Appl. Radiat. Isot. Vol. 43, No. 6, pp. 777-779, 1992 Int. J. Radiat. Appl. lnstrum. Part A Printed in Great Britain. All rights reserved

0883-2889/92 $5.00 + 0.00 Copyright © 1992 Pergamon Press Ltd

A Modification of the Emission-transmission Method

Determination of Trace and Elements by XRF

for the Minor

A. MARKOWICZ* and N. HASELBERGER

International Atomic Energy Agency, Agency's Laboratories Seibersdorf, Instrumentation Unit, 2444 Seibersdorf, Austria

(Received 4 September 1991)

The paper deals with a modified version of the emission-transmission method which can be applied to the determination of minor (and/or major) elements by x-ray fluorescence analysis. A method for the additional correction for the absorption edges of such elements is presented and all steps involved in the calculation described thoroughly. An example of practical application of the procedure proposed is also given.

Introduction

The emission-transmission method [E-T: Leroux and Mahmud (1966)] is a very efficient technique for the correction of matrix absorption effects in x-ray fluorescence (XRF) analysis. Its relative simplicity and versatility is supplemented by good accuracy, particularly in trace element analysis. In this case one additional measurement carried out with a multi- element target enables one to calculate the absorption correction factors for all the elements to be deter- mined (Giauque et al., 1979). Applying a simple interpolation and/or extrapolation procedure for the results obtained from experiments is possible only for trace element analysis. In some cases, however, such a simple approach can produce inaccurate results, particularly in the analysis of materials containing minor and/or major elements. The reasons for this are discontinuities in the mass absorption coefficient vs energy relationship.

In this paper a method dealing with the existence of the absorption edges of some elements is presented. The necessity of applying such a modified version of the E-T method is demonstrated for the XRF analysis of real samples.

*Author for correspondence at: Institute of Physics and Nuclear Techniques, Academy of Mining and Metallurgy, A1. Mickiewicza 30, 30059 Cracow, Poland.

Modif icat ion of the E - T M e t h o d

For homogeneous intermediate thickness samples (Markowicz, 1979) and monochromatic excitation, the mass per unit area of the ith element, mi, can be calculated from the following expression:

I, m i = ~.F i (1)

where/i is the intensity of the characteristic x-rays for the ith element, Si is the calibration factor (or sensi- tivity) usually determined experimentally on standard samples of known composition (Markowicz et al., 1992a), and Fi is the absorption correction factor for the ith element.

The F~ factor can be determined by the E-T technique by using the equation

/2Tin F i -

1 - exp(--/~T m) = - -

In A (2)

1 1 - - - -

A

with

li T / i - - I i T + S-------~/ (2a)

where/~T is the total mass absorption coefficient of the primary and characteristic radiation in the whole sample (involving the incident and emerging angles), m is the total mass per unit area for the sample to be analyzed, IT and IT + s are the net x-ray intensities of

777

778 A. MARKOWICZ and N. HASELBERGER

the ith element from the target alone and from sample plus target, respectively.

In practice, the values of A determined for a few energies of the characteristic x-rays of some elements to be present in a multielement target are used to construct a curve In In A vs In E which enables one to calculate the absorption correction factors for any energy. In many cases the relationship of In In A vs l n E is a straight line and if no minor (major) element is present in the unknown samples, it does not exhibit any discontinuity.

However, in the case when one or more minor constituents are present in the unknown sample a drop can be observed in the relationship of In In A vs In E. The drop corresponds to the absorption edge of the minor element. An approach which can be adapted in this case requires fitting two (or more) different straight lines for the predefined energy regions. It can simply be done when at least two experimental points are obtained for each energy region. A problem arises when only one or no experimental point is available.

To explain the procedure proposed in this case let us assume that a multielement target consisting of Ca, Ti, Fe, Zn, St, Zr and Pb, and the material to be analyzed contains some minor elements, such as Fe and Ca. From the E-T measurements the values of A are easily obtained for higher energies, e.g. for the characteristic x-rays of Fe, Zn, Sr, Zr and Pb in this case (see Fig. 1). First a straight line is fitted to the points corresponding to Zn, Pb, Sr and Zr (region I). Secondly a straight line of the same slope and passing through a point for Fe is constructed (region II). If no experimental point is available for Ca the dis- continuity for the K absorption edge of Ca has to be taken into account by applying a computation routine. In the first step the following product AI = Wca(i- /above-/- /below) is calculated, where Wc. is the weight fraction of Ca obtained by using a direct

<

t q I

,, exper imen ta l po in ts

III

° \ ' -

i Sr ,

C a K a b s F e K a b s - - I=,.- I n E

Fig. 1. Graphical explanation of the idea for the modified version of the E-T method (see text for details).

extrapolation of the curve II, #~bo~ and/,/below are the mass absorption coefficients just above and below the K absorption edge of Ca, respectively (Poehn et al.,

1985). Next the corrected value of the total mass absorption coefficient #~,or = (ln A ) / m -- Al csc~O2 is calculated for the energy of the CaK,b , edge, where A is taken from curve II and q;2 is the emerging angle for the characteristic x-rays (Hallak and Saleh, 1985; Markowicz et al., 1992a). Based on the #~,or value a straight line passing through point C and having the same slope as that one in region II is constructed (the coordinates of the point C are" x = l n CaKa~, y = ln[ln A - mA 1 cscl,O2] ). In the next step the values of In ptrn and the absorption correction factors F,. are calculated for the energy of Ca characteristic x-rays based on the straight line for region III. Since the true value of the weight fraction for Ca is unknown all calculations for the absorption edge of Ca (region III) are iterated until the following convergence is obtained

( W c a ) n - ( W c a ) n - I 0.001 (3)

(wc.)"

where (Wc.)" and (Wca) "-l are the values of the weight fractions for Ca obtained in the sequential iterations.

