Citation |

- Permanent Link:
- https://ufdc.ufl.edu/UF00098391/00001
## Material Information- Title:
- Double modulation - optical scanning and mechanical chopping - in atomic absorption spectrometry using a continuum source
- Creator:
- Elser, Robert Cooper, 1941- (
*Dissertant*) Winefordner, James D. (*Thesis advisor*) Savory, John (*Reviewer*) Schmid, Gerhard F. (*Reviewer*) Sander, Eugene G. (*Reviewer*) - Place of Publication:
- Gainesville, Fla.
- Publisher:
- University of Florida
- Publication Date:
- 1971
- Copyright Date:
- 1971
- Language:
- English
- Physical Description:
- xiii, 91 leaves. : illus. ; 28 cm.
## Subjects- Subjects / Keywords:
- Absorption spectra ( jstor )
Flame spectroscopy ( jstor ) Flames ( jstor ) Monochromators ( jstor ) Noise spectra ( jstor ) Radiance ( jstor ) Signal detection ( jstor ) Signals ( jstor ) Spectral bands ( jstor ) Wavelengths ( jstor ) Absorption spectra ( lcsh ) Atomic spectra ( lcsh ) Chemistry thesis Ph. D Dissertations, Academic -- Chemistry -- UF Spectrometer ( lcsh ) - Genre:
- bibliography ( marcgt )
non-fiction ( marcgt )
## Notes- Abstract:
- Atomic absorption spectrometry using a continuum source (AAC) presents several advantages distinct from atomic absorption using lino 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 i.ts operation derived. It is shown that both first and second derivatives of the transmitted spectrum can be obtained. The first derivative appears at 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, Or, Cu, Fe, Mg and Ni.
- Thesis:
- Thesis--University of Florida, 1971.
- Bibliography:
- Bibliography: leaves 88-89.
- General Note:
- Manuscript copy.
- General Note:
- Vita.
## Record Information- Source Institution:
- University of Florida
- Holding Location:
- University of Florida
- Rights Management:
- Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
- Resource Identifier:
- 030437474 ( AlephBibNum )
17063952 ( OCLC ) AES1424 ( NOTIS )
## UFDC Membership |

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'.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, . . . 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 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 l-o ,: 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 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. .' 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 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 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 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 .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 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 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 C) H 4, fr); w P. 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, 4, H nI;; cd bO Frz (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 H I I 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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PAGE 1 Double Modulation Optical Scanning 'and Mechanical Chopping ~ in Atomic Absorption Spectrometry Using a Continuum Source By ROBERT COOPER A DIS IC'l PRES INTED TO THE GRADUATE COUNCIL OF EB C UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF ; ': ! R >U] ffiMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 1971 PAGE 2 UNIVERSITY OF FLOR'CJA | 3 1262 08552 4816 PAGE 3 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 bo her and to her understanding that I dedicate this dissertation. PAGE 4 ACKNOWLEDGMENTS 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 Lo 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. Winefordner 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 needed most. 111 PAGE 5 TABLE 0? CONTENTS Page ACKNOWLEDGMENTS . iii LIST 0? TABLES vi LIST OF FIGURES vii KEY TO SYMBOLS ' ix ABSTRACT. . . . . . . xli Chapter I. INTRODUCTION, I II. THEORETICAL CONSIDERATIONS 7 Mechanical Chopper Modulation 7 Refractor Plate Modulation ........ 9 Intensity Expressions. , 3A Limits of Detection. ........... 55 Signal ~to-Noise Ratio 57 III. EXPERIMENTAL SYSTEM AND PROCEDURES 53 Description of System 53 Source ..... 58 Burner and Nebulizer ! '-S Monochromator and Optics 4-9 ; sctronic Components 55 Solutions 57 ;:rimental Procedure . 