Crystal Equilibrium and Lattice Dynamical Study of α-Iron and Chromium

1977 ◽  
Vol 32 (12) ◽  
pp. 1495-1502 ◽  
Author(s):  
O. P. Gupta ◽  
M. P. Hemkar
Keyword(s):  
Short Range ◽  
Phonon Dispersion ◽  
Mean Square Displacement ◽  
Waller Factor ◽  
Dynamical Study ◽  
Ion Interactions ◽  
Debye Waller Factor ◽  
Screening Parameter ◽  
The Mean ◽  
Ionic Lattice

Abstract Studies of the phonon dispersion, the temperature dependence of Debye-Waller factor, the Debye temperature, and the mean square displacement of α-iron and chromium have been made by means of a lattice dynamical model proposed by the authors. The model considers short range pairwise forces effective up to the second neighbours and electron-ion interactions on the lines of Bhatia using an appropriate value of the screening parameter. The volume force is aver­ aged over the whole Wigner-Seitz sphere. The ionic lattice is in equilibrium in a medium of electrons. The computed results compare well with experimental data.

Lattice Dynamical Properties of Potassium

1981 ◽  
Vol 36 (11) ◽  
pp. 1242-1245
Author(s):  
O. P. Gupta
Keyword(s):  
Equilibrium Condition ◽  
Short Range ◽  
Phonon Dispersion ◽  
Waller Factor ◽  
Crystal Stability ◽  
Debye Waller Factor ◽  
Dynamical Properties ◽  
Experimental Values ◽  
Theoretical Results ◽  
Good Agreement

The phonon dispersion, temperature dependence of the Debye temperature, Debye-Waller factor, and Grüneisen parameter of potassium are calculated using a realistic lattice dynamical model. The model considers short range pairwise forces effective upto second neighbors and an improved electron ion interaction on the lines of Bhatia. An equilibrium condition, which preserves the crystal stability, is obtained. The theoretical results are found to be in good agreement with the experimental values.

Debye Waller Factors of fee Metals by the Modified Angular Force Model

1977 ◽  
Vol 32 (6) ◽  
pp. 570-576 ◽  
Author(s):  
Hira Lai Kharoo ◽  
O. P. Gupta ◽  
M. P. Hemkar
Keyword(s):  
Characteristic Temperature ◽  
Mean Square Displacement ◽  
Waller Factor ◽  
Force Model ◽  
Debye Waller Factor ◽  
Different Temperatures ◽  
Temperature Parameter ◽  
The Mean ◽  
Experimental Values ◽  
Theoretical Results

Abstract A modified form of the non-central force model which takes account of the electron-ion inter­ action term of the Kreb's model in the Clark, Gazis and Wallis type angular forces is considered to calculate the Debye-Waller exponents at different temperatures for five fee metals: copper, silver, gold, aluminium and nickel. The results are compared with the available x-ray measurements in terms of the temperature parameter Y of the Debye-Waller factor, the Debye characteristic temperature ΘM and the mean square displacement of the atoms. The theoretical results are found to be in reasonably satisfactory agreement with the experimental values.

In Situ Observation of the Oxygen Nucleation in Silicon with X-Ray Single Crystal Diffraction

2011 ◽  
Vol 178-179 ◽  
pp. 353-359 ◽  
Author(s):  
Johannes Will ◽  
Alexander Gröschel ◽  
Christoph Bergmann ◽  
Andreas Magerl
Keyword(s):  
Single Crystal ◽  
Waller Factor ◽  
Dynamical Theory ◽  
Mean Value ◽  
Single Crystal Diffraction ◽  
X Ray ◽  
Float Zone ◽  
Debye Waller Factor ◽  
The Mean

The measurement of Pendellösungs oscillations was used to observe the time dependent nucleation of oxygen in a Czochralski grown single crystal at 750°C. It is shown, that the theoretical approach of the statistical dynamical theory describes the data well. Within the framework of this theory it is possible to determine the static Debye-Waller-factor as a function of the annealing time by evaluating the mean value of the Bragg intensity and the period length. The temperature influence on the Pendellösungs distance was corrected for by measurement of a Float-zone sample at the same temperature.

