Efficient calculation method for glancing angle x-ray techniques

PÉREZ, ROBERTO DANIEL; SÁNCHEZ, HECTOR JORGE; RUBIO, MARCELO

X-RAY SPECTROMETRY

JOHN WILEY & SONS LTD

Año: 2002 vol. 31 p. 296 - 299

0049-8246

General depth profiling involves all kind of concentration profiles. The most complex samples present a wide variation of elemental composition with depth. In those cases, calculations of x-ray propagation a grazing angles are done by representing the sample as a stratified structure in order to obtain an analytical solution of the problem. The density of each layer is an average of the real density inside the layer, and a large number of surface layers may be necessary for a correct representation of the sample. This involves a large number of mathematical operations and therefore an efficient calculation method of x-ray propagation at glancing angles is required. In this paper, a mathematical algorithm for the calculation of x-ray propagation at grazing angles is presented. It applies a new formalism introduced recently in the field. This formalism uses a matrix approach to take advantage of well-known mathematical results such as Hessenberg´s matrix properties. The model allows one to reduce the number of mathematical operations for glancing angle x-ray techniques. The method was used to study surface oxidation of copper and roughness of a glass surface by the grazing exit XRF technique. Data analysis in these samples shows the advantage of the present mathematical algorithm since both samples present a continuous depth profile. Copyright © 2002 John Wiley & Sons, Ltd.