Prediction of X-Ray Fluorescent Intensities and Interelement Effects BETTY J. MITCHELL Research and Development Analytical laboratory, Technology Department, Union Carbide Metals Co., Division o f Union Carbide Corp., Niagara Falls, N.
b A method for the accurate prediction of x-ray fluorescent intensities requires only the measurement of an element's intensity in a few key matrix materials. The variation in the intensity of the x-radiation with the atomic number of its matrix i s generally inverse to the variation in its mass absorption coefficient. An intensity-matrix correlation, except for certain discontinuities, is a continuous-type curve from which previously unmeasured intensities may b e read. The discontinuities are explained by the proximity of emission line and absorption edges. The complete pattern of intensities for molybdenum and iron in matrices from atomic number 20 to 90 has been developed.
T
he study of x-ray spectra offers a perfect example of natural law. The systematic decrease in nave length R ith increased atomic number n as first recorded by hloseley and stated in the law commonly given his name. The regularity in the relationship of x-ray spectra to absorption edges and to absorption coefficients makes possible the determination of patterns of emission lines and absorption edges, of absorption coefficients and atomic nunibers, and of abqorption coefficients and mave length which may be used for the qualitative prediction of interelement d e c t s (5) and for the accurate prediction of x-ray fluorescent intensities. Quantitative x-ray spectrographic analyis is made possible by the relationship of fluorescent intensities to composition. Xs5uming controlled conditions of the x-ray spectrograph and the physical and chemical state of the sample under study, the line intensity of a n element will vary with total sample composition, as well as that element's concentration, because of the absorption effects which are c o r nionly designated as "interelement effects." These effects may be corrected for by using one of a variety of techniques for sample preparation and intemity - composition correlations. Qualitative knon ledge of the sample matrix makes possible general prediction of the interelement effects occurring therein, intelligent selection of the best correction method, and the
Y.
choice of analytical lines subject to the minimum effects. It also makes practicable a simple but accurate estimation of a n element's fluorescent intensity. MASS ABSORPTION COEFFICIENT-WAVE LENGTH CORRELATION
Absorption effects are a consequence of the variation in the mass absorption coefficient of a given material with wave length, or conversely the variation in the mass absorption coefficient for a given nave length with atomic number of the absorbing matrix. Valuable information is made available for x-ray analysis if tabular absorption data are plotted as continuous curves. A typical logarithmic plot of mass coefficient LIS. wave length for tin is shown in Figure 1. Except for several points where it drops abruptly, the coefficient increases 15-ith increased wave length of the radiation. These discontinuities occur a t the K and L series absorption edges, in this case the SnK edge a t 0.43 A., and the Sn L edges a t 2.8, 3.0, and 3.2 .4. Curves of this type are useful for qualitative evaluation of absorptions. They are not intended to represent the fine structure of the ab-
sorption edges, as has been determined by various workers. Figure 1 reveals that radiation on the short wave length side of an absorption edge is absorbed to a greater extent by the given matrix material than radiation just on the long side of the edge. The K series of the rare earths-for example, La K a a t 0.37 A. on the low side of the Sn K edge-is absorbed more strongly by a tin matrix than Cd K a a t 0.54 -4.on the high side of the tin edge. As K a at 1.18 A. is even more highly absorbed by tin than either lanthanum or cadmium, although it is far on the high side of the Sn K edge and far on the short side of the L edges of tin. Ca K a a t 3.36 A. suffers more absorption than these cadmium, arsenic, or lanthanum lines. The complementary effect of this absorption by a material is the enhancement or excitation of its fluorescent radiation; the enhancement is especially effective if the wave length of the absorbed radiation is just short of its absorption edge, in the case of tin by La K a a t 0.37 -4.or T' K a a t 2.5 A. Absorption-enhancement effects due to the proximity of emission lines and absorption edges have been described by L
I urn
Figure 1 . Mass coefficientwave length correlation for Sn material
5WAVELENGTH
(A. 1
VOL. 33, NO. 7, JUNE 1961
917
I - TI K a 2 7 5 A 3- U La, 0 9 1 A . 4-LaKa 0 3 7 A
I
5
IO
50
100
A T O M I C NUMBER
Figure 2. Mass coefficient-atomic number correlations for Ti, Fe, U, and La radiation