A calculation procedure applied for the Ca absorp- tion edge can easily be repeated for any other absorp- tion discontinuity at a lower energy and finally a total absorption curve In In A vs In E is obtained.

The program for the calculation involved in the modified version of the E-T method was written in MS-QuickBasic version 4 and is available on request.

Results

The method proposed in this paper has been applied for XRF analysis of coal samples. Finely ground coal powder has been pelletized without any binder (total mass of the samples ca 0.5 g; sample diameter 2.5 cm). For the excitation of the character- istic x-rays a ~°9Cd radioisotope (ca 9 mCi) has been used. XRF measurements have been carried out with an energy-dispersive spectrometer consisting of a Si/Li solid state detector and a Canberra multi- channel analyzer.

For the E-T experiments an infinitely thick multi- element target has been used. Spectrum evaluation has been performed using the AXIL routine (Van Espen).

Table 1 shows the results of the analysis of a coal sample obtained with different versions of the E-T method.

As can be seen from Table 1 neglecting the absorp- tion edges of Fe and Ca of the concentration of ca

1% can result in considerable errors of the analysis. This example, which is representative for coal analysis, clearly demonstrates the importance of the additional correction for the discontinuities of the absorption properties of the sample to be analyzed.

A modification o f the E -T method

Table I. The results of XRF analysis of a coal sample for different version of the E-T method (in ppm)

779

Element

With corrections For FeK.~ Relative difference

With corrections (experimental) No correction for FeK,b~ and CaK°~ ( A ) - (C) 100 (B) - (C)

for edges (experimental) (iterative routine) (C) (C)

(A) (a) (C) (%) (%)

- - . 1 0 0

Ca 1.24% _+ 0.05%* 8940 + 340 7600 _+ 220 63.2 17.6 Ti 1620 _+ 80 1180 _ 60 1180 _+ 60 37.3 37.3 Fe 1.48% _+ 0.04% 1.17% _+ 0.03% 1.17% -I- 0.03% 26.5 26.5 Cu 31.3 + 3 31.3 + 3 31.3 + 3 - - - - Zn 25.6 __. 2.3 25.6 + 2.3 25.6 _ 2.3 - - - - Ga 14.3 ___ 1.7 14.3 5- 1.7 14.3 _+ 1.7 - - - - Sr 474.1 _+ 10.4 474.1 _+ 10.4 474.1 _+ 10.4 - - - - Y 15.1 +0.7 15.1 +0.7 15.1 +0.7 - - - - Zr 83.7+2.1 83.7+2.1 83.7+2.1 - - - - Pb 20.5 + 2.8 20.5 + 2.8 20.5 + 2.8 - - - -

*Total error of the E-T method is given (Markowicz et al., 1992b).

Conclusion

A p r o c e d u r e p r e s e n t e d in th is p a p e r e n a b l e s o n e to

iden t i fy the c o n t r i b u t i o n o f the a b s o r p t i o n edges o f

r a i n o r ( o r / a n d m a j o r ) e l e m e n t s p r e s e n t in the u n -

k n o w n s a m p l e s to the e r r o r o f the s i mp l e s t ve r s i on o f

the E - T m e t h o d [ resul ts in c o l u m n (A) o f T a b l e 1].

M o r e o v e r , by t a k i n g in to a c c o u n t the ex i s t ence o f s u c h

c i s c o n t i n u i t i e s in t he r e l a t i o n s h i p o f l n In A vs In E the

app l i cab i l i t y r a n g e o f the E - T m e t h o d c a n be con -

s i de r ab ly e x t e n d e d . T o faci l i ta te an u n d e r s t a n d i n g o f

toe m e t h o d o l o g y o f t he c o r r e c t i o n invo lved , a specific

c o n f i g u r a t i o n h a s been s t ud i ed in detai l . Neve r t he l e s s ,

t a e w h o l e p r o c e d u r e is d i rect ly app l i cab le to a n y

ana ly t i ca l case w h e n m i n o r ( a n d / o r m a j o r ) e l e m e n t s

l~ave to be d e t e r m i n e d by the E - T m e t h o d .

References (~iauque D. R., Garrett R. B. and Goda L. Y. (1979)

Determination of trace elements in light element matrices by X-ray fluorescence spectrometry with incoherent scat-

tered radiation as an internal standard. Anal. Chem. 51, 511.

Hallak A. B. and Saleh N. S. (1985) Geometry consider- ations in radioisotope X-ray fluorescence spectrometry. J. Phys. E: Sci. Instrum. lg, 9.

Leroux J. and M a h m u d M. (1966) X-ray quantitative analysis by an emission-transmission method. Anal. Chem. 38, 76.

Markowicz A. (1979) A method of correction for absorption matrix effects in samples of intermediate thickness in E D X R F analysis. X-Ray Spectrom. 8, 14.

Markowicz A., Haselberger N. and Mulenga P. (1992a) Accuracy of calibration procedure for energy dispersive X-ray fluorescence spectrometry. X-Ray Spectrom. (in press)

Markowicz A., Haselberger N., El Hassan H. S. and Sewando M. S. A. (1992b) Accuracy of the emission- transmission method applied in XRF analysis of inter- mediate thickness samples. J. Radioanalytical Nucl. Chem. (in press).

Poehn Ch., Wernisch J. and Hanke W. (1985) Least-squares fits of fundamental parameters for quantitative X-ray analysis as a function of Z ( 1 1 ~ < Z ~ 8 3 ) and E (1 keV ~ E ~ 50 keV). X-Ray Spectrom. 14, 120.

Van Espen P., Janssens K. and Swenters I. AXIL X-ray Analysis Software. Canberra Packard, Benelux.