Matrix Effects

Abstract

The basis of quantitative X-ray fluorescence spectrometry is to follow the identification of a certain element in a mixture of elements (the matrix) with a measurement of the intensity of one of its characteristic lines, then to use this intensity to estimate the concentration of that element. By use of a range of standard materials a calibration curve can be constructed in which the peak response of a suitable characteristic line is correlated with the concentration of the element. Fig. 6.1 illustrates a typical case where the peak counting rates (R _b ) from a range of elements (1–5) are plotted against the concentration of a certain element i. By fitting the calibration curve parameters into the equation for a straight line

$$\begin{array}{*{20}{c}} y \hfill & {=mx+v} \hfill \\ {\left( {{{R}_{p}}} \right)i} \hfill & {={{m}_{i}}\left( {\%i} \right)+\left( {{{R}_{b}}} \right)i} \hfill \\ {\%i} \hfill & {=\frac{{\left( {{{R}_{p}}} \right)i-\left( {{{R}_{b}}} \right)i}}{{{{m}_{i}}}}} \hfill \\ \end{array}$$

((6.1))

it will be seen that the slope of the curve “m” is equal to counts per second per percent and this can be used as a calibration factor for the element in that specific matrix. Once m has been established from standards the net peak minus background response can be divided by m to give the concentration of the element in an unknown but similar matrix. If such a curve were constructed in practice, by an experienced operator using a series of completely homogeneous standards it would be found that, on repeating each measurement a number of times, a certain degree of spread in the count data would occur. This spread is due to certain random errors associated with each reading and would define the precision of the measurement.