17
V O L U M E 2 1 , N O . 1, J A N U A R Y 1 9 4 9 mono-olefins. For esample, this technique i.5 suitable for the dctermination of butadiene in mixtures of Ca hydrocarbons, particularly at low concrntrations ( 2 7 ) . Similarly, it has been used, for the determination of cyclopentadiene and methylcyclopentadiene (26) and for the analysis of CS aromatic mixture ( 1 8 ) . A quantitative analyak of ternary mistures of naphthalene, 1inethyhaphthalrne, and 2-methylnaphthalene (12 ) has been reported. An ultraviolet method for the determination of benzene and tolurnr in gasoline ( 1 , 2 ) has been written by an A.S.T.M. group (Committee D-2, Subcommittee XXP, Section F). This does not begin to esliaust the possibilities of ultraviolet spectrophotometric methods of analysis. Acetone at low concentrations ha.: b w n accurately determined ( 5 ) . The analysis of mixtures of phcnol anti the isomeric cresols has been described ( 2 6 ) . llisturcs of aniline, Al--niethylaniline, arid S,S-dimethylaniline have hcen successfully analyzod (28). The value of thc ultravio1t.t method in the determination of certain inhibitors ill polymers has heeri demonstrated ( 3 . In order to dccidv whether ultraviolet spectrophotometry would be useful in a particular analytical problem, it is helpful to have at hand the spectra of the compounds of interest. The appearance in the literature of the ultraviolet absorption spectra of many compounds is obviously very valuable. As an example, one recent paper (22) presents the spectra of about a dozen anthracene derivative.. The catalog of ultraviolet spectra issued by .hierican Petroleum Institute Research Project 44 at the Sational Bureau of Standards (14) is particularly useful for hydrocarbon analysis, although the spectra of some nonhydrocarbons are also included. TERMINOLOGY
absorbance to the product of c3ncentiation arid optical path length is called the “absorptivity” (symbd a ) Thia quantity is a specific property of a material or substance and the suffix “-ivity” denotes that fact. With these term3 and their wmbols, Beer’s law can be expressed as follows: A = - logr abc where T is the tiansmittance, h i, tlie optical path length, and c i s tlie concentration. Widespread adoption of these terms would semi to br desira1,lt..
LITER-iTURE CITED Soc. Testing JIat,erials, ”Compilation of d.S.T.N. Standards on Petroleum Products and Lubricants,” p. 690, 1948. Am. Soc. Testing Materials, Proceedings, 1948. Banes, F. IT., and Eby, L. T., ISD.ENG.CHEM.,.IN.~T, ED., 18, 535 (1946). Barnes, R. H., Rusoff, I. I., Miller, E. S.,and Burr, G. O., I b i d . , 16,385 (1944). Barthauer, G. L., Jones, F. \-., and Metler, -1.V., Ibid., 18, 354 (1946). Beadle, B. W., and Kraybill, H. R., 6.Am. Chem. SOC.,66, 1232 (1944). Brice, B. .\., and Swain, M. L., J . Optical S O C .4m., . 35,532(1945). Brode, W.R . , Patterson, J. W., Brown, J. B., and Frankel, J., IND. ENG.CHEX.,AN.AL.ED..16,77 (1944). Burdett, R. A , , and Jones, L. C., Jr., J . Optical S O C .A m . , 37, 554 (1947). Cary, H. H., and Beckman, A . O., Ibid., 31, 682 (1941). Chance, B., Rev. Sci. Instruments, 18, 601 (1947). Cleaves, A. P., Carver, M. S., and Hibbard, 11. K., S a t l . Advisory Com. Aeionautics, R e p t . TN1608 (1947). Coor, T., Jr., and Smith, D. C., Rev. Sci. Instruments, 18, 173 (1947). Demmerle, R. L., Chem. Eng. .Yews, 25, 904 (1947). Ewing, G. W., and Parsons, T., Jr., . ~ N . A L .CHEhf., 20, 423 (1948). Fletcher, M .H., White, C. E., and Sheftel, J,l. S.,ISD. ENQ. CHEM., .\SAL. ED.,18,204 (1946). Gibson, K. S.,and Balcorn, M .M., J . Optical S O C .Am., 37,593 (1947). Gordon, R. R., Powell, H., and Tadayyoii, J., -1.Inst. Petroleum, 33, 103 (1947). Graff, M. M.,O’Connor, It. T., and Skau. E. L.. IND.ENQ. CHEM..AXIL. ED.. 16. 5,56 (1944). Halpern,’G.R., Ibid.; 18; 621 (l946j. Hogness, T. R., Zscheile, F. P.. and Sidmell, A. IZ.,J . Phys. Chem., 41, 379 (1937). Jones, R. N., Chem. R ~ P 41, . , 353 (1947). Xeal, R. H., and Luckinann, F. H., ISD. ENG.CHEM.,hzra~. ED..16, :358 (1944). O’Connor, R. T., Heinzelnian, D. C., Freeman, -1. F.,and Pack, F.C . , Ibid., 17,467 (1945). Powell, J. S., and Edson, K. C., .\x.AL. CHEM., 20, 510 (1948). Robertson, W.W.,Ginshurg, N., and Matsen, F., ISD.Ezra. CHEM.,.~N.AL. ED.,18, 746 (1946). Roienbaurn, E. J., and Stanton, L., rlra~. CHmf., 19,794 (1947). Tunnicliff, D. D., Ibid., 20, 828 (1948). I‘andenbelt, J. >I., Forsyth, J., and Garrett. .1.,IND.ENQ. CHEX.AXAL.ED..17.235 (1945). RECEIVED Kovember 16, 1948. .\in.