58 iv PAGE 6 LIST OE TABLES Table Page 1. Breakdown of Intensity Expression Bm(X ,t) . . 22 2. Optical Components HI 3. Electrical Components 4-3 4. Verification of Theory . . , 61 5. Limits of Detection 84VI PAGE 7 Chapter Pago 17. RESULTS AND DISCUSSION 60 Verification of Theory 60 Analytical Curves and Limits of Detection 66 Conclusions 85 LIST 0? REFERENCES 33 BIOGRAPHICAL SKETCH 90 PAGE 8 LIST OP FIGURES Figure Page la. Refraction of an axial beam incident to the refractor plate at an angle, a 11 lb. Refraction of a non-axial beam incident; to the refractor plate at an angle, 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 . . 29 3b. Second derivative of Ca resonance line profile Â° -1 ab 4-227 A at a concentration of 25 ug ml . . 29 o 4. Theoretical curve of growth for Ca at 4227 A by first derivative analysis 32 5. 31ock diagram of experimental system 40 G. 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 bimorph 53 9. Circuit for chopper reference signal" 54 10. First derivative signal intensity versus spectral modulation amplitude (slit image : )Â•.';Â•: stral b idwidth of 0.40 A ~. 63 o 11. Analytical curve Cor silver A. Â• 68 o 12. Analytical curve for calciu a at 4227 A . 70 o 13. ! for cadmium taken a 88 A . 72 o 14. ^.al curve for ' en at 35' Â• 74 PAGE 9 Figure Page 15. Analytical curve for copper taken at 324-7 A . 76 o 16. Analytical curve for iron taken at 3719 A . . 78 17. Analytical curve .for magnesium taken at 2852 A . . . 80 o 18. Analytical curve for nickel token at 34-14A . 82 Vlll PAGE 10 JY TO SYMBOLS o a = Lateral displacement of refracted beam, A. A = Atomic weight, amu, B = Factor accounting for noise contribution from dynodes , no units. 3. = Unmodulated source spectral radiance, watts cm" K o -1 -1 sr nm c -2 B, = Modulated source spectral radiance, watts cm ' Â° sr" 1 nm" 1 . c -2 B, m = Radiance transmitted through flame, watts cm xm = Radiance transmitted through flame, /V -1 Â„.-l nm Bm(\ ,t) Modulated spectn ed by phototube, watts. c = Speed of light, cm sec" . C = Minimum detectable solution concentration, w.g ml . m 7 d = Lateral brie displacement of refracted beam, mm. -19 e = Electronic charge, 1.6 x 10 coulomb* E. = Excitation energy of state i, ev. Af = Frequency interval over which amplifier readout sys ponds, Hz. -Statistical weight ol state i. H = Monochromator sli , Ai = rms noise s" ] bo the photodetector, amperes. J = Total Lantum number. -S -1 k = Bo] on constant, 3.6 L V x 10 y ev Â°K IX PAGE 11 k = Peak atonic absorption coefficient for the minimum -1 detectable concent3?ation, cm k = Atomic absorption coefficient at the absorption line -1 center, cm " . k\ = Modified atomic absorption coefficient, era" . 1 = Length of flame, cm. M = Multiplication (amplification) -factor of photodetector, no units. n = Total atomic concentration of species of interest, aoom cm . n = Total minimum atomic concentration of species of interest in flame, atom cm . n = Minimum atomic concentration of species of interest in state i in flame, atom cm , z -1 Q = Plow rate of unburned gases, cm sec Rn = Reciprocal linear dispersion of monochromator, A rim Hi = Reciprocal linear dispersion of monochromator, A cm" . Rr = Phototube load resistor, ohms, s = Spectral bandwidth of monochromator, A. Â• S(\) = Slit function of the monochromator, no units. , = Pirst derivative signal, volt. S, = Second derivative signal, volt, T = Absolut perature, Â°K. T^> = Transmission factor of instn I system of lenses, monochromator ond flame. T(\) = Transmission of flame cell. PAGE 12 t -Thickness of Refractor plate, im, W = Monochromator 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, 3 = Factor to account for incomplete atom formation and losses due to ionization, no units. f = Phototube sensitivity factor, amp watt . 5 = Parallel displacement of refracted beam, mm. o A ^ Apparent half-width of absorption line , A. 6 = Efficiency of nebulizabion and atomization processes, o X Any wave length, A. X Wavelength at center of exit slit corresponding to grating setting, A. X Wavelength at center of absorption line profile, A. o AA. A = Half -width of absorption line, A. 2 rce ore i r\~2 2 -1 Â— Â— =s 2.65 x 10 cm sec p Coefficient to correct k . 1 o 2 " ?r ' dulal Ion, sec" . xi |