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.

Mechanical and thermodynamic properties of AlX (X = N, P, As) compounds

2017 ◽  
Vol 31 (23) ◽  
pp. 1750167 ◽  
Author(s):  
Lifang Xu ◽  
Wei Bu
Keyword(s):  
Thermodynamic Properties ◽  
Specific Heat ◽  
Atomic Number ◽  
Phonon Dispersion ◽  
Theoretical Data ◽  
Constant Volume ◽  
Vibrational Entropy ◽  
Debye Temperatures ◽  
The Difference ◽  
Good Agreement

The Vickers hardness of various AlX (X = N, P, As) compound polymorphs were calculated with the bond resistance model. Thermodynamic properties, such as vibrational entropy, constant volume specific heat and Debye temperatures, were calculated using phonon dispersion relations and phonon density of states (DOS). The calculated values are in good agreement with the previous experimental and theoretical data. For the same structure of AlX (X = N, P, As) compounds, their hardness and Debye temperatures both decrease with the X atomic number. The wurtzite (wz) and zincblende (zb) structures of the same compounds AlX share an almost identical hardness, but have different Debye temperatures. The difference between wz and zb structures increases as the atomic number of X increases. The thermodynamic properties reveal that the constant volume specific heat approaches the Dulong–Petit rule at high temperatures.

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.

Application of Statistical Moment Method to Thermodynamic Properties and Phase Transformations of Metals and Alloys

2008 ◽  
Vol 138 ◽  
pp. 209-240 ◽  
Author(s):  
K. Masuda-Jindo ◽  
Vu Van Hung ◽  
P.E.A. Turchi
Keyword(s):  
Thermodynamic Properties ◽  
Phase Transformations ◽  
Moment Method ◽  
Structural Phase ◽  
Equilibrium Phase ◽  
Statistical Moment ◽  
Metals And Alloys ◽  
Thermodynamic Quantities ◽  
Specific Heats ◽  
Statistical Moment Method

The thermodynamic properties and phase transformations of metals and alloys are studied using the statistical moment method, going beyond the quasi-harmonic approximations. Including the power moments of the atomic displacements up to the fourth order, the Helmholtz free energies and the related thermodynamic quantities are derived explicitly in closed analytic forms. The thermodynamic quantities, like thermal lattice expansion coefficients, specific heats, Grüneisen constants, elastic constants calculated by using the SMM are compared with those of other theoretical schemes and the experimental results. The hcp-bcc structural phase transformations observed for IVB elements, Ti, Zr and Hf, are discussed in terms of the anharmonicity of thermal lattice vibrations. The equilibrium phase diagrams are calculated for the refractory Ta-W and Mo-Ta bcc alloys. In addition, the temperature dependence of the elastic moduli C11, C12 and C14 and those of the ideal tensile and shear strengths of the bcc elements Mo, Ta and W are studied: We also discuss the melting transitions of metals and alloys within the framework of the SMM and estimate the melting temperatures through the limiting temperature of the crystalline stability.

scholarly journals FP-LAPW investigation of mechanical and thermodynamic properties of Na2X (X = S and Se) under pressure and temperature effects

2015 ◽  
Vol 33 (3) ◽  
pp. 649-659 ◽  
Author(s):  
Kada Bidai ◽  
Mohammed Ameri ◽  
Djillali Bensaid ◽  
Nour-Eddine Moulay ◽  
Y. Al-Douri ◽  
...  
Keyword(s):  
High Pressure ◽  
Thermal Expansion ◽  
Thermodynamic Properties ◽  
Elastic Constants ◽  
Ground State ◽  
Temperature Effects ◽  
Lattice Parameter ◽  
High Pressure And Temperature ◽  
Pressure And Temperature Effects ◽  
Good Agreement

Abstract Structural, elastic and thermodynamic properties of sodium chalcogenides (Na2X, X = S, Se) have been calculated using FP-APW+1o method. The ground state lattice parameter, bulk moduli have been obtained. The Zener anisotropy factor, Poisson’s ratio, shear modulus, Young’s modulus, have also been calculated. The calculated structural and elastic constants are in good agreement with the available data. We also determined the thermodynamic properties, such as heat capacities CV and CP, thermal expansion α , entropy S, and Debye temperature θD, at various pressures and temperatures for Na2X compounds. The elastic constants under high pressure and temperature are also calculated and elaborated.