~I
For many years it has generally been recognized that the tcrminology of absorption spectrophotometry is in a n unsatisfactorv Ptate. Such poor terms as “optical density” (almost invariably abbreviated t o density) arid “extinction coefficient” (absorption coefficient, absorption index) have become entrenched through use. With a large and increasing number of m-orkers (many of whom are not spectroscopists) using qpectrophotometric niethods for chemical analysis, the need has become more apparent for a set of ternis less Confusing than that employed up to now and more consistent with usage in other branches of physics. Several organizations, including the Xational Bureau of Standards, the American Society for Testing Materials, and the Society for h p plied Spectroscopy, have become aware of the need and are considering suggestions for improving the situation. -4set of terms for the quantities involved in Beer’s law which has much to commend it has been used in a proposed A.S.T.M. test method ( 1 , 2 ) . The word “absorbance” (symbol A ) is used for the logarithm of the reciprocal of the transmittance, which has previously been called the optical density. The ratio of the
X-RAY ABS0 RPTlON HERMAN A. LIEBHAFSKY General Electric Company, Schenectady, ,V. Y
I
S THE past, when the analytical chemist has used x-rays. he has taken advantage primarily ,of their diffraction ( 1 5 ) by crystalline substances, or of the emission of characteristic spectra. Within recent years, hoxTever, it has become possible for the first time t o measure x-ray absorption a t once precisely and conveniently. As a consequence, x-ray absorptiometry (23) will probably become increasingly important as a method of chemical analysis and of chemical control, for the distinctive characteristics of x-rays lead to results unobtainable with the radiant energy now commonly used for these purposes. Meas-
urements of x-ray absorption will not noticeably alter the sample, and a single measurement can often be made in a matter of seconds once the sample is in the beam. FUNDAMENTAL INFORMATION
The advantages and limitations of x-ray absorptiometry are in general deducible from the known characteristics of x-rays, for a thorough discussion of which the reader is referred to several excellent books ( 5 , 7,1.4,67). rln attempt is made here to illustrate these characteristics by comparing the absorption of x-rays by
ANALYTICAL CHEMISTRY
18 bromine with the absorption of the 2537 A. resonance lihe of mercury vapor, which resembles more closely the type of process common in absorptiometry as practiced by analvtical chemists today. The outstanding characteristic of x-rays, from which certain otbers derive, is their high energy, or small wave length (near 1 A,). Because of this characteristic, the absorption of x-rays usually involves only electrons near the atomic nucleus. The absorption of ultraviolet, visible, or infrared rays, on the other hand, affects the electrons that determine the chemical properties of the elements. X-ray absorption is thus essentially an atomic process and therefore virtually independent of the chemical or physical state. For purposes of chemical analysis, the statements made below concerning x-ray absorption by bromine remain quantitatively valid so long as the mass of bromine is unchanged-be the bromine solid, liquid, or gaseous, elementary or combined, hot or cold, crystalline or amorphous.
