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A fundamental parameter-based calibration model for an intrinsic germanium X-ray fluorescence spectrometer
95
Nuclear Instruments and Methods 193 (1982) 95-98 North-Holland Publishing Company
A F U N D A M E N T A L P A R A M E T E R - B A S E D C A L I B R A T I O N M O D E L FOR AN INTRINSIC G E R M A N I U M X-RAY F L U O R E S C E N C E S P E C T R O M E T E R Leif H0jslet C H R I S T E N S E N * and Niels P I N D Department of Chemistry, Aarhus University, DK-8000 Aarhus C, Denmark
A matrix-independent fundamental parameter-based calibration model for an energy-dispersive X-ray fluorescence spectrometer has been developed. This model, which is part of a fundamental parameter approach quantification method, accounts for both the excitation and detection probability. For each secondary target a number of relative calibration constants are calculated on the basis of knowledge of the irradiation geometry, the detector specifications, and tabulated fundamental physical parameters. The absolute calibration of the spectrometer is performed by measuring one pure element standard per secondary target. For sample systems where all elements can by analyzed by means of the same secondary target the absolute calibration constant can be determined during the iterative solution of the basic equation. Calculated and experimentally determined relative calibration constants agree to within 5-10% of each other and so do the results obtained from the analysis of an NBS certified alloy using the two sets of constants.
1. Introduction The quantitative interpretation of an X-ray fluorescence spectrum is complicated by the interaction of the primary (exciting) and secondary (fluorescence) radiation with the sample matrix through scattering and photoelectric absorption processes. In a recent paper [1], we described an iterative computational method based on the fundamental p a r a m e t e r approach [2--4], and on experimentally determined calibration constants. T h e present work describes an extension of the method where empirically determined calibration constants are replaced by constants c o m p u t e d from tabulated physical constants and detector specifications.
absorption correction, A,, and the enhancement Hi, constituting the matrix effects [1]. They are calculated from a knowledge of tabulated mass absorption coefficients, various other fundamental parameters, and the unknown weight fractions. The latter dependency requires a recursive solution of eq. (1). The calibration constant for a particular element and a particular line, F~, is given by Fi = P K i e,.
(2)
In the fundamental p a r a m e t e r approach the working equation relating observed fluorescence intensity, /~, from a sample of infinite thickness and weight fraction, W~, is given by
T h e primary b e a m intensity or the absolute calibration constant, P, depends on (1) the highvoltage generator setting, (2) the secondary target material, and (3) the irradiation geometry. Usually P has to be determined experimentally by measuring one pure element standard per secondary target. When all elements can be analyzed by means of the same secondary target, P may be interpreted as a weight percentage scaling factor and determined during the iterative solution of eq. (1). For a given excitation energy, e.g. the weighted K~ and Ka energies of the secondary target, the excitation probability, K,, is given by
/, = F~ A, (1 +/-/~) W~.
K, = ~', (1 - 1/J~) to, a, T~,
2. Theory
(1)
We have treated in detail elsewhere the matrix *Present address: The Isotope Division, Rise National Laboratory, Postbox 49, DK-4000 Roskilde, Denmark.
(3)
where r, is the photoelectric cross section, £ the absorption j u m p ratio, to, the fluorescence yield, al the fractional radiative rate, and T~ a hole
0029-554X/82/0000-0000/$02.75 O 1982 North-Holland
II. DETECTORS
96
L.H. Christensen, N. Pind / Calibration model for X-ray fluorescence spectrometer
transfer factor. For the K shell and for any s subshell the hole transfer factor is unity. The various parameters are tabulated in refs. 5-9. The photopeak efficiency model described by Hansen et al. [10] and Cohen [11] has been applied to our intrinsic G e detector. The efficiency, ~, includes an intrinsic efficiency, ex accounting for both the absorption in the sensitive volume and the Ge Ks and K~ escape peak probabilities [12]. The efficiency also includes transmission factors accounting for absorption in (1) the beryllium window (fBe), (2) the gold frontal layer (fAu), (3) the germanium dead layer (fd), and (4) the air path between sample and detector (f~r). Two factors have been omitted compared to the work of Cohen. The photon energy-dependent geometric factor does not deviate significantly from unity for energies below 50 keV. Further, the radial dependent efficiency is assumed to be uniform for the intrinsic Ge detector [10]. All the corrections have been discussed in detail by Cohen [11] and we confine ourselves to presenting the equation for e~ Ei = ~zfBefAufOfair.
