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 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 Свойства движущихся дискретных бризеров в бериллии

2018 ◽  
Vol 60 (5) ◽  
pp. 978
Author(s):  
O.B. Бачурина ◽  
P.T. Мурзаев ◽  
A.C. Семенов ◽  
E.A. Корзникова ◽  
C.B. Дмитриев
Keyword(s):  
Energy Transport ◽  
Interatomic Potential ◽  
Maximum Velocity ◽  
Face Centered Cubic ◽  
Sound Waves ◽  
Many Body ◽  
Hexagonal Close Packed ◽  
Bcc Lattice ◽  
Face Centered ◽  
The Many

AbstractDiscrete breathers (DBs) have been described among pure metals with face-centered cubic (FCC) and body-centered cubic (BCC) lattice, but for hexagonal close-packed (HCP) metals, their properties are little studied. In this paper, the properties of standing and moving DBs in beryllium HCP metal are analyzed by the molecular dynamics method using the many-body interatomic potential. It is shown that the DB is localized in a close-packed atomic row in the basal plane, while oscillations with a large amplitude along the close-packed row are made by two or three atoms, moving in antiphase with the nearest neighbors. Dependences of the DB frequency on the amplitude, as well as the velocity of the DB on its amplitude and on parameter δ, which determines the phase difference of the oscillations of neighboring atoms, are obtained. The maximum velocity of the DB movement in beryllium reaches 4.35 km/s, which is 33.7% of the velocity of longitudinal sound waves. The obtained results supplement our concepts about the mechanisms of localization and energy transport in HCP metals.

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.

Temperature-dependent atomic B factor: an ab initio calculation

2019 ◽  
Vol 75 (4) ◽  
pp. 624-632 ◽  
Author(s):  
Cristiano Malica ◽  
Andrea Dal Corso
Keyword(s):  
Ab Initio ◽  
Harmonic Approximation ◽  
Debye Model ◽  
Waller Factor ◽  
Temperature Dependent ◽  
Atomic Displacements ◽  
Debye Waller Factor ◽  
Diffraction Peaks ◽  
Effects Of Temperature ◽  
Quantum Espresso

The Debye–Waller factor explains the temperature dependence of the intensities of X-ray or neutron diffraction peaks. It is defined in terms of the B matrix whose elements B αβ are mean-square atomic displacements in different directions. These quantities, introduced in several contexts, account for the effects of temperature and quantum fluctuations on the lattice dynamics. This paper presents an implementation of the B factor (8π2 B αβ) in the thermo_pw software, a driver of Quantum ESPRESSO routines that provides several thermodynamic properties of materials. The B factor can be calculated from the ab initio phonon frequencies and displacements or can be estimated, although less accurately, from the elastic constants, using the Debye model. The B factors are computed for a few elemental crystals: silicon, ruthenium, magnesium and cadmium; the harmonic approximation at fixed geometry is compared with the quasi-harmonic approximation where the B factors are calculated accounting for thermal expansion. The results are compared with the available experimental data.

scholarly journals Symmetry of Terms in the Temperature Factor for Bragg Diffraction of X Rays or Neutrons

1985 ◽  
Vol 38 (3) ◽  
pp. 421
Author(s):  
SL Mair
Keyword(s):  
Point Group ◽  
Waller Factor ◽  
Bragg Diffraction ◽  
Group Symmetry ◽  
X Rays ◽  
Point Group Symmetry ◽  
Many Body ◽  
Crystal Potential ◽  
Debye Waller Factor ◽  
Particle Potential

Terms in the anharmonic Debye-Waller factor, taken as a perturbation about the harmonic case to second order in the van Hove ordering parameter, are classified according to the point-group symmetry of the vibrating atom. The classification is valid for a fully interacting (many-body) crystal potential. It is pointed out that certain terms, which are symmetry-allowed for such a general crystal potential, are excluded if an effective one-particle potential is employed.

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.

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.

Debye–Waller factor and the Lindemann parameter of some hexagonal close-packed metals

1980 ◽  
Vol 58 (3) ◽  
pp. 384-387 ◽  
Author(s):  
A. Ramanand ◽  
R. Ramji Rao
Keyword(s):  
Distribution Function ◽  
Harmonic Approximation ◽  
Normal Modes ◽  
Waller Factor ◽  
Hexagonal Close Packed ◽  
Debye Waller Factor ◽  
Anisotropic Temperature ◽  
Modes Of Vibration ◽  
The Mean ◽  
Temperature Factors

The Debye–Waller factor has been calculated as a function of temperature for the four hexagonal close-packed (hcp) metals cobalt, ruthenium, erbium, and scandium, using a lattice-dynamical model to evaluate the normal mode frequencies and eigenvectors in the harmonic approximation. The calculation of the anisotropic temperature factors for these metals requires a knowledge of the eigenvectors for the various normal modes of vibration. The frequency distribution function is also used to calculate the mean-square amplitude of displacement of the atoms, in the cubic approximation. The first and second negative moments of the distribution function are used to calculate the low- and high-temperature limits of [Formula: see text], respectively. The value of the Lindemann parameter obtained from the present calculations is consistent with the value quoted by Gschneidner.

scholarly journals Atomic disorder of Li0.5Ni0.5O thin films caused by Li doping: estimation from X-ray Debye–Waller factors

2015 ◽  
Vol 48 (6) ◽  
pp. 1896-1900 ◽  
Author(s):  
Anli Yang ◽  
Osami Sakata ◽  
Ryosuke Yamauchi ◽  
L. S. R. Kumara ◽  
Chulho Song ◽  
...  
Keyword(s):  
Thin Film ◽  
Thin Films ◽  
Debye Model ◽  
Waller Factor ◽  
Structural Parameter ◽  
X Ray Diffraction ◽  
Atomic Disorder ◽  
X Ray ◽  
Li Doping ◽  
Debye Waller Factor

Cubic type room-temperature (RT) epitaxial Li0.5Ni0.5O and NiO thin films with [111] orientation grown on ultra-smooth sapphire (0001) substrates were examined using synchrotron-based thin-film X-ray diffraction. The 1\overline{1}1 and 2\overline{2}2 rocking curves including six respective equivalent reflections of the Li0.5Ni0.5O and NiO thin films were recorded. The RTB1factor, which appears in the Debye–Waller factor, of a cubic Li0.5Ni0.5O thin film was estimated to be 1.8 (4) Å2from its 1\overline{1}1 and 2\overline{2}2 reflections, even though the Debye model was originally derived on the basis of one cubic element. The corresponding Debye temperature is 281 (39) K. Furthermore, theB2factor in the pseudo-Debye–Waller factor is proposed. This parameter, which is evaluated using one reflection, was also determined for the Li0.5Ni0.5O thin film by treating Li0.5Ni0.5O and NiO as ideal NaCl crystal structures. A structural parameter for the atomic disorder is introduced and evaluated. This parameter includes the combined effects of thermal vibration, interstitial atoms and defects caused by Li doping using the two Debye–Waller factors.

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