Debye-Waller factor of bcc metals: A comparison of the lattice-dynamics and molecular-dynamics results for Li and Rb

1982 ◽  
Vol 25 (6) ◽  
pp. 3649-3657 ◽  
Author(s):  
Ramesh C. Shukla ◽  
Raymond D. Mountain
Keyword(s):  
Molecular Dynamics ◽  
Lattice Dynamics ◽  
Waller Factor ◽  
Bcc Metals ◽  
Debye Waller Factor ◽  
Molecular Dynamics Results

ISOTOPIC EFFECT IN DEBYE–WALLER FACTOR OF CRYSTALLINE GERMANIUM

2013 ◽  
Vol 27 (26) ◽  
pp. 1350191
Author(s):  
HO KHAC HIEU ◽  
VU VAN HUNG
Keyword(s):  
Lattice Dynamics ◽  
Mass Difference ◽  
Relative Displacement ◽  
Waller Factor ◽  
Isotopic Effect ◽  
Mean Square ◽  
X Ray ◽  
Debye Waller Factor ◽  
X Ray Absorption ◽  
Crystalline Germanium

The statistical moment method has been used to study the effect of isotopic mass difference on extended X-ray absorption fine structure (EXAFS) Debye–Waller factor of crystalline germanium. The effects on the parallel mean-square relative displacement and the atomic mean square displacements have been considered. This research also exposed that isotopic effect is noticeable where the correlated atomic motion is concerned. Numerical calculations have been performed for two isotopes 70 Ge and 76 Ge in range of temperature from 0 K to 600 K. Our results are compared with available experimental EXAFS data [J. Purans et al., Phys. Rev. Lett.100 (2008) 055901] as well as with lattice dynamics calculations [A. Sanson, Solid State Sci.12 (2010) 1988] and the good agreements are found.

Are Common Atom Form Factors in HREM-Simulations Accurate Enough for Quantitative Image Matching?

1997 ◽  
Vol 3 (S2) ◽  
pp. 1159-1160
Author(s):  
G. Möbus ◽  
T. Gemming ◽  
W. Nüchter ◽  
M. Exner ◽  
P. Gumbsch ◽  
...  
Keyword(s):  
Molecular Dynamics ◽  
Image Matching ◽  
Form Factors ◽  
Waller Factor ◽  
Dynamics Simulation ◽  
Simulated Image ◽  
Thermal Diffuse Scattering ◽  
Hartree Fock ◽  
Debye Waller Factor ◽  
Quantitative Image

1.Introduction:If digital image matching between an experimental HREM-image and the simulated image fails, one of the suggested reasons is the “inaccuracy of the atomic form factors“ describing the electron scattering in common simulation packages using the free and neutral atom approximation from Hartree-Fock calculations [1]. In detail, three contributions within the usual form factor calculations are mainly missing: (i) the redistribution of charge in ionic crystals, (ii) the accumulation of charge away from atom sites in covalent crystals, (iii) the inclusion of thermal diffuse scattering (TDS) as well as the correlated vibration of atoms beyond the Einstein-approximation within the Debye-Waller factor (DWF) theory. Each of the three effects have been checked separately:2.Simulations of TDS by Coupling of Molecular Dynamics Time Series to HREM- Multislice Calculations:70 snap shots of a series of structures of NiAl (4.9 × 5.1 × l0nm) are stored from an equilibrated molecular dynamics simulation with vibration amplitudes corresponding to room temperature.

Surface Lattice Dynamics of Silver. I. Low-Energy Electron Debye-Waller Factor

1966 ◽  
Vol 151 (2) ◽  
pp. 476-483 ◽  
Author(s):  
Edwin R. Jones ◽  
James T. McKinney ◽  
Maurice B. Webb
Keyword(s):  
Lattice Dynamics ◽  
Waller Factor ◽  
Low Energy ◽  
Energy Electron ◽  
Surface Lattice ◽  
Debye Waller Factor ◽  
Low Energy Electron

Lattice Dynamics of Molybdenum and Chromium

1980 ◽  
Vol 35 (2) ◽  
pp. 230-235
Author(s):  
B. P. Singh ◽  
L. P. Pathak ◽  
M. P. Hemkar
Keyword(s):  
Experimental Data ◽  
Temperature Dependence ◽  
Lattice Dynamics ◽  
Waller Factor ◽  
Mean Square ◽  
Frequency Wave ◽  
Debye Waller Factor ◽  
Nearest Neighbours ◽  
The Mean ◽  
First Time

Abstract The frequency-wave vector dispersion relations, the frequency spectrum, the Debye temperature, the temperature dependence of the Debye-Waller factor and the mean square displacements of the atoms molybdenum and chromium, the metals for which long range forces are also important, have been computed on the basis of the extended improved Fielek model for BCC transition metals. The model considers, for the first time the d shell-d shell central interactions upto next-nearest-neighbours. The calculated results show a satisfactory agreement with the available experimental data.

The effect of temperature on high-resolution TEM image contrast

1995 ◽  
Vol 53 ◽  
pp. 640-641
Author(s):  
T. Geipel ◽  
W. Mader ◽  
P. Pirouz
Keyword(s):  
Form Factor ◽  
Inelastic Scattering ◽  
Accurate Method ◽  
Waller Factor ◽  
Effect Of Temperature ◽  
Specimen Thickness ◽  
Influence Of Temperature ◽  
Debye Waller Factor ◽  
Influence Of Temperature On ◽  
Atomic Form Factor

Temperature affects both elastic and inelastic scattering of electrons in a crystal. The Debye-Waller factor, B, describes the influence of temperature on the elastic scattering of electrons, whereas the imaginary part of the (complex) atomic form factor, fc = fr + ifi, describes the influence of temperature on the inelastic scattering of electrons (i.e. absorption). In HRTEM simulations, two possible ways to include absorption are: (i) an approximate method in which absorption is described by a phenomenological constant, μ, i.e. fi; - μfr, with the real part of the atomic form factor, fr, obtained from Hartree-Fock calculations, (ii) a more accurate method in which the absorptive components, fi of the atomic form factor are explicitly calculated. In this contribution, the inclusion of both the Debye-Waller factor and absorption on HRTEM images of a (Oll)-oriented GaAs crystal are presented (using the EMS software.Fig. 1 shows the the amplitudes and phases of the dominant 111 beams as a function of the specimen thickness, t, for the cases when μ = 0 (i.e. no absorption, solid line) and μ = 0.1 (with absorption, dashed line).

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