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

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Nguyen Ba Duc ◽  
Nguyen Van Hung ◽  
Ha Dang Khoa ◽  
Dinh Quoc Vuong ◽  
Tong Sy Tien
Keyword(s):  
Thermodynamic Properties ◽  
Present Theory ◽  
Debye Model ◽  
Near Neighbor ◽  
Atomic Interaction ◽  
Single Pair ◽  
Many Body ◽  
Anharmonic Effects ◽  
X Ray Absorption ◽  
Analytical Expressions

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.

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

2017 ◽  
Vol 33 (3) ◽  
Author(s):  
Nguyen Van Hung
Keyword(s):  
Metallic Copper ◽  
Pair Potential ◽  
Debye Model ◽  
Near Neighbor ◽  
Atomic Interaction ◽  
Perturbation Approach ◽  
Single Pair ◽  
Many Body ◽  
The Many ◽  
Analytical Expressions

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.

Correlation effects studied based on Debye–Waller factors. Application to fcc crystals

2019 ◽  
Vol 33 (20) ◽  
pp. 1950237
Author(s):  
Nguyen Van Hung ◽  
Dinh Quoc Vuong
Keyword(s):  
Mean Square Displacement ◽  
Relative Displacement ◽  
Debye Model ◽  
Atomic Interaction ◽  
Single Pair ◽  
Mean Square ◽  
Correlation Effects ◽  
Many Body ◽  
The Difference ◽  
Experimental Values

Correlation effects described by the displacement–displacement correlation function [Formula: see text] have been studied based on Debye–Waller factors presented by the mean square displacement (MSD) [Formula: see text] and mean square relative displacement (MSRD) [Formula: see text] in X-ray Absorption Fine Structure. Analytical expressions have been derived for [Formula: see text] based on the anharmonic correlated Debye model (ACDM) and for [Formula: see text] based on anharmonic Debye model (ADM) or uncorrelated Debye model. Many-body effects have been taken into account in the present one-dimensional model by a simple measure based on the anharmonic effective potentials that include interactions of absorber and backscatterer atoms with their nearest neighbors. Morse potential is used for describing single-pair atomic interaction. The reasons for the difference between MSRD and MSD have been discussed in detail. The theory is applied to fcc crystals and can be generalized to any crystal structure. Numerical results for Cu are found to be in good agreement with the experimental values and with those taken from the measured Morse parameters, as well as with the values of [Formula: see text] calculated using the other theories.

Impurity effects in Debye–Waller factors of bcc crystals based on anharmonic correlated Einstein model

2019 ◽  
Vol 33 (07) ◽  
pp. 1950078 ◽  
Author(s):  
Dinh Quoc Vuong ◽  
Nguyen Van Hung
Keyword(s):  
Effective Potential ◽  
Pair Potential ◽  
Atomic Interaction ◽  
Single Pair ◽  
Impurity Effects ◽  
Pure Material ◽  
Einstein Model ◽  
The Difference ◽  
X Ray Absorption ◽  
Analytical Expressions

Impurity effects in Debye–Waller factors (DWFs) describing thermodynamic properties of bcc impure crystals included in X-ray absorption fine structure (XAFS) have been studied based on the anharmonic correlated Einstein model. The impurity is obtained by replacing absorber of host element by an atom of doping element. Analytical expressions of DWFs presented in terms of cumulant expansion up to the third-order and thermal expansion coefficient of impure crystals have been derived. Anharmonic effective potential of impure crystal includes interactions of absorber and backscatterer atoms with their first shell near neighbors. Morse potential is assumed to describe single-pair atomic interaction. The obtained expressions for impure crystal can also be used for calculating the considered XAFS quantities of pure material based on replacing all data of the doping atoms by those of pure host element. The advantage of using the anharmonic effective potential is shown by its possibility of defining the difference of XAFS quantities between the two inverse doping processes, which cannot be obtained by using the single-pair potential. Numerical results are found to be in good agreement with experiment for the impure Fe doped by Mo or inversely for Mo doped by Fe, as well as for pure Fe and Mo.