(4)
No attempt has been made to determine experimentally the above-mentioned factors individually, i.e. ei is calculated solely from the detector specifications given by the manufacturer. In order to obtain calibration constants independent of the high-voltage generator setting, they are normalized to one of the elements within a secondary target group, the relative calibration constant, F~.R, is given by Fi.R : ( K i E i ) / ( K ~ ¢ ~ ) ,
thickness of 5 mm. The thickness of the beryllium window, the gold frontal layer, the dead layer, and the air path between sample and detector is 33/xm, 0.05 Izm, 0.25/zm, and 6.2 cm, respectively (manufacturer specifications).
4. Results and discussion Fig. 1. is a graphical representation of calculated and experimentally determined relative calibration constants for Ks lines measured by means of the Se and Mo secondary targets. The constants are taken relative to Fe and Sr, respectively. Similar curves can be drawn for any other secondary target as well as for K~, L~, and L~ lines. The precision of the experimentally determined relative calibration constants measured as one standard deviation is better than 2% as long as the counting statistics are not the limiting factor. The uncertainty of the calculated constants is difficult to assess. Applying the error of propagation to eq. (3) and using the uncertainties quoted in refs. 5-9 would give an overall variation of Ki of the order of 5-10%. However, as pointed out by Krause et al. [9], the uncertainty
F~,R Se
2£ x o
(5)
Mo
where s denotes the element used as reference. o
1.0 o
3. Experimental Our energy-dispersive X-ray fluorescence spectrometer, spectrum analysis routine, fundamental parameter approach program, and experimental relative calibration procedure are described in detail elsewhere [1, 13]. The spectrometer is based on the secondary target excitation principle. The intrinsic G e detector used has an active area of 5 0 m m 2 and a sensitive
e
0.5
® 6 0 o
× 5 e
I
2O
x I
25
I
30
I
35
Z~ ,O
Fig. 1. Calculated and experimentally determined relative calibration constants, F,.R [eq. (5)], for K,, lines measured by means of the Se and Mo secondary targets. (× : calculated values, C): experimental values, D: reference element.)
L.H. Christensen, N. Pind / Calibration model for X-ray fluorescence spectrometer
of the relative excitation probability may be reduced to 1-2% for K~ lines and to 3-4% for La lines. This reduction is due to the systematic nature of the error. The assessment of the uncertainty of ~, eq. (4), is even more difficult. An accurate knowledge of the appropriate detector specifications is not available. The magnitude of the intrinsic efficiency above the G e K absorption edge and below 30 keV is determined primarily by the escape peak probability, which has been shown by Christensen [12] to vary from 0.16 to 0.04. The uncertainty of ~x is less than 1%. The magnitude of the absorption corrections and the estimated percentage variations of these due to assumed marginal variations in the thickness of the beryllium window, the gold layer, the dead layer, and the air path between sample and detector are shown in table 1. The attenuation of the fluorescence radiation between the sample and the sensitive volume of the detector is significant for energies below 5 keV, and so are the estimated percentage variations in the jr. parameters. In conclusion, the estimated uncertainty of ¢~ is probably within 15% for energies below 5 keV
97
and above within 5%. The relative efficiency may, however, be more accurate. The graphical representation of the relative calibration constants given in fig. 1 is unsuited to a comparison of the two sets of constants, i.e. the comparison would depend on the choice of element used for the normalization. A least-squares analysis of the relationship between the relative calibration constant and the atomic number, In FR = In A + B In Z, eliminates the problem of normalization. Such an analysis discloses a 2-3% deviation between the slopes of the calculated and experimental data, and this difference is within one standard deviation of the slope
(-5%). The ultimate proof of the validity of any calibration procedure is, however, given by applying the procedure to one or more certified samples. Furthermore, certified samples provide a common basis for comparing various procedures. This has been accomplished for three different calibration procedures based on (a) an experimental absolute and relative calibration, (b) an experimental absolute calibration and a calculated relative calibration, and (c) a calculated absolute and relative calibration, by applying these to the analysis of a certified N i - F e - C r
