where μi and Wi are respectively the mass absorption coefficient and the mass fraction of element i.
The relation between the intensities of the incident radiation Io and the fluorescent radiation IF is
complex, i.e.
where φ is the fluorescence yield factor, equation (8.7), μx the mass absorption coefficient of element x
for the incident radiation. Wx is the mass fraction of element x, and μ and μ' are the mass absorption
coefficients of the matrix for incident and fluorescent radiations respectively (derived from equation
(8.9)). It will be seen from equation (8.10) that even for a simple two component mixture the signal
from one component will be modified by the other, and the extent of the modification will depend upon
the mass fractions of the two elements. Working curves need to be prepared (Figure 8.39) to enable
corrections to be applied. Where the matrix is more complex, this simple solution is not possible and
great care needs to be taken in preparing standards for calibration purposes. For a heavy matrix,
measurements may sometimes be improved by dissolution of the sample in a light solvent such as water
or in a solid such as borax by a fusion procedure. Samples may also be mounted as thin layers on filter
paper disks. In this way, matrix absorption problems may be minimized but the dilution of the sample
can result in a reduction of the overall sensitivity of the measurement. The maximum depths within the
sample at which X-ray emission
Figure 8.39
Analytical curves for the
determination of iron and chromium in
a mixture of the two.