scholarly journals Lattice Vibrations in Vanadium

1974 ◽  
Vol 27 (4) ◽  
pp. 471 ◽  
Author(s):  
Satya Pal
Keyword(s):  
Specific Heat ◽  
Frequency Distribution ◽  
Phonon Dispersion ◽  
Sampling Technique ◽  
Experimental Measurements ◽  
Lattice Vibrations ◽  
Phonon Dispersion Curves ◽  
Characteristic Temperatures ◽  
Lattice Specific Heat ◽  
Root Sampling

The phonon dispersion curves, frequency spectrum and specific heat of vanadium have been calculated on the basis of the lattice dynamical model of Sharma and Joshi (1963). The frequency distribution has been derived according to Blackman's (1937, 1955) root-sampling technique by the numerical sampling of 192000 frequencies corresponding to 64000 points considered in the first Brillouin zone. This computed frequency distribution has then been used to calculate the lattice specific heat of vanadium. The resulting values of the specific heat have been compared with experimental measurements in terms of the Debye characteristic temperatures.

Lattice Dynamical Properties of Nickel

1973 ◽  
Vol 51 (17) ◽  
pp. 1869-1873 ◽  
Author(s):  
Satya Pal
Keyword(s):  
Experimental Data ◽  
Specific Heat ◽  
Frequency Spectrum ◽  
Reasonable Agreement ◽  
Sampling Technique ◽  
Waller Factor ◽  
Characteristic Temperatures ◽  
Debye Waller Factor ◽  
Root Sampling ◽  
Theoretical Results

The frequency spectrum of nickel has been calculated on the basis of the lattice dynamical model of Sharma and Joshi. The frequency spectrum has been computed with the help of Blackman's root sampling technique for a discrete subdivision in the reciprocal space. The computed frequency distribution has been employed for the calculation of the specific heat and the temperature variation of the Debye–Waller factor of nickel. The theoretically computed values of specific heat are compared with the experimental data in terms of the Debye characteristic temperatures. The theoretical results are in reasonable agreement with the experimental data.

Temperature-dependent X-ray dynamical diffraction: Darwin theory simulations

1999 ◽  
Vol 55 (1) ◽  
pp. 14-19 ◽  
Author(s):  
Jin-Seok Chung ◽  
Stephen M. Durbin
Keyword(s):  
Phonon Dispersion ◽  
Lattice Vibrations ◽  
X Ray Diffraction ◽  
Temperature Dependent ◽  
Phonon Dispersion Curves ◽  
Dynamical Diffraction ◽  
X Ray ◽  
Ergodic Hypothesis ◽  
Thermal Vibrations ◽  
Good Agreement

Thermal vibrations destroy the perfect crystalline periodicity generally assumed by dynamical diffraction theories. This can lead to some difficulty in deriving the temperature dependence of X-ray reflectivity from otherwise perfect crystals. This difficulty is overcome here in numerical simulations based on the extended Darwin theory, which does not require periodicity. Using Si and Ge as model materials, it is shown how to map the lattice vibrations derived from measured phonon dispersion curves onto a suitable Darwin model. Good agreement is observed with the usual Debye–Waller behavior predicted by standard theories, except at high temperatures for high-order reflections. These deviations are discussed in terms of a possible breakdown of the ergodic hypothesis for X-ray diffraction.

THEORETICAL STUDY OF LATTICE DYNAMICAL PROPERTIES IN FERROELECTRIC LiTaO3

1992 ◽  
Vol 06 (20) ◽  
pp. 3279-3293 ◽  
Author(s):  
YIMIN JIANG ◽  
CHENG GOU
Keyword(s):  
Specific Heat ◽  
Theoretical Study ◽  
Phonon Dispersion ◽  
Dispersion Curves ◽  
Optical Data ◽  
General Function ◽  
Zero Temperature ◽  
Phonon Dispersion Curves ◽  
Maximum Value ◽  
The One

We present the phonon-dispersion curves, the one-phonon density of states, the lattice specific heat cv(T) and the Debye temperature Θ(T) of the ferroelectric LiTaO 3, based on full lattice dynamical model whose parametèrs are fitted to the optical data and neutron measured dispersion curves. A model theory is developed to describe the transition from Debye to non-Debye behaviors observed in the low temperature part of the cv/T3 curve. The cv/T3 function, when is properly scaled, can be fitted by a general function derived from the model. It can be characterized by the temperature T max at which it has maximum, its maximum value (cv/T3)T=T max and its value at zero temperature (cv/T3)T=0. These results are considered useful in searching possibly anomalous phonon behavior from the specific heat cv(T).

scholarly journals Dispersion of Phonons in Ideal Crystals

1969 ◽  
Vol 22 (4) ◽  
pp. 471 ◽  
Author(s):  
NP Gupta
Keyword(s):  
Experimental Data ◽  
Phonon Dispersion ◽  
Zero Point ◽  
Lattice Vibrations ◽  
Rare Gases ◽  
Point Energy ◽  
Phonon Dispersion Curves ◽  
Debye Theory ◽  
Specific Heats ◽  
Theoretical Frequency

A quasiharmonic central force rigid-atom model has been used to study the lattice vibrations of frozen rare gases. The model takes care of interactions up to fourth neighbour and estimates zero-point energy and its volume derivatives by the Debye theory of specific heats. The theoretical frequency distribution and phonon dispersion curves are found to compare reasonably well with the available experimental data. Various causes of the discrepancies and possibilities of improvement of the results are discussed.

