Lattice dynamical study of face centred tetragonal indium

1983 ◽  
Vol 61 (1) ◽  
pp. 58-66 ◽  
Author(s):  
V. Ramamurthy ◽  
S. B. Rajendraprasad
Keyword(s):  
Frequency Distribution ◽  
Phonon Frequency ◽  
Phonon Dispersion ◽  
Dynamical Study ◽  
Atomic Interactions ◽  
Characteristic Features ◽  
Experimental Values ◽  
First Time ◽  
Good Agreement ◽  
Phonon Dispersion Relations

The phonon dispersion relations and the phonon frequency distribution function of fct indium have been deduced, for the first time, using a lattice dynamical model which expresses the atomic interactions in terms of central, angular, and volume forces. Six elastic constants, four zone boundary frequencies, and an equilibrium condition were used in the evaluation of the force constants. It is shown that this model is elastically consistent and conforms with the translational symmetry of the lattice; the phonon frequencies of indium deduced from it are in very good agreement with the experimental values of Reichardt and Smith and the theoretical values of Garrett and Swihart, but disagree with the theoretical values of Chulkov et al. as well as those of Gunton and Saunders at several wave vectors and polarizations. In addition the phonon frequency distribution curve obtained from this model is in overall agreement with those obtained from the electron tunnelling data, the inelastic scattering of neutrons as well as a pseudopotential model. The apparent characteristic features of these curves, the implications of the crystallographic equivalence between fct and bet lattices, and their relevance in the lattice dynamical study of indium are discussed.

scholarly journals Phonon Dispersion Relations for Chromium and Tantalum

1975 ◽  
Vol 28 (1) ◽  
pp. 57 ◽  
Author(s):  
Jyoti Prakash ◽  
LP Pathak ◽  
MP Hemkar
Keyword(s):  
Force Constant ◽  
Phonon Dispersion ◽  
Normal Modes ◽  
Inelastic Neutron ◽  
Neutron Spectroscopy ◽  
Phonon Dispersion Curves ◽  
Modes Of Vibration ◽  
Experimental Values ◽  
Good Agreement ◽  
Phonon Dispersion Relations

Phonon dispersion curves for the normal modes of vibration in chromium and tantalum are calculated along the symmetry directions [100], [110] and [111] using the five force-constant model of Behari and Tripathi (1970a). The results are compared with experimental values obtained from inelastic neutron spectroscopy and reasonably good agreement is found.

A lattice dynamical study of Cu and Ni based on a new empirical many-body potential

1995 ◽  
Vol 73 (3-4) ◽  
pp. 143-146 ◽  
Author(s):  
I. Akgün
Keyword(s):  
Potential Energy Function ◽  
Many Body ◽  
Dynamical Study ◽  
Dynamical Behaviors ◽  
Atomic Interactions ◽  
The Face ◽  
Experimental Values ◽  
Three Body ◽  
Body Potential ◽  
Good Agreement

In the present work, a recently developed empirical many-body potential-energy function (PEF) is first used, as an application, to investigate the dynamical behaviors of the face-centred-cube d-band metals, Cu and Ni. The new PEF contains both two- and three-body atomic interactions. The two-body potential is a kind of hybrid function and the three-body potential is expressed in terms of the two-body interactions. The parameters defining the PEF for the metals are computed following a procedure similar to a method given by Girifalco and Weizer. The input data for evaluating the necessary parameters are independent of the phonon frequencies and elastic constants of the metals. The phonon frequencies along the principal symmetry directions of Cu and Ni are calculated using the computed two- and three-body force constants. The results are found to be in good agreement with the corresponding experimental values.

Atomistic simulation of phonon dispersion for body-centred cubic alkali metals

2008 ◽  
Vol 86 (6) ◽  
pp. 801-805 ◽  
Author(s):  
Y Xie ◽  
J -M Zhang
Keyword(s):  
Cohesive Energy ◽  
Atomistic Simulation ◽  
Alkali Metals ◽  
Phonon Frequency ◽  
Phonon Dispersion ◽  
Atomistic Simulations ◽  
Phonon Dispersion Curves ◽  
Embedded Atom ◽  
Atomic Force ◽  
Good Agreement

Atomistic simulations of phonon dispersion for body-centred cubic alkali metals were carried out using the modified analytic embedded atom potentials. The expressions for atomic force constants are derived, the cohesive energy and elastic constants are calculated, and the phonon dispersion curves of Li, Na, K, Rb, and Cs are calculated along five principal symmetry directions. The calculated results are in good agreement with the available experiments. For all of the five alkali metals, in the same direction, a similar phonon dispersion curve is obtained in spite of the successive phonon frequency decreases for Li, Na, K, Rb, and Cs, which may be related to the atom mass increases or the cohesive energy decreases. PACS Nos.: 63.20.Dj, 71.20.Dg, 31.15.Ct

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.

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.