scholarly journals X-ray Absorption Fine Structure of bcc Crystals Studied Based on High-order Expanded Debye-Waller Factors

2017 ◽  
Vol 27 (1) ◽  
pp. 55
Author(s):  
Nguyen Van Hung ◽  
Trinh Thi Hue ◽  
Ha Dang Khoa ◽  
Tong Sy Tien
Keyword(s):  
Fine Structure ◽  
High Order ◽  
Atomic Interaction ◽  
Perturbation Approach ◽  
Single Pair ◽  
Many Body ◽  
X Ray ◽  
Absorption Fine ◽  
The Many ◽  
X Ray Absorption

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.

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

2021 ◽  
Vol 28 (5) ◽  
Author(s):  
Tong Sy Tien
Keyword(s):  
Axial Ratio ◽  
Debye Model ◽  
Waller Factor ◽  
Calculation Model ◽  
Near Neighbor ◽  
Perturbation Approach ◽  
Many Body ◽  
Hexagonal Close Packed ◽  
Debye Waller Factor ◽  
The Many

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.

scholarly journals EXAFS Debye-Waller Factors of B2-FeAl Alloys

2021 ◽  
Vol 37 (2) ◽  
Author(s):  
Nguyen Thi Hong ◽  
Nguyen Ba Duc ◽  
Ho Khac Hieu
Keyword(s):  
Debye Model ◽  
Al Alloys ◽  
Temperature Dependent ◽  
X Ray ◽  
Debye Frequency ◽  
X Ray Absorption ◽  
Analytical Expressions ◽  
Theoretical Results ◽  
B2 Structure ◽  
Good Agreement

This work develops the anharmonic correlated Debye model to study the temperature-dependent extended X-ray absorption fine structure (EXAFS) Debye-Waller factors (DWFs) of B2-FeAl alloys. We derived the analytical expressions of the EXAFS DWF and Debye frequency as functions of temperature. Numerical calculations were performed for Fe1-yAly alloys with various Al concentration (y = 0.35, 0.40, 0.45 and 0.50) in which Fe-Al alloys still maintained B2 structure. The good agreement between our theoretical results with previous data verifies our developed theory. Our calculations show that DWFs of Fe1-yAly alloys increase robustly when temperature and/or Al concentration in Fe1-yAly alloys increase. The increasing of DWF will cause the reduction of the amplitude of EXAFS.

Pressure effects on the EXAFS Debye–Waller factor of iron

2020 ◽  
Vol 27 (5) ◽  
pp. 1372-1375
Author(s):  
Ho Khac Hieu ◽  
Nguyen Ba Duc ◽  
Nguyen Van Hung ◽  
Pham Thi Minh Hanh ◽  
Tran Thi Hai
Keyword(s):  
Relative Displacement ◽  
Debye Model ◽  
Waller Factor ◽  
Pressure Effects ◽  
Displacement Curve ◽  
Mean Square ◽  
Debye Waller Factor ◽  
Debye Frequency ◽  
X Ray Absorption ◽  
Analytical Expressions

The pressure effects on atomic mean-square relative displacement characterizing the extended X-ray absorption fine structure (EXAFS) Debye–Waller factor of iron metal have been investigated based on the Debye model. The analytical expressions of the Debye frequency and EXAFS Debye–Waller factor have been derived as functions of crystal volume compressibility. Based on the well established equation-of-state including the contributions of the anharmonic and electronic thermal pressures, numerical calculations have been performed for iron up to a pressure of 220 GPa and compared with experimental data when possible. These results show that the Debye frequency increases rapidly with compression, and beyond 150 GPa it behaves as a linear function of pressure. Meanwhile the mean-square relative displacement curve drops robustly with pressure, especially at pressures smaller than 100 GPa. This phenomenon causes the enhancement of EXAFS signals at high pressure. Reversely, the increasing of temperature will reduce the amplitude of EXAFS spectra.

