X-Ray Fluorescence Analytical Techniques - CNSTN : Centre ...

preparation of a thick sample, and when preparation of a thin sample is difficult or even
impossible. Such cases might occur in the analysis of biological and environmental
specimens.
In recent years a number of approaches have been developed for quantitation in XRF
analysis of intermediate thickness samples. Some of them are based on the emissiontransmission
(E-T) method. The original version of the E-T method requires the
measurements of the specific X-ray intensities from the sample alone and from the sample
and a certain target positioned behind it in a fixed geometry. Alternative correction
procedures are based on the use of scattered primary radiation which suffers similar matrix
absorption as fluorescent peaks and behaves similarly with instrumental variations. The
scattered radiation peaks also provide the only direct spectral measure of the total or average
matrix of the analysed materials when these contain large quantities of light elements such as
carbon, nitrogen and oxygen, usually observed by their characteristic X-ray peaks.
For homogeneous, intermediate thickness samples, the mass per unit area of the element
i, mi can be calculated from the following equation:
Ii
mit Si
= , (II.10)
where Ii is the measured intensity of the characteristic X-rays of the ith element and t is the
absorption factor, given by:
1−exp { − [ µ ( Eo) cosecφ+µ ( Ei) cos ecψ] m}
t =
. (II.11)
⎡µ ( E ) cos ecφ+µ ( E ) cos ecψ⎤m ⎣ o i ⎦
In the E-T method, the t-factor, representing the combined attenuation of both the
primary and fluorescent radiations in the whole specimen, is determined individually for each
sample. This is done by measuring the X-ray intensities with and without the specimen from a
thick multi-element target located at a position adjacent to the back of the specimen, as shown
in Figure II.11. If (Ii)S, (Ii)T and (Ii)o are the intensities, after background correction, from the
sample alone, from the sample plus target and from the target alone, respectively, then the
combined fraction of the exciting and fluorescent radiations transmitted through the total
sample thickness is expressed by:
( Ii) − ( I
T i)
S
exp{ − ⎡
⎣µ ( Eo) cos ecφ+µ ( Ei) cos ecψ ⎤
⎦ m} = = T.
(II.12)
( I )
Since the parameter T is determined experimentally, the following equation for the tfactor
is obtained:
1 − T
t =
−lnT
. (II.13)
It is necessary to emphasize that the E-T method can only be applied in quantitative
XRF analysis of homogeneous samples of masses per unit area smaller than the critical value
mcrit, defined as:
−lnTcrit
mcrit
= , (II.14)
µ ( Eo) cos ecφ+µ ( Ei) cos ecψ
where Tcrit is the critical transmission factor, Equation (II.12) is equal, in practice, to 0.1 or
0.05. A number of more complex and more versatile versions of the E-T method have been
developed.
i o