E~~OY~WE
BROKEN CENTER LINE REPRESENTS WAVELENGTH OF Ka OF (1.04 h OR OF RESONANCE L : O F MERCURY VAPOR(2537d I
bromine. (3) In the direction of increasing wave length, the discontinuity In the absorbancy curve for mercury vapor is in the direction of increasing absorbancy and coincides in wave length with the emitted line. With bromine, this discontinuity is in the direction of decreasing absorbancy and occurs a t a wave length over 10% lower than that of the emitted line. These differences are readily explained in terms of the atomic processes involved under the simplest conditions. Wit; mercury vapor a t low pressures, the absorption of the 2537’A. line raises one of the outermost electrons in the mercury atom from the ground state to a higher energy level. The emission of this line accompanies the return of this electron to the ground state. With, bromine, the absorption of a n x-ray in the region below 0.92 A. ejects one of the innermost, or K , electrons from the atom. The resulting vacancy is then filled by an L electron from the neighboring electron shel;, and the characteristic K a bromine line with wave length 1.04 A. is emitted. The latter wave length thus measures the energy of this electron transfer, which is some 10% less than the energy needed to eject a K electron from the atom. This explains why the critical absorption wave length is less than that of the corresponding emitted line. The established “absorbancy index” for x-rays is the mass absorption coefficient, pm, which is defined by Equat,ion 5 . In contrast with absorbancy indexes for the radiant energy commonly used in analytical work, mass absorption coefficients can be expressed as the following approximate function of wave length and of atomic number 2 : pm =
( 2 4
x 3)SC/A
(1)
where N is Avogadro’s number, A is the atomic weight, and C is assumed to be constant in the range between adjacent critical absorption wave lengths. The scattering of x-rays by electrons gives rise to an additive term, usually unimportant except a t low 2 and A, that has been omitted from Equat,ion 1. Because x-ray absorption is an atomic process, the mass absorption coefficient of a sample usually stands in a simple additive relationship to those of the elements present. If, for example, sample S contains elements A , B , and C in the proportions by weight x, y, and (1-x-y), respectively, then P:
+ Y d + (l--z-Y)d
= ZPC%
(2)
without restiction as to the chemical or physical state of S , .4, B , or C. For the purposes of chemical analysis, t>hemass absorption coefficient of a sample depends only on its ultimate composition and on the wave length of the x-ray beam if the beam is monochromatic. K i t h polychromatic beams, there may occasionally be departures from Equation 2 (“deviations from additivity”) which are not discussed in this review (51, Figure 4). .0.59.4 - 0 3 4 . 2 -0.1 00+0.1~0.2r0.3+0.4t0.5 CHANGE IN WAVELENQTH FROM O E N T L R ( ~ I I
Figure 1.
Comparison of X-Rays and Resonance
Radiation In Figure 1, the broken center line represents a t once an xray (the KCYline at, 1.04 A.) emitted by bromine, and an ultraviolet line (2537 A.) emitted by mercury vapor. The solid curves show how the corresponding absorbancy indexes (25) vary in the wave-length region about the emitted line. The emitted lines are represented identically in Figure 1, but the absorbancy curves differ widely. Curve 11, which was calculated from information given by Mitchell and Zemansky (ZO), is symmetrical about the emitted lines, and (on Figure 1) indistinguishable fopom it except near the bottom, where it is approximately 0.04 A. wide. Elsewhere in Figure 1, curve I1 coincides with the abscissa. Curve I, on the other hand, is composed of tvio continuous branches not obviously related to the emitted line and separated from each other by a sharp discontinuity a t the “critical absorption wave length” (0.92.&. in Figure 1). There are three important differences between curves I and 11: (1) Bromine absorbs x-rays appreciably a t all the wave lengths shown, whereas mercury vapor is highly transparent over most of Figure 1. (2) For a mass of 1 gram, the maximum absorbancy index is about a million times greater for mercury vapor than for
TYPES OF X-RAY ABSORPTIOMETRY
X h y absorptiometry may be subdivided into absorption spectrometry, absorptiornetry with filtered beams, and absorptiometry with polychromatic beams, the order being that of decreasing restrictions on wave length. It will not be necessary to discuss the intermediate subdivision, for its usefulness can be estimated from t,hat of the limiting cases for any particular problem. In absorption spectrometry, the x-ray beam is made monochromatic before it strikes the sample, or the wave-length distribution of the emergent beam is measured by diffraction methods. When this type of absorptiometry is ca;ried out near a critical absorption wave length-e.g., near 0.92 A. in Figure 1it can yield both qualitative and quantitative information. Whe.1 such work is done in regions of continuous absorption, it may usually be considered as a simplified case of absorptiometry with polychromatic beams. Absorptiometry with a polychromatic x-ray beam somewhat resembles colorimetry with white light. Its most fundamental limitation as an analytical tool is implicit in Equation 1. As all atoms absorb x-rays, such measurements cannot be specific: they cannot ordinarily identify unknown elements in a sample, and (as a corollary) they cannot give the composition of a sample