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 first-principles studies on TlX (X=P, As)

Open Physics ◽  
2008 ◽  
Vol 6 (4) ◽  
Author(s):  
Yasemin Ciftci ◽  
Kemal Colakoglu ◽  
Engin Deligoz
Keyword(s):  
Thermodynamic Properties ◽  
Ab Initio ◽  
Density Functional ◽  
Lattice Parameter ◽  
Functional Theory ◽  
Zinc Blende ◽  
The Density Functional Theory ◽  
Pseudopotential Approach ◽  
Theoretical Results ◽  
Good Agreement

AbstractWe present an ab initio study of the structural, electronic and thermodynamic properties of TlX(X=P,As). The plane-wave pseudopotential approach to the density-functional theory within the LDA and GGA approximations implemented in VASP (Viena Ab-initio Simulation Package) is used. The calculated lattice parameter, elastic constants, and band structures are compared with other available theoretical results, and good agreement is obtained. In addition, we have calculated the transition pressure (P t) from zinc-blende (ZB) to (rock-salt) NaCl structures, and have examined some thermodynamic properties.

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 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.

The Percus–Yevick approximation near the triple point of argon

1969 ◽  
Vol 47 (23) ◽  
pp. 2709-2713 ◽  
Author(s):  
R. O. Watts
Keyword(s):  
Distribution Function ◽  
Perturbation Theory ◽  
Thermodynamic Properties ◽  
Radial Distribution Function ◽  
Radial Distribution ◽  
Triple Point ◽  
Triple Point Of Argon ◽  
Experimental Values

The radial distribution function and thermodynamic properties of argon are calculated using the (12, 6) potential and the Percus–Yevick approximation. The results are compared with experimental values for argon, the machine calculations of Verlet and of McDonald and Singer, and with the perturbation theory of Barker and Henderson.

The structural, electronic, elastic and thermodynamic properties of V2AX (A = B, Al, Ga, In and TI; X = C and N): A DFT calculation

2019 ◽  
Vol 33 (30) ◽  
pp. 1950359
Author(s):  
Chunying Zuo ◽  
Baishu Chen ◽  
Cheng Zhong ◽  
Jianhua Zhao
Keyword(s):  
Thermodynamic Properties ◽  
Shear Modulus ◽  
Mechanical Stability ◽  
Phonon Dispersion ◽  
Shape Change ◽  
Theoretical Data ◽  
Total Density ◽  
Barrier Coating ◽  
Machinability Index ◽  
Experimental Values

The structural, electronic, elastic and thermodynamic properties of [Formula: see text] ([Formula: see text], Al, Ga, In and TI; [Formula: see text] and N) phase have been systematically investigated by the first principles. The optimized lattice parameters are in good agreement with the experimental values and better than the available theoretical data. We calculated the elastic constants [Formula: see text] and the total density of states, which verified mechanical stability and electronic structural stability, respectively. The other elastic parameters including bulk modulus, shear modulus, Young’s modulus, Cauchy pressure, shear anisotropy factor, linear compressibility coefficients, Pugh’s ratio, Poissons’s ratio, microhardness parameter and machinability index are calculated and discussed in this work. The results show that the compounds we studied are stable in mechanics and are anisotropic materials; the compressibility along [Formula: see text]-axis is lower than that along [Formula: see text]-direction except for [Formula: see text] ([Formula: see text] and N); the compounds of [Formula: see text] ([Formula: see text]) and [Formula: see text] ([Formula: see text]) are brittle in nature, and [Formula: see text] and V2TIN are ductile in nature; the shear modulus [Formula: see text] limits the mechanical stability of the materials under consideration; the ability to resist shape change and the stiffness of [Formula: see text] are stronger compared with [Formula: see text] when A takes B, Al, Ga, In, TI, respectively. Finally we have estimated the Vickers hardness which shows that the hardness of the [Formula: see text] ([Formula: see text], Al, Ga, In, TI) would decrease when C is replaced by N. At last, we investigated the thermodynamic properties of [Formula: see text] by calculating the phonon dispersion, Debye temperature and minimum thermal conductivity. The results show that all structures are dynamical stable and the compounds of [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] are candidates for thermal barrier coating (TBC) materials.

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