Effect of the non-ideal axial ratio c/a on anharmonic EXAFS oscillation of h.c.p. crystals

Abstract

The temperature and wavenumber dependence of the extended X-ray absorption fine-structure (EXAFS) oscillation of hexagonal close-packed (h.c.p.) crystals have been calculated and analyzed under the effect of the non-ideal axial ratio c/a. The anharmonic EXAFS oscillation is presented in terms of the Debye–Waller factor using the cumulant expansion approach up to the fourth order. An effective calculation model is expanded and developed from the many-body perturbation approach and correlated Debye model using the anharmonic effective potential. This potential, depending on the non-ideal axial ratio c/a, is obtained from the first-shell near-neighbor contribution approach. A suitable analysis procedure is performed by evaluating the influence of EXAFS cumulants on the phase shift and amplitude reduction of the anharmonic EXAFS oscillation. The numerical results for crystalline zinc are found to be in good agreement with those obtained from experiments and other theoretical methods at various temperatures. The obtained results show that the present theoretical model is essential and effective in improving the accuracy for analyzing the experimental data of anharmonic EXAFS signals of h.c.p. crystals with a non-ideal axial ratio c/a.

Application of Anharmonic Correlated Debye Model in Investigating Anharmonic XAFS Thermodynamic Properties of Crystalline Silicon

“…Recently, an anharmonic correlated Debye (ACD) model was efficiently used to investigate the anharmonic XAFS oscillation of many materials [27][28][29][30]. The advantage of this model is that using it one can calculate all first four cumulants, even in low-temperatures (LT) region of crystals that have low symmetry and isotropy with multiple acoustic phonons [29,30]. Still, it has not yet been used to analyze the anharmonic XAFS oscillation of c-Si.…”

“…The ACD model [27][28][29][30] is derived from the dualism of an elementary particle in quantum theory and is perfected based on the correlated Debye model [38] using the AE potential [35] and the manybody perturbation approach [39]. In this model, the atomic vibrations can be quantized and treated as a system consisting of many phonons, in which each atomic vibration corresponds to a wave that has a frequency   q  and is described via the dispersion relation [27,28]:…”

“…In this model, the correlated Debye frequency D  and temperature D  of c-Si characterize the atomic thermal vibrations in the crystal lattice [29][30]. They can be obtained using the effective force constant 0 k from Eq.…”

“…The general expressions of the anharmonic XAFS cumulants in the ACD model were calculated in the temperature dependence by Hung et al, [27]. Still, these obtained expressions are not optimized yet because they depend on the lattice constant a [30]. Therefore, we have extended the previous ACD model to calculate the temperature-dependent TE coefficient and XAFS DW factor of c-Si.…”

Calculation of Temperature-Dependent Thermal Expansion Coefficient of Metal Crystals Based on Anharmonic Correlated Debye Model

“…It is because EXAFS spectroscopy can contain information on local structures around X-ray absorbing atoms and gives interatomic distances and coordination numbers in crystal lattices [9]. This resulted in the EXAFS technique being developed and expanded greatly based on the rapid development of synchrotron radiation facilities worldwide [10]. In reality, thermal disorders can disturb the EXAFS oscillation [6,9], so the TE coefficient is also sensitive to EXAFS oscillation under the influence of temperature.…”