Calculation of the XAFS Debye-Waller Factor with Spherical-Wave Corrections

Abstract

To calculate XAFS spherical-wave corrections and multiple scattering contributions have to be included improving the single scattering plane-wave approximation. A suitable method is described to include such corrections. The temperature dependence of the spectra is determined by a Debye-Waller factor in the plane-wave approximation. An additional temperature dependence arises in a spherical-wave description. An approximative expression is developed, which is valid for the exact angular momentum expansion and any spherical-wave approximation. Due to the thermal movement of the atoms the elements of the t-matrix tl have to be replaced by tlTD=tl+k2 σ102 \ ildetl where \ ildet is a modified t-matrix. σ102 is the average relative atomic displacement between the emitter and the scatterer. t and \ ildet have a different k-dependence. The consequence is as shift in the peaks of the absolut value of the fouriertransformed spectrum. For Ni and NiO we get a shift up to 0.1 atomic units for the nearest and next nearest neighbour.