Efficient calculation method for glancing angle x‐ray techniques

Abstract

AbstractGeneral 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 at 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.