateral geometric displacement of refracted bear, mm.
-.19
e = Electronic charge, 1.6 x 1019 coulomb.

E = Excitation energy of state i, ev.

Af = Frequency interval over which amplifier readout system
responds, Hz.

i = Statistical weight of state i.

H = ilonochromator slit height, cm.

Ai rms noise signal due to the photodetector, amperes.

J = Total angular momentum quantum number.

k = Boltzrnjnn constant, 8.64 x 10- ev OK-.










km = Peak atomic absorption coefficient for the minimum
-1
detectable concentration, cm .

ko = Atomic absorption coefficient at the absorption line
center, cm-1

k, = Modified atomic absorption coefficient, cm-1

1 = Length of flame, cm.

M = Multiplication (amplification)-factor of photodetector,
no units.

n = Total atomic concentration of species of interest,
atom cm-.

n = Total minimum atomic concentration of species of
-3
interest in flame, atom cm .

nm = minimum atomic concentration of species of interest
in state i in flame, atom cm3.

Q = Flow rate of unburned gases, cm sec-I.
o -1
Rd Reciprocal linear dispersion of monochronator, A mm -
R' -1
R = Reciprocal linear dispersion of monochromator, A cm

RL = Phoottube load resistor, ohms.

s = Spectral bandwidth of monochrom!ator, A.-

S(X) = Slit function of the nonochromator, no units.

S, 1 42 = First derivative signal, volb.

S, = Second derivative signal, volt,

T = Absolute temperature, OK.

T. = Transm.ission factor of instrumental system of lenses,
S monochraomator and flame.

T(X) = Transmission of flame cell.









t = ThickIu- c z of 'r. ; fr .': V.: :.v :i L. nI,.

W = Honochronator slit width, cm.

Z(T) = Electronic partition function, no units.

a = Angle of beam incident to refractor plate, rad.

a' = Angle of refracted beam within refractor plate, rad.

P = Factor to account for incomplete atom formation and
losses due to ionization, no units.

= Phototube sensitivity factor, a-np watt-.

S = Parallel displacement of refracted beam, run.
o
A = Apparent half-width of absorption line, A.

e. = Efficiency of nebulization and atomization processes.
0
X = Any wavelength, A.

Xc = Wavelength at center of exit; slit; corresponding to
grating setting, A.
0
0- = Wavelength at center of absorption line profile, A.

AXA = Half-width of absorption line, A.
2
2e -2 2 --1
L-- 2.65 x 102 cm sec1.
mc
S= Coefficient to correct ko.
S= Flow rate of solution into nebulizer, cm3 nmin-

Mi = Solid angle of radiation collected by the mono-
chr'omaaor, sr.

i 1 = Froquency of source modulation, soc-.
p= Frequeoncy olf wavelengtLh modulation, sc.-
02 = Vrequency of wavwloneth modulation, sece










Ai:,:,;.t of Dissertation Presented to the Graduate Council
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy


DOUBLE MODULATION
OPTICAL SCANNING AND M3ECIIANICAL CHOPPING -
IN ATOMIC ABSORPTION SPECTROMETRY USING A CONTIITUUM SOURCE

By

Robert Cooper Elser

June, 1971-

Chairman: James Dudley Winefordner
Major Department: Chemistry

Atomic absorption spectrometry using a continuum

source (AAC) presents several advantages distinct from

atomic absorption using line sources. Among these are a

saving in time of analysis, saving in cost of sources and

the capability of non-resonance line absorption measurements.

An instrumental system employing double modulation -

mechanical chopping of source radiation and wavelength

modulation of radiation transmitted by the absorption cell -

offers advantages over normal AAC. Improvement in signal-to--

noise ratios and decreased sensitivity to background as

compared to normal AAC are the most important advantages.

In this work, a doubly modulated system is described and

the theory underlying its operation derived. It is shown

that both first and second derivatives of the transmitted


xii










spectrumn . i I L i. T .-'ir~.l. i L 'irC :, .i.:-ri-: i..- o ', ,-, ::u- t

a frequency equal to the sum or the difference of the two

modulation frequencies,while the second derivative appears

at the sum or the difference of the chopping frequency and

twice the wavelength modulation frequency. Experiments

are described which verify the validity of the theoretical

expressions. Analytical curves and limits of detection

are presented for the following eight elements: Ag, Ca,

Cd, Cr, Cu, Fe, Ig and Ni.


xiii












CHAPTER I


INTRODUCTION


Atomic absorption spectrometry has proven its utility

as a practical analytical tool in laboratories throughout

the world over the past fifteen years since Walsh [1]

introduced it in 1955. In his classic paper, he indicated

that the measurement of the atomic absorption line profile

of an element in a flame should provide a clue as to the

atomic concentration in the flame. However, in order to

resolve the spectral profile of an absorption line,

monochromators having nearly unattainable resolving power

would be required. Furthermore, the question of whether a

continuum would have sufficient spectral energy in an

interval of the size of an absorption line, that is 0.01

to 0.03 A, to provide an acceptable signal-to-noise ratio

led him to propose that measurement of the peak atomic

absorption coefficient at the line center using a line

source would provide similar quanti ative information.

Because an atomic line source concentrates most of its

spectral output into the resonance lines characteristic of

thab element, it would provide sufficient energy in the









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arguments, the development of atomic absorption instrumen-

tation has excluded the use of continuum sources to a large

extent. It is unfortunate that this has been the case since

continuum sources offer several advantages over line sources.

These have been enumerated by several authors [2,3,4,5,6]

and include Lhe requirement of having only one source

instead of a source for each element (or small groups of

elements) of interest; the saving of time in source align-

ment, and ease of background correction. In addition,

McGoc and WIinefordnor [2] and Fassel etf al. [5] have shown

that the limits of detection by atomic absorption using a

continuum source approaches that using line sources for

many elements. At low concentrations of absorber, however,

the absorption line half-width becomes ins:ignificanb with

respect bo the spectral bandwidth of the monochronator and

while the line may be discerned, the signal-to-noise ratio

is low. It was thought that the weak signal due to the

absorption line profile could be extracted from' the noise

and enhanced by using a derivative bochniquo which has been

o ployed successfully in other areas of spectroscopy.










The technique of derivative spectroscopy, that is,

taking the derivative of the transmitted spectrum with

respect to time or wavelength, was first introduced in 1955

by Giese and French [7]. They demonstrated its theoretical

utility in resolving overlapping absorption bands having

as much as 90 per cent overlap. Collier and Singleton [8]

applied the technique to infrared absorption spectra by

taking the second derivative of the spectrum electronically.

However, as Bonfiglioli and Brovetto [9] and Perregaux and

Ascarelli [10] point out, analog differentiation of the

defector outpii results in treatment of the noise component

contained in the signal as well as the information component.

The frequency spectrum of the noise component differs from

the frequency spectrum of the information component. There-

fore, the noise in the derivative signal may become a greater

proportion than in the original signal with the result that

the signal-to-noise ratio of the derivative signal is lower

than that of the original signal. Bonfiglioli and Brovetto

developed the theory for a self-modulating derivative

optical spectrometer [9] which employed a vibrating mirror

to modulate the image of the spectrum. They showed, as

will be derived in Chapter II, that by modulating the

spectrum spatially and detecting at the appropriate

frequency, the derivative of the transmitted spectrum may be

obtained. In this manner, only the derivative of the desired










signal is obtained, i it the -: oia ,I'.T-; ronrL 11 Of i- ct i- 1

maintaining its relative proportion or even. decreasing, In

fact, noise arising from random fluctuations in phototube

output proved to be the limiting noise in the derivative

system. Since this type of photon noise has a constant

spectral noise power over the entire frequency spectrum,

its contribution to the signal will be identical for both

modulated and unmodulated systems. Their system proved

efficacious in the analysis of complex molecular absorption

bands [11] of rare earth nitrates in aqueous solutions.

Various ingenious techniques have been employed in

obtaining a modulated spectrum, Stauffer and Sakai [12]

used a rotating mirror stopped along one diameter to modu-

late the spectrum image by a discrete amount. Balslev [15]

modulated the exit slit of his monochromator by mechanically

linking it to a loudspeaker vibrating at 175 Hz. The

derivative spectrum obtained was used to study the influence

of stress on the indirect optical absorption edge in silicon

and germ.anium: crystals. Williams and Hagor [14-] also

employed an oscillating exit slit bo study the second

derivative absorption spectra of Caseous atmospheric pol-

lutants. Porregaux and Ascarelli [10] studied the first

derivative absorption spectrum of 12 in an incandescent lamp

using a gl.ss refractor plate to modulate the spectrum. In

their system, the plate was cpoxiad to a sbeel ribbon which









was oscillated by means of a piezoelectric bimorph. Shaklee

and Rowe [15] used a fused. silica refractor plate to modu-

late the reflectance spectra of InP and GaP at several

temperatures. Snelleman et al. [16] modulated the emission

spectra of elements in a flame using a quartz refractor

plate and by operating in the second derivative mode were

able to detect Ba in the presence of large amounts of Ca;

The first application of derivative spectrometry to atomic

absorption was by Snelleman [17] who used a mirror to scan

the image of the dispersed spectrum across the exit slit

of the monochromator. It was primarily his work which led

to the development of the present system.

