Temperature-dependent X-ray absorption fine structure Debye–Waller factor of Pb influenced by thermal disorder

Thermodynamic properties of bcc crystals have been studied based on the anharmonic correlated Debye model high-order expanded Debye-Waller factors and X-ray absorption fine structure (XAFS). The many-body effects are taken into account in the present one-dimensional model based on the anharmonic effective potential that includes interactions of absorber and backscatterer atoms with their first shell near neighbors, where Morse potential is assumed to describe the single-pair atomic interaction. Analytical expressions for dispersion relation, correlated Debye frequency and temperature and four first temperature-dependent XAFS cumulants of bcc crystals have been derived using the many-body perturbation approach. The obtained cumulants are applied to calculating XAFS spectra and their Fourier transform magnitude. Numerical results for Fe, a ferrite crystal, are found to be in good agreement with experiment.

An analysis of the Debye-Waller (DW) factor in the anharmonic X-ray absorption fine structure (XAFS) of crystalline platinum (Pt) has been conducted under the influence of thermal disorder. This factor was calculated in explicit and simple forms from the calculation model developed using the anharmonic effective potential and classical statistical theory based on the correlated Debye model. The thermodynamic parameters of Pt have considered the influence of nearest neighbors on the backscattering and absorbing atoms. The numerical results of the Pt at temperatures from 0 to 800 K fit well with those obtained from the experimental data and other methods. The obtained results indicate that the present calculation model can efficiently investigate the anharmonic XAFS DW factor of Pt.

In this work, the temperature dependence of the anharmonic X-ray absorption fine structure (XAFS) and thermodynamic properties of the crystalline silicon (c-Si) have been investigated. The thermodynamic parameters are derived from the influence of the absorbing and backscattering atoms of all their nearest neighbors in the crystalline lattice with thermal vibrations. The Debye-Waller factor and thermal expansion coefficient in the anharmonic XAFS of c-Si were calculated in explicit forms using the anharmonic correlated Debye (ACD) model. This calculation model is developed from the many-body perturbation approach and correlated Debye model using the anharmonic effective potential. The numerical results of c-Si in temperature ranging from 0 to 1500 K are in good agreement with those obtained by the other theoretical procedures and experiments at several temperatures. The analytical results showed that the ACD model is useful in analyzing the experimental XAFS data on c-Si.

Anharmonic correlated Debye model high-order expanded interatomic effective potential and Debye-Waller factors of bcc crystals

In this work, X-ray absorption fine structure (XAFS) of bcc crystals and it Fourier transformmagnitude have been studied based on the anharmonic correlated Debye model high-order expandedDebye-Waller factors. The many-body effects are taken into account in the present one-dimensionalmodel based on the anharmonic effective potential that includes interactions of absorber andbackscatterer atoms with their first shell near neighbors, where Morse potential is assumed to describethe single-pair atomic interaction. Analytical expressions of four first temperature-dependent cumulantsof bcc crystals have been derived using the many-body perturbation approach. The obtained cumulantsare applied to calculating XAFS spectra and their Fourier transform magnitudes. Numerical results forFe are found to be in good agreement with experiment.

Debye-Waller factors (DWFs) of metallic Cu (fcc crystal) in X-ray absorption fine structure (XAFS) presented in terms of cumulant expansion have been studied using the anharmonic correlated Debye model (ACDM). This ACDM is derived using the many-body perturbation approach and the anharmonic effective potential that includes the first shell near neighbor contributions to the vibration between absorber and backscatterer atoms. Analytical expressions of three first XAFS cumulants of Cu have been derived involving more information of phonon-phonon interactions taken from integration over the first Brillouin zone. Morse potential is assumed to describe the single-pair atomic interaction. Numerical results for Cu using the present ACDM show their good agreement with experiment and with those of other theories, as well as their advantage compared to those calculated using the single-pair potential.

