Monte Carlo simulation of an anharmonic Debye–Waller factor to theT4order

2017 ◽  
Vol 73 (2) ◽  
pp. 151-156 ◽  
Author(s):  
Kun-lun Wang ◽  
Xian-bin Huang ◽  
Jing Li ◽  
Qiang Xu ◽  
Jia-kun Dan ◽  
...  
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Fourth Order ◽  
Taylor Expansion ◽  
Harmonic Approximation ◽  
Perturbation Expansion ◽  
Waller Factor ◽  
Bragg Diffraction ◽  
Atomic Interaction ◽  
Debye Waller Factor

In an increasing number of cases the harmonic approximation is incommensurate with the quality of Bragg diffraction data, while results of the anharmonic Debye–Waller factor are not typically available. This paper presents a Monte Carlo computation of a Taylor expansion of an anharmonic Debye–Waller factor with respect to temperature up to the fourth order, where the lattice was a face-centred cubic lattice and the atomic interaction was described by the Lennard–Jones potential. The anharmonic Debye–Waller factor was interpreted in terms of cumulants. The results revealed three significant points. Firstly, the leading term of anharmonicity had a negative contribution to the Debye–Waller factor, which was confirmed by Green's function method. Secondly, the fourth-order cumulants indicated a non-spherical probability density function. Thirdly, up to the melting point of two different densities, the cumulants up to the fourth order were well fitted by the Taylor expansion up toT4, which suggested that the Debye–Waller factor may be calculated by perturbation expansion up to the corresponding terms. In conclusion, Monte Carlo simulation is a useful approach for calculating the Debye–Waller factor.

scholarly journals MELTING OF THE VORTEX LATTICE IN LAYERED SUPERCONDUCTORS

2009 ◽  
Vol 23 (05) ◽  
pp. 661-672 ◽  
Author(s):  
BO FENG ◽  
ZHIGANG WU ◽  
DINGPING LI
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Vortex Lattice ◽  
Waller Factor ◽  
Layered Superconductor ◽  
Melting Line ◽  
Loop Order ◽  
Debye Waller Factor ◽  
Simulation And Experiment ◽  
Good Agreement

The structure function of the vortex lattice of layered superconductor is calculated to one-loop order. Based on a phenomenological melting criterion concerning the Debye–Waller factor, we calculate the melting line of the vortex lattice, and compare our results to Monte Carlo simulation and experiment. We find that our results are in good agreement with the Monte Carlo results. Moreover, our analytic calculation of the melting line of BSCCO fits the experiment reasonably.

MONTE CARLO SIMULATION USING JOHNSON POTENTIAL ON Gd–Mg ALLOY FOR DEBYE–WALLER FACTOR AND DEBYE TEMPERATURE

2002 ◽  
Vol 13 (05) ◽  
pp. 707-715 ◽  
Author(s):  
S. CHITRA ◽  
K. RAMACHANDRAN
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Thermal Properties ◽  
Debye Temperature ◽  
Waller Factor ◽  
Mg Alloy ◽  
X Ray ◽  
Specific Heats ◽  
Debye Waller Factor ◽  
Present Simulation

Monte Carlo simulation (MCS) on the thermal properties in Gd–Mg alloy becomes essential as there are only limited experiments available. A realistic Johnson potential is used to workout the specific heats for various temperatures and hence the Debye temperature. The results from the present simulation technique are very well compared with our shell model calculation. The need of better X-ray measurements for Debye–Waller factor and Debye temperature other than the measurements of Subadhra and Sirdeshmukh, is discussed in detail.

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.

EFFECT OF LATTICE DISTORTION ON THE DEBYE–WALLER FACTOR: I. EXTENDED INTERNAL DEFECTS

1967 ◽  
Vol 45 (8) ◽  
pp. 2651-2660 ◽  
Author(s):  
J. Vail
Keyword(s):  
Nearest Neighbor ◽  
Harmonic Approximation ◽  
Waller Factor ◽  
Potential Interaction ◽  
Coupling Constants ◽  
Extended Defects ◽  
Extended Defect ◽  
Cubic Crystal ◽  
Perfect Lattice ◽  
Debye Waller Factor

A model is introduced in which a Mössbauer atom in an extended internal defect is replaced by a point defect in a perfect lattice, with coupling equal to that in the extended defect. Lattice distortions are considered which are typical for extended defects, with 5 and 10% dilatation and compression, effective coupling constants in nearest-neighbor harmonic approximation are estimated for these cases for a monatomic cubic crystal with Morse potential interaction, and Visscher's data are then used to estimate the fractional change in the Debye–Waller factor, e−2W. Decreases of 14 and 38% are found in e−2W for 5 and 10%, respectively, of lattice dilatation in extended defects, using parameters that are typical of monatomic metals.

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.

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.

Electron Scattering in Solids

1990 ◽  
Vol 48 (2) ◽  
pp. 4-5
Author(s):  
Ryuichi Shimizu ◽  
Ze-Jun Ding
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Angular Distribution ◽  
Elastic Scattering ◽  
Electron Scattering ◽  
Cross Sections ◽  
Expansion Method ◽  
Electron Excitation ◽  
Partial Wave Expansion ◽  
Backscattered Electrons

Monte Carlo simulation has been becoming most powerful tool to describe the electron scattering in solids, leading to more comprehensive understanding of the complicated mechanism of generation of various types of signals for microbeam analysis.The present paper proposes a practical model for the Monte Carlo simulation of scattering processes of a penetrating electron and the generation of the slow secondaries in solids. The model is based on the combined use of Gryzinski’s inner-shell electron excitation function and the dielectric function for taking into account the valence electron contribution in inelastic scattering processes, while the cross-sections derived by partial wave expansion method are used for describing elastic scattering processes. An improvement of the use of this elastic scattering cross-section can be seen in the success to describe the anisotropy of angular distribution of elastically backscattered electrons from Au in low energy region, shown in Fig.l. Fig.l(a) shows the elastic cross-sections of 600 eV electron for single Au-atom, clearly indicating that the angular distribution is no more smooth as expected from Rutherford scattering formula, but has the socalled lobes appearing at the large scattering angle.

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).

Determination of Stoichiometry of GaAs Component in (Gaas)Ge Epitaxially Grown Thin Films by Electron Microprobe X-Ray Analysis

1990 ◽  
Vol 48 (2) ◽  
pp. 264-265
Author(s):  
D. R. Liu ◽  
S. S. Shinozaki ◽  
R. J. Baird
Keyword(s):  
Thin Film ◽  
Thin Films ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Compound Semiconductors ◽  
Energy Dispersive Analysis ◽  
X Ray ◽  
Metastable Alloys ◽  
Lower Voltage

The epitaxially grown (GaAs)Ge thin film has been arousing much interest because it is one of metastable alloys of III-V compound semiconductors with germanium and a possible candidate in optoelectronic applications. It is important to be able to accurately determine the composition of the film, particularly whether or not the GaAs component is in stoichiometry, but x-ray energy dispersive analysis (EDS) cannot meet this need. The thickness of the film is usually about 0.5-1.5 μm. If Kα peaks are used for quantification, the accelerating voltage must be more than 10 kV in order for these peaks to be excited. Under this voltage, the generation depth of x-ray photons approaches 1 μm, as evidenced by a Monte Carlo simulation and actual x-ray intensity measurement as discussed below. If a lower voltage is used to reduce the generation depth, their L peaks have to be used. But these L peaks actually are merged as one big hump simply because the atomic numbers of these three elements are relatively small and close together, and the EDS energy resolution is limited.

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