I
V O L U M E 21, NO. 1, J A N U A R Y 1 9 4 9
19
containing unknown elements though they can usually show whether such a sample has an assumed composition or not. The measurement of x-ray absorption does not differ in principle from similar measurements common in analytical laboratories. For example, polychromatic x-rays from a source (usually a standard x-ray tube) might be passed through the sample contained in a cell, whereupon the emergent beam would enter a detector (photoelectric detector, Geiger counter, ionization chamber) to yield an electric current, i, proportional to the beam intensity, I . When absorption spectrometry is being done, there must be provision for suitably diffracting the beam before i t strikes the sample (to render it monochromatic) or after emergence (to analyze it). Seither operation is possible without radically reducing the intensity (say, by several powers of 10) below that of the polychromatic beam. Under the simplest conditions, the decreases in beam intensity and in output current that measure x-ray absorption by a sample in a cell follow the usual exponential law, which may be written: log[Za/Z] = log[io/i] = km
(3)
when Io and i o refer to the empty cell, k is a proportionality constant that contains the information of chemical interest, and m is the mass of the sample. The effect of certain departures from “simplest conditions” (“deviations from linearity”) is discussed below. (For other, less important departures, see the original literature, especially 10, SO, S I .) By deviation from linearity is meant a curvature in a plot of i on a logarithmic ordinate against m (or thickness); in other words,
I
I
I
1
I
I
I
1
a variation in k , the slope of such a plot, and a departure from Equation 3. Such a deviation will occur even with a monochromatic beam if the detection and amplification system becomes nonlinear so that i no longer varies directly as 1. One remedy is to restrict the range of operation until satisfactory linearity is achieved. For example, when the range of sample masses is chosen large enough from the viewpoints of convcnience and precision, io may equal 1000 i. For samples of masses m, and rnzl however, Equation 2 takes the more practical form log[11/Z*] = log
[il/iZ]
= klm2
- rnl]
( 4)
Xnot’her important deviation from linearity peculiar to polychromatic beams is a consequence of the fundamental nature of x-ray absorption. The proportionality constant, IC, is related as follows to the mass absorption coefficient of the sample p,
= 2.303 a k
(5).
where a is the cross-sectional area (sq. em.) of the cell containing the sample. For most elements, p m is ltnoivn to increase approximately tTith the cube of the wave length (Equation 1) between adjacent critical absorption wave lengths. Consequently, when a polychromatic beam passes through a sample, the longer wave lengths are the more strongly absorbed, so that the beam becomes “harder” as i t progresses. It follows that k xi11 decrease as m, the mass of sample, increases. This point is extremely important to the analytical chemist who plans to use polychromatic beams for precise work. The effect of the deviation just discussed can often be estimated if the change in the “effective wave length” of the poiychromatic beam is known. (The effective wave length of a polychromatic beam is defined as that of a monochromatic beam absorbed to the same extent under the experimental conditions.) Figure 2 illustrates the points discussed (16, pp. 862-3).
I X-RAY ABSORPTION SPECTROMETRY
Absorption measurements near a critical wave length can yield qualitative as well as quantitative information. Glocker and Frohnmayer ( 1 2 ) ,using photographic methods, did the classical work in this field 25 years ago with results that were excellent for the times. Their method will be illustrated briefly with reference to Figure 1, the assumed problem being to determine the proportion of total bromine (free or combined) x in a sample weighing nc grams. The experimental data will be the results of absorbancy measurements a t n-avc lengths just above and just below ( h and h‘, respectively) the, critical absorption wave length, 0.92 (more precisely, 0.918) A . On the basis of Equations 2, 3, and 5,
+ h m ( 1 - z) ( A > 0.92 A,) logZL/Z‘ = kL,mx + kgm(1 - x) < 0.92 d.)
