Thickness inhomogeneity effect in EXAFS spectroscopy

In many cases x-ray absorption spectra measured in transmission mode are degraded by an inhomogeneity in thickness of the samples. As a result, the EXAFS amplitude is decreased and information about the coordination numbers is distorted. To avoid this influence, it is necessary to prepare a homogeneous sample. But, for powder samples, thick inhomogeneous foils, and sputtered films this is not possible. Absorption spectra on these samples should be corrected for the thickness inhomogeneity effect.To correct an absorption spectrum it is necessary to know the sample thickness distribution function. We propose a method of solving an integral equation for a distribution function as an inverse problem. We use and compare the experimental pre-edge absorption behaviour with the theoretical Victoreen function. We apply the Tikhonov regularization algorithm to determine the distribution function. Model calculations are carried out to check the reproducibility of the calculations. This method is applied to preliminary procession of x-ray absorption spectra for high quality foils of crystalline Cu, crystalline Cu powder samples, and an inhomogeneous foil of ordered Ni50Mn50 alloy. We estimate the thickness inhomogeneity effect on the coordination numbers in the cases before and after correcting the spectra.