Von Hevesey (4),Glocker and Schreiber (S), and Adler and Axelrod (1) in their studies on internal standardization. The results of these relationships on fluorescent intcnsities are illustrated in the following sections. MASS ABSORPTION COEFFICIENT-ATOMIC NUMBER CORRELATION
A somewhat more useful form of the absorption coefficient data is shown in Figure 2, in which the coefficient is plotted against atomic number of the matrix material for several given wave lengths. (In this figure and those following it, atomic number refers to the number of the matrix material.) For a given wave length the absorption increases with increased atomic number. As a result, disregarding temporarily the discontinuities, the intensity of an element's fluorescent radiation should be reduced progressively as the atomic number of its matrix increases. As has been pointed out by others (2), a light element emitting long wave length radiation in a heavy matrix is strongly absorbede.g., Ti K a a t 2.75 A. in a tantalum (No. 73) matrix with an absorption coefficient about 600. The absorption of the radiation from a heavy element by a light matrix is small--e.g., U Lai at 0.911 A. in calcium (No. 20) with an absorption coefficient about 40. Also, since the L series radiation of a n element is softer (or longer) than its K series
0
Per Cent
TiOz
100
Figure 3. Intensity-concentration curves for Ti02
918
ANALYTICAL CHEMISTRY
radiation, the L series lines will be more highly absorbed than K series linese.g., La1 at 2.665 A. is more highly absorbed by calcium (absorption coefficient about 850) than is La K a at 0.371 A. with an absorption coefficient less than 10. The shapes of the fluorescent intensity-concentration curves resulting from various absorption conditions are illustrated in Figure 3. The intensity of Ti02 in NbzOs, W-03, and Taz06 (curves 2, 3, and 4) illustrates a higher absorption than the intensity of TiOz in Fez08 (curve 1). The absorption of Sn K a a t 0.49 A. is shown in Figure 4. The absorption coefficient increases until Atomic No. 46 is reached, drops down a t No. 47, then gradually increases again. Apparently this discontinuity occurs between the two elements whose absorption edges are just longer and just shorter than the tin line, the Sn K a line a t 0.491 A. being absorbed highly by palladium (Atomic No. 46) with its K absorption edge at 0.509 A, and to a much lesser degree by silver (Atomic No. 47) with R edge a t 0.486 A. The increase in the coefficient from No. 47 up forms a curve parallel to the first. This should mean that for this tin line there are two series of elements with similar absorptions. Sn K a intensity should be similar in certain low-numbered materials to its intensity in certain highnumbered ones. (Referring to Figure 2, we note three parallel lines which indicate three sets of elements in which titanium and iron should give the same intensities.) INTENSITY-ATOMIC NUMBER CORRELATIONS
Figure 5 shows the effect on tin fluorescent intensity of its mass coefficient-atomic number pattern. Although oxides were used in this study because of their availability and ease of handling, and in many cases, their absorption coefficients are not in the same order of magnitude as the metals themselves, the results obtained are applicable to metals, as either powders or solids. A plot of the intensity of 10% SnOz as measured in various oxide matrices follows a pattern inverse to that of Figure 4. The vertical scale represents the intensity of 10% SnOz; the horizontal scale, the atomic number of the matrix. As expected, the intensity follows the inverse pattern from the mass absorption coefficient relationship; the intensity decreases as the atomic number increases until NO. 46 is reached; it increases abruptly, then decreases again with increasing atomic number. For certain matrix pairs, tin intensity is the same or very nearly the same-.g., niobium (No. 41) and tantalum (No. 73), iron (No. 26) and barium ( S o . 56). According to
WAVELENGTH 100-
50
049 A
Sn Ka
-
c
g ::
'0-
V
Y
5-
0
z
P a
I
0
104
the information in Figure 4, the mass coefficient is a t a maximum a t No. 46 and a t a minimum a t Xo. 47, which should result in an intensity minimum a t KO.46 and maximum a t No. 47. However, the intensity of tin, although low a t KO.46, does not go up directly to a peak a t No. 47 as expected. Instead it rises gradually t o a peak a t Xo, 54 before dropping. This discrepancy was checked using molybdenum and iron oxides in various matrices and was found to occur in the same manner. A careful study of the line-edge relationships for these materials showed that an enhancement of the fluorescent radiation from the element was occurring because its matrix element emitted a strong line
'i
'OOt
z
W
I-
E
400:
6
300
2oor
IOOl
I
I
1
I l l 10
30
46
ATOMIC
54
70
90
I 100
NUMBER
Figure 5. Fluorescent intensity-atomic number pattern for 10% SnOz
'0°[
i 5
"2;
I \
l 4oo/
" w rn
J 300
u
_
!