A continuum source and double modulation, that is,

modulation of the radiation falling on the flame and

emerging from it, was employed in this experimental system.

A theory was developed to predict the response of the

instrumentation to variation of experimental parameters.

Several authors [9,13,14,15,18,19] have developed theoretical

intensity expressions for derivative spectrometers. How-

ever, none have used. their expressions as quantitative

predictors of experimental signals, The derivation of

theoretical expressions in this work closely parallels the

derivations of Bonfiglioli and Brovetto [9] and Shaklee and

Rowe [15]. The quantitative predictions of the theory were

investigated and the system was used to construct analytical











curv: C r, C' 1 F i i ic. .' Cd, Cr, Cu, Fe, TI, and Ni.












CHAPTER II


THEORETICAL CONSIDERATIONS


Mechanical Chopper IHodulation


In atomic absorption spectrophotometry, ib is

important to eliminate any signal arising in the absorption

cell which is not due to absorption of source radiation.

Since in most atomic absorption systems the absorption

cell is a flame, there are three possible spurious sources

of signal arising in the cell: emission due to flame gas

combustion products; atomic emission and/or fluorescence

of analyto atoms in the flame, and Rayleigh scattering of

source radiation by small unovaporated solvent droplets or

other small particles. Fortunately, in most cases, none of

these has much effect upon the radiation passing through

the flame. However, because atomic absorption signals are

due to the attenuation of source radiation by absorbing

species in the flame, any emission due to flame gas products

or analyte atoms will decrease this attenuation and cause an

apparent decrease in absorption which would be interpreted

as a smaller concentration of absorbers in the absorption

cell. Likewise, Rayloigh scattering of source radiation










. .':.i.'-. Inc'r:-- :c.. I-'.:: ll:r".ri '':L:.n t, i.hc i "li' c' O i'- .2:..ini,
ILJ'.: ]jt-[ l i": ri.. '1 ..* r .- 'lm L I iii:.: rc e. :.. 1'
i'' *- '. L-' O:= i -.) i *I m -i: 1, : i n s f' i ? .L1 : T ." ii. ;r : i.'1i ] =

there.

By modulating the source radiation and measuring the

detector signal at the modulation frequency and with the

correct phase relationship, omission from the flame cell

can be rejected. The effect of Raylcigh scattering is

eliminated by wavelength modulation. As a result of the

source modulation, the signal due to absorbing species

appears as an ac component, at the frequency of modulation,

superimposed upon the de signal due to flame coll omission.

In practice, source modulation is usually accomplished by

mechanical chopping using a motor driven disk having

alternating transparent and opaque sectors which intersect

the bean of radiation emanating from the source along the

optical path of the system.

The modulated source radiation, if it is focused

on the chopper disk, is actually nearly square-wave modu-

lated, IHo:rover, in order to treat tho system r.abhe'oatically,

it is convenient to assume the source radiation is sinu--

soidally modulated. In this case, the modulated source
c -2 -L
spectral radiance, B (w.atts canti.atetr- sberadian
-10
nanometur ), m;a be expressed as;


S- /'B (1 + cos it) (1)
xo o X









where Bo is thb unmodulated source spectral radiance
-2 -l -1
(wat ts cm -sr -nmr- ) and ei is the frequency of source

modulation. In Equation (1) it is assumed thab there are

equally sized transparent and opaque sectors and therefore


Bc = B o (2)
XAvg X

where BC is the average source spectral radiance incident
AAvg
upon the flame cell.

Refractor Plate Iodulation

The wavelength modulation of the system is

accomplished in this work by the use of an oscillating

quartz plate. Because the index of refraction of the quartz

plate is different fro; n that of air, a beam of light inci-

dent on the plate will be refracted if its angle of

incidence varies from 0. The lateral displacement of the

refracted beam may be expressed as


d = t-cos a (tan a tan a') (3)

where d is the lateral displacement (ram), t is the plate

thickness (mm), a is the angle of incidence and a' is the

angle of refraction. It may be clearly seen front Figure la

that the following relations hold


, tan a' = Z (4-)


t
Cos U. = yy Ir tan a i


















-~~~ i)-* L~cr[- cC 1a tci~ b' 1nju.ictL


Figo. lb.---Refraciion of a non-axial beat incidlen
bo the refractor plate at an ar le, ca.









II





dn


!-- t -1


a- a,









By rearranging and substituting, one obtains Equation (3).
From Snell's law


n tan a = n' tan a' (5)

where n and n' are the index of refraction of air and the

plate, respectively. Substitution of Equation (5) into

Equation (3) yields the exact expression for the lateral-

displacement

d = t'cos cc (tan a t tmn a) (6)

For very snail angles cos a is nearly unity and

sin a is approximately a. Considering n to be unity, the

small angle approximation for the lateral displacement

becomes

d = t a (1- --) (7)

It is clear from this equation that the lateral displacement

of the incident been from the optical axis is proportional

to the thickness of the refractor plaot and to the ;nIgle it

makes with the incident bean.

The lateral dispLacemaent of the image of the en-

trance slit at the exit slit plane in wavelength units, A, is

a d (8)

where Rd is the reciprocal linear dispe -rion of the nono-

chromfitor (A am-1.










The result of oscillating the refractor plate

periodically so that the angle of the incident beam varies

periodically from u. to -ca at some angular frequency c2 is

to oscillate the entrance slit imago about some nean wavc-

length, Xc, which corresponds to the position of the grating

of the monochromabor with the refractor plate perpendicular

to the entering light beam. The position of the mobile

spectrum with respect to the grating setting, X may be

expressed as


X = X c- a sin w2 t (9)

where X is bhe mean wavelength passing through the exit

slit.

The Rayleigh :scattering mentioned in the preceding

section is accounted for by wavelength modulation. Since

Rayleigh scattering is independent of wavelength over a

small wavelength range for a given particle size, any

scattering will be the same at the absorption line and

close by it. Thus, there will be a constant difference

between the baseline signal and the absorption signal

whether scattering is present or not.

In addition to causing a lateral displacement of an

axial beam incident upon it ab some angle a, the refractor

plate also causes a displacement of non-axial beams parallel

to the optical axis, Figure lb,










S- *i.. -in ,:< (10)


where S is the parallel displacement of the image (ui). By

substituting the small angle approximation for d and for

sin a the following result is obtained


S= t( 1-) (11)


For the case of quartz, this means that the image of the

incident bean is displaced a distance of approximately

one-third the thiccncss of the refractor plate. In practice

the result is a slight defocussing of the exit image which

can be neglected.


Intensity E:_pressions


Intensity expressions which allow quantitative pre-

diction of experimental signals will be derived in the

following section. It will be shown that signals corres-

ponding to both first and second derivatives of the

tr.?nosmitted spcctrum are predicted. The oxpresssions do-

rived for this sysite.i are general and apply equally to

spectra containing narrow or broad lines.

The oxperimienbal arrangement for which the expres-

sions will be derived i; illustrated in 2igurc 2. The

source employed must be a continuum for tho expressions to

hold. The source radiance and the radiance at each impor-

bant point a3re also indicated in Figure 2.



















I 0

4J 0

I I *
C dr 4' O O
M r- H-P 0 0 H
CM rH 1 c 4' )

c I O O

0 -P 0 0 4- 0 4- r 0
SE I-Cr-I -I -H o
H 4- P To o Al A A o i d a
0 O CU 4- 0 4 O 0
-pH I O 80 10 10 d ,0 o rH


o1 05-oo o ]e d
d r C 0 0 i 4-I
fr~~, p ci pi (A C) -P a L o i

C -P H o H-
C) ci N (\I C 0 ri C


O 0 +Pd H 01 0r) P 0 d





o0c a rJ rd a e o
oi '-' o c c i o o o



l 4000
c' r-i 4i O 4 C ) fC5 ) 0 i
0i 0 0 c 0 0 0 4' rH oH
-P ci 0 '-I *- n

. i 0 d 0 0 0 0 4
0 )-P 0 C -P P p


o o d o a .o .- -p .- _- O ,- o,
CI 'd H 1 * -P 'H E C) C
Al C0 ci 5 m^ Ci CM 'H C 0 0 C)0H
+d fl *4 tH N I Cj C C




S00 C) i 4' M C M -P 0) 0 P (
Cd C O) 0 U) -!4 PA



I
O 0 H 0 0 C0 1 O ON

cO H O H I 0 0 0 0 5 ) 0
oU 'di Pi ) C-i C -i C l 10 o 0)

0I A CO 0- P 0C 0 03 0

1 II II II 0 II o
,l 0 0 1i -C CO -I





60
-rt


























I-
0 -<

0)

C,)


n.
0.
0
1:

It


I Li









The continuum source spectral radiance, B is
o
focused onto the blade of a chopper wheel rotating at an
c*
angular frequency (,)I. The modulated spectral radiance, B

is then focused onto a flane absorption cell into which

analyte absorbing species may be introduced. The radiance

transmitted through the absorption cell, B T, is related to

the incident radiance, B by the absorption law [5,20]
o
B, c Bc exp(- 1) (12)


where kx is a modified atomic absorption coefficient defined

by Equation (15) and 1 is the path length of the flame.

