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 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 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 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.

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 Thermal and Quantum Fluctuation Effects in Quasiperiodic Systems in External Potentials

2019 ◽  
Vol 4 (4) ◽  
pp. 93
Author(s):  
Fabio Cinti ◽  
Tommaso Macrì
Keyword(s):  
Monte Carlo ◽  
Quantum Monte Carlo ◽  
Quantum Fluctuation ◽  
Pair Potential ◽  
Many Body ◽  
Harmonic Confinement ◽  
Intrinsic Length ◽  
Fluctuation Effects ◽  
The Many ◽  
Quantum Monte Carlo Methods

We analyze the many-body phases of an ensemble of particles interacting via a Lifshitz–Petrich–Gaussian pair potential in a harmonic confinement. We focus on specific parameter regimes where we expect decagonal quasiperiodic cluster arrangements. Performing classical Monte Carlo as well as path integral quantum Monte Carlo methods, we numerically simulate systems of a few thousand particles including thermal and quantum fluctuations. Our findings indicate that the competition between the intrinsic length scale of the harmonic oscillator and the wavelengths associated to the minima of the pair potential generically lead to a destruction of the quasicrystalline pattern. Extensions of this work are also discussed.

MECHANICS OF NANOTUBES FILLED WITH C60, C36 AND C20

2003 ◽  
Vol 17 (26) ◽  
pp. 4667-4674 ◽  
Author(s):  
Z. X. ZHANG ◽  
Z. Y. PAN ◽  
Q. WEI ◽  
Z. J. LI ◽  
L. K. ZANG ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Critical Strain ◽  
Md Simulation ◽  
Pair Potential ◽  
Small Strain ◽  
Critical Value ◽  
Many Body ◽  
Long Distance ◽  
The Many ◽  
Brenner Potential

The mechanical properties of single-walled nanotubes (SWNTs) filled with small fullerenes (C20, C36 and C60) were investigated using molecular dynamics (MD) simulation. The interaction between carbon atoms was described by a combination of the many-body Brenner potential with a two-body pair potential. We found that below the critical value of the strain, the stress of SWNT increases linearly with the strain and the Young's modulus of certain SWNT with different filling densities is almost the same for small strain. It was also observed that the buckling force, which corresponds to the critical strain, becomes higher as the filling density of SWNT is increased in general. However, in the case of SWNT of larger radius filled with smaller fullerenes, the dependence of the buckling force on the filling density is expected to be different, which was attributive to the long-distance attractive interaction between atoms of fullerene and those of SWNT.

The scattering of light. II. The complex refractive index of a molecular fluid

1987 ◽  
Vol 321 (1559) ◽  
pp. 305-360 ◽  
Keyword(s):  
Refractive Index ◽  
Complex Refractive Index ◽  
Pair Potential ◽  
Many Body ◽  
Effective Polarizability ◽  
Reaction Field ◽  
Many Body Theory ◽  
The Many ◽  
Molecular Resonance ◽  
Body Theory

We treat the complex refractive index of a finite molecular fluid on the basis of a classical many-body theory; the surface problem is handled through surfacedependent propagators. We develop a density expansion generalizing the Lorentz-Lorenz relation and sum all two-body terms to a closed form with intermolecular correlations determined by a Lennard-Jones pair potential; the dependence on density, temperature and frequency is discussed and the case when the frequency is near a molecular resonance is considered. The refractive index and the extinction coefficient are compared with experiments for gases. We also derive a generalization of the macroscopic relation of Onsager and Bottcher from the many-body theory, essentially as an expansion in an effective polarizability of a molecule in the many-body system. Exact microscopic expressions for an effective polarizability and for a reaction field are identified, and it is shown that they are related like the Bottcher polarizability and the Onsager reaction field in a well-defined decorrelation approximation. The relation with, and validity of, the macroscopic formulae of Lorentz and Bottcher are analysed in depth.

A Simple Real-Space Channelling Theory for Electron Diffraction and HREM

1990 ◽  
Vol 48 (1) ◽  
pp. 64-65
Author(s):  
D. Van Dyck
Keyword(s):  
High Resolution ◽  
Electron Diffraction ◽  
Direct Method ◽  
Real Space ◽  
Zone Axis ◽  
Phase Object ◽  
High Resolution Images ◽  
The Many ◽  
Analytical Expressions ◽  
Electron Wavefunction

The computation of the many beam dynamical electron diffraction amplitudes or high resolution images can only be done numerically by using rather sophisticated computer programs so that the physical insight in the diffraction progress is often lost. Furthermore, it is not likely that in this way the inverse problem can be solved exactly, i.e. to reconstruct the structure of the object from the knowledge of the wavefunction at its exit face, as is needed for a direct method [1]. For this purpose, analytical expressions for the electron wavefunction in real or reciprocal space are much more useful. However, the analytical expressions available at present are relatively poor approximations of the dynamical scattering which are only valid either for thin objects ((weak) phase object approximation, thick phase object approximation, kinematical theory) or when the number of beams is very limited (2 or 3). Both requirements are usually invalid for HREM of crystals. There is a need for an analytical expression of the dynamical electron wavefunction which applies for many beam diffraction in thicker crystals. It is well known that, when a crystal is viewed along a zone axis, i.e. parallel to the atom columns, the high resolution images often show a one-to-one correspondence with the configuration of columns provided the distance between the columns is large enough and the resolution of the instrument is sufficient. This is for instance the case in ordered alloys with a column structure [2,3]. From this, it can be suggested that, for a crystal viewed along a zone axis with sufficient separation between the columns, the wave function at the exit face does mainly depend on the projected structure, i.e. on the type of atom columns. Hence, the classical picture of electrons traversing the crystal as plane-like waves in the directions of the Bragg beams which historically stems from the X-ray diffraction picture, is in fact misleading.

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