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 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.

scholarly journals Application of Path-integral for Studying EXAFS Cumulants

2014 ◽  
Vol 24 (3S1) ◽  
pp. 40-44
Author(s):  
Ho Khac Hieu ◽  
Nguyen Manh Hai
Keyword(s):  
Experimental Data ◽  
Path Integral ◽  
Effective Potential ◽  
Perturbation Approach ◽  
X Ray ◽  
First Order ◽  
Einstein Model ◽  
X Ray Absorption ◽  
Analytical Expressions ◽  
First Order Perturbation

In this work, the path-integral effective potential (PIEP) method has been applied to re-study the temperature dependence of extended X-ray absorption fine structure (EXAFS) cumulants of materials. Using the trial density matrix and effective potential expression, we derived the analytical expressions of the first three EXAFS cumulants in the first shell of materials. The cumulant relation is also calculated to determine the temperature range in which the PIEP method could be applied. Our results are compared with available experimental data as well as with those calculated by the first-order perturbation approach in anharmonic Einstein model and the reasonable agreements are achieved.

High-order expanded XAFS Debye–Waller factors of HCP crystals based on classical anharmonic correlated Einstein model

2014 ◽  
Vol 28 (21) ◽  
pp. 1450174 ◽  
Author(s):  
Nguyen Van Hung ◽  
Tong Sy Tien ◽  
Ngyen Ba Duc ◽  
Dinh Quoc Vuong
Keyword(s):  
Effective Potential ◽  
Interatomic Interaction ◽  
High Order ◽  
Cumulant Expansion ◽  
X Ray ◽  
Einstein Model ◽  
Atomic Vibrations ◽  
X Ray Absorption ◽  
Analytical Expressions ◽  
Good Agreement

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.

ANHARMONIC EFFECTIVE POTENTIAL, LOCAL FORCE CONSTANT AND EXAFS OF HCP CRYSTALS: THEORY AND COMPARISON TO EXPERIMENT

2008 ◽  
Vol 22 (29) ◽  
pp. 5155-5166 ◽  
Author(s):  
NGUYEN VAN HUNG ◽  
TONG SY TIEN ◽  
LE HAI HUNG ◽  
RONALD R. FRAHM
Keyword(s):  
Thermal Expansion ◽  
Fine Structure ◽  
Thermal Expansion Coefficient ◽  
Force Constant ◽  
Expansion Coefficient ◽  
Effective Potential ◽  
X Ray ◽  
X Ray Absorption ◽  
Analytical Expressions ◽  
Good Agreement

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.

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.

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 Study the Temperature Dependence of EXAFS Cumulants of Si and Ge by the Anharmonic Correlated Einstein Model

2011 ◽  
Vol 21 (1) ◽  
pp. 25 ◽  
Author(s):  
Vu Van Hung ◽  
Ho Khac Hieu
Keyword(s):  
Fine Structure ◽  
Temperature Dependence ◽  
X Ray ◽  
Einstein Model ◽  
Silicon And Germanium ◽  
Experimental Values ◽  
X Ray Absorption ◽  
Analytical Expressions ◽  
Theoretical Results ◽  
Good Agreement

In present article, the anharmonic correlated Einstein model has been used to study the temperature dependence of Extended X-ray absorption fine structure (EXAFS) cumulants of silicon and germanium crystals. The analytical expressions of the first, second and third cumulants of silion and germanium have been derived. Our numerical calculations are compared with the experimental values and also with other theoretical results showing the good agreement.

scholarly journals Thermodynamic parameters depend on temperature with the influence of doping ratio of the crystal structure metals in extended X-Ray absorption fine structure

2021 ◽  
Vol 4 (10) ◽  
pp. 5-10
Author(s):  
Ba Duc Nguyen ◽  
Quang Tho Vu ◽  
Phi Hiep Trinh ◽  
Quynh Lam Nguyen Thi
Keyword(s):  
Crystal Structure ◽  
Fine Structure ◽  
Thermodynamic Parameters ◽  
Effective Potential ◽  
Single Pair ◽  
Face Centered Cubic ◽  
X Ray ◽  
Absorption Fine ◽  
X Ray Absorption ◽  
Doping Ratio

The effects of the doping ratio and temperature on the cumulants andthermodynamic parameters of crystal structure metals and their alloys wasinvestigated using the anharmonic correlated Einstein model, in extended X-ray absorption fine structure (EXAFS) spectra. We derived analytical expressions for the EXAFS cumulants, correlated Einstein frequency, Einstein temperature, and effective spring constant. We have considered parameters of the effective Morsepotential and the Debye-Waller factor depend on temperature and the effects of the doping ratio of face-centered-cubic (fcc) crystals of copper (Cu-Cu), silver (Ag-Ag), and hexagonal-close-packed (hcp) crystal of zinc (Zn-Zn), and their alloys of Cu-Ag and Cu-Zn. The derived anharmonic effective potential includes the contributions of all the nearest neighbors of the absorbing and scattering atoms. This accounts for three-dimensional interactions and the parameters of theMorse potential, to describe single-pair atomic interactions. The numericalresults of the EXAFS cumulants, thermodynamic parameters, and anharmonic effective potential agree reasonably with experiments and other theories.

scholarly journals Anharmonic EXAFS and its Parameters of HCP Crystals: Theory and Comparison to Experiment

2007 ◽  
Vol 14 (2) ◽  
pp. 74-83
Author(s):  
Nguyen Van Hung ◽  
Dao Xuan Viet
Keyword(s):  
Fine Structure ◽  
High Temperature ◽  
Ab Initio Calculation ◽  
Harmonic Model ◽  
X Ray ◽  
Einstein Model ◽  
Experimental Values ◽  
X Ray Absorption ◽  
Analytical Expressions ◽  
Exafs Function

A new theory for ab initio calculation of the anharmonic Extended X-ray Absorption Fine Structure (EXAFS) and its parameters of hcp crystals has been developed based on the single- shell model. Analytical expressions for the anharmonic contributions to the amplitude and to the phase of EXAFS and a new anharmonic factor have been derived. The EXAFS cumulant expressions are formulated based on the anharmonic correlated Einstein model. The EXAFS function and its parameters contain anharmonic effects at high temperature and appoach those of the harmonic model at low temperature. Numerical results for Zn agree well with the experimental values.

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