Ordinarily, I the true atomic absorption coefficient for

an atomic vapor is used in Equation (12) and is a function

of wavelength; the peak atomic absorption coefficient, ko;

and the half-width of the absorption line, lAA [213. How-

ever, when medium resolution monochromators having spectral

bandwidths equal to or larger than the half-width of the

absorption line are used, the apparent half-width of the

spectral profile viewed by the nonochromator is approximately

the same as the spectral bandwidth [22]. The apparent

balf-width is herein defined as

A 2 s AV (15)


A is the apparent half-width (A) and s is the spectral band-

width of the monochromator (A)


(14)


s = R'W









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Lu ,o r ,: ,7 ,! ': i t : .' ( .'2 . : L .i L ,' ', '.t r ': i -,.\ ~ _'v a L ,e .' ) I : :' -''
the p:;'i!: itu.%i ,' ,jb:*.,r-. ';C;C.::l ,, 1 LCt i,.ni; 'i.: Ll i e c_'.rt.r,

.L. ., !.-. 1 ,. r'j.S' i .:.', :i (, '.. ,, ,. Il ",., i,.'. f -_ ? *r.. ,, -

chromator. Kostkowski and Bass [23] have calculated the
obs
change in k0s for various spectral bandwidth-to-absorption

line half-width ratios, For ratios greater than 2, which

is generally the case for real analytical situations in--

volving atomic lines, kb varies from 75 per cent to less

than 50 per cent of the true k According to the above

discussion, k nmay be expressed as


S= k exp- (15)


hero 0 is a coefficient less than 1.0 to account for the

diminution of kobs due to finite spectral bandwidth and X
o o
is the wavelongth at the center of the absorption line

profile. This expression only approximates reality since

it describes a line haviaig a Gaussian type of profile.

IHowover, considering the line as having a simple shape

instead oC its true shape thich results from the several

broadening processes occurring in flames, the expression

becomes ancluab.le ;o iiathomatical brcatmcnL;. Equal;ion (12)

may be rewritten n a form which indicates more clearly

that the c.:ponential teor simply e:qpresses the transmission








of : I:!. ft L e -.:1L -i fui-ction of wavelength


T X B T(A) (16)

The radiance transmitted through the absor.ption cell

is focused upon the entrance slit of a monochror.ator after

which it passes through a refractor plate modulated at an

angular frequency o,2. The effect of the displacement of the

image (described in the previous section) is to cause the

spectrum produced by the grating of the monochromator to

periodically oscillate about a mean wavelength, X ,

corresponding to the central wavelength of the spectral

band of radiation emerging from the exit slit when the

monocbmhroaitor is used i i its conventional mode. The wave-

length of the oscillating spectrum which is viewed by the

center of the exit slit at any time t is given by Equation

(9)

X = X + a sin'2 t

Therefore, the radiation emerging from the exit slit of the

modulated system, B,,(c ,t), is a function of the periodic

oscillation of the spectrum about the center of the exit

slit. Also, as a result of the finite width of b1o exit

slit, B9(1 ,t) is also a function of the spectral bandwidth

of the monochronator. The modulated spectr'u~ passing the

exit slit may be expressed in the form of an integral of







2,)


'- ,, 1 v l*uzc .--'1', 1 :;i :.r, .-1 it l0.u2.;1i1o.f. Of h H r !rO.2,2"-, i'r,

S(X), eralju_::c.1 :. i.r. .e*: r :I. ;Ti.' "- i. CL '.' rI.C:'i)'"

chromatror

X + s/2

BT(XC,t) = B S(X)d (17)

I s/2

In the case of a monochromator having equal entrance

and exit slits and unit magnification within the mono-

chromator, S(X) is a triangular function and is expressed

as

S(X) = 1 IXI = | X | < s
(18)
S(W) = 0 |XI = Ix -- XcI s

c
Bx, as e:coresscd by Equation (16) may be rewritten

as a function of the modulated spectrum and the slit width.

B = BxC (\c +- a sin-2+ t + IX )T(Xc + a sing2 b + 1XI)

(19)
uubstitution of Equationi (18) and (19) into the

interal. of Zquaticn (17) yields


Fr(-,l,-) =

X + s/2

B (X\ + a sinao t i- II1)T(X, + a sin.y2 t F I1I)
o
c -- z/2
-. I ax VU).- /i-.


(I U ) dx


(,U)









A Taylor series expansion may be performed on the
terms of Equation (19).


B( (X) = BO (X ) + (a sin t2 t + IXI )Bk(\) +
No0 0 20


I-X--- (c ) ......
0

T(X) = T(Xc) + (a since2 t IXI )T'(Xc) +


(a sinms2 t+ 1XI )2
------ --- T"(Xc) + 1)

where the prices indicate the derivative of the expression
with respect bo N evaluated at X For the purposes of

arriving at the desired expression in this derivation, the

expansion was only carried to the second order in (a sino2 t -

IXI ), A more precise expression could be obtained by ex-
panding the series to higher order terms, but it will be
shown that, for practical purposes, second order terms are

sufficient and can either be accounted for experimenbally
or are negligible, Multiplication of all terms and subse-

quent integration over the spectral bandwidth results in the

expression (see Table 1)














S 'd d p
(U o 'do
(D 0 rd (D
.P -P p ri -P o
oI .M -p o a <
S -rl r 0 ) 00
(4 n ,r 0H (o r*
S d P .p,
--i Md o I o
Srd 1 P 0d f- i a C --A
.P H-4 PP N( 4-r- -P 3 to
p: 0 ED 0 D 0U CM iH

0 H -1 'd -rl 'd G
d P 4o 'H o '1-1 iH
. Po -po .-)
P 0 o Fi > b I > > i




-A D P F -r ) p N
o +P.1 rd (04

S) 1 -E
0U Pd > r 0
RI 0 *H = C) 0 0 -4 C O'




00






+ o
r9-1 v -- C) 1
H R








I rq NI l"
N 0
pi I





F 5 :11



I El l 0


r RU F- Rl 4I
1M 0 Cl C-1 MlR I- F-
ei E -d r o


















r ) 0 0
SEl M OJ a
R: Fp d| [. 1 i



O) '- '.) m P-P
0o o


Pi l P-
PI i- r- m *



51 0 0 l rH1

PI 0C *-e 1 'U1) .1
n o Rn
C -) ) r 'U 4l l
4O 0 f) rl R



c' ) E-l r(iu 0/ 0 I
(- C -H 0 0
ri 'Ud 4o C/ 0-









2
BT(X,,t) = sBT + (BT" i- 2B'T' + B"T)
2


2
+ sa sin 2 2 t[BT" + 2 B'T' + B"T]
4--

+ higher harmonics (22)


where all superscripts ond subscripts have been omitted to

simplify the expression.

The first two terms of the expression represent the

dc signal output of the multiplier phototube detector.

Of the terms appearing at the fundamental frequency

L2, the first term describes the first derivative of the
transmitted spectrum; the second term is zero if the source

radiance is constant or a constant if the radiance increases

or decreases linearly over the spectral modulation interval,

a; the third term is zero at the wavelength of the first

derivative maximum and the fourth term is zero if the source

spectrum has no fine structure over the spectral modulation

interval.

Of the tbrm.s appearing at the second harmonic, 2 -j,

the first describes the second derivative of the transmitted

spectrum; the second is zero at the wavelength of the second

derivative maximum; the third is zero if the source spectrum

has no fine structure over the spectral modulation interval.














sa sin.)2 t B (k) T'(X) (25a)

and the first bermi at the second harmonic frequency

sa- sin 202 t BA ( ) T"(X) (25b)

Each of those expressions may be expanded by substitution
of the appropriate derivatives.

