Investigation of the anharmonic EXAFS oscillation of distorted HCP crystals based on extending quantum anharmonic correlated Einstein model

2021 ◽  
Vol 60 (11) ◽  
pp. 112001
Author(s):  
Tong Sy Tien
Keyword(s):  
Einstein Model

EINSTein Model Validation

2002 ◽  
Author(s):  
Randall R. Klingaman ◽  
William B. Carlton
Keyword(s):  
Model Validation ◽  
Einstein Model

Correlated Einstein model for the equilibrium properties of solids

1984 ◽  
Vol 29 (7) ◽  
pp. 4108-4119 ◽  
Author(s):  
Robert J. Hardy ◽  
Michael A. Day
Keyword(s):  
Einstein Model

ICSC: a program for calculating inelastic scattering cross sections for fast electrons incident on crystals

2003 ◽  
Vol 36 (3) ◽  
pp. 940-943 ◽  
Author(s):  
M. P. Oxley ◽  
L. J. Allen
Keyword(s):  
Inelastic Scattering ◽  
Cross Sections ◽  
Dark Field ◽  
Fast Electrons ◽  
Scattering Coefficients ◽  
Einstein Model ◽  
Annular Dark Field ◽  
Inner Shell Ionization ◽  
Scattering Cross Sections ◽  
Shell Ionization

A computer program which calculates inner-shell ionization and backscattering cross sections for fast electrons incident on a crystal is presented. The program calculates the inelastic scattering coefficients for inner-shell ionization, pertinent to electron energy loss spectroscopy and energy dispersive X-ray analysis, using recently presented parameterizations of the atomic scattering factors. Orientation-dependent cross sections, suitable for atom location by channelling enhanced microanalysis, may be calculated. Inelastic scattering coefficients that allow the calculation of orientation-dependent annular dark-field and Rutherford backscattering maps are calculated using an Einstein model. In all cases, absorption due to thermal diffuse scattering, also calculated using an Einstein model, can be included.

scholarly journals A Bose–Einstein model of particle multiplicity distributions

2007 ◽  
Vol 784 (1-4) ◽  
pp. 515-535 ◽  
Author(s):  
A.Z. Mekjian ◽  
T. Csörgö ◽  
S. Hegyi
Keyword(s):  
Particle Multiplicity ◽  
Einstein Model ◽  
Multiplicity Distributions ◽  
Bose Einstein

scholarly journals Diffusion Coefficients of Methane in Methylbenzene and Heptane at Temperatures between 323 K and 398 K at Pressures up to 65 MPa

2020 ◽  
Vol 41 (8) ◽  
Author(s):  
Malyanah Binti Mohd Taib ◽  
J. P. Martin Trusler
Keyword(s):  
Diffusion Coefficients ◽  
Infinite Dilution ◽  
Hydrodynamic Radius ◽  
Taylor Dispersion ◽  
Relative Uncertainty ◽  
Dispersion Method ◽  
Solvent Density ◽  
Einstein Model ◽  
Taylor Dispersion Method ◽  
Simple Empirical Model

Abstract We reported experimental measurements of the diffusion coefficient of methane at effectively infinite dilution in methylbenzene and in heptane at temperatures ranging from (323 to 398) K and at pressures up to 65 MPa. The Taylor dispersion method was used and the overall combined standard relative uncertainty was 2.3%. The experimental diffusion coefficients were correlated with a simple empirical model as well as the Stokes–Einstein model with the effective hydrodynamic radius of methane depending linearly upon the solvent density. The new data address key gaps in the literature and may facilitate the development of an improved predictive model for the diffusion coefficients of dilute gaseous solutes in hydrocarbon liquids.

Detailed Calculations of Thermal Diffuse Scattering

1997 ◽  
Vol 3 (S2) ◽  
pp. 1153-1154
Author(s):  
D.A. Müller ◽  
B. Edwards ◽  
E.J. Kirkland ◽  
J. Silcox
Keyword(s):  
Diffuse Scattering ◽  
Single Point ◽  
Scanning Transmission Electron Microscope ◽  
Diffraction Spot ◽  
Thermal Diffuse Scattering ◽  
Transmission Electron ◽  
Einstein Model ◽  
Scanning Transmission ◽  
Convergent Beam ◽  
Thermal Diffuse

Convergent beam electron diffraction (CBED) produces a diffraction pattern from a single point on the specimen using a focused probe in the scanning transmission electron microscope (STEM). Because the incident wavefunction is a focused probe, each diffraction spot is enlarged to a disk the size of the objective aperture. Thermal vibration in the specimen reduces the intensity of the diffraction disks and introduces scattering in between the disk. This normally forbidden scattering between the diffraction disks is referred to as thermal diffuse scattering (TDS). The effects are most pronounced at large scattering angles, where TDS scattering can greatly reduce the intensity of the higher order Laue zone (HOLZ) lines. Previous work on modeling the TDS intensity involved the so-called frozen phonon method and the Einstein model of lattice vibration. The Einstein model assumes that each atom in the specimen vibrates independently of every other atom in the specimen and possible correlations among adjacent atoms are ignored.

A thermodynamic description of data for pure Pb from 0 K using the expanded Einstein model for the solid and the two state model for the liquid phase

Calphad ◽  
2018 ◽  
Vol 60 ◽  
pp. 144-155 ◽  
Author(s):  
A.V. Khvan ◽  
A.T. Dinsdale ◽  
I.A. Uspenskaya ◽  
M. Zhilin ◽  
T. Babkina ◽  
...  
Keyword(s):  
Liquid Phase ◽  
Thermodynamic Description ◽  
State Model ◽  
Einstein Model ◽  
Two State Model

Elastic constants and anisotropic pair correlations in solid hydrogen and deuterium

1979 ◽  
Vol 57 (2) ◽  
pp. 136-146 ◽  
Author(s):  
S. Luryi ◽  
J. Van Kranendonk
Keyword(s):  
Elastic Constants ◽  
Phonon Dispersion ◽  
Debye Model ◽  
Elasticity Tensor ◽  
Pair Correlations ◽  
Nearest Neighbours ◽  
Einstein Model ◽  
The One ◽  
Central Forces ◽  
Phonon Dispersion Relations

The anisotropic displacement–displacement correlation function for the two types of pairs of nearest neighbours in solid hep hydrogen and deuterium is studied. Two mechanisms contributing to the deviation of the pair distribution function from axial symmetry around the pair axis are identified. The one is due to the anisotropy of the phonon dispersion relations and is treated in a generalized Debye model parameterized in terms of the elastic constants. The elasticity tensor is decomposed into rotationally irreducible parts, and certain new relations between the elastic constants of hep crystals with central forces are derived. The other mechanism arises from the immediate, anisotropic environment of a pair and is treated using a generalized Einstein model. The relevance of these results for the interpretation of the microwave spectrum of pairs of orthohydrogen molecules in parahydrogen is also discussed.

Sign in / Sign up

Export Citation Format

Share Document