Table 1 Estimated percentage variations in the f-parameters, eq. (4), due to a s s u m e d variations in the thickness of (1) the beryllium window, (2) the evaporated gold layer, (3) the g e r m a n i u m dead layer, and (4) the air path between sample and detector Parameter
Thickness 0x m)
Energy (keV)
f
A (%)
fB~
33 ± 2.5
3 5 10 20
0.8637 0.9676 0.9957 0.9994
1.1 0.3 0 0
fAu
0.05 ± 0.02
3 5 10 20
0.8694 0.9355 0.9887 1.0000
5.7 2.6 0.5 0
fd
0.25 -- 0.10
3 5 10 20
0.8740 0.9672 0.9950 0.9944
5.5 1.3 0.2 0.2
fair
(6.2 -+ 0.31) × 104
3 5 10 20
0.2767 0.7618 0.9682 0.9950
6.5 1.3 0.15 0.03
II. D E T E C T O R S
L.H. Christensen, N. Pind / Calibration model for X-ray fluorescence spectrometer
98
Table 2 Analysis of the NBS SRM 1198 alloy using three different calibration procedures: (a) P and Fi.R [eqs. (2) and (5)] determined experimentally, (b) P determined experimentally and F,,R calculated, and (c) F/,a calculated and P included in refinement procedure Element
W(%) a
W(%) b
W(%) c
W(%) Certified
Ti Cr Mn Fe Co Ni Mo
2.53 12.8 0.3 36.4 0.6 40.4 6.7
2.58 13.1 0.3 36.8 0.6 39.6 6.8
2.73 12.7 0.6 36.0 0.2 42.2 5.6
2.59 12.9 (0.49) 36.2 0.70 40. I 6.0
alloy. The SRM 1198 alloy was analyzed by means of the Se and Ag secondary targets. Fe and Mo pure metal standards were used for the experimental absolute calibration. The matrix effects were calculated by means of our fundamental parameter approach program. The results of the analysis are shown in table 2 together with the certified values. Calibration procedures (a) and (b) both use the same netto peak intensities, and the results obtained using these two calibrations agree to within 2-3% of each other. This agreement is comparable to the accuracy of the method ( - 5 % ) [1]. Calibration procedure (c) makes use of an iteratively determined absolute calibration constant for the Ag secondary target. The significant discrepancies between some of the results obtained in this case and those just mentioned can be attributed to enhanced spectrum analysis problems due to poorer counting statistics. The Ge I ~ escape peak caused by Mo K~ radiation impedes an accurate determination of the Ni K~ intensity. This in turn influences the accuracy of the Ni concentration.
5. Conclusion It has been demonstrated that a fundamental
parameter-based calibration model accounting for both the excitation and detection probability provides results with an accuracy comparable to that which can be obtained using an experimental calibration. Due to the lack of accurate detector specifications calculated calibration constants should only be used for elements with fluorescence energies above, say, 3--4 keV.
We are grateful to the Danish National Science Research Council for covering the cost of the germanium detector and for a research fellowship to L.H.C. The authors thank S.E. Rasmussen, J.O. Schmidt, and K. Heydorn for their comments on the preparation of the paper, and A. Lindahl for preparing the figure.
References [1] L.H. Christensen and N. Pind, X-Ray Spectrom. (1981) to be published. [2] C.J. Sparks, Jr., Adv. X-Ray Anal. 19 (1976) 19. [3] E. Giilam and H.T. Heal, Brit. J. Appl, Phys. 3 (1952) 3. [4] T. Shiraiwa and N. Fujino, Jpn. J. Appl. Phys. 5 (1966) 886. [5] W.H. McMaster, N. Kerr Del Grande, J.H. Mallett and J.H. Hubbell, Compilation of X-ray cross sections UCRL 50174, Sec. 1 and 2, Rev. 1, Lawrence Radiation Laboratory, University of California, Livermore (t969). [6] Wm. J. Veigele, At. Data 5 (1973) 51. [7] W. Bambynek, B. Crasemann, R.W. Fink, H.U. Freund, H. Mark, C.D. Swift, R.E. Prince and P. Venugopala Rao, Rev. Mod. Phys. 44 (1972) 716. [8] Mr. R. Khan and M. Karimi, X-Ray Spectrom. 9 (1980) 32. [9] M.O. Krause, C.W. Nestor, Jr., C.J. Sparks, Jr., and E. Ricci, ORNL-5399, Oak Ridge National Laboratory (1978). [10] J.S. Hansen, J.C. McGeorge, D. Nix, W.D. Schmidt-Ott, I. Unus and R.W. Fink, Nucl. Instr. and Meth. 106 (1973) 365. [11] D.D. Cohen, Nucl. Instr. and Meth. 178 (1980) 481. [12] L.H. Christensen, X-Ray Spectrom. 8 (1979) 146. [13] L H . Christensen, S.E. Rasmussen, N. Pind and K. Henriksen, Anal. Chim. Acta 116 (1980) 7.