T(X) = exp(-1)
dlEX


T"(X) 1 exp(-1f.) + -- exp(- \1)

Substitution inbo the expressions (24) may be
accomplished by taking the appropriate derivabivos of
Equation (15).

dlck 2pko X-^o2
d -. -- ('-Xo)exp (25a)




4-

ex (25b)








By substituting expressions 25a and 25b into expressions 24
and evaluating at one obtains
c

2pk 0\ 0-* 2
T(, ) = --2- 1( )e ------ exp(-1)

(26)
and

"() 2 k0 1 ex-p [- 1 1(X, X)2
122

e o c-]2
L-2

+ 1(A X,)ex - exp( 1)
(27)
The location of the maximum or minimum of Equation
(25a) can be found by setting Equation (25b) to zero,
substituting X, for X and solving for X At the maximum
or minimum

c = + -A (28)

The maxima or minima of Equation (27) can be located
d3I
by setting c3 equal to zero and solving for X Three
values are obtained, of which \ = X is the maximum.

x = xo
(29)
XC OX - ,72 A










becomes
2ko
T'(X) -- o 13 exp(-.) o(~p(-.~il) (50)

Evaluating Equation (27) at X = \ one obtains
2k
T"(X ) = --- 1 exp(-il) ()1)

These expressions may be substituted back into
Equations (23a) and (23b) and Equation (1) substituted for
B '1hen this is done, Equation (23a) becomes
o
sa sinac2t B (X )TR(Xc = sa*sin:J2t 'B0 (1 +


cos .t) o1 eo(~)exo(-1)


I'ul.tipl.ying through and discarding any terms not having both
N'1 and '2 appearing inl them,one obtains

sas [in:2t cBC e). sin(l1I -I- )t
c 3 &2)t +

sa Bo0 ok 1 e ox (-k1)
sin('t1 2) 1
2VJi A
(32)
*'iuat.ioa (32) predicts that the first dorivativo of
the branimitted :upccrun should appear at both blhe sm and
the difference of the modulation frequencies. Similar
substitut. ioin can be maloe into Equation (25b) wil.h lhe result









being

sa2sin2o2,t B c (X )'"(Ic = sin(., + 2c.2)t + sin( -

sa2 B kol exp(-1)

\ 8 0
2o2) -- -- 8 A P (33)


Equation (33) predicts that the second derivative of the
transmitted spectrum should appear at the sum of the
chopping frequency and twice the wavelength modulation
frequency and also at their difference. Examples of first
and second derivative signals are shown in Figure 3.
Equations (32) and (33) may nou be written as input
signals to the phase lock amplifier at their appropriate
frequencies of detection and phase so that the sin tcrms
are equal to unity.

WHO T yL, saB k 1 ex~p(-) exp(- )
S o (34)
(2 %- c2 2 / A

where and H are the .width and height of the monochromator
slit, respectively, in cm, N, is the solid angle of radiation
collected by the nonochromator in sberadians, Tf is the
transmission factor of the opbics of the system, Y is the
phototube radiant sensitivity in amperes watt-'1, and RL is
the phototube load resistor in ohbas.

S Rsa l exp (-1)
f 0 ( IA


8 L\


'- fi + t'2 =


k 3)
























OJ


d-




4-


a
0

ri




o0l
*Hf



*




o b
H '








4-1
0 n

OH
Od
o
CIH
t H
0



o


o r
rd o
04-P
Hi c
i*H -I







*rI


CoJ
(1

-P
-,
'l

CI)
r-l

0




r-I
O


H


C ll




o
0
Sa o
'I




url
- o
*,- -P
i d
> -P

' o

rd rO
o
Ori
0) -lP


I
I






ri


















*20C C' 3 (
6 o 2


;--i-.









Equations (4!-) and (55) predict that the First

derivative signal should be larger than the second by the

ratio



41 c"2 22AZ p
2 0 + c) e(-) (36)
b1 + -^2


They represent the final expressions which arc used to

predict the shape of the curves of growth for the derivative

system, A theoretical first derivative growth curve is

shown in Figure 4.,

That there is an optimum spectral modulation ampli-

tude is shown by. Balalcv [13] who gives the resolution for

a conventional monochromator as s1 + s2 = s where s1 and s2


are the spectral slit widths of the entrance slit and exit

slit, respectively. For the case of a I.onochromabor modified

to produce a derivative si.nal. and having a spectral modu-

la;ion amplitude s3 bhe resolution is given as

s + s2 -I- s
----A-)- -----r


Cince the signal of the derivati.ve spectrometeor, according

to Balleov, is propot ljional to ,S1 2S, the besb choice for

sli.- widths and modulation unplitudde for optimum resolution

anid signal i3 s = 2 = 5." In the p-ocendLng derivation,

























-P
4)

'to
vI














rH
0-4
C\J



C"j




0


4-1









Id,,
0
















P Pd
F-4










,44
o to






















































































(clI;AOJ J I~ J I ii'ii;!S


ci


Co



o tI
SE


C
C
a
'

C) C
C c
C



EE
a









the assumption that s- = s2 has already been made. Con-

sidering now the size of s3 one see; that if s3 < S1 reso-

lution will be improved but the signal will decrease and if

s.3 > s1 the signal will increase but resolution will suffer.

In the previous equations, a is equivalent to s3. For the

optimum case a should be chosen equal to s]. Equation (36)

then predicts that the ratio of the first to second deriva-

tive signals should be 1.7.'


Limits of Detection


Vinefordnor and Vickers [20] have derived expressions

for calculating the theoretical concentration of analyte

at the limit of ldebctability in atomic absorption flame

spectrometry for a system employing a hollow cathode dis-

charge lamp as a source and dc detection of the signal. In

theLr derivation, they defined the limit of detectability as

the concentration of analyze atoms in a flame which produces

a change in signal equal to twice the root-mean-square noise

signal- due to all sources of noise present in the system.

The major sources of noise precut in any system are (i)

fluctuations in the signal arising fro-m the phobodetector

or photon noise; (ii) fluctuations in signal arising front

source intensity fluctuations or source flicker noise, and

(iii) fluctuations in the signal arising from fluctuations

in the intensity of background flame emission intensity or

flame flicker noise. Of these sources of noise, flame








j "
li ,*L _... :,',J~'~' g '.l' .-: o r ':i". '.: r :'i" ." "j :" 11"' 1/l"

~.'.-a'L'~:i^, !. ;, [ :i i- : i fc .? '.c i .tC thi i'i I"i:', V i-rcI '.t';.*:,'i ,OJi. ,' ,




.'.qr:.:. ~::-.:tr,. Thlor'eifre, one should expect to en-

counter only photon noise in ac detection systems operating

at frequencies greater than about -00 Hz. The following

derivation of the analyto concentration at the limit of

detectability is based on the assumption that the system is

photon noise limited. The phoboanodic current due to

photon noise may be riLtten as [20]

i =. 2BMe fOTB s (38)


where B is a factor characteristic of the pho;;odetector

dynodes, H is the multiplication (amplification) factor of

the photodetector, e is the charge on the electron

(coulomabs), Af is the frequency response bandwidth (secl),

and all other terms have been previously defined. Because

phobon noise is frequency independent, it will be detected

alon wiith the signal. At the limit of dctcectabili;y, the

signal due io analyze absorbing species will be equal to

twice teo phobon noise. Por bhe Cirst.derivative system

Sm1in 2RL 1 i (50)
"j., *K 1-12







35

The term in the signal expression (Equation 34) which

relates the signal size to the number of analyze absorbers

is k The value of kin for the minimum detectable number
O o
of atoms in the flame, n is given by [21]


in 2 l n2(Xo)2 2 if
kmin 0 e (40)
o /T AX nDmc


where n is the minimum detectable number of aboms in the ith

state per cm3 of flame gases, A\D is the Doppler half-width
0
(A), f is the oscillator strength for the a-tom:ic transition

and c is the speed of light (cm sec- ). n1" rayt be calcu-

lated using the Boltzmann Equation (20)


i ng.
n =ng3 (41)

where n is the total number of atoms in all states; gi is

the statistical weight of state i, 2J + 1; and Z(T) is the

partition function of the atom, Z(T) = X giexp(-Ei/kT),

where Ei is the energy of state i above the ground state,

k is the Boltzi.ann constant, T is the absolute temperature,

and the summation is over all states of the atom.

Equations (34,38,40 and 41) nay be substituted into

Equation (39) and the resulting expression solved for an to

yield a general equation for the minimum number of atoms

detectable in a flame.







'1-






The minimum detectable concentration o-f -ii;oms

cn-3 of flame gases, n can be converted to minimum

detectable solution concentration in,ug ml- ,C by use of

the following Equation C20].