,001
1
IO
30 ATOMIC
50
70
90 100
NUMBER
Figure 6. Fluorescent intensity-atomic number pattern for 10% Fez03
just short of its absorption edge. The proximity of line and edge, with its resulting enhancement, is most pronounced, not in the matrix of lower absorption, No. 47 for tin, but in the matrix, No. 54, several atomic numbers higher. Similarly, for 10% Fe203, although the mass coefficient indicated the intensity should reach a maximum in manganese (No. 25), the peak occurred in nickel ( S o . 28) (Figure 6) u i t h its K a line a t 1.66 A, just short of the iron absorption edge at 1.74 A. As indicated for F e K a by its coefficient-atomic number plot (Figure 2), there should be three series of matrices in uhich its absorption and consequently its intensities are the same. The intensity-atomic number pattern proves this to be the case for matrix oxides in the groups from KO.21 to 24, 44 to 47, and 72 to 84. An unpredicted group of similar intensities also appears from S o . 60 to 63. An interejting illustration occurred in the determination of wide concentrations of Fe203 (Figure 7) in combinations of titanium ( S o . 22), niobium (No, 41), tantalum (KO. 73), and tungsten (KO. i 4 ) . Although the matrices varied grmtly in atomic number, iron fluoresc m t intensities varicd very little. Curves 1 to 4 represent niobium, tungsten, titanium, and tantalum oxide matrices, respectively. The discrepancy between the expected inverse relationship of absorption coefficient-atomic number and intensity-atomic number which occurs in the case of a matrix element emitting K series radiation is complicated in the case of a matrix element emitting strong L series radiation. Variations in absorption of the line of interest, due to variations in its location between the L series edges of matrix elements, occur, plus variations in its enhancement by strong L series lines. A careful study
of this situation n-as made in the cases of iron, chromium, and titanium (Table I). The first F e K a intensity maximum (Figure 6) occurred in nickel, as has been explained. From atomic numbers 57 to 62 (lanthanum, cerium, praseodymium, neodymium, samarium) Fe K a is absorbed in relation to a variety of edge combinations. In lanthanum it is on the low wave length side of all three L edges, in cerium of two edges. in praseodymiuni and neodymium of one edge, and in samarium of no edges. Since the strongest lines of these rareearth elements do not occur on the short wave length side of the iron absorption edge, its intensity pattern is not complicated by enhancement. Iron K a intensity was found to follow the pattern indicated by its location in respect to the L edges-Le., it is low in lanthanum (No. 57), increases from cerium (No. 58) to praseodymium (No. 59), t o neodymium (Yo. 60), to samarium (No. 62).
Table I.
