PERFORMANCE OF TXRF and GI-XRF ANALYSES - Total-Reflection X-Ray Fluorescence Analysis and Related Methods - page 284

reflection defined by Equations 2.29a, b and 2.40a, b. This model is only
applicable to surfaces and interfaces with a small roughness (some
nanometers).
2. For the second model it is assumed that the distribution of the height of
the respective surface or interface over the xy plane shows a Gaussian
profile. In that case, the Fresnel coefficients r j and t j can be modified in
general. This model can be applied for a small roughness ( σ j << thickness
of the respective layer).
3. The third model uses so-called effective densities. It was first used by
Nevot etal . [94,95] and seems to be rather successful. For a simple flat
substrate, it describes the zone of roughness as a stack of virtual plane-
parallel layers with a stepwise increasing density [89,91]. The uppermost
layer may show zero density, while the lowest layer should have the bulk
density. For a layered sample, the near-surface layer and also deeper
layers are split into a stack of thin slices with subnanometer thickness. The
total sample is treated as numerous slices with different densities but with
sharp interfaces and zero-roughness between them. The density is esti-
mated in accord with the respective volume; decrement and attenuation
coefficient of the refractive index n i are corrected accordingly.
Several examples for a characterization of nanostructured materials are
described in the literature [82,83,87-92]. Thin layers or thin films and also lots
of single particles with nanometer dimensions deposited on or below the
surface of a flat substrate have been characterized by GI-XRF. Such thin
layers were made of pure metals, metal alloys, semiconductors, oxides or
nitrides, metal-organic compounds, and polymers. Different kinds of layers,
such as monolayers, double layers, multilayers, Langmuir-Blodgett films, and
biofilms were investigated [47,79,80,90,96,97]. Some examples will be given in
Chapter 5.
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