3.3 x lO 19 n TQn
C = (4L3)


where T is the flame temperature in OK; nT is the number of

noles of combustion products at temperature T; r298 is the

number of moles present at 298K; Q is the flow rate of

unburned gases in cm sec-1 at room temperature and one

atmosphere pressure; is the flow rate of solution in
3 -1
cm minute "; a is the efficiency of atomization and nobuli-

zation processes; P is a factor to account for ilcomp!lete

dissociation and atomic losses due to ionization; and the

atoli.c weight is expressed in grams mole-, and A is the

atonic weight of the ;nalyte. 'The constant contains the

nueioric.al factors 29 0K, Avog..dro's number and conversion

factors front minutes to seconds and from grams to micro-

grans. It thus has units of (moles atoe.n) (seconds

ninubo-1) (nicrograns grai--) (K-1).







357

Sij gnaNl-to--Hoi se Ratio

The signal-to-noise ratio of the system in the first
derivative node is written as


WHIt, PTBo 0 EiMeAfs S
S/H = 0 IC l -exp(-4)exp(-kl)


Equation (44) predicts that y he signal- bo-noise ratio will
improve with the square root of the source intensity.












r1I.'l."' R ITi


.i-. ,- :..^i,, ;,,,r, ,,L .2'd F .C I i


D :rri rt 0r .r t r-i


The instrumental system is pictured in a block

diagram in Figure 5. Each of the individual components is

discussed in detail below. The entire system was mounted

on a one inch thick steel plate using quick-release magnetic

mounts. This arrangement facilitated the location and

physical stabilization of components while at the same time

allowing rapid aind easy experj.mcntal ruarrangement.

Components used are listed in Tables 2 and 3.


Source


Continuun sources were-employed in all of the experi-

nents. A 150 watt high pressure xenon arc having a colli-

mabted beam 'was used for all analytical experiments. The

spectr.al distribution of radiant flux for the lamp as given

by the manufacturer':; specificabions is shown in Figure 6.

Source inbeasibt, below 5200 A is only about one-oenth of the

output around 4'500 A. Since most ab'onic reson anco lines for

cle;.ents which ordinarily are neasuoed by atomic absorption


















04







0



-


r *ri
-1 0 0
Pi C) C


*l ,0 P0 4 ml

r-l + r-I 0 5
4o 0 0 ., 0 0
'D) 0 o d)
,o .p F0 0
0) (1 g r-l rli
P00 54 0 0 r-p

Fl ,rl P 0 0 C)

vS P 0 0 ci
A -I 5 -l


r0 i o 1 a p

40 0 h


I 54 54 5
C CO OI 5 4 4




Cl 0 CS CR i- p a o'
0 FiCi PI PA F


g0 PS II II s
o II II II
oII
vO >I N. 1 M
PS rP PA -i




f'
.ct
*l-

































_____ _____-J


CO
cl) C"








., j
0
3





C"







(v
sm:












0 F -

0 0 > -!
S:- 0 r * *
I >aj ( > N -4 F- I M .'4,< 0p 00
-I P..U 0 *H 4 *q 0 F-' C I _-
Sr-I .-i 4o o PI rH 0 e( j o o
E0,0-- 40 ,C 0C50 OH O) f
51 d 0% O c3.H *rI.H rl F, -I
q .,-I .- i 0o o


'drJ r- ti 0 cim
S rl l Pi P -1 l -I l r 0
p o n o .p a ,< od 1 r oHO ii .ori Li

J 4- 0 0 F 0 l .0 (-t l .i (4 r
S -ID d l- 0 0 o o
o o p a o c 0 o (D -




'ld rd NO 1d *8 i
"u 0 Fl o t rd l 5 *- *rV i l





Q) PA Q : 3 )= r


*rl 'o r 0 ; 0
I--{ i l-l d 'Ir~-l r l -H ?

C. F 0 0


>: P o 1 Pf
D I 0 -1 'I rI c4 P Ir 0


o II 0. l I I -1 I 0
P0i 00) 1 , -P

1 CI1 0p I H 0 W H 0
00 0 r-0 o P0 0O 0 ,O
S-i 0i o a- P 0d

o 0 P0 l-I 0 .- 0 U
S0 I P r-o O
0r i Fi f G rl ri P4



O M 0 4- -d 0 0 r 0)
H *; F) < ( ri 0d r > 0 r0
E1 1 o3 ~4 P, to h rC P,
> c 0 0 0 l
00 '-H 0 d l Cr i \O 0
02-rH Ll rl t f--1 S, 0
S O t ni -P O u ,

00 l Fi 1 i rg -
>I' F, )) 0 i fkI Q

dO I A ('Pdo PA
01-1 0 0 o 0 0 P
03ri L n (! C p .



00 r-4 O Eo a to t -
SO ( r 0 t 1 a r- P i
00 M p c! L r --,1 El( 0H E )


1w: n-l 0 PI P o 0f 0







a o r-i o u j to r-- 0 a
I r P pi 0 *rl0
0 0 O0H 0 >s i--I 1H H -I 0


ri0 r) M| TJ f-I VI(') ii I i


















0 -:
0 0I) C
0

1 0








4 o




it
I 0



H-ri










O0
O -,

O 1-I)







40) c





0 Orl
C) o












0
fIri




















0
0 0
-i4 <-


l *



4 0





I 4 0p




CO0 4- 4
0 t

>O I




0


0-,
U-1'

S-P H


















Fo






oo
0 0


,-Ig













Md
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S0
Sci 0-
O -P





























cd
oO
iH





O -l
























(12
F:
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OO




co

0





















00


. -
Li
*1

1 H

oP
0 -P

r-1










0 -f
r *d F-










o &
or H






O 0


























O .rl
g o


cd


U






0
-w







0 *


0 *
-PM
0






o'o
10
'ci 0
0 &0








F-i r-t

Pi
O















M p
o 0
F-ti


)0 Li
CLO







1 I-I
C) U) C
41 t) r -l
,O



'
o 2 0 I 02 1



-P -4i ,N I
0 00
1,ci 41 41 41



,c*ic riOC0]
C) 0
4 o ii Ii Ti
05 H 1 Iri K


0I
0F 0.

o rC)
i-l c)


,d o
0) *


O43



P1 0
0)
43 --
'i o



Ol
0














tcc
da
12

























IN
F 0










0(







,-I 0
0 !

N
ci









*r4 0
r L
S*H




n'
-PO









0I
C)i 0







,-I



i- i--i
Io Cr


fl'd
rc
000



-0 0



H,,l "0_
H0- 0-

S04) (I 'cd
0 *ri i-C o
0 ( ( ) P
O PI M







ro
0

ri







.1i
LA









Od
0









(11
In



S0





lOl
0



Pi

0
-lC
O
0fl


H O

* 0 fI










L)5


*d
0 r-i 0
0d -l rl 0 .d

Sd r- ( r- Pi 0 H *d O

( II Hd ob o) p) Hp *b ,

Pi I 1 P 0 ,c 0 0 o 0,c1 0 to 0 1
S -p dri -i -P o d p -P 0 -P 3 O
eDCO (P P, o ) 0l -io ( c I cI c
0 oo 01 0cj0 oElI ,_o
1 0 0) r -I ,'0 c l oe 43l -O
0 H H C- l H rn ,C ci j l
( uL ei 0 i 4r --l- -P B D
--1 i ~1 P o Pi p i H- -H N CA












i O ?O o C
CI -0I 0 r-i



P 0 P1) .1 :: IH 0
H -P43 H 0-H P d
0O ic r-l ,00 P0 1i 0






Si d ,m n I





o c4 ), o ) C )
cH H U-








o 0 CO~'0 ., 0 0-0
R !^l -P r-l d
M d o M o p, d o


o d o 0o H .,


P01-1 0 P Cy "I *rl rlP



S 'di ) Md z Pc i
I 0 O *r Po i P0 oO -0W



E I 51 f~ nr O







r-l r, il .0 P .ri M I
'-HO "' C o 1 -C- > 0I









0- -H -o o a 00 *,o-
P *d r) P .] 0 (i 0 P-







3 0 r- r-Hl 0- -Hr

o 30d .'I o 0 ,
0 0 od 0 N*\ 4-)
0 r- cN 1 10 -A Lf, -,A CO -
(j O '- n n ,-
O Oa I n -q 1 -1 O- U -P-
0 a co(0 0 Q) o
C d )d d .r *d z d d 'd --! 0
0 C 0 r-1 0 0 'OA OaCO





rl 0 (D i1 r 0
i r' *d > (U 0 0 Pi ,P

0 r-l *d r| 0 .* .*-4 0
D-i -P. rP 'I p) +-P
l-i rd 0 r *d 13 r-l Pi 1 Pi O
o '-- o y. 01 oi M -1 &Pi 0 ,
O O 0 CO o cl As J l
















i
4 Cd
O P 0H\


oi f2 ri o o 0 u
P -- 0 -H d C
i Pi 0 cI +H ,

S1 ,C0 -r
I .p 60 o uN 0
orl1d d oH-I







03

p ,d



















PI-
o o
O 0 1FI
*P 'd 2
Pi 0 0 >





1 0 J





o o -P
P &o o



SOR
iI 'd




,-1 r)






0 p c
-d Pi p0 0
a~, rn 0F


' F1 IpO O
5 l O Tc aO




































00w





0 0





'H I
4)Oo

:ri U) =







o P (a


4) C) ?

