Geometrical probability can be used as a basis for the quantification of XPS-signals stemming from random samples such as, for instance, supported heterogeneous catalysts. From a study of three ideal cases, namely extended layers of constant thickness, equally sized spheres and hemispheres on a randomly oriented support, it has been established that the effects of angular and layer thickness averaging are interconnected in such a way that a general model can be derived. It has been found that signal ratios as measured by XPS for convex particles are determined by the surface/volume ratios of the supported phases, nearly independent of particle shape.

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