Nuclear Instruments and Methods 193 (1982) 95-98 North-Holland Publishing Company
A F U N D A M E N T A L P A R A M E T E R - B A S E D C A L I B R A T I O N M O D E L FOR AN INTRINSIC G E R M A N I U M X-RAY F L U O R E S C E N C E S P E C T R O M E T E R Leif H0jslet C H R I S T E N S E N * and Niels P I N D Department of Chemistry, Aarhus University, DK-8000 Aarhus C, Denmark
A matrix-independent fundamental parameter-based calibration model for an energy-dispersive X-ray fluorescence spectrometer has been developed. This model, which is part of a fundamental parameter approach quantification method, accounts for both the excitation and detection probability. For each secondary target a number of relative calibration constants are calculated on the basis of knowledge of the irradiation geometry, the detector specifications, and tabulated fundamental physical parameters. The absolute calibration of the spectrometer is performed by measuring one pure element standard per secondary target. For sample systems where all elements can by analyzed by means of the same secondary target the absolute calibration constant can be determined during the iterative solution of the basic equation. Calculated and experimentally determined relative calibration constants agree to within 5-10% of each other and so do the results obtained from the analysis of an NBS certified alloy using the two sets of constants.
1. Introduction The quantitative interpretation of an X-ray fluorescence spectrum is complicated by the interaction of the primary (exciting) and secondary (fluorescence) radiation with the sample matrix through scattering and photoelectric absorption processes. In a recent paper [1], we described an iterative computational method based on the fundamental p a r a m e t e r approach [2--4], and on experimentally determined calibration constants. T h e present work describes an extension of the method where empirically determined calibration constants are replaced by constants c o m p u t e d from tabulated physical constants and detector specifications.
absorption correction, A,, and the enhancement Hi, constituting the matrix effects [1]. They are calculated from a knowledge of tabulated mass absorption coefficients, various other fundamental parameters, and the unknown weight fractions. The latter dependency requires a recursive solution of eq. (1). The calibration constant for a particular element and a particular line, F~, is given by Fi = P K i e,.
(2)
In the fundamental p a r a m e t e r approach the working equation relating observed fluorescence intensity, /~, from a sample of infinite thickness and weight fraction, W~, is given by
T h e primary b e a m intensity or the absolute calibration constant, P, depends on (1) the highvoltage generator setting, (2) the secondary target material, and (3) the irradiation geometry. Usually P has to be determined experimentally by measuring one pure element standard per secondary target. When all elements can be analyzed by means of the same secondary target, P may be interpreted as a weight percentage scaling factor and determined during the iterative solution of eq. (1). For a given excitation energy, e.g. the weighted K~ and Ka energies of the secondary target, the excitation probability, K,, is given by
/, = F~ A, (1 +/-/~) W~.
K, = ~', (1 - 1/J~) to, a, T~,
2. Theory
(1)
We have treated in detail elsewhere the matrix *Present address: The Isotope Division, Rise National Laboratory, Postbox 49, DK-4000 Roskilde, Denmark.
(3)
where r, is the photoelectric cross section, £ the absorption j u m p ratio, to, the fluorescence yield, al the fractional radiative rate, and T~ a hole
0029-554X/82/0000-0000/$02.75 O 1982 North-Holland
II. DETECTORS
96
L.H. Christensen, N. Pind / Calibration model for X-ray fluorescence spectrometer
transfer factor. For the K shell and for any s subshell the hole transfer factor is unity. The various parameters are tabulated in refs. 5-9. The photopeak efficiency model described by Hansen et al. [10] and Cohen [11] has been applied to our intrinsic G e detector. The efficiency, ~, includes an intrinsic efficiency, ex accounting for both the absorption in the sensitive volume and the Ge Ks and K~ escape peak probabilities [12]. The efficiency also includes transmission factors accounting for absorption in (1) the beryllium window (fBe), (2) the gold frontal layer (fAu), (3) the germanium dead layer (fd), and (4) the air path between sample and detector (f~r). Two factors have been omitted compared to the work of Cohen. The photon energy-dependent geometric factor does not deviate significantly from unity for energies below 50 keV. Further, the radial dependent efficiency is assumed to be uniform for the intrinsic Ge detector [10]. All the corrections have been discussed in detail by Cohen [11] and we confine ourselves to presenting the equation for e~ Ei = ~zfBefAufOfair.