4)
C)W -

4)


' d


























\8





-co
O


'tA
IC3



o







co
ol
L

I o









o
1







^^..-,
--' -r_ 01? ~-4
r- a a a










techniques fall below 3600 A (Al, Ba, Ca, Cs, K, Li, Na, Rb,

Sr and most rare earths have useful resonance lines above

3600 A), a very powerful source is required to yield

appreciable intensity in this low wavelength region of the

spectrum. The xenon arc source used had an effective
0 --
spectral radiance in the region of 4000 A of between 10
-3 -2 -1 -1
and 10- watts cm sr am and correspondingly lower

spectral radiance at the lower wavelength resonance lines.

The measured spectral radiance of the source at the wave-

lengths employed is also plotted in Figure 6 as relative

values. The spectral radiance ab '-227 A is arbitrarily

assigned a value of 1. The estimation of source spectral

radiance was made by measuring the phototube signal which

resulted when the source was focused on the slit of the

monochromatoir under kno-wn conditions. Equation (45) was

used to calculate B To. The transmission factor was in-

eluded in the calculated value since an accurate estimation

of its value could not be made; however, all other para-

mctors were known.

Signal = Bo T W .Isy (45)


where the signal is the phototube signal in amperes; .I and

II are the Atidth and height of the monochromator slits,

respectively, in cm; CI is the solid angle of radiation

collected by Uhe monochronator in steradians; s is the










spectral b ar.in .lt h o l ta.: i.'. 'l,, I' r .t' i L' 'I').i t L -,h-

radiant sensitivity of the photobube in amperes watt-.

Source flicker was nob observed to be a problem.

This finding is in agreement with Snelleman [17] and others

[24] .who have shown that source flicker at frequencies

greater than 100 Hz is negligible.

A tungsten-iodine projector lamp having a quartz

envelo-ps was used in an experiment to verify photon noise

limitations. Its power supply is indicated in Table 2.


Burner and iNbulizor


An adjustable nebulizor and mixing chamber assembly

was employed in all experiments. The efficiency of the

nobulizer in delivering aspirated sample into the flame

was on the order of 5 to 10 per cent. The nebulizer chamber

was equipped with a 3-slot burner head 10 cm in length. The

burner supported an acetyleno-air flame for. all experi-

mental noasurenients. The entire nebulizer-burner assembly

is nrou"tcd on an alurninum shaaft w.hi.ch could be set at

various heights by iaeans of an adjustable lockin; collar.

The collar was i-ounted on a quick-roloase magnetic mount

which nlIlowe d r;?pid align;aent of the burner head ;ith

respect to the optical ai.s of the system.







L!.9


Honochromator and Optics


A 0.5 meter scanning Eberb monochromator was employed

in this study. It was mounted on a 1 inch thick aluminum

plate which was supported by three adjustable posts mounted

on quick-release magnetic mounts. The monochromator was

initially roughly leveled using a spirit level while pre-

cise leveling was accomplished by using a small, low power

helium-neon laser., The laser was set to the appropriate

height and its beam made parallel to the steel plate by the

use of glass plates which were epoxied to adjustable rods

mounted on quick-release magnetic mounts and which hed an

"X" inscribed on one face, These were positioned such that

the centers of the "X"'s coincided with the horizontal

plane containing thle optical axis of the system. By placing

these in the path o.f the laser beam at various distances

from the laser 'vperture, the laser could easily be adjusted

so that the beam coincided with the centers of the "X"'s and

thus was conta.ined in the optical plane of the system, The

nonochromator was leveled by illurn.inating the center of the

entrance slit with the leveled laser beam and adjusting the

height and level of the monochroma.bor until the beam

emerging from the exit slit was contained in the optical

plane.

The lenses used to focus the source radiation were

aligned in the same manner as the monochromator. They were










placed in 3 .rp.:.::.r.t..1- y t:lel .,i fr : 1 o:,.. '. ici on '.h : .pi:i.al

bench and :-I ju ::;,cd v* rti.., ll ,.f i.. .i c l .I: *.--.' r.;: .:-re ..jn-

tained in rl: omto LC.:.1 : : in ..:it-: t ..: . -

mrission of the laser beam. Initially, their position along

the optical axis was defined by l;he criterion of obtaining

a 1:1 image of the source at the entrance slit,. When this

arrangement was made, it was discovered that the center of

the grating was dark as were the centers of the collinating

mirrors of the monochronator. Due to the construction of

the source, this phenomenon was understandable. The anode

of the lamp is supported by a iletal spider noun;cd ir:uiedi--

ately behind the sapphire front window and is directly in

frout of the arc. This unilluminated portion of the source

image coincides with its center and accounts for the dark

areas observed. To correct this problem, a domagnified

image of the source was formed on the slit by relocation

of the lenses with subsequent complete illumination of the

grating.

The quar;tz refractor plate used to displace the ir,mage

of the entrance slit was mounted in a brass electrode holder

as shown in Figure 7. The clectrode holder was located on

the nanochro.ator cha:.:;;is a a distaico front the cntr.ance

.;11it such that tDo wi.Idthi of the plate .was sufficient to

totally intersect the solid angle of radiation collected by

the collinat;or mirror. The refractor *l..ite :.as epoxied to a
















































Fig. 7.--Electrode holder for piezoelectric transducer.

a = Brass electrodes.
b = Brass holder block.
c = Piezoelectric bimorph transducer.
d = Quartzq refractor plate.
e = Teflon insulator block.










piczo lec triOc L .. .: . .1 i i : '' Fr':, '1-1.-'.

was accomplished by supplying the piezoclecbric binorph

with a sinusoidally varying voltage. The optimum per-

formance of the piezoelectric bimorph was expected to occur

at its resonance frequency. The approximate resonance

frequency was calculated using Equation (4-6) [25,26]

35o (0,6)
C') -2-0


where L is the free length of the vibrating member in

inches; c was calculated to be 56 IIz. Ex:eperimentally the

resonance frequency was found to be 55 Hz. Consequently,

the bii.iorph .ras driven at 55 Hz by a voltage of The

appropriate nagnibude to attain the desired def.lction and

thereby the desired spectral] modulation interval (Figure 8).

The mechanical chopper used to interrupt the source

radiation falling on the flame was constructed in the

chemistry department machine shop. It consisted of an 8

inch diameiter wheel having 10 apertures driven by a

synchronous 5600 rpi motor, The ratio of bhe amotor pulley

wheel to bhe chopper blade pulley wheel was O,~5-30 which

resulted in a chopping frequeacy of 253 lz.

A reference signal of this fcequency was generated

bi a s:.ill pohotorebtector systu:t built into the chopper

housing,. 'heo referenLce system used a 6.2 volt radio lamp

and a phoi;oLtansist:or i-n. bho circuit di.agr-nmmed in Figure 9.











































0 20 40 60 80 100
Voltage to Bimorph



Fig, 8.--Spectral maodulation aoplitumle (slit i~a(e diis-
placement) versus voltage supplied bo bhe binoriph.













-1 6 volts


-- A OGnd












?i:'. 9,---Ciccuit for chopper rofer'erce sic ia,1.

1 = 2N51-.12.

2 = LSG'0O (Texas Instrumcnt, Inc.) photo-
*tr..!nsi.;o s .'.

K = Radiia;ion incident on phobotra.nsistor.

A i Signi-i outpub.










'The lamp and phototransistor were mounted beside each oti.r::t

on the face plate of the chopper housing. Directly opposite

them a mirror w.as attached bo the roar plate of the housing.

When an aperture presented itself between the lamp and the

mirror, light was reflected onto the phototransistor, its

resistance decreased to a low value causing Q1 to turn off.

When 01 was off, point A dropped to zero volts. As an

opaque portion of the chopper interrupted the light falling

on the phototransistor, its resistance became high, Q1 was

turned on and point A rose to 6 volts,. In this manner, an

approximate square wave signal of frequency /01 was generated

at point A for each interruption of the xenon source.