This work reviews the contributions of author to the developments and applications of Photoelectron Spectroscopy (PES) and X-ray Absorption Fine Structure (XAFS) to materials studies. Focusing on Angle resolved PES (ARPES) the energy distribution is discussed for angle-resolved photoemission from valence bands of single crystals. The important influence of the spectrometer angle of acceptance on the results of X-ray PES (XPS) is investigated in detail. The Plane Density of States (PDOS) is introduced as a new property of the electronic structure. Most meaningful contributions to XAFS consist of the developments of multiple-scattering and anharmonic XAFS theory. Anharmonic correlated Einstein model (ACEM) and anharmonic correlated Debye model (ACDM) have been derived to obtain Debye-Waller factors (DWF) presented in terms of cumulant expansion which describe the thermodynamic properties and anharmonic effects in XAFS of substances contributing to their accurate structural determination. The anharmonic effective potential (AEP) procedure and first shell near neighbor contributions approach have developed to include many-body effects in the one-dimensional model by a simple measure. Based on DWFs a thermodynamic lattice theory has been derived for studying melting curve and eutectic points of binary alloys. Several applications of the derived methods are performed and the good agreement of the calculated results with experiment illustrate the advantages and efficiencies of the achieved developments.

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.

In this paper, high-order expanded anharmonic effective potential and Debye–Waller factors in X-ray absorption fine structure (XAFS) of hcp crystals have been studied based on classical anharmonic correlated Einstein model. Here XAFS Debye–Waller factors are presented in terms of cumulant expansion up to the fourth order and their analytical expressions have been derived based on classical statistical theory. They contain the parameters of a derived high-order anharmonic effective potential that takes into account all nearest neighbors of absorber and backscattering atoms, where Morse potential is assumed to describe interatomic interaction included in this derived anharmonic effective potential. The dependence of the derived cumulants on atomic vibrations is described by their proportionality to the correlated Einstein frequency. This model avoids full lattice dynamical calculations yet provides good agreement of numerical results for Zn and Cd with experiment at several temperatures.

This study aims to calculate the anharmonic thermal expansion (TE) coefficient of metal crystals in the temperature dependence. The calculation model is derived from the anharmonic correlated Debye (ACD) model that is developed using the many-body perturbation approach and correlated Debye model based on the anharmonic effective potential. This potential has taken into account the influence on the absorbing and backscattering atoms of all their nearest neighbors in the crystal lattice. The numerical results for the crystalline zinc (Zn) and crystalline copper (Cu) are in agreement with those obtained by the other theoretical model and experiments at several temperatures. The analytical results show that the ACD model is useful and efficient in analyzing the TE of coefficient of metal crystals.

Analytical expressions for the anharmonic effective potential, local force constant, Displacement-displacement Correlation Function (DCF) CR and Debye-Waller factor described by the Mean Square Relative Displacement (MSRD) sigma 2 and by the Mean Square Displacement (MSD) u2of bcc crystals in the X-ray Absorption Fine Structure (XAFS) have been derived. The effective interatomic potential of the system has been considered by taking into account the influences of nearest atomic neighbors, and it contains the Morse potential characterizing the interaction of each pair of atoms. Numerical results for u 2 , sigma 2 and CR of Fe and W are found to be in good agreement with experiment. The ratios CR/u 2 and CR/sigma 2 approach constant values at high temperatures showing the same properties obtained by the Debye model.

The anharmonic X-ray absorption fine structure (XAFS) Debye-Waller (DW) factor of the crystalline tungsten (W) has been investigated in the temperature-dependent. This DW factor is calculated in explicit forms using the quantum anharmonic correlated Einstein model developed from the correlated Einstein model based on the anharmonic effective potential and the quantum statistical theory. The numerical results of W in the temperature range from 0 to 900 K are in good agreement with those obtained by the other theoretical models and experiments at several temperatures. The analytical results show that the anharmonic correlated Einstein model is suitable for analyzing the experimental XAFS data of metals.

Thermodynamic properties and anharmonic effects in X‐ray absorption fine structure (XAFS) have been studied based on the anharmonic correlated Debye model Debye–Waller factors presented in terms of cumulant expansion. The derived analytical expressions of three first XAFS cumulants involve more information on phonon‐phonon interactions taken from integration over the first Brillouin zone. Many‐body effects are taken into account in the present one‐dimensional model based on the first shell near neighbor contributions to the vibrations between absorber and backscatterer atoms. Morse potential is assumed to describe single‐pair atomic interaction included in the derived anharmonic interatomic effective potential. The present theory can be applied to any crystal structure including complex systems. Numerical results for Cu and Ni are found to be in good agreement with experiment and with those of the other theories.

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.

Temperature dependence of theoretical and experimental Debye-Waller factors, thermal expansion and XAFS of metallic Zinc