PRINCIPLES OF TOTAL REFLECTION XRF - Total-Reflection X-Ray Fluorescence Analysis and Related Methods - page 105

Figure2.18. Fluorescence signal of small particles or thin films deposited on a silicon substrate used
as sample carrier. The intensity was calculated for particles, thin films or sections of different
thickness but equal mass of the analyte, and plotted against the glancing angle α . A Mo-K α beam
was assumed for excitation. Particles or films more than 100 nm thick show double intensity below
the critical angle of 0.1 ° . Figure from Ref. [1], reproduced with permission. Copyright1996, John
Wiley and Sons.
where m x is the mass of the analyte element x on top of the substrate. The
constant value of the intensity is (1 + R )-fold, which is asymptotically approxi-
mated. It is nearly double the amount observed for angles beyond the total
reflection zone. The doubling can easily be explained by the fact that particles
are excited equally by the incoming and the reflected beam. Thus, if the
glancing angle falls short of the critical angle, the fluorescence intensity will
step up to the double value.
For quantitative analyses, it is important to get an intensity that is
independent of particle size or film thickness and also of glancing angle.
This ideal behavior is realized for granular or thin-film-like samples of about
100 nm. However, several particles of various thicknesses may also be
applied, as frequently happens in practice. A broad size distribution can
average over the oscillations [21]. On the other hand, the particles have to be
small enough in order to avoid absorption effects [19]. In any case, the need
for internal standardization is obvious. A standard may be added to the
particles and distributed homogeneously over the height of the particles. In
particular, the standard must not be enriched in the nodes or antinodes of the
primary field but should be uniformly mixed with the sample. In the case of a