Electronic Comuonents


The driving voltage to the piezoelectric bimorph was

supplied at the proper frequency by using a variable ampli-

tude wide band oscillator feeding into a fixed gain power

amplifier rhich was capable of supplying up to 120 volts

(rus) without distortion of the output wave form. The

amplifier used in thick experiment was constructed in the

chemistry department electronics shop and not optimized to

the load Iwhich the piezoelectric presented.1


A suitable commercial amplifier would be the Iodel DCA-10,
Krohn--ite Power Afiplifier, Irohn-Hite Corp., 580
Has.ssachuoebtts Ave., Cambridge, IIassachusetts.










The refcrc ce iEn'I for t'l phitl -o.ci.:tric tr: ai uccr

irequency, 02' was taken at the oscillator output. When

the system \as operated in the first derivative mode, this

signal and the reference signal from the mechanical chopper

were used as inputs to a multiplier. The result of multi-

plying two periodic functions together is given by Equation

(47)

sin(a) cos(b) = %(sin (a+b) + sin(a-b)) (47)

In the present system, the frequency of the multiplier out-

put was of interest because it was to be used to supply the

reference signal to the phase-lock amplifier. In order to

differentiate between the sum and difference frequencies in

the multiplier output, a tuned amplifier of high Q was used

to select the proper frequency to be used as the reference

signal to the lock-in. For the first derivative spectrum,

the sum frequency was 313 Hz and the difference frequency

was 203 Hz.

For operation of the system in the second derivative

mode, the reference signal from the oscillator was fed into

a squarer to obtain a signal at twice the oscillator

frequency, 202. The output of the squarer and the chopper

reference signal were fed into the multiplier as for first

derivative operation and the selective amplifier tuned

appropriately to either 368 Hz(d1 + 2)2) or 148 Hz(&1 2w)2









The multiplier phototube detector signal current was-

dropped across a 16.2 KR. load resistor to provide an

input signal voltage to the phase-lock amplifier. The

value of the load resistor was chosen to yield the lowest

noise in the system compatible with reasonable input

voltages for the range of signal current expected. With

this load resistor, phototube signals of between 10-5 and
_Q
10 amperes yielded voltages of between 160 millivolts and

16 microvolts-which nearly spanned the input signal range

of the phase-lock amplifier.

The output of the phase-lock amplifier was 1 volt

full scale for the sensitivity range in use. A voltage

divider was constructed to permit a signal one-hundredth

of the output to be used to drive a 10 millivolt recorder

full scale.

Solutions


Solutions of each element to be analyzed were pre-

pared from reagent grade chemicals. Stock solutions for Ag,

Ca, Cd, Cr, Cu, Fe, Mg and Ni were made from AgNO3,

Ca(C2H302)2'H20, CdC12"*2H20, K2Cr207, CuS04'5H20,

FeSO4 7H20, MgSO4, Mg(C104)2 and NiS04O6H20, respectively.

Three solutions of relative concentration 1.00, 0.50 and

0.25 were prepared for each decade of concentration examined.

All solutions were prepared as aqueous solutions using high









Ia u lity i,,: i -,: I .t.' ::?,?,c-; :.r th. i_' ,4);, i U .i.- 3

;,I.ch were prepared in absolute ethanol.


Exoerinental Procedure

The practical analytical operating conditions for the

system were either the manufacturer's recommended conditions

or were experimentally chosen to give the optimum signal.

The source was run at 12 amperes and 12.5 volts dc. The

spectral bandwidth, s, and the spectral modulation ampli-

tude, a, were maintained at a ratio of 1. The actual

spectral bandwidth used in the experiments varied between
0 0
0.3 A and 0.5 A. The slit height was kept at 2 nm. Due to

the variation in source intensity from wavelengths around
0 0
4000 A to 2500 A, the sensitivity setting of the phase-lock

amplifier was adjusted to a level compatible with acquiring

the phototube signal without overloading either the input

or output amplifiers. The time constant employed in most

experiments was 300 milliseconds although for very small

signals a 1 second time constant was employed. The phase

setting of the phase-lock amplifier was adjusted at the

beginning of each experiment to yield the maximum signal.

Data were taken with the monochromator in the non-scanning

mode. The wavelength was set manually to give the maximum

signal deflection on the recorder. Thermal drift of the

monochromator away from the preset wavelength did not prove







59

to be a problem and an entire set of data could be collected

without the necessity for readjustment of the monochromator.

A nearly stoichiometric flame was used for all analyses

except for Ca and Cr for which a fuel-rich flame was used.

The acetylene-air flame supported on the 3-slot burner was

very "soft" and had a marked tendency to waver about the

optical axis due to drafts of air in the laboratory. This

condition was remedied by placing sheets of aluminum behind

and in front of the flame extending from the bench top

nearly to the exhaust hood.












C .'-' I,. T;V


RESULTS AND DISCUSSION


Verification of Theory


Various experiments were performed to test the

validity of the theoretical expressions derived in Chapter

II. The results of these are discussed below and summarized

in Table 4.

Optimum Slit Width to Hodulation Amplitude Ratio

The experiment to determine the optimum spectral

bandwidth-to-spectral modulation amplitude ratio to verify

Balslev's prediction [15] involved using a set of fixed

straight slits of spectral bandwidth 0.40 A. The signal

resulting from the aspiration of a solution of 10 pg ml-1

Ca into the flame was measured as a function of spectral

modulation amplitude. The results are plotted in Figure 10.

It may be seen that the theoretical optimum and the experi-

mental optimum agree within about 3 per cent which is within

experimental error.

First Derivative Mode Versus Second Derivative Mode

Equation (36) predicts that when the spectral modu-

lation interval is equal to the spectral bandwidth, the








61



4--r

,-- 4 I I



0 4 0

o 0 ) *




p *H u KM o o-






0 p-04 d


m .0 P 4-)
S m r ~4 H a

-o o d > a1o
0 or\





E- C- 0r1 Ao
0 P O H Idp
3O

H ; )'d *A pa

o I M| I
O (d >
$ 0 ri Td 0 C4`

H O -- I H Ad 4'
1--l m 00 A-I 0
H 0 P r-I $ $40
0) c l 0 cd r- 0 ( D
0 li 4 0 P P 4 P
$; o 0 1 O H *' 9 a) o

Ed - *r -l P rd :$
r-4 co N N -1P


A -PO 0 I *d *100
H O P H rco .--I
a) Fj dP i- o ) - a

SU -l 0 -P r 0 0 0 -H
P d -P -ri OMO :: r V) d -
r d -i -N 0 o I
'd a *r\ hr-\ pp' a+' a-pe f-








f 0 -l oi +q N 1 3
b-o d a F1 P -P U




S r-4 0o 0 ao oo nr'1 0 o oc

SI -p : d -
0 9 -0 d( 43


*p as o 4 <44 ars r
0 O 4 -P O 0-a!
0 0Td rd J'd 0 -l

S -r4 O 0 H Od n OO M
H M -PC o a d4% 0 o r

















0( W

















pd
*H i
km









o (





PAP

m -















tfl
0











0
o
a








0
0





-ct
0


0
II
HIC'
N*


(D

a) a)
C 0 g
50 B: :0
Zi2 ',04 C0 Wa

H H H --I H
I 0 | *r- I *H





0 004 L J
*CO *(M1 *\J
'Pr-H II HzS It OC\J U






0)

0 0
a)



0









o

dH '
O et
H H


H r-


o
0 _








c 0 0p
0 cd
QCQS





o. 0
-rP r -1d P

a+a
+3 .rl(U )
o Q 3 n
Rm) 0'


0(
0
*-

n










oI

00
4
. o
d
o









0-P



o w


*, d
P00

O P
*-I 1 r- l
00
0 4
tcl 0
*rloP*r
ri o ar


H
H

0 *r- *--
Q)1* I * *

nd rlM-ir 0 a
0 0 c 0 0 0
t%\ -H 0 rl _d.





0 ( ., ) 0 )
cl) cU) ) j) 0' co
CO Q 0 O'd 0
49000~W







70 Theoretical 65
Optimum


60 -








S40-



30



20




10-





.100 .200 .300 .400 .500

Slit Image Displacement,a (A)


Fig, 10.--First derivative signal intensity versus
spectral modulation anplitude (slit inage
displacement) at constant spectral bandwidth
of 0,40 A.










ratio of the magnitudes of the first and second derivative

signals is equal to 1.7. An experiment was performed at

three different slit widths but at the same a/'s ratio of

unity. The mean ratio was found experimentally to be 1.4.