(4)
No attempt has been made to determine experimentally the above-mentioned factors individually, i.e. ei is calculated solely from the detector specifications given by the manufacturer. In order to obtain calibration constants independent of the high-voltage generator setting, they are normalized to one of the elements within a secondary target group, the relative calibration constant, F~.R, is given by Fi.R : ( K i E i ) / ( K ~ ¢ ~ ) ,
thickness of 5 mm. The thickness of the beryllium window, the gold frontal layer, the dead layer, and the air path between sample and detector is 33/xm, 0.05 Izm, 0.25/zm, and 6.2 cm, respectively (manufacturer specifications).
4. Results and discussion Fig. 1. is a graphical representation of calculated and experimentally determined relative calibration constants for Ks lines measured by means of the Se and Mo secondary targets. The constants are taken relative to Fe and Sr, respectively. Similar curves can be drawn for any other secondary target as well as for K~, L~, and L~ lines. The precision of the experimentally determined relative calibration constants measured as one standard deviation is better than 2% as long as the counting statistics are not the limiting factor. The uncertainty of the calculated constants is difficult to assess. Applying the error of propagation to eq. (3) and using the uncertainties quoted in refs. 5-9 would give an overall variation of Ki of the order of 5-10%. However, as pointed out by Krause et al. [9], the uncertainty
F~,R Se
2£ x o
(5)
Mo
where s denotes the element used as reference. o
1.0 o
3. Experimental Our energy-dispersive X-ray fluorescence spectrometer, spectrum analysis routine, fundamental parameter approach program, and experimental relative calibration procedure are described in detail elsewhere [1, 13]. The spectrometer is based on the secondary target excitation principle. The intrinsic G e detector used has an active area of 5 0 m m 2 and a sensitive
e
0.5
® 6 0 o
× 5 e
I
2O
x I
25
I
30
I
35
Z~ ,O
Fig. 1. Calculated and experimentally determined relative calibration constants, F,.R [eq. (5)], for K,, lines measured by means of the Se and Mo secondary targets. (× : calculated values, C): experimental values, D: reference element.)
L.H. Christensen, N. Pind / Calibration model for X-ray fluorescence spectrometer
of the relative excitation probability may be reduced to 1-2% for K~ lines and to 3-4% for La lines. This reduction is due to the systematic nature of the error. The assessment of the uncertainty of ~, eq. (4), is even more difficult. An accurate knowledge of the appropriate detector specifications is not available. The magnitude of the intrinsic efficiency above the G e K absorption edge and below 30 keV is determined primarily by the escape peak probability, which has been shown by Christensen [12] to vary from 0.16 to 0.04. The uncertainty of ~x is less than 1%. The magnitude of the absorption corrections and the estimated percentage variations of these due to assumed marginal variations in the thickness of the beryllium window, the gold layer, the dead layer, and the air path between sample and detector are shown in table 1. The attenuation of the fluorescence radiation between the sample and the sensitive volume of the detector is significant for energies below 5 keV, and so are the estimated percentage variations in the jr. parameters. In conclusion, the estimated uncertainty of ¢~ is probably within 15% for energies below 5 keV
97
and above within 5%. The relative efficiency may, however, be more accurate. The graphical representation of the relative calibration constants given in fig. 1 is unsuited to a comparison of the two sets of constants, i.e. the comparison would depend on the choice of element used for the normalization. A least-squares analysis of the relationship between the relative calibration constant and the atomic number, In FR = In A + B In Z, eliminates the problem of normalization. Such an analysis discloses a 2-3% deviation between the slopes of the calculated and experimental data, and this difference is within one standard deviation of the slope
(-5%). The ultimate proof of the validity of any calibration procedure is, however, given by applying the procedure to one or more certified samples. Furthermore, certified samples provide a common basis for comparing various procedures. This has been accomplished for three different calibration procedures based on (a) an experimental absolute and relative calibration, (b) an experimental absolute calibration and a calculated relative calibration, and (c) a calculated absolute and relative calibration, by applying these to the analysis of a certified N i - F e - C r