Per
0
Cent
Fez03
100
Figure 7. Intensity-concentration curves for F e n 0 3
The determination of chromium using Cr K a and Cr Kg radiation was also evaluated under similar absorption edge conditions. Cr K a at 2.29 A. is short of the three edges of iodine (No. 53), of the tn-o edges of cesium (KO. 55), and of a single edge of barium (No. 56), and is on the high side of lanthanum (No. 57) edges. Cr Kp a t 2.085 A. varies in edge proximity from cesium (No. 55) to praseodymium (No. 59)
Absorption-Enhancement Conditions for Tin, Iron, Chromium, and Titanium
Element Sn (No. 50) Fe (No. 26)
Cr (KO.24)
~ ~ Absorbing i Edges,@ ~ A. ~K Edge, i Enhancing ~ Linea,O ~ A. Line, A. No. A. No. K a 0.491 46 Pd K 0.509 0.425 54 X K a 0.418 24 Cr K Kcu 1.937 2.070 1,744 28 Ni K a 1.659 60 Nd L I I I 1.995 1.682 65 Tb L& 59 Pr L I11 2.077 1.710 66 DY LBi 58 Ce L I11 2.164 1.623 LP2 57 L a L I 1.973 1.647 67 HOLp1 L I1 2.103 1.567 LP2 L I11 2.259 1.587 68 E r LB1 56 B a L I 2.068 1.514 LP2 L I1 2.204 1.726 69 Tm LaI L I11 2.363 1.530 K a 2.291
25 hln Kp, 26 Fe K a Fe Kp
1.463 1.672 1.910 1.937 1.757
60 Nd LPz
2.035
2.070
25 Mn KP1 26 Fe K a Fe K p 60 Nd L& 62 Sm Lo1 LP2
1.998 1.882 1.920 1.812 2.046 1.847 1.746 1.910 1.937 1,757 2.035 1.998 1.882
2.407
50 Sn L I L I1
23 24 56 57
51 Sb L I1
58
52 Te L I11 2.856
59
22
Ti K
2.497
2.070
56 Ba L I11 2.363
K p 2.085
Ti (No. 22)
Kcu 2,750
23 V K 22 Ti K
2.269 2.497
58 Ce L I11 57 La L I1 L I11 56 Ba L I I L I11 55 Cs L I LII L I11 21 Sc K
2.164 2.103 2.259 2.204 2.363 2.167 2.314 2.474 2.758
L I11 L I11
La; L82
2.285 2.291 2,404 2.458 2.303 2.356 2.208 2.463 2.259 2.119
Only those pertinent to the discussion are listed. ~~~~
VOL. 33, NO. 7, JUNE 1961
919
changes very little from KO.56 to 60, although a general decrease occurs. Thus a small general decrease with increased atomic number appears to be the pattern in spite of variations in enchancement. The intensity of Cr K a and Cr Kp in samarium (No. 62) confirms this; in spite of the SmLpl line a t 2.00 A. (Cr K edge a t 2.07 A.), their intensities are less than in No. 59 (Figure 8). The pattern for Fe K a (Figure 6) between 63 and 72 may be approximated as fairly constant.
700 -
600-
CrKn
>
&z 500W
E +
400-
z
W
u W VI
300Cr Kg
-I
100-
I
I
10
30
-50
70
90
ATOM I C NUMBER
Figure 8. Intensity-atomic number pattern for 10% CrtO,
A plot of the kind in Figure 5, 6, or 8 makes obvious an extremely valuable method for predicting intensities. By measuring the intensities of an element in a certain few key matrices and plotting a continuous curve therefrom, its intensity may be estimated very accurately in other completely different matrices without ever running a standard. This was illustrated using 10% Sn02, 10% Moo3, and 10% Fez03
As in the case of iron, strong lines of these elements are on the high side of the chromium edge. The intensities of the chronlium lines followed the pattern shown in Figure 8. Cr K a peaks a t No. 57 and Cr Kp a t No. 59 as expected. The intensity of Cr Kp in Nos. 56 and 57 is reversed from that predicted by the order of the line and edgesLe., it is somewhat higher in No. 56 0 100 than in No. 57. This is probably due to PER CENT M o o 3 the fact that since CrpOa was prepared Figure 9. Estimated M o inin BaC03 as matrix No. 56 and La203 tensity pattern for atomicas matrix No. 57, the higher proportion numbered elements from 20 of lanthanum (85.3%) in Laz03 than to 92 barium (69.6%) in BaC03 resulted in a greater absorption of Cr Kp radiation. The same reversal is evident for Fe in various oxide matrices. The plot K a (Figure 6) in matrices Nos. 73 and of tin intensities, as in Figure 5, was 74 represented by Ta& (81.9% tanused to read the expected intensities of talum) and W03 (79.3% tungsten), 10% SnO2 in matrices which had not and in matrices Nos. 25 and 27 reprebeen previously determined-Le., NizOa sented by h h 0 2 (63.2% manganese) and COO (78.7% cobalt). (No. 28), v205 (No. 23), and Smz03 (No. 62). The plot