Normal AAC Compared with Derivative AAC

Comparisons-of different analytical technFques are

usually not valid since one experimentalist may compare

results obtained with his system to those obtained in

another laboratory under different conditions with different

instrumentation in many cases. The only way to obtain a

truly fair comparison is to perform both analytical tech-

niques under the same laboratory conditions using as many

common pieces of instrumentation as possible. In this

manner, differences which arise may be attributed to the

differences in technique. To this end, both normal atomic

absorption spectrometry using a continuum source (AAC) and

derivative AAC were performed using the same instrumenta-

tion. All experimental conditions, slit width and height,

source power, flame conditions and analyte concentrations

were identical for both techniques. The only difference

between the techniques was oscillation of the refractor

plate in the derivative technique.

The signals predicted by theory for normal AAC [20]

and for the first derivative signal by Equation (34) for

25 pg ml1 of Ca were calculated and compared with experi-










mental values. The results are listed-in Table 4 and are- -

in good agreement. Furthermore, even though the signal

magnitude for normal AAC was five times larger than for the

first derivative AAC signal, the S/N ratio was about five

times poorer. -

Direct comparison of results obtained with the

present system with the best previous results by normal AAC

[5] were unfavorable to the derivative system. However, the

systems were different enough that the arguments raised-in

the first paragraph apply. When comparison -was made on

equal terms, that is, using ethanolic solutions of analyte

and the same instrumentation, the derivative system proved

to have an advantage in S/N ratio.

Photon Noise Limitation

All signal-to-noise and minimum detectable concentra-

tion expressions derived above have been predicated on the

assumption that photon noise is the limiting noise in the

present system. Equation (44) predicts that for all other

parameters being constant, S/N should vary as the square

root of the source radiance, B By using two sources the

ratio of whose radiances is known, one can verify the pre-

diction of Equation (44). Writing Equation (44) for the

two sources and taking the ratio results in the following

expression










(3..1 1(H(B )151
1 1

), I) 2 W22 %( 242


Experimentally, a tungsten-iodine lamp and xenon arc

were used as-the sources and had a radiancy ratio of 0.16
0 -1
at the wavelength of measurement, 4227 A. A 1 g ml solu-

tion of Ca was used as the experimental probe. The ratio.

calculated from the appropriate experimental parameters was

0.3 while the-experimentally determined ratio was found-to-

be 0.5.

Frequency of Detection

Equation (32) predicts that the first derivative

signal should appear at both the sum and difference

frequencies. An experiment measuring three concentrations

of Cu (5.0 /g ml-1, 1.0,ug ml1 and 0.5/ag ml-1 ) was

carried out at the sum and difference frequencies. The

results are tabulated in Table 4 and are in close agreement.

Analytical Curves and Limits of Detection

Analytical curves were constructed from measurements

made with the system in the first derivative mode for Ag,

Ca, Cd, Cr, Cu, Fe, Mg, and Ni and are illustrated in
Figures 11 through 18, respectively. The analytical lines
employed, the type of transition which occurred [27], de-

gree of atomization [28], statistical weight of the state

























cdl
0
cc
CM

4,
as






0




"A
0
a)




fr






4,



P-4
Ci

-r1




































c-

c



0

C)



C>





















COJ Ic Co


(S1IOAOJ3!IU) I2U~3iS


























IN
Cd
4,


Cd






cI
4,


0
C.)







0




rjl
F4
04




4-IJ








70

h


(SHIOAOJ3!LW) Ieu'!s




























cO
cO










C-1








(1,
*0





0
rl
4,







r\



r-4


















































(sIIOAOJO!Wu) jeui!S




























ON


I,-




LrIA







0




0





(1)



(H
























































(SIIOAOJDIU) jeu2!s





































C-




P,

0
41,

'I)

0
V

0

0


qH

W


c,





0
w







rA

















































































LL~L-LLJ....?#
0a 0~


- LI I I II I I


(SIIOAOJ!IUW) Ieu2!s


c



0
CD


a
CL
0
U
0)
0.
0.


























ON






Cd
4,
C)


0
0
p


0
el-i


0



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4,
fr);



w
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H



bfl


Fri


























































( OJ

(St|OAOJD!Wu) ieu2is
























cm
4,

ci







U2


0
0
F-i









0
"-4
4,
'-I


hD

r(4









































































C (S
(SU|OAOJZiW) |eu!S







































C,





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(silOAOJC3u! ) |eu2!S










from which absorption-occurred [27]-,the oscillator strength

for the transition [27], the electronic partition function

[29], the theoretical limits of detection calculated using

Equation (43) and the experimental limits of detection are

tabulated in Table 5. Experimental limits of defection

were obtained by extrapolating the analytical curves to the

point where the signal was equal to twice the rms noise-and

reading the corresponding concentration.

Because the derivative spectrometer is sensitive to

small, but rapid,changes in the slope of the spectrum it

views, both the source and flame background spectra were

examined over an interval of 5 A on either side of the

analytical lines used. In all cases, the source background

varied linearly and had no fine structure in its spectrum.

In the cases of Mg, Cr, and Fe, there were some flame

emission lines within the 10 A interval, but these were far

enough away from the analytical lines not to interfere.

It should be noted that the general shape of all

analytical curves follows that of the theoretical curve of

growth in Figure 3 having a slope of 1 at low concentra-

tions and a slope of less than 1 at concentrations greater

than 10 /g ml-1 which corresponds approximately to an

atomic concentration in the flame of 1010 atoms cm3.












,-I"
I
rl
i-
Stoi)

u a




O .



4 E
u 0
A U



N

m
E0 U
'-N












m
c-N











0


4,










4PP
-4 41
*Hrlb















4,
0















0
E-
COCM
r>

0l
*^


o-

O r-


I I I






0 0 0



I I- r-I

d-- NJ .--4


N N E 't t\ co
SN ,- N 0 N


r- -I i M O\ J l- E- 0 r--I


* *
ON
OC; -'


t ir CN co
0 l\ 0 0 A U\ N
* r- * *-
,-I


- H-I r o n LN N- O0 r-4
OJ r-

r-4
CO 0 03 0 cN 4 N
r\ 0 oO c- 0 O 0
9 I .
0 r-1 0 0 0

N N
- K\ K\ 0 tc* n
N N P4 P4 p P4i t: P-4
.r- H N N 0 C [ LN rl
I I I I I I I I
Co co p a C to
H- r-i N N KC\ N- LUN r-


Co N N- 0 CT\
0o n t o 0 r- c
N co N CN 4 Ur\
(\J \1 I l >c rf


-8 .
*H 0 O Z 0 0 a -E
S0 r> M o 0 o
S c O -Il *rl 0 rH
o a o 0 u O H 0


0
w
0
L
Sa





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0
0 0 0 ("J








j Cj -4
CJ (J ,-
L 0 0 0

oJ D- ou








85

Conclusions


The advantages of using a continuum source in atomic

absorption spectrometry versus line sources have been

enumerated earlier. In addition to the cost and time

saving advantages, one further important capability is

present. When using line sources, the analyst is restricted

to utilizing resonance transitions, that is, transitions

arising from the ground state, since these are usually the

most strongly emitted lines of the source. However, in

certain cases, for example. Ni, and Fe, there are very low

lying states having large transition probabilities which

may be appreciably populated at the temperature of the

flame. Systems employing continuum sources may take

advantage of these more favorable transitions while those

using line sources generally may not.

It is shown in Table 4 that the signal obtained for

identical concentrations of analyte was larger for normal

mode AAC than for the first derivative mode by a factor of

about 5. Why, then, use the derivative mode in favor of the

normal mode? The answer is that the signal-to-noise ratio

of the derivative mode is 5 times that of the normal mode.

In addition, if the absorption peak happens to be super-

imposed on a slowly increasing or decreasing background, no

background baseline correction need be applied since the

first derivative of such a slope is a constant.










The advantage of using double-modul3tion over just

wavelength modulation as in Snelleman's system [17] is that

all of the signal arising from the flame due to emission is

totally rejected. In addition, the use of a piezoelectric

transducer to drive the refractor plate simplifies the

system to the extent that no major modifications need to be

made to the monochromator as in other systems employing.,

rotating mirrors or refractor plates or vibrating slits.

All that is required to revert to the normal mode is to.

stop the oscillation of the refractor plate.

An additional capability of the system allows first

or second derivative operation in the emission mode, as in

Snelleman et al. [16], by simply turning off the source and

chopper and detecting at 02 or 20 for the first or second

derivative signal, respectively.

The chief limitation of the present system is that

the radiancy of the source is insufficient to push the

minimum detectable concentration into the 10 to 102

pg ml-1 range where it could compete more favorably with

line source atomic absorption spectrometry.

Several possibilities to improve the system suggest

themselves. The first is to utilize a source of con-
0 0
siderably greater radiancy between 2500 A and 4200 A. The

second is to improve the transmission of light through the

system. The latter could be accomplished by using mirrors

instead of quartz lenses. A third would be to substitute




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