Dispersion relations and lattice thermal expansion of dysprosium

The lattice dynamics, second and third order elastic constants and the lattice thermal expansion of dysprosium have been calculated using Keating's approach. The ten third order elastic constants are calculated using four anharmonic parameters. The present model reproduces the measured pressure derivatives of the second order elastic constants of dysprosium well. The low and high temperature limits γ?_I and γ?_H of the lattice thermal expansion are evaluated and the agreement between the calculated γ?_H and that obtained from the thermal expansion and specific heat data is satisfactory.     

Lattice dynamics,third order elastic constants and thermal expansion of rhenium

A systematic investigation of the lattice dynamics, second and third order elastic constants and thermal expansion has been carried out in rhenium using Keating's approach. The ten third-order elastic constants of rhenium are calculated using four anharmonic parameters. The present model reproduces the measured pressure derivatives of the second order elastic constants well. The low and high temperature limits γ̄L and γ̄H of the lattice thermal expansion are calculated. The agreement between the calculated γ̄H and that obtained by Gschneidner from the thermal expansion and specific heat data of rhenium is satisfactory.     

Lattice dynamics,third order elastic constants and thermal expansion of Cadmium

The lattice dynamics, second and third order elastic constants, pressure derivatives of the second order elastic constants and the temperature variation of the lattice thermal expansion of Cadmium have been worked out utilising Keating's approach. The ten TOE constants are calculated using four anharmonic parameters. The model used here reproduces the measured pressure derivatives of the SOE constants of Cadmium extremely well. The low temperature limit of the volume Gruneisen function γ_L is found to be nearer to the value of Andres. The high temperature limit γ_v(T) is in good agreement with the value calculated by Gschneidner Jr. from the Cv data for Cadmium. The lattice dynamics of Cadmium is found to be essentially similar to that of Zinc.     

Third order elastic constants and thermal expansion of terbium

The third-order elastic constants and the temperature variation of the effective Grüneisen functions of terbium have been calculated on the basis of Keating's method. The pressure derivatives of the second order elastic constants of terbium have been obtained by interpolation of the experimental pressure derivatives of gadolinium and dysprosium. The ten third order elastic constants of terbium are calculated using four third order anharmonic parameters obtained from its interpolated pressure derivatives. The low and high temperature limits $\text{λ}{}_{\mathrm{L}}$ and $\text{λ}{}_{\mathrm{H}}$ of the lattice thermal expansion are evaluated. The agreement between the calculated $\text{λ}{}_{\mathrm{H}}$ and that obtained from thermal expansion and specific heat data of terbium is good.     

Grüneisen parameter and thermal expansion of V3Si and V3Ge

The Grüneisen parameter and lattice thermal expansion of the A-15 compounds V₃Si and V₃Ge at room temperature are evaluated on the basis of the method due to Brugger and Fritz [1] from the third order elastic constants reported earlier [2]. The calculated values are compared with available experimental values and are found to fit satisfactorily.     

Lattice dynamics,third order elastic constants and low temperature lattice thermal expansion of zirconium

The lattice dynamics and the anharmonic properties of the hexagonal Zirconium are worked out using Keating's approach. The dispersion curves are fitted using twelve second order parameters and the six second order elastic constants are evaluated. The ten third order elastic constants are calculated using five third order parameters. The experimental measurements on the pressure derivatives of the second order elastic constants in Zirconium are in good agreement with the calculated values. The low-temperature limit of the lattice thermal expansion is calculated which agrees well with the value obtained from thermal expansion data. The variation of the generalised GPs of the elastic modes with the direction of propagation is illustrated by polar diagram.     

用赝势方法计算简单金属的弹性常数

本文利用单参数Heine-Abarenkov模型势及Hubbard-Sham介电函数计算了七种简单金属(Li,Na,K,Rb,Cs,Al和Pb)的二阶与三阶弹性常数,两个可调参数用零温零压下晶体的弹性常数C₄₄与晶格常数的实验值来确定,计算结果与实验值或其他作者的理论计算值符合得比较好,尤其是Al的三阶弹性常数,本文的计算结果比其他作者的计算结果更接近于实验值。 关键词：     

Ab-initio study of electronic and elastic properties of B2-type ductile YM (M=Cu, Zn and Ag) intermetallics

A theoretical study of structural, electronic, elastic, thermal and mechanical properties of nonmagnetic intermetallics YM (M=Cu, Zn and Ag), which crystallize in CsCl-type structure, is performed using first principles density functional theory based on full potential linearized augmented plane wave (FP-LAPW) method. The calculations are carried out within the generalized gradient approximation (GGA) for the exchange correlation potential. The calculated ground state properties such as lattice constants, bulk modulus and elastic constants agree well with the experiment. From energy dispersion curves, it is found that these compounds are metallic in nature. The ductility of these intermetallics is determined by calculating the bulk to shear ratio B/G_H. The calculated results indicate that YAg is the most ductile amongst the present YM compounds. The results obtained are compared with the available experimental and theoretical results. The mechanical and thermal properties are predicted from the calculated values of elastic constants.     