Diffuse X-ray scattering by 2,3-dimethylnaphthalene

1999 ◽  
Vol 32 (2) ◽  
pp. 309-321 ◽  
Author(s):  
R. Schreier ◽  
J. Kalus
Keyword(s):  
Correlation Coefficients ◽  
Waller Factor ◽  
Mutual Orientation ◽  
X Rays ◽  
Static Disorder ◽  
Diffuse Intensity ◽  
X Ray Scattering ◽  
Debye Waller Factor ◽  
Isotropic Displacement Parameter ◽  
The Mean

The diffuse intensity distribution of X-rays scattered from a dipolar disordered single crystal of 2,3-dimethylnaphthalene (2,3-DMN) has been measured and was found to be nearly independent of temperature in some restricted regions of the reciprocal space. This behaviour was related to a static disorder of the crystal. Lattice parameters were determined between room temperature and 9 K and phase transitions at 227 K and 112 K were observed. The results of the data analysis at 298 K are: the equivalent isotropic displacement parameterUeqfor the thermal Debye–Waller factor is (0.18 Å)2; the displacement parameters describing the static disorder are U\raise.15em{_{xx}}\kern-.65em^C\le(0.05 Å)2, U\raise.15em{_{yy}}\kern-.65em^C=[0.22\,(2) Å]2and U_{zz}^C= [0.35\,(3) Å]2. The molecules show an orientational Gaussian distribution around thexaxis with a width of 5.0 (8)°. All these results refer to the molecular inertia system. Correlation coefficients characterizing the mean mutual orientation of neighbouring molecules were determined. The highest correlation coefficient was found along [010]: C=-0.231\pm 0.004.

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.

scholarly journals Calculation of X-ray absorption structure above K-edge of laser shock-compressed aluminum

1990 ◽  
Vol 8 (1-2) ◽  
pp. 319-325 ◽  
Author(s):  
A. Djaoui ◽  
T. A. Hall ◽  
R. C. Albers ◽  
J. J. Rehr ◽  
J. Mustre
Keyword(s):  
Mean Free Path ◽  
Waller Factor ◽  
Normal Density ◽  
Structure Model ◽  
Exchange Correlation ◽  
Debye Waller Factor ◽  
Correlation Potential ◽  
The Mean ◽  
X Ray Absorption ◽  
Band Structure Model

Aluminum sandwich foils can be compressed to more than twice the normal density by the use of shock waves generated by laser beams. We present calculations of the K-edge absorption structure of two fold compressed aluminum, and compare the results with experimental data. The atomic potential is calculated using a spherical band-structure model with Fermi-Dirac statistics for the electrons. The structure above the K-edge is calculated according to the Müller-Shaich formula for the propagating photo-electron. The mean free path of the electron is taken into account through a complex exchange correlation potential. An appropriate Debye-Waller factor is used to represent the effect of the relatively high temperature encountered in these experiments.

Dependence of critical voltages in Cu-based alloys on composition, temperature and short range order

1978 ◽  
Vol 36 (1) ◽  
pp. 192-193
Author(s):  
K. Kuroda ◽  
Y. Tomokiyo ◽  
T. Eguchi
Keyword(s):  
Short Range ◽  
Short Range Order ◽  
Mean Square Displacement ◽  
Dynamical Theory ◽  
Range Order ◽  
Critical Voltage ◽  
Middle Line ◽  
The Mean ◽  
Degree Of Order ◽  
Minimum Intensity

Introduction Since the critical voltage effect in electron microscopy was discovered [1, 2], a number of its applications have been proposed [3-9]. As the critical voltage Vcof an alloy depends primarily on the scattering factors of constituent atoms, not only the compositional change but also the degree of order and the mean square displacement (msd) of the atoms affect the value of Vc. In the present paper the effect of alloying on Vc is studied in Cu-based alloys containing 14.8 at% Al, 4.9 or 14.9 at% Au. These alloys are of interest because Al is lighter and Au heavier than Cu atom, and furthermore the alloys develop a short range order. The critical voltages were determined using JEM-1000 HVEM by observing of the minimum intensity of 2g Kikuchi line and the reversal of the contrast of middle line at lg spot. The measured Vc was analyzed by the 10-beam dynamical theory.

On the Debye-Waller Factor and Debye Temperature of Dendrite-Shaped PbTe

2013 ◽  
Vol 678 ◽  
pp. 17-21
Author(s):  
R. Karunamoorthi ◽  
P. Indra Devi ◽  
K. Ramachandran
Keyword(s):  
Dispersion Curve ◽  
Shell Model ◽  
Debye Temperature ◽  
Phonon Dispersion ◽  
Lead Telluride ◽  
Waller Factor ◽  
Phonon Dispersion Curve ◽  
Thermal Parameters ◽  
Experimental Results ◽  
Debye Waller Factor

In this study, the phonon dispersion curve of dendrite-shaped lead telluride (PbTe), a nano structured material is obtained by shell model and the thermal parameters are calculated and compared with experimental results.

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