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 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 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 Dynamic response of some atoms: Many-body calculations

2005 ◽  
Vol 3 (2) ◽  
pp. 129-140 ◽  
Author(s):  
Aleksandar Tancic ◽  
M. Nikolic
Keyword(s):  
Random Phase Approximation ◽  
Random Phase ◽  
Atomic Interaction ◽  
Correlation Effects ◽  
Many Body ◽  
Hartree Fock ◽  
Many Body Theory ◽  
Correlation Potential ◽  
Body Theory ◽  
True Correlation

The frequency-dependent polarizability in the Hartree-Fock (HF) approximation has been corrected for true correlation effects by means of many-body theory. The polarizability has been computed in the Random Phase Approximation with Exchange (RPAE) for He, Ar Xe, Kr, Li, Ca through the second (and some higher) order in the correlation potential. With this polarizability as input we obtained the values of some atomic interaction constants.

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.

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.

Averages of additive quantities for the master equation description of the dynamics of a system

1988 ◽  
Vol 420 (1859) ◽  
pp. 407-417
Keyword(s):  
Diffusion Coefficient ◽  
Master Equation ◽  
Thermal Equilibrium ◽  
Linear Response ◽  
Mean Square Displacement ◽  
Time Correlation ◽  
Time Correlation Functions ◽  
Mean Square ◽  
Many Body ◽  
Diffusive Systems

Stationary ensemble averages such as < X n >, < XY > etc. where X and Y are stochastic variables whose changes in the course of time t are additive, are examined for a system with dynamics described by a master equation. Results are obtained for the two important cases of ( a ) thermal equilibrium and ( b ) steady-state situations brought about by the imposition of external fields. The averages are expressed as integrals with respect to time of appropriate time-correlation functions. For appropriate quantities of this type one may express corresponding linear response coefficients in terms of these averages. The results represent many-body generalizations of the elementary Einstein relations between diffusion coefficient and mean-square displacement, and between mobility and mean-square displacement. While the former type of relation holds only for normal diffusive systems the second type holds also for anomalous diffusive systems.

The metachor as a characteristic of the association of electrolytes in aqueous solutions

1984 ◽  
Vol 49 (5) ◽  
pp. 1061-1078 ◽  
Author(s):  
Jiří Čeleda ◽  
Stanislav Škramovský
Keyword(s):  
Aqueous Solutions ◽  
Apparent Volume ◽  
Solutions Of Electrolytes ◽  
Molal Volumes ◽  
The Difference ◽  
High Concentrations ◽  
Experimental Values ◽  
Suitable Characteristic ◽  
Association Of Ions ◽  
Very High

Based on the earlier paper introducing a concept of the apparent parachor of a solute in the solution, we have eliminated in the present work algebraically the effect which is introduced into this quantity by the additivity of the apparent molal volumes. The difference remaining from the apparent parachor after substracting the contribution corresponding to the apparent volume ( for which the present authors suggest the name metachor) was evaluated from the experimental values of the surface tension of aqueous solutions for a set of 1,1-, 1,2- and 2,1-valent electrolytes. This difference showed to be independent of concentration up to the very high values of the order of units mol dm-3 but it was directly proportional to the number of the free charges (with a proportionality factor 5 ± 1 cm3 mol-1 identical for all studied electrolytes). The metachor can be, for this reason, a suitable characteristic for detection of the association of ions and formation of complexes in the solutions of electrolytes, up to high concentrations where other methods are failing.

scholarly journals Effect of Terminal Groups on Thermomechanical and Dielectric Properties of Silica–Epoxy Composite Modified by Hyperbranched Polyester

Polymers ◽  
2021 ◽  
Vol 13 (15) ◽  
pp. 2451
Author(s):  
Jianwen Zhang ◽  
Dongwei Wang ◽  
Lujia Wang ◽  
Wanwan Zuo ◽  
Lijun Zhou ◽  
...  
Keyword(s):  
Dielectric Constant ◽  
Dielectric Properties ◽  
Binding Energy ◽  
Epoxy Resin ◽  
Volume Fraction ◽  
Epoxy Composite ◽  
Mean Square Displacement ◽  
Mean Square ◽  
Hyperbranched Polyester ◽  
Free Volume Fraction

To study the effect of hyperbranched polyester with different kinds of terminal groups on the thermomechanical and dielectric properties of silica–epoxy resin composite, a molecular dynamics simulation method was utilized. Pure epoxy resin and four groups of silica–epoxy resin composites were established, where the silica surface was hydrogenated, grafted with silane coupling agents, and grafted with hyperbranched polyester with terminal carboxyl and terminal hydroxyl, respectively. Then the thermal conductivity, glass transition temperature, elastic modulus, dielectric constant, free volume fraction, mean square displacement, hydrogen bonds, and binding energy of the five models were calculated. The results showed that the hyperbranched polyester significantly improved the thermomechanical and dielectric properties of the silica–epoxy composites compared with other surface treatments, and the terminal groups had an obvious effect on the enhancement effect. Among them, epoxy composite modified by the hyperbranched polyester with terminal carboxy exhibited the best thermomechanical properties and lowest dielectric constant. Our analysis of the microstructure found that the two systems grafted with hyperbranched polyester had a smaller free volume fraction (FFV) and mean square displacement (MSD), and the larger number of hydrogen bonds and greater binding energy, indicating that weaker strength of molecular segments motion and stronger interfacial bonding between silica and epoxy resin matrix were the reasons for the enhancement of the thermomechanical and dielectric properties.

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