scholarly journals Thermodynamic properties of semiconductor compounds studied based on Debye-Waller factors

Open Physics ◽  
2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Nguyen Van Hung ◽  
Nguyen Cong Toan ◽  
Nguyen Ba Duc ◽  
Dinh Quoc Vuong
Keyword(s):  
Thermodynamic Properties ◽  
Mean Square Displacement ◽  
Close Relation ◽  
Relative Displacement ◽  
Mean Square ◽  
Many Body ◽  
Zinc Blende ◽  
Semiconductor Compounds ◽  
The Mean ◽  
Analytical Expressions

AbstractThermodynamic properties of semiconductor compounds have been studied based on Debye-Waller factors (DWFs) described by the mean square displacement (MSD) which has close relation with the mean square relative displacement (MSRD). Their analytical expressions have been derived based on the statistical moment method (SMM) and the empirical many-body Stillinger-Weber potentials. Numerical results for the MSDs of GaAs, GaP, InP, InSb, which have zinc-blende structure, are found to be in reasonable agreement with experiment and other theories. This paper shows that an elements value for MSD is dependent on the binary semiconductor compound within which it resides.

scholarly journals Contributions to Developments of Photoelectron Spectroscopy and X-ray Absorption Fine Structure Applied to Materials Studies

2021 ◽  
Vol 31 (2) ◽  
pp. 113
Author(s):  
Nguyen Van Hung
Keyword(s):  
Fine Structure ◽  
Photoelectron Spectroscopy ◽  
Melting Curve ◽  
Debye Model ◽  
Near Neighbor ◽  
X Ray ◽  
Absorption Fine ◽  
Valence Bands ◽  
The One ◽  
X Ray Absorption

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.

scholarly journals Pressure effect of the mechanical, electronics and thermodynamic properties of Mg–B compounds A first-principles investigations

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
GuoWei Zhang ◽  
Chao Xu ◽  
MingJie Wang ◽  
Ying Dong ◽  
FengEr Sun ◽  
...  
Keyword(s):  
Thermodynamic Properties ◽  
First Principles ◽  
Boron Content ◽  
Structural Parameters ◽  
Debye Model ◽  
Total Density ◽  
First Principle ◽  
Volume Deformation ◽  
Temperature And Pressure ◽  
Total Density Of States

AbstractFirst principle calculations were performed to investigate the structural, mechanical, electronic properties, and thermodynamic properties of three binary Mg–B compounds under pressure, by using the first principle method. The results implied that the structural parameters and the mechanical properties of the Mg–B compounds without pressure are well matched with the obtainable theoretically simulated values and experimental data. The obtained pressure–volume and energy–volume revealed that the three Mg–B compounds were mechanically stable, and the volume variation decreases with an increase in the boron content. The shear and volume deformation resistance indicated that the elastic constant Cij and bulk modulus B increased when the pressure increased up to 40 GPa, and that MgB7 had the strongest capacity to resist shear and volume deformation at zero pressure, which indicated the highest hardness. Meanwhile, MgB4 exhibited a ductility transformation behaviour at 30 GPa, and MgB2 and MgB7 displayed a brittle nature under all the considered pressure conditions. The anisotropy of the three Mg–B compounds under pressure were arranged as follows: MgB4 > MgB2 > MgB7. Moreover, the total density of states varied slightly and decreased with an increase in the pressure. The Debye temperature ΘD of the Mg–B compounds gradually increased with an increase in the pressure and the boron content. The temperature and pressure dependence of the heat capacity and the thermal expansion coefficient α were both obtained on the basis of Debye model under increased pressure from 0 to 40 GPa and increased temperatures. This paper brings a convenient understanding of the magnesium–boron alloys.

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