A METHOD FOR ACCURATE QUANTITATIVE XPS ANALYSIS OF MULTIMETALLIC OR MULTIPHASE CATALYSTS ON SUPPORT PARTICLES

A mathematical formalism for the quantitative analysis of X-ray photoe lectron spectroscopy (XPS) intensities for supported, multiphase catal ysts is presented. Such powdered catalysts are modeled as spherical su pport particles, covered in regions (islands) by different stratified layers of phases. It specifically considers the variation in photoelec tron take-off angle over the surface of the particles, by integrating the signal over the particle's volume. The evaluation of this integral can be done numerically, but for certain particle sizes it is simplif ied by a new approximation to the exponential integral function presen ted here, which introduces an error of <4%. The results show that the common assumption of normal emission usually leads to large errors (fa ctors of 2-5). A simpler approximation to this new formalism, using th e unweighted average take-off angle of photoelectrons from the local s urface normal of 57.3 degrees, introduces an error of <23% except for species whose main intensity arises from an underlayer that is buried by another phase of average depth greater than 1.3 lambda (lambda is a photoelectron's inelastic mean free path). It is useful for the initi al optimization of parameters when searching for structural models of catalysts that are consistent with their XPS spectra. These formalisms are also applicable in treating other shapes of catalysts than those treated explicitly here, provided the phase's surface-to-volume ratio is the same as chosen in this model and that the BET surface area is l ess than about 35 m(2)/g. More complex expressions which treat higher surface area samples are also presented. The formalisms can also be us ed in quantitative Auger electron spectroscopy (AES), if the XPS sensi tivity factors are replaced by AES sensitivity factors. (C) 1995 Acade mic Press, Inc.