(6)
l a =Z A and k , = IC;
( 9)
logZo/Z = ks,mx
(At (7) where k& > kBr (see Figure 1) (8) I n these equations, S refers to the sample less the bromine, and the la’s usually apply to the empty cell. Now, the more nearly identical are A and A’, the more nearly (in the simplest case)
If Equation 9 is valid, then by substitution and by subtracting Equation 7 from Equation 6, one obtains logZ’/Z = (kBr - kA,)mx = -cmx
1,000
I
I
I
0.10
0.20
I
I
I
0.30 0.40 a30 THICKNESS OF ALUMINUM CM X 5 0 CURVE A CM. :CURVE B
I
ow
I 0.70
Figure 2. X-Ray Absorbancy Curves for Aluminum over Two Ranges of Thickness Decrease i n effective Rave length with increasing thickness of sample is principally responsible f o r curvature shown which grows more pronounced as wave length increased.
(10) The constant c, which is characteristic for each element and for each absorption discontinuity, can be determined empirically or calculated from known mass absorption coefficients by Equation 5. When either part of Equation 9 does not hold, the effect is to introduce into Equation 10 factors that can be determined by making additional measurements, Glocker and Frohnmayer determined the characteristic constant c for nine elements (12, Table 4)ranging in atomic numbers from 42 (molybdenum) to 90 (thorium). They proved that iden-
ANALYTICAL CHEMISTRY
20 tical results could be obtained with the sample in the primary (polychromat’ic) or in the diffracted (monochroniatic) beam. The method was applied with good results t o the determination of barium in glass; of antimony in a silicate; of hafnium in the mineral alvite; and of molybdenum, antimony, barium, and lanthanum in a solution of their salts-for example, 5.45y0 barium was found on 90-minute exposure by the x-ray method for a glass that yielded 5.8% on being analyzed chemically. Andrews ( 2 ) used an ionization chamber as detector to determine iron (0.44%) in beryllium according to a procedure resenibling that just described. Engstrom succeeded in applying the method to microscopic sections of tissue and claimed that “in analyses of calcium and phosphorus in biological material, quantities of to lo-” gi’ani have been determined by the method with an error of 10%’’ (8). Limitations. The element to be determined may be present in an amount so small that the absorbancy of the rest of the sample near the cribical wave length is great enough to make the method insensitive (see Equations 6, 7, and lo), or the char: acteristic constant c may be so small that the precision desired is unattainable. Measurements a t certain critical absorption wave lengths-e.g., the K series for the light elements-are difficult t o make. There may be interference owing to the nearness of critical wave lengths characteristic of other elements in the sample-e. g., the K wave lengths of lead and thallium differ by only 0.004 A. The seriousness of these limitations can sometimes be reduced by selecting a more favorable critical absorption wave length. More important, however, is the prom-
ise of progress in this direction that is held out by recent improvements in the equipment available for such work. Dow Spectrometer. An outstanding example of such equipment is the Dow automatic x-ray absorption spectrometer being developed by Frevel and North (3, 9, I O , I S ) , who are now preparing to publish an account of their work. A cone of polychromatic x-rays passes through the sample and strikes a multiplecrystal “lens” comprising four sodium chloride cryst,als, the monochromatic beams from lvhich are focused on a Geiger counter so hhat the sum of their intensities can be automatically recorded as an output current’. Variation of wave length is accomplished by having a lathe lead screw move the lens and the detector (at twice the lens speed) along the optical axis. “Voltage is stable to within 0.05% during measurement, . , The probable error of the mean of a single intensity measurement is 0.5% for all measurements made for a period of approsiniately 5 niinutes at rates of 10,000 counts per minute and higher. Repeated measurements give agreement within 1%. The time for an Ill0 measurement is 10 to 15 minutes” (9). hfter the values of In Ill0 measured above and below the absorption edge have been extrapolated t o the corresponding critical wave length, the results may be calculated according to Equation 10. Figure 3 shows the output current records obtaiued on the Don, instrument, for iso-octane and for a solution of ethyl bromide in that solvent. In other words, these may be considered experimental data for the problem assumed near the beginning of this section. d s regards precision, time required, and range of determinable elements (now down to atomic number 22), Frevel
175-
-
150-
z
1
2
2 2 cz
,918
8.C
.918
A
8.-A
I
125-
6
>. t m
,Is
loo-
8
c
E
9 V
75-
c
2
2
50-
25
-
DIRECTfON OF OECREASING WAVELENGTH
-
COURTESY DOW C H E M I C A L COMPANY
Figure 3. Geiger-Counter Output Currents Recorded by Dow Automatic X-Ray Absorption Spectrometer “Superposed records on left are x-rny absorptiomeiric curves for iso-octane and a solution containing ethylene dibroinide, whereas traces a t right illustrate recording of transmitted intensities a i fixed wave lengths Apparent change in x-ray absorption of solvent in going through bromine absorption edge is result of marked slope of white radiation distribution curve a t 0.9 A,’’ ( 1 0 ) .