of Fez03 intensities I n matrices from atomic number 63 as in Figure 6 and of Moo3 was similarly to 72, it is more difficult to predict the employed. The intensities of molybintensity pattern for Fe K a , or the Cr denum in unknown matrices CeOz K lines. Many of the elements in this (No. 58) and Sn02 (No. 50), and of iron group emit L series lines which may in Vz05 (No. 23) and CuO (KO. 29) cause iron or chromium line enhancement--e.g., Dy Lp2 a t 1.62 A,, Ho L ~ I were estimated. The estimated intensities were then checked by preparation a t 1.65 A., or Yb Lal a t 1.67 A,, on the and measurement of appropriate oxide low side of the Fe K edge a t 1.74 A , ; standards. The accuracy of the estiGd La1 a t 2.05 A., E u Lp1 a t 1.92 A.; mated readings is illustrated in Table I1 or SmLpl a t 2.0 A. on the low side of the by comparing them with the standard Cr K edge a t 2.07 A. (Table I). Bereadings. Although the intensity of the cause of the expense of these matrix Mo K a second-order line a t 1.42 A. materials (Nos. 63 to 72), a similar situawas measured, its intensity-atomic tion of enhancement-absorption of Ti number pattern was the same as would K a was studied using Ti02 in matrices be predicted for hlo KCYfirst order a t Eos. 50 to 60, which were more easily 0.710 A. The mass absorption coefobtained. As previously described for iron and chromium, the Ti K a intensity ficient-atomic number pattern for 1.42 A. is different from that for 0.710 A., increases as the number of higher wave being a three-parallel line pattern similength edges decreases. Its intensity 920
ANALYTICAL CHEMISTRY
II. Accuracy
of Estimated Fluorescent Intensities
Element
Estimated Matrix Inten- Measured No. sity Intensity
10% SnOz Ni203 28 VeO6 23 Smz03 62
400
191.5 407.4 169.4
10% hfoot CeOI 58 SmzOs 50
135
95
93.7 139.4
10% Fez03 VrOs
185 608
183 610
CuO
INTENSITY PREDICTION
200-
1
Table
23 29
185 170
lar to that for Fe K a and Ti K a . This fact indicates that higher order lines may not be used to avoid interelement effects occurring on the firstorder line, but are subject to the same effects. The prediction of intensities may be extended to wider concentration ranges, as desired, and even complete systems of calibration curves constructed. On the basis of the measured intensities of MOO, [Mo K a (S)] in eight matrices, a complete system was projected for molybdenum and M O O 3 in matrices from calcium (No. 20) to uranium (No. 92). A few representative curves are shown in Figure 9. The top and bottom curves represent maximum and minimum intensities and the intensity of Mool in any combination of elements will fall within these limiting curves. Interpolations between appropriate curves may be made for combinations of elements. A projection of the complete system for iron or Fe&,
> k v) W z I-
z
100
0
PER CENT F e z 0 3
Figure 10. Estimated Fe intensity pattern for atomic-numbered elements from 20 to 90
based on its intensity-atomic number pattern, is shown in Figure 10. CONCLUSIONS
With a minimum of information based on the relationship of mass absorption coefficients to atomic number and wave
length, it is possible to predict fluorescent intensities for a particular x-ray spectrograph over wide variations in concentration and matrix. General calibration curve shapes or intensity systems may be worked out for every element analyzed by x-ray fluorescence in any matrix. Knowledge of these systems offers the possibility of develop-
ing basic correlations of x-ray intensity with concentration and matrix which will be valuable to all x-ray spectrographers. LITERATURE CITED
(1) Adler, I., .4xelrod, J. M., Spectrochim.
7, 91 (1955). ( 2 ) Birks, L. S., Brooks, E. J., ANAL.
CHEM.
30, 19 A (October 1958).
(3’pE:$ki5,lf&:$$$‘er,
Ann. (4) H ~ c;. van,~ ‘[Chemical ~ ~ ~ ~~ by X-Rays and Its Applications,” McGraw-Hill, New York, 1932. (5) Mitchell, B; J., “Encyclopedia of Spectroscopy, G. L. Clarh, ed., pp. H.j
736-44, Reinhold, New York, 1960.
RECEIVED for review December 12, 1960. Accepted March 20, 1961.
X-Ray Fluorescent Intensity of Elements Evaporated from Solution onto Thin Film E.
L. GUNN
Humble
Oil & Refining Co., Baytown, Tex.
b The x-ray fluorescence emission properties of six metallic elements deposited from aqueous solutions as thin film have been studied with the objective of defining the range in which linearity between intensity and concentration may b e expected in microanalysis. linearity was found up to 100 y of deposit for iron, copper, and titanium, up to 400 y for calcium, and up to 2000 y for strontium; for molybdenum the relationship still was linear a t 20,000 y. The data were analyzed to determine in each case the concentration a t which the rate of departure from linearity was greatest. Sensitivities of the six elements were compared and found to vary b y as much as approximately 1 00-fold. Emission and absorption measurements on the same film deposits are compared to illustrate the relationship between them. An example of a microanalysis is given, in which an internal standard is employed.
T
HE advantages of the use of thin film for determining microgram amounts of elements by x-ray fluorescence have been pointed out and utilized by several workers (2, 4, 6, 6). The chief advantages are that film techniques are highly sensitive and, within limits, free from absorption effects. The ideal support for a microdeposit would be one which contributes no background whatsoever to the fluorescent spectrum, allowing the sample deposit virtually to float in the x-ray beam. Such a support does not exist, of course. But materials of low atomic number, such as paper, cork, polymers, or beryllium, magnesium, and aluminum metals, do contribute very low background when employed in the form of thin film. A common disadvantage which all these substances have as supports for evaporated solution deposits is the difficulty
of obtaining uniform thickness and area on the film. This well known limitation is recognized, hon ever, and this laboratory, among others, has successfully utilized film techniques n i t h filter paper and other materials as support in the analysis of microdeposits. The fluorescent emission characteristics of microdeposits are of pertinent interest in this or any laboratory where thinfilm analytical methods are employed. Mylar, a polymer film supplied by D u Pont, has been used as a support for deposits of selected elements. This material possesses favorable qualities as a sturdy, durable support; yet it contributes a very low background. The present paper reports the results of measurements of emission and absorption of thin deposits of six selected metals and the influence of concentration on linearity, sensitivity, and change in sensitivity of the nieasurements. Specifically, the concentration range over which the relationship to intensity is linear is defined for each element. THEORY
The theory of x-ray fluorescent emission has been adequately discussed in recent books (1, 3 ) . The theory pertaining t o thin film deposits has been presented as follow. Assume that a thin, uniform film deposit is irradiated by an x-ray beam and that a characteristic fluorescent line of an element is thereby excited. The intensity, I , of the fluorescent line from a minute element of volume in the deposit having a depth, dx, is given by the following expression: where
C is a proportionality constant +I
is the angle between the incident beam and the sample surface
+2
pl
p
is the angle between the emergent beam and the sample surface is the effective absorption coefficient of the incident beam is the sample density
and 2
is the sample thickness
If the sample deposit is kept very thin, the absorption of x-rays by it will be very small or practically zero. This signifies that the exponential term of the foregoing equation approximates a value of unity, or dI = C csc $1 IO dx
Incrementally, one may write AI = C
CSC
41 Io AX
For a constant deposit area, AI-A‘v
where N is the number of atoms of the element in the deposit which emit fluorescence. Hence A I = C’
CBC 41 Io
AN
Thus, in the region of limited thickness, the physical significance of this expression is that a direct linear proportionality between Concentration and intensity will be observed. As long as sample absorption is negligible, this proportionality will be maintained. EXPERIMENTAL
A Mylar support for a deposit was prepared b y the use of a glass cylinder cut from glass tubing, 11/4 inches in outside diameter, 13/16 inches in inside diameter, and 5 / * inch in depth. A taut diaphragm of 1/4-mil Mylar was stretched over the cylinder and held in place by several turns of a rubber band. Aqueous solutions roll off the diaphragm very easily, and it therefore must be pretreated in some manner before it will retain the solution on a given area of the surface. This was Deposit
Preparation.
VOL. 33, NO. 7, JUNE 1961
921
~~
