Local thermal expansion in copper: Extended x-ray-absorption fine-structure measurements and path-integral Monte Carlo calculations

Abstract

A combined approach has been used to study thermal effects on the extended x-ray absorption fine-structure ͑EXAFS͒ of copper between 4 and 500 K. A phenomenological data analysis shows that the thermal expansions measured from the first and third cumulants significantly differ between each other and from the crystallographic thermal expansion. Path-integral Monte Carlo calculations of EXAFS cumulants have been performed, using a many-body potential. The good reproduction of experimental values validates the phenomenological analysis and opens more perspectives for applications to more complex systems. It is shown that the reproduction of EXAFS parameters allows for a test of the interaction potentials with regard to anharmonicity.

Anharmonic correlated Debye model Debye-Waller factors of metallic Copper compared to experiment and to other theories

“…Morse potential is assumed to describe the single-pair atomic interaction included in the derived anharmonic interatomic effective potential. Numerical results for Cu (Section 3) using the present ACDM show their good agreement with those calculated using the anharmonic correlated Einstein model (ACEM) [4], the Path-integral Monte-Carlo (PIMC) [5] and with experiment [5][6][7][8], as well as their advantages compared to those calculated from the single-pair potential (SPP) [9,10].…”

“…[6] and to those calculated using the SPP. calculated using the present theory compared to those calculated using the ACEM [4], the PIMC [5], the SPP, and to the experimental values Expt. [6,8] for…”

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).…”

“…Such a shift of the potential energy, corresponding to a shift of the mode of the distribution, has been confirmed by theoretical simulations: path-integral Monte Carlo for Cu (a Beccara & Fornasini, 2008) and molecular dynamics for Ge (Sanson, 2010). In both cases, the simulations show that for the first shell the asymmetry contribution (17) to thermal expansion slightly prevails, due to the relatively high values of the third cumulant, with respect to the contribution of the shift of the maximum of the distribution; for the outer shells the asymmetry contribution is much weaker, and the thermal expansion is mainly accounted for by the shift of the maximum of the distribution.…”

“…By a simple phenomenological approach, Van Hung & Rehr (1997) derived an anharmonic correlated model for the effective potential taking into account the interaction of absorber and backscatterer atoms with their nearest neighbours via a Morse potential; the method was applied to calculations for Cu and Ni (Van Hung & Fornasini, 2007) and for Zn and Cd (Van Hung et al, 2014a) and extended to Si and Ge using StillingerWeber potentials ((Van Hung et al, 2014b). Following the pioneering work of Benfatto and co-workers (Benfatto et al, 1989), the cumulants have been evaluated by sampling a configurational space obtained by molecular dynamics, both classical (Edwards et al, 1997;Sanson, 2010) and ab initio (Vila et al, 2012),), as well as by path-integral techniques, based on the use of effective potentials (Yokoyama, 1998;Miyanaga & Fujikawa, 1998) or on Monte Carlo sampling (a Beccara et al, 2003;a Beccara & Fornasini, 2008). 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.…”