'.rt;icl .',c. rI'nii ": :I i:c".i ,nic? l Chojr;'!" 
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, . . .
SignaltoIToise 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 nonaxial 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 4227 A at a concentration of 25 ug mlI 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 weight, amu.
B = Factor accounting for noise contribution from dynodes,
no units.
B = Unmodulated source spectral radiance, watts cm2
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 c2
1 1
sr 1m .
BT(c,, ) = Modulated spectrum viewed by phototube, watts.
JI
c Speed of light, cm sec.
C = HIinimim detectable solution concentration, pg ml1
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, cm1
k, = Modified atomic absorption coefficient, cm1
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 secI.
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, anp watt.
S = Parallel displacement of refracted beam, run.
o
A = Apparent halfwidth 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 = Halfwidth 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 nonresonance 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 signalto
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 signaltonoise 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
c. ;:.l'* ; ir i n .;v.:.J:,1. pf it.1 re;,t ii 3,_ l.t: .ju t . .vi. 'I. , jr '.j
',_' ",l' i., ,',,.';, co ',i. i i.x'r ,. l , t.e r.i,. i,.:,.:; t'l ,I l l;o ,: tO 'i.., ; ,.if
hu.:i/ L lo ,: 1 ,a.'j',l].i'tt; ,Lf L..r, :1' i.:ol l:t ,;h,' .Ie'', ?l;jr l. t.in,:
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 halfwidth becomes ins:ignificanb with
respect bo the spectral bandwidth of the monochronator and
while the line may be discerned, the signaltonoise 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 signaltonoise ratio of the derivative signal is lower
than that of the original signal. Bonfiglioli and Brovetto
developed the theory for a selfmodulating 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 squarewave 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 = tcos 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 nonaxial 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 am1.
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 nonaxial 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
onethird 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 HP 0 0 H
CM rH 1 c 4' )
c I O O
0 P 0 0 4 0 4 r 0
SE ICrI 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 05oo o ]e d
d r C 0 0 i 4I
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' ri 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 ) Ci 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 halfwidth of the absorption line, lAA [213. How
ever, when medium resolution monochromators having spectral
bandwidths equal to or larger than the halfwidth of the
absorption line are used, the apparent halfwidth of the
spectral profile viewed by the nonochromator is approximately
the same as the spectral bandwidth [22]. The apparent
balfwidth is herein defined as
A 2 s AV (15)
A is the apparent halfwidth (A) and s is the spectral band
width of the monochromator (A)
(14)
s = R'W
Trin L.,ra.it n ( 1 ) ;. i.s the .1Ir. 'i'l.li oI t)1 i, n.r f.7i. ALor
( ..L) _r,.i ..r.I ii.. t.;i: i'" :.,,c.,:]:,l ]..r,:L :r *l.i 'p .c: liou .)J th'
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 bandwidthtoabsorption
line halfwidth 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 fuiction 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 sin2+ 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
IX (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 H4 PP N( 4r P 3 to
p: 0 ED 0 D 0U CM iH
0 H 1 'd rl 'd G
d P 4o 'H o '11 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
r91 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 C1 MlR I F
ei E d r o
r ) 0 0
SEl M OJ a
R: Fp d [. 1 i
O) ' '.) m PP
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' ) El 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 exp [ 1 1(X, X)2
122
e o c]2
L2
+ 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 '
41
0 n
OH
Od
o
CIH
t H
0
o
o r
rd o
04P
Hi c
i*H I
*rI
CoJ
(1
P
,
'l
CI)
rl
0
rI
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 pocendLng derivation,
P
4)
'to
vI
rH
04
C\J
C"j
0
41
Id,,
0
P Pd
F4
,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 rootmeansquare 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 from 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 ircI '.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 112
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 halfwidth
0
(A), f is the oscillator strength for the atom: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 of ii;oms
cn3 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 sec1 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
ninubo1) (nicrograns grai) (K1).
357
Sij gnaNltoHoi se Ratio
The signaltonoise 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 bonoise 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 ri
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 quickrelease 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 wereemployed 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 oneoenth 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
rl + rI 0 5
4o 0 0 ., 0 0
'D) 0 o d)
,o .p F0 0
0) (1 g rl rli
P00 54 0 0 rp
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 _
SrI .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 ll 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 r0 o P0 0O 0 ,O
Si 0i o a P 0d
o 0 P0 lI 0 . 0 U
S0 I P ro 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
02rH Ll rl t f1 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
011 0 0 o 0 0 P
03ri L n (! C p .
00 r4 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: nl 0 PI P o 0f 0
a o ri o u j to r 0 a
I r P pi 0 *rl0
0 0 O0H 0 >s iI 1H H I 0
ri0 r) M TJ fI VI(') ii I i
0 :
0 0I) C
0
1 0
4 o
it
I 0
Hri
O0
O ,
O 1I)
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,
U1'
SP H
Fo
oo
0 0
,Ig
Md
.4 o
S0
Sci 0
O P
cd
oO
iH
O l
(12
F:
I>
OO
co
0
00
. 
Li
*1
1 H
oP
0 P
r1
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
Fi rt
Pi
O
M p
o 0
Fti
)0 Li
CLO
1 II
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)
il 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 ii
Io Cr
fl'd
rc
000
0 0
H,,l "0_
H0 0
S04) (I 'cd
0 *ri iC 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 ri 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 ri
P 0 P1) .1 :: IH 0
H P43 H 0H P d
0O ic rl ,00 P0 1i 0
Si d ,m n I
o c4 ), o ) C )
cH H U
o 0 CO~'0 ., 0 00
R !^l P rl d
M d o M o p, d o
o d o 0o H .,
P011 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
rl 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 rHl 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 r1 0 0 'OA OaCO
rl 0 (D i1 r 0
i r' *d > (U 0 0 Pi ,P
0 rl *d r 0 .* .*4 0
Di P. rP 'I p) +P
li rd 0 r *d 13 rl 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 oHI
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 known 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 tungsteniodine projector lamp having a quartz
envelops 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 3slot burner head 10 cm in length. The
burner supported an acetylenoair flame for. all experi
mental noasurenients. The entire nebulizerburner 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 iounted on a quickroloase 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 quickrelease magnetic mounts. The monochromator was
initially roughly leveled using a spirit level while pre
cise leveling was accomplished by using a small, low power
heliumneon 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 quickrelease 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':, '11.'.
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 (46) [25,26]
35o (0,6)
C') 20
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,~530 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 in. bho circuit di.agrnmmed 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 Signii 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 DCA10,
Krohnite Power Afiplifier, IrohnHite 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(ab)) (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 phaselock 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 lockin. 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 phaselock 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 105 and
_Q
10 amperes yielded voltages of between 160 millivolts and
16 microvoltswhich nearly spanned the input signal range
of the phaselock amplifier.
The output of the phaselock amplifier was 1 volt
full scale for the sensitivity range in use. A voltage
divider was constructed to permit a signal onehundredth
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 phaselock
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 phaselock amplifier was adjusted at the
beginning of each experiment to yield the maximum signal.
Data were taken with the monochromator in the nonscanning
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 fuelrich flame was used.
The acetyleneair flame supported on the 3slot 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
bandwidthtospectral 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 ml1
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
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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
Comparisonsof 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 listedin 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 raisedin
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 signaltonoise 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 tungsteniodine lamp and xenon arc
were used asthe 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 theexperimentally determined ratio was foundto
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 ml1, 1.0,ug ml1 and 0.5/ag ml1 ) 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
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as
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from which absorptionoccurred [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 noiseand
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 ml1 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
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m
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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 signaltonoise 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 doublemodul3tion 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 ml1 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
