Thermal and structural damping of the multiple-scattering contributions to the x-ray-absorption coefficient

We present a method to calculate both the thermal and the structural damping of the multiple-scattering (MS) contributions to the x-ray-absorption coefficient. In the thermal case the correlation matrices between the coordinates of the atoms connected by MS paths are calculated, in the harmonic approximation, using the high-temperature expansion for the vibrational correlation function. When an additional structural disorder is present equivalent correlation matrices can be obtained from proposed models. These matrices define the widths of the corresponding Gaussian peaks in the n-body structural correlation functions. We present two different methods of calculation which can be generalized to non-Gaussian distributions: the first consists of a simple random sampling over the distribution of displacements, the second uses the Taylor expansion of the MS signal around the equilibrium position of the atoms in the path. The results are equivalent and indicate that only for ${\chi }_2$ the dominant damping is given by a simple Debye-Waller-type correction in the amplitude. Both for the ${\chi }_3$ and for the ${\chi }_4$ signals, phase effects become important and can alter the effective damping. Implications on the convergence of the MS series will be discussed. In the case of structural disorder we show how the MS signal present in the x-ray-absorption spectra is capable of providing new structural information and will allow us to distinguish between various proposed models.