Theoretical x-ray absorption Debye-Waller factors

Abstract

An approach is presented for theoretical calculations of the Debye-Waller factors in x-ray absorption spectra. These factors are represented in terms of the cumulant expansion up to third order. They account respectively for the net thermal expansion σ(1) (T ), the mean-square relative displacements σ 2 (T ), and the asymmetry of the pair distribution function σ (3) (T ). Similarly, we obtain Debye-Waller factors for x-ray and neutron scattering in terms of the mean-square vibrational amplitudes u 2 (T ). Our method is based on density functional theory calculations of the dynamical matrix, together with an efficient Lanczos algorithm for projected phonon spectra within the quasiharmonic approximation. Due to anharmonicity in the interatomic forces, the results are highly sensitive to variations in the equilibrium lattice constants, and hence to the choice of exchangecorrelation potential. In order to treat this sensitivity, we introduce two prescriptions: one based on the local density approximation, and a second based on a modified generalized gradient approximation. Illustrative results for the leading cumulants are presented for several materials and compared with experiment and with correlated Einstein and Debye models. We also obtain Born-von Karman parameters and corrections due to perpendicular vibrations.

Local vibrational properties of GaAs studied by extended X-ray absorption fine structure

“…The experimental values of the asymptotic ratios lim T →∞ u 2 ⊥ / u 2 = 2ξ are 2.2 for Cu, 5.78 for Ge, 7.44 for GaAs, and 9.15 for CdTe, in good agreement with the values calculated ab initio by Vila et al, 15 2.36 for Cu at 500 K and 7.2 for diamond lattices at 600 K.…”

“…(b) EXAFS gives original information on the local vibrational dynamics, whose reproduction is a quite unique benchmark for theoretical calculations, including the phase relations between eigenvectors of the dynamical matrix and the anharmonicity contributions. 15 (c) In recent years, a number of crystals with the diamondzincblende structure, affected by negative thermal expansion (NTE) at low temperatures, has been investigated: Ge, 9 CdTe, 12 CuCl, 16 InP. 17 The results suggest that a correlation exists between the bond ionicity, the NTE properties and some of the parameters determined from EXAFS analysis.…”

On EXAFS Debye-Waller factor and recent advances

“…The agreement of the temperature dependence of the polynomial coefficientsC C n with theoretical expectations (7)- (16) can be a self-consistent check of the convergence properties of the cumulants series, in order that polynomial coefficients could be considered as good estimates of the cumulants C n (Dalba et al, 1999;Fornasini et al, 2004). The soundness of the procedure is supported by the reproduction of experimental EXAFS cumulants by theoretical simulations (a Beccara et al, 2003;Vila et al, 2007;Sanson, 2010).…”

“…An effort to take into account the anharmonicity effects on the vibrational density of states of many-atomic systems and its connection to EXAFS cumulants has been recently made by Vila et al (2007).…”

“…Poiarkova & Rehr (1999) used the equation of motion method, which involves the Fourier transform of the time dependence of the molecular dynamics, to calculate the DW factor of multiple-scattering paths in Cu, Ge and Zn tetraimidazole. Ab initio calculations based on the density functional theory (DFT) formalism were performed for several molecules by Dimakis & Bunker (1998); a critical evaluation of the different approximations to DFT was made by Vila et al (2007), who further exploited the Lanczos algorithm to diagonalize the dynamical matrix.…”