Angular Forces and Normal Vibrations in Platinum

1977 ◽  
Vol 32 (12) ◽  
pp. 1490-1494
Author(s):  
H. L. Kharoo ◽  
O. P. Gupta ◽  
M. P. Hemkar
Keyword(s):  
Phonon Dispersion ◽  
Inelastic Neutron Scattering ◽  
Sampling Technique ◽  
Inelastic Neutron ◽  
Dynamical Study ◽  
Normal Vibrations ◽  
Specific Heats ◽  
Debye Temperatures ◽  
Root Sampling ◽  
Good Agreement

Abstract A lattice dynamical study of platinum has been made on the basis of the improved Clark-Gazis-Wallis model considering volume forces of Krebs' nature. The phonon dispersion relations obtained for the three symmetry directions have been compared with the recent inelastic neutron scattering experiments. The specific heat at constant volume has been calculated by Blackman's root sampling technique for temperatures above Θ/10, and below this temperature the calculations are carried out by employing the modified Houston spherical six-term integration procedure. The computed lattice specific heats in terms of the effective Debye temperatures Θ are compared with the available calorimetric data. The theory is in good agreement with the experimental data.

LATTICE DYNAMICS OF YBa2Cu3O7 IN THE IONIC MODEL

1989 ◽  
Vol 03 (04) ◽  
pp. 611-615 ◽  
Author(s):  
V. R. BELOSLUDOV ◽  
M. Yu. LAVRENTIEV ◽  
S. A. SYSKIN
Keyword(s):  
Lattice Dynamics ◽  
Short Range ◽  
Phonon Dispersion ◽  
Lattice Vibrations ◽  
Coulombic Interaction ◽  
Ionic Model ◽  
Phonon Dispersion Curves ◽  
Short Range Repulsion ◽  
Ir And Raman ◽  
Density Of Phonon States

A simple model of interatomic interactions in YBa 2 Cu 3 O 7, which takes into account long-range Coulombic interaction and short-range repulsion of the Born-Mayer type, is presented. On the basis of this model the calculation of lattice vibrations in YBa 2 Cu 3 O 7 is performed, and phonon dispersion curves and density of phonon states are found. A comparison with experimental data on IR and Raman spectra is presented.

scholarly journals LATTICE DYNAMICAL STUDY OF TITANIUM (TI) BY USING CGW-VTBFS MODEL

2021 ◽  
Vol 9 (07) ◽  
pp. 124-129
Author(s):  
U.C Srivastava ◽  
◽  
Shyamendra Pratap Singh ◽  
Keyword(s):  
Experimental Data ◽  
Specific Heat ◽  
Shell Model ◽  
Body Force ◽  
Phonon Dispersion ◽  
Dispersion Curves ◽  
Dynamical Study ◽  
Phonon Dispersion Curves ◽  
Phonon Dynamics ◽  
Experimental Values

In measurements of the phonon dynamics of bcc Titanium (Ti), In the present paper we have reported the lattice dynamical calculations which are performed by using the Clark-Gazis-Wallis (CGW) and Van der Waalsthree body force shell model (VTBFS).The theory is used to compute the phonon dispersion curves(PDC), the Specific heat variation &frequency distribution with the used temperature. The frequencies along the symmetry directions have plotted against the wavevector to obtain the phonon dispersion curves(PDC)from the present models, with the help of available experimental values. The obtained results are agreed well with experimental data.

Lattice Dynamics and Thermal Expansion of Ruthenium

1979 ◽  
Vol 34 (6) ◽  
pp. 724-730 ◽  
Author(s):  
R. Ramji Rao ◽  
J. V. S. S. Narayana Murthy
Keyword(s):  
Thermal Expansion ◽  
Distribution Function ◽  
Bulk Modulus ◽  
Specific Heat ◽  
Temperature Variation ◽  
Frequency Distribution ◽  
Lattice Dynamics ◽  
Pressure Variation ◽  
Frequency Distribution Function ◽  
Lattice Specific Heat

Abstract The lattice dynamics, lattice specific heat and thermal expansion of ruthenium are worked out using the model of Srinivasan and Ramji Rao, based on Keating’s approach. A total number of 50,880 frequencies has been used in constructing the frequency distribution function. The anharmonic parameters are obtained from the data of Clendenen and Drickamer on the pressure variation of the lattice parameters of ruthenium. The Anderson-Grüneisen parameter δ is calculated using the theoretical TOE constants, and the temperature variation of the bulk modulus is explained using Anderson’s theory.

Second-Order Raman Spectra and Phonon Dispersion in GaP

1973 ◽  
Vol 51 (1) ◽  
pp. 63-76 ◽  
Author(s):  
R. M. Hoff ◽  
J. C. Irwin
Keyword(s):  
Specific Heat ◽  
Phonon Dispersion ◽  
Second Order ◽  
Phonon Density ◽  
Specific Heat Data ◽  
Phonon Dispersion Curves ◽  
Point Analysis ◽  
The One ◽  
Critical Point Analysis ◽  
Heat Data

The second-order Raman spectrum of GaP has been investigated experimentally. The experiments were performed on oriented single crystals at both 300 and 77 °K. A critical point analysis of the data has been carried out with the aid of the polarization selection rules. The resulting frequencies are also consistent with a theoretical model which in turn is used to calculate the phonon dispersion throughout the Brillouin zone. The one- and two-phonon density of states and the specific heat have also been calculated and compared to our spectra and available specific heat data. The calculated quantities have also been compared to similar quantities obtained from neutron scattering experiments. This comparison provides information on the accuracy and reliability of phonon dispersion curves obtained from Raman scattering experiments.

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