Abstract
The effects of structural and vibrational disorder on the EXAFS signals are parameterized in terms of the Debye Waller (DW) factor. Here the vibrational contribution is addressed, which for most systems can be singled out by studying the temperature dependence of the EXAFS DW factor, which corresponds to a good accuracy to the parallel mean square relative displacement (MSRD) around the inter-atomic equilibrium distance. By comparing the first-shell EXAFS thermal expansion with the crystallographic thermal expansion one can evaluate the perpendicular MSRD. The results of recent measurements on copper and on several tetrahedral semiconductors are here critically compared and some properties of the MSRDs are discussed, such as the dependence of correlation, force constants and vibrational anisotropy on crystal structure and bond ionicity as well as the relative merits of the correlated Debye and Einstein models. The anharmonic contribution to the parallel MSRD of CdTe has been evaluated and a quasi-harmonic analysis has been attempted, leading to an estimation of the bond Grüneisen parameter.
Highlights
EXAFS spectra are damped by the effect of disorder, of both vibrational and structural origin (Lee et al, 1981; Rehr & Albers, 2000; Fornasini, 2015a)
Less obvious is the fact that when the temperature interval is reduced the absolute values of the Debye model undergo a larger modification than the absolute values of the Einstein model; this effect is much more significant for CdTe than for Cu. These results suggest that the Einstein model could be preferable to the Debye model for non-primitive crystals, such as CdTe or Ge
It is worth remembering that, while force constants are directly obtained from EXAFS results, correlation functions are obtained by comparing the EXAFS parallel mean square relative displacement (MSRD) with the mean square displacements (MSDs) from Bragg scattering or from theoretical calculations, whose accuracy can significantly differ for different systems
Summary
EXAFS spectra are damped by the effect of disorder, of both vibrational and structural origin (Lee et al, 1981; Rehr & Albers, 2000; Fornasini, 2015a). Different theoretical approaches have been attempted to evaluate the vibrational contribution to the EXAFS cumulants, and to the DW factor. In x4–x6, recent experimental results on Cu and on some crystals with the diamond–zincblende structure are critically discussed: x4 is dedicated to the harmonic analysis of the first shell, with emphasis on correlation and anisotropy as well as on strengths and limitations of the correlated Debye and Einstein models; in x5 the anharmonic contributions to the first-shell parallel MSRD of CdTe are evaluated and an estimation of the bond Gruneisen parameter is attempted; in x6 the correlation, the force constants and the Debye temperatures of the outer coordination shells are analysed. With the exception of a few seminal papers, only the literature posterior to 1997 is cited
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