Insight into structural,mechanical, electronic and thermodynamic properties of intermetallic phases in Zr–Sn system from first-principles calculations

The structural, phase stabilities, mechanical, electronic and thermodynamic properties of intermetallic phases in Zr–Sn system are investigated by using first-principles method. The equilibrium lattice constants, enthalpy of formation (ΔH^form) and elastic constants are obtained and compared with available experimental and theoretical data. The configuration of Zr₄Sn is measured with reasonable precision. The ΔH^form of five hypothetical structures are obtained in order to find possible metastable phase for Zr–Sn system. The mechanical properties, including bulk modulus, shear modulus, Young's modulus and Poisson's ratio, are calculated by Voigt–Reuss–Hill approximation and the Zr₅Sn₄ and Zr₅Sn₃ show excellent mechanical properties. The electronic density of states for Zr₅Sn₄, Zr₅Sn₃ and cP8-Zr₃Sn are calculated to further investigate the stability of intermetallic compounds. Through the quasi-harmonic Debye model, the Debye temperature, heat capacity and thermal expansion coefficient under temperature of 0–300 K and pressure of 0–50 GPa for Zr₅Sn₃ and Zr₅Sn₄ are deeply investigated.     

Elasticity of a magnetic lattice near the magnetic critical point

The isothermal elastic constants and the coefficient of anomalous thermal expansion of a magnetic lattice are discussed. The spin system is described by the Ising model with an exchange coupling depending on lattice spacing. A behavior of the elastic constants and the coefficient of thermal expansion is found which is in qualitative agreement with experiments. The isothermal compressibility remains positive nearT _c and no thermo-mechanical instability occurs (which would lead to a first-order phase transitions), in contrast to earlier theories.     

Ab initio calculations of elastic constants and thermodynamic properties of Li2O for high temperatures and pressures

The elastic constants and thermodynamic properties of Li₂O for high temperatures and pressures are calculated by the ab initio unrestricted Hartree-Fock (HF) linear combination of atomic orbital (LCAO) periodic approach. The lattice constant, elastic constants, Debye temperature, and thermal expansion coefficient obtained are in good agreement with the available experimental data and other theoretical results. It is found that at zero pressure the elastic constants C₁₁, C₁₂ and C₄₄, bulk modulus B and Debye temperature Θ_D decrease monotonically over the wide range of temperatures from 0 to 1100 K. When the temperature , C₁₂ approaches zero, consistently with the transition temperature 1200 K. However, with increasing pressure, they all increase monotonically and the anisotropy will weaken.     

高温高压下Zr2AlC的结构及热学性质的第一性原理

利用密度泛函理论研究了高温高压下Zr₂AlC的结构和热力学性质,计算得到Zr₂AlC的晶格参数与实验值符合较好．研究了Zr₂AlC的弹性常数、体模量、剪切模量和杨氏模量等力学性质随压力变化的趋势．同时研究了维氏硬度随压力的变化趋势．通过计算得到的杨氏模量预测了Zr₂AlC的弹性各向异性．最后,基于准简谐德拜模型,成功预测了Zr₂AlC的德拜温度、热容、热膨胀系数和Grüneisen参数随着压强和温度的变化关系.     

Structural,mechanical and thermal properties of some Holmium Pnictides under pressure: A theoretical approach

The high pressure structural, elastic and thermal properties of holmium pnictides HoX (X=N, P, As and Bi) were investigated theoretically by using an inter-ionic potential theory with modified ionic charge parameter. We have predicted a structural phase transition from NaCl (B₁) to CsCl (B₂)-type structure at pressure of 139 GPa for HoN, 52 GPa for HoP, 44 GPa for HoAs and 26 GPa for HoBi. Other properties, such as lattice constant, bulk modulus, cohesive energy, second and third-order elastic constants were calculated and compared with the available experimental and theoretical data. In order to gain further information the brittle behaviour of these compounds was observed. Some other properties like Shear modulus (G), Young's modulus (E), Poisson's ratio (ν), anisotropy factor (A), sound velocities, Debye temperature (θ_D) were calculated. The variation of elastic constants (C₁₁ and C₄₄