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.

scholarly journals The Description of Heat Capacity by the Debye – Mayer – Kelly Hybrid Model

2020 ◽  
Author(s):  
Valery P. Vasiliev ◽  
Alex F. Taldrik
Keyword(s):  
Heat Capacity ◽  
Hybrid Model ◽  
Heat Capacities ◽  
Model Description ◽  
Experimental Uncertainty ◽  
Pure Silicon ◽  
Experimental Values ◽  
First Time ◽  
Similarity Method ◽  
Good Agreement

The universal Debye – Mayer – Kelly hybrid model was proposed for the description of the heat capacity from 0 K to the melting points of substance within the experimental uncertainty for the first time. To describe the heat capacity, the in-house software on the base of commercial one DELPHI-7 was used with a 95% confidence level. To demonstrate the perfect suitability of this model, a thermodynamic analysis of the heat capacities of the fourth group elements, and some compounds of the AIIIBV and AIIBVI phases was carried out. It produced good agreement within the experimental uncertainty. There is no a similar model description in literature.The Similarity Method is a convenient and effective tool for critical analysis of the heat capacities of isostructural phases, which was used as an example for diamond-like compounds. Phases with the same sum of the atomic numbers of elements (Z), such as diamond and B0.5 N0.5 (cub) (Z = 6); pure silicon (Si) and Al0.5 P0.5 (Z=14); pure germanium (Ge) and Ga0.5 As0.5 (Z = 32)); pure grey tin (alpha-Sn) and In0.5 Sb0.5, and Cd0.5 Te0.5 (Z = 50) have the same heat capacity experimental values in the solid state. The proposed models can be used to both different binary and multicomponent phases. It helps to standardize the physicochemical constants.

Calculation of Phonon Dispersion for 3d Transition Metals Cr and Fe by Modified Analytic Embedded Atom Method

2011 ◽  
Vol 411 ◽  
pp. 532-536
Author(s):  
You Xie ◽  
Jian Min Zhang
Keyword(s):  
Experimental Data ◽  
Transition Metals ◽  
Phonon Frequency ◽  
Phonon Dispersion ◽  
Phonon Dispersion Curve ◽  
Embedded Atom Method ◽  
Body Centered Cubic ◽  
Phonon Dispersion Curves ◽  
Embedded Atom ◽  
Good Agreement

The modified analytical embedded atom method is applied to calculate the phonon dispersion of body-centered cubic 3d transition metals Cr and Fe along five symmetry directions [q 0 0], [1 q q], [q q q], [q q 0] and [1/2 1/2 q]. Our results of phonon dispersion curves are in good agreement with the available experimental data. For the two transition metals Cr and Fe, along the same direction, a similar phonon dispersion curve is obtained in spite of the phonon frequency decreases for Cr and Fe due to the atom mass increases. There are no experimental results for comparison along the directions [1 q q] and [1/2 1/2 q], further experimental measurement are needed.

Anharmonic perturbation theory to 0(λ4): Equation of state for Kr from the Aziz potential

1992 ◽  
Vol 70 (1) ◽  
pp. 31-39 ◽  
Author(s):  
Ramesh C. Shukla ◽  
Hermann Hübschle
Keyword(s):  
Perturbation Theory ◽  
Thermodynamic Properties ◽  
Potential Function ◽  
Phonon Dispersion ◽  
Perturbation Expansion ◽  
Lattice Parameter ◽  
Thermodynamic Quantities ◽  
Specific Heats ◽  
Experimental Values ◽  
Good Agreement

We carry out a complete calculation of the thermodynamic properties of Kr from a potential function, the Aziz potential, including the three-body Axilrod–Teller contribution, and the (λ4) anharmonic perturbation theory proposed by Shukla and Cowley (Phys. Rev. B: Solid State, 3, 4055 (1971)), where λ is the Van Hove ordering parameter. Along with the λ4 results, in the high-temperature (HT) limit (T > θD, where θD is the Debye temperature), we also present the results for the quasi-harmonic (QH) theory (calculated for all temperatures), the lowest order (λ2) perturbation theory (PT), as well as results from those theories that involve a subset of diagrams (contributions) of 0(λ4), both in the HT limit. This work represents the first calculation of the thermodynamic properties of Kr with the λ2 and λ4 anharmonic PT from a potential function not fitted to the crystal data. The Aziz potential gives an excellent description of phonon-dispersion curves in the three principal symmetry directions. The QH results are in good agreement with the experimental values for most of the thermodynamic quantities for temperatures up to <Tm/3 (Tm is the melting temperature) except for the isothermal bulk modulus (BT) where the agreement is poor in 0 K < T < 25 K and good up to 2Tm/3. The λ2 PT results are only slightly better than the corresponding QH results in the temperature range of < Tm/2. The inclusion of the λ4 PT enhances the results for the Aziz potential significantly. The calculated lattice parameter (a0) is in excellent agreement with experimental values up to 3Tm/4. For T > 3Tm/4, a0 rises rapidly and there is an indication of the breakdown of the perturbation expansion. The values for specific heats at constant volume (Cv) and constant pressure (Cp) and volume expansion (β) are in very good agreement with experiment up to 60% of Tm. The other schemes (with the exception of Ladder) that utilize a subset of diagrams of 0(λ4), which were so successful for the model of a Lennard–Jones solid (viz., ISC (improved self-consistent), λ4-Ladder etc.), are not so useful for this potential. This is due to the heavy cancellation of diagrams in these sets. The ring diagram scheme proposed here for the Aziz potential gives better results than the ISC scheme.

Non-pair forces and lattice dynamical properties of hexagonal close-packed lattice

1978 ◽  
Vol 56 (1) ◽  
pp. 63-67 ◽  
Author(s):  
S. K. Mishra ◽  
S. S. Kushwaha
Keyword(s):  
Specific Heat ◽  
Phonon Dispersion ◽  
Axial Ratio ◽  
Experimental Results ◽  
Hexagonal Close Packed ◽  
Dynamical Properties ◽  
Hcp Structure ◽  
Good Agreement ◽  
Phonon Dispersion Relations ◽  
The Ideal

Cadmium is a highly anisotropic hcp metal like zinc. It has an axial ratio (c/a = 1.8855) that is much higher than the ideal axial ratio for the hcp structure. The successful study of the lattice dynamical properties of Zn and Tl by the modified Cheveau model has created an interest in studying the phonon dispersion relations and specific heat of cadmium. The computed results are in reasonably good agreement with the experimental results.

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