Anharmonic Effective Potential, Local Force Constant and Exafs of HCP Crystals: Theory and Comparison to Experiment

Abstract

Anharmonic effective potential, Extended X-ray Absorption Fine Structure (EXAFS) and its parameters of hcp crystals have been theoretically and experimentally studied. Analytical expressions for the anharmonic effective potential, effective local force constant, three first cumulants, a novel anharmonic factor, thermal expansion coefficient and anhamonic contributions to EXAFS amplitude and phase have been derived. This anharmonic theory is applied to analyze the EXAFS of Zn and Cd at 77 K and 300 K, measured at HASYLAB (DESY, Germany). Numerical results are found to be in good agreement with experiment, where unnegligible anharmonic effects have been shown in the considered theoretical and experimental quantities.

Diffuse Neutron Scattering of KBr at Room Temperature and Its Application as Background Function in Rietveld Analysis

“…The values of DCF and MSD are important factors in the analysis of lattice dynamics of crystals by EXAFS (Extended X-ray Absorption Fine Structure) method [10]. The values are also can be used to predict effective potential and local force constant between atoms in crystals [11]. The ratio of DCF and MSD is similar to the correlation effects in our analysis.…”

Thermodynamic Properties and Anharmonic Effects in XAFS Based on Anharmonic Correlated Debye Model Debye–Waller Factors

“…ese results are also found to be in good agreement with those calculated using the ACEM [9] and the PIMC [19] for Cu. e cumulant ratio σ (1) σ 2 /σ (3) is often considered as a standard for cumulant studies to identify the temperature above which the classical limit is applicable [9][10][11][12][13][14]. Figure 6 shows that in the present ACDM this temperature is the Debye temperature (θ D 334 K for Cu and 376 K for Ni) while such temperature for ACEM is the Einstein temperature [9] because from this temperature the ratio reaches the classical value of 1/2 [9,10,14] and classical limit is applicable.…”

“…distances and can be connected to the force constants of a one-dimensional e ective pair potential [5,[9][10][11][12][13][14][15]34]. In particular, the rst three cumulants measure the average value, the variance, and the asymmetry of the distribution, respectively [25].…”

“…e anharmonic correlated Einstein model (ACEM) [9] has been derived for the calculation and analysis of DWFs presented in terms of cumulant expansion up to the third order. Its simplicity and efficiency in XAFS studies is demonstrated by calculating and analyzing XAFS cumulants of fcc [9][10][11][12][13], hcp [14], and crystals and in studying pressure-dependent XAFS [15]. e statistical moment method [16,17] has been applied to calculate the mean square relative displacement (MSRD) including anharmonic contributions of some crystals.…”

A thermodynamic lattice theory on melting curve and eutectic point of binary alloys. Application to fcc and bcc structure

“…The atomic oscillating amplitude is characterized by the MSD or Debye-Waller factor (DWF) [9,18,[20][21][22][23] which has the form [18]…”