Table 1 Estimated percentage variations in the f-parameters, eq. (4), due to a s s u m e d variations in the thickness of (1) the beryllium window, (2) the evaporated gold layer, (3) the g e r m a n i u m dead layer, and (4) the air path between sample and detector Parameter
Thickness 0x m)
Energy (keV)
f
A (%)
fB~
33 ± 2.5
3 5 10 20
0.8637 0.9676 0.9957 0.9994
1.1 0.3 0 0
fAu
0.05 ± 0.02
3 5 10 20
0.8694 0.9355 0.9887 1.0000
5.7 2.6 0.5 0
fd
0.25 -- 0.10
3 5 10 20
0.8740 0.9672 0.9950 0.9944
5.5 1.3 0.2 0.2
fair
(6.2 -+ 0.31) × 104
3 5 10 20
0.2767 0.7618 0.9682 0.9950
6.5 1.3 0.15 0.03
II. D E T E C T O R S
L.H. Christensen, N. Pind / Calibration model for X-ray fluorescence spectrometer
98
Table 2 Analysis of the NBS SRM 1198 alloy using three different calibration procedures: (a) P and Fi.R [eqs. (2) and (5)] determined experimentally, (b) P determined experimentally and F,,R calculated, and (c) F/,a calculated and P included in refinement procedure Element
W(%) a
W(%) b
W(%) c
W(%) Certified
Ti Cr Mn Fe Co Ni Mo
2.53 12.8 0.3 36.4 0.6 40.4 6.7
2.58 13.1 0.3 36.8 0.6 39.6 6.8
2.73 12.7 0.6 36.0 0.2 42.2 5.6
2.59 12.9 (0.49) 36.2 0.70 40. I 6.0
alloy. The SRM 1198 alloy was analyzed by means of the Se and Ag secondary targets. Fe and Mo pure metal standards were used for the experimental absolute calibration. The matrix effects were calculated by means of our fundamental parameter approach program. The results of the analysis are shown in table 2 together with the certified values. Calibration procedures (a) and (b) both use the same netto peak intensities, and the results obtained using these two calibrations agree to within 2-3% of each other. This agreement is comparable to the accuracy of the method ( - 5 % ) [1]. Calibration procedure (c) makes use of an iteratively determined absolute calibration constant for the Ag secondary target. The significant discrepancies between some of the results obtained in this case and those just mentioned can be attributed to enhanced spectrum analysis problems due to poorer counting statistics. The Ge I ~ escape peak caused by Mo K~ radiation impedes an accurate determination of the Ni K~ intensity. This in turn influences the accuracy of the Ni concentration.
5. Conclusion It has been demonstrated that a fundamental
parameter-based calibration model accounting for both the excitation and detection probability provides results with an accuracy comparable to that which can be obtained using an experimental calibration. Due to the lack of accurate detector specifications calculated calibration constants should only be used for elements with fluorescence energies above, say, 3--4 keV.
We are grateful to the Danish National Science Research Council for covering the cost of the germanium detector and for a research fellowship to L.H.C. The authors thank S.E. Rasmussen, J.O. Schmidt, and K. Heydorn for their comments on the preparation of the paper, and A. Lindahl for preparing the figure.
References [1] L.H. Christensen and N. Pind, X-Ray Spectrom. (1981) to be published. [2] C.J. Sparks, Jr., Adv. X-Ray Anal. 19 (1976) 19. [3] E. Giilam and H.T. Heal, Brit. J. Appl, Phys. 3 (1952) 3. [4] T. Shiraiwa and N. Fujino, Jpn. J. Appl. Phys. 5 (1966) 886. [5] W.H. McMaster, N. Kerr Del Grande, J.H. Mallett and J.H. Hubbell, Compilation of X-ray cross sections UCRL 50174, Sec. 1 and 2, Rev. 1, Lawrence Radiation Laboratory, University of California, Livermore (t969). [6] Wm. J. Veigele, At. Data 5 (1973) 51. [7] W. Bambynek, B. Crasemann, R.W. Fink, H.U. Freund, H. Mark, C.D. Swift, R.E. Prince and P. Venugopala Rao, Rev. Mod. Phys. 44 (1972) 716. [8] Mr. R. Khan and M. Karimi, X-Ray Spectrom. 9 (1980) 32. [9] M.O. Krause, C.W. Nestor, Jr., C.J. Sparks, Jr., and E. Ricci, ORNL-5399, Oak Ridge National Laboratory (1978). [10] J.S. Hansen, J.C. McGeorge, D. Nix, W.D. Schmidt-Ott, I. Unus and R.W. Fink, Nucl. Instr. and Meth. 106 (1973) 365. [11] D.D. Cohen, Nucl. Instr. and Meth. 178 (1980) 481. [12] L.H. Christensen, X-Ray Spectrom. 8 (1979) 146. [13] L H . Christensen, S.E. Rasmussen, N. Pind and K. Henriksen, Anal. Chim. Acta 116 (1980) 7.