V O L U M E 21, NO. 1, J A N U A R Y 1 9 4 9
21
and North have improved the method of Glocker and Frohnniayer to the point where it deserves serious consideration by analytical chemists. -4nalyses for t,he lighter elements can of course be carried out on the Dow instrument by making measurements a t various wave lengths in t,he region of continuous absorption; this is the other type of spectrometric method mentioned above. The early work of Winghrdh ( 2 9 ) forms a basis for assessing what might be done by this method with modern equipment. The improved diffraction equipment (15) currently becoming available-e.g., Xorelco and G.E. XRD-3-can be used, not only for emission spectrometry, but for x-ray absorptiometry of all kinds as well. As this fact becomes mqre generally appreciated, the importance of s-ray absorption i n analytical chemistry \ - d l grow. X-RAY ABSORPTIOMETRY WITH POLYCHROMATIC BEAJIS
The use of monochromatic s-ray beanis is desirable i n chemical analysis because it simplifies the interpretation of results, but there are many applications in which the conconlitant reduction in beam intensity cannot (or need not) be tolerated. In general, owing to thrir higher intensities, polychromatic beams can be used with simpler apparatus. In particular, absorpt:ometry with polychromatic beams has been made sinlple and easy by the invention of the multiplier phototube (26, SR), which can be readily SECONDARY ELECTRONS
PHOTOELECTRONS
X-RAY
converted into a photoelectric r-ray detector by the use of a suitable phosphor (see Figure 4). Morgan ( Z I ) , who had been investigating photoelectric cells for the control of roentgenographic exposures, \\-as the first to discover the usefulness of the multiplier phototube in the detection of x-rays. Independently and somewhat Inter, Smith (26) and Moriarty ($2)made the same discovery in successfully completing a war assignment not fundamentally different from many problems in chemical control. Fuse Testing. This assignment mas the devising of an infallible, nondestructive, rapid method of inspecting hand-grenade fuses ($2, 2%). If a fuse contains too little powder, the hand grenade esplodes prematurely. Fuses to be tested were mounted upright on a belt that carried them through an x-ray beam. The absorbance of a fuse containing the proper amount of powder was great enough so that the intensity of the transmitted beam, as measured by a multiplier phototube, was too low to trip the detector circuit. With a defective fuse in the beam, however, the increased output current from the tube set into pperation four means of identifying the defective fuse. The equipment inspected fuses a t a rate near 4000 an hour, and this rate was not limited by the detecting or recording apparatus. Thickness of Steel Strip. Clapp and Pohl (4) solved another important control problem by using a polychromatic x-ray beam to measure the thickness of steel strip. During the measurement, the strip is hot (1400' to 1700" F.), moving (say, 2000 feet per minute horizontally with possible vertical vibrations up to several inchec: in amplitude), and subjected to a spray of cooling water. As is being done to an increasing extent in instrumental analysis, the ineasurement is accomplished by means of a servo system, whose main features are indicated in Figure 5 . The top and the bottom x-ray detector each contains a multiplier phototube coated with phosphor. This tube compares the intensity of the x-ray beam entering the detector with that of the light from the reference standard, a discharge lamp. The reference beam is part of a circuit that maintains the s-ray source a t constant intensity. The deviation wedge comes to rest when the intensities of the transmitted x-ray beams stand in a predetermined ratio. At this point, the unbalance in the servo system has been compensated, and the position of the deviation wedge consequently indicates the thickness of the strip.
I t seems reasonable to hope t,hat s-ray absorptiometry with polychromatic beams can be used to solve various other production problems, such as assessing roughly the quality of crushed Phosphor coni.erts x-rays into light t h a t liberates electrons minerals on a conveyer belt, or controlling the addition of a from photocathode 0. These are guid,ed electrically t o t h e successive dynodes 1 t o 9, n h e r e multiplication t o give secondmaterial-cl.g., tetraethyllead to gasoline-to a moving "base ary electrons occurs. T h e greatly (105 t o 106 times) amplified beam is finally gathered by anode 10 for subrequent exstock.)' ternal amplification (over 104 times in photometer of Figure Chemical Analysis. The use of polychromatic x-ray beanis in 61, if desired chemical analysis is not new. Fuller ( 1 1 ) used photographic means to compare the absorbance of TOP DETECTOR ,---alloys for the purpose oi establishing their coniposition. Xborn and Brown ( I ) , acting upon a suggestion of George Calingaert, applied absorptiometry of this type to the determination of tetraethyllead in gasoline and used an ionization chamber as detector. Recently, Sullivan and Friedman (28J rlmployed a Geiger counter for the same purpose. I The successful solution of the fuse-testing probGAGE I 1 N D I CATOR Irm led to an investigation of the photoelectric I s-ray drtector as a tool for chemical analysis (17). I The laboratory photometer incorporating this deI tpctor is shown in Figure 6. Early work on solids, I liquids, and gases was done by the direct method (16). The intensity of the x-ray beam was adjusted to a standard initial value by varying the x-ray tube I I voltage until the desired output current was obI 1 - 1 tained with a standard thickness of aluminum in the beam, the voltage across the detector and the amplifier setting being fixed. Output currents obZERO ADJ. tained with known weights of sample in the beam were then used to give information about the Figure 5 . Block Diagram of General Electric X-Ray Thickness Gage Figure 4. Schematic Diagram of Simple Photoelectric X-Ray Detector
Inr
I
-
8
ANALYTICAL CHEMISTRY
22
composition of the sample. In general, these output currents are plotted as in Figure 2, and the slopes of the curves (or straight lines, Equation 4) are interpreted according to Equations 5 and 2. To illustrate such an interpretation, a common analytic$ problem-the determination of chlorine in a chlorinated hydrocarbon polymer--will be briefly discussed (16).
The direct method has been used in this laboratory in pointto-point explorations of impregnated materials t o test their uniformity. For this work, the diameter. of the x-ray beam was reduced (in some ca6es to 0.15 cm.), and thousands of outpub current readings were taken. Each reading gave in a matter of seconds i obtain bj methods have bee] riding COI Thougl and yields rrsuirti pre~rat:eiwurii wr L L Q U ~ puryuaau, t b 1s ' ~ u v j e m to uncertainties arising from voltage fluctuations and from changes in the effective wave length of the polychromatic beam (31). Far an unfiltered beam of this kind, the variation of outp u t current with primary voltage is much more pronounced than for a monochromatic beam because the change in the total xray output affects the current reedings in the former case. Rapid commutation in the beam between the unknown and 8. suitahle standard can reduce the uncertainties due t o both causes, and the comparative method of x-ray absorptiometry uses this procedure. Readings of output currents are taken alternately for standard and unknown. From these readings, the amount of standard equivalent in absorbancy to the unknown can he calculated. As a consequence, the interpretation of the results does not directly involve output currents, and this is the great advantage of the comparative method. In many cases, aluminum is a satisfactory standard. The laboratory photometer was used in carrying out the following three types of determinations by the comparative method (5'1): identifications of certain new compounds, determination of tetraethyllead fluid in gasoline, and determinatiou of sulfur in
Figure 6. X-Ray Absorption Apparatus ~~
Phoaphor and multiplier phototube. B. Sample cell. C. Sample. D. (CA-5) x-ray tube and houaing. E . Milliammeter. F. Amplifier and rectifier Y B O U U ~tubes. (i. Regulated power a n m b for amplifier tubes and phototube anode voltage. H . Control panel A.
Figure 7 contains the k values derived from output current
kind &her when one element replrtces &other-.&
chlorine
in Figum 7), i t is obvious that these data
