Extended x-ray-absorption fine-structure measurements of copper:  Local dynamics, anharmonicity, and thermal expansion

Abstract

Extended x-ray-absorption fine-structure (EXAFS) of copper has been measured from 4 to 500 K and analyzed by the cumulant method, to check the effectiveness of EXAFS as a probe of local dynamics and thermal expansion. The comparison between parallel mean square relative displacements (MSRD) of the first four coordination shells has allowed detecting a significant deviation from a pure Debye behavior. The firstshell EXAFS thermal expansion is larger than the crystallographic one: the difference has allowed evaluating the perpendicular MSRD, whose Debye temperature is slightly larger than the one of the parallel MSRD, due to anisotropy effects. High-order first-shell cumulants are in good agreement with quantum perturbative models. The anharmonic contribution to the first-shell parallel MSRD amounts to less than 1.5 percent. The third cumulant cannot be neglected in the analysis, if accurate values of the first cumulant are sought; it cannot however be used to directly estimate the thermal expansion. The shape of the effective pair potential is independent of temperature; a rigid shift, partially due to the relative motion perpendicular to the bond direction, is however observed.

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

“…10,16 As a first procedure, the ratio method 7,20,21 has been utilized for the first coordination shell, whose contribution can be neatly isolated ( Figure 2) and where MS effects are absent. For each of the two sets of measurements (Ga and As edges), the first-shell EXAFS signals have been obtained by Fourier back-transform of the corresponding peaks in r-space (Fig.…”

“…More recently, the difference between the thermal expansions measured by EXAFS and by Bragg diffraction in crystals was experimentally detected, leading to the evaluation of the perpendicular MSRD; the role of the third cumulant was clarified too. 9,10 a) Permanent address: Ain Shams University, Cairo, Egypt. b) Author to whom correspondence should be addressed.…”

Bayes-Turchin analysis of x-ray absorption data above the FeL2,3-edges

“…The first term in the sum of ␦R j,L s ͑k͒ is customarily used and expresses the difference between the real and effective first cumulants that correspond to the real and effective average values of the radial distribution. It has been pointed out by Fornasini et al 26 that disorder perpendicular to the scattering path also affects the average distance measured by EXAFS. This is taken into account by the second term ␦R j,Ќ in the argument of the sin function using the approximation…”

“…In Ref. 26 experimental values of Ќ 2 / ʈ 2 for the first shell of copper were determined and resulted in values larger than 2 and smaller than 3. Considering the first scattering path in Fe with R 1 = 2.470 Å at T = 295 K, for example, the cumulant correction yields 0.011 Å and the correction term due to perpendicular vibrations yields 0.002 Å.…”

Thermal properties of nanoporous gold

“…In order to extract thermal and structural parameters of NPG from EXAFS data we applied correlated Einstein model 27 that proved effective in many previous studies of bulk 28,29 and nanoscale [30][31][32][33] metals. In this model, parameters 0 k and 3 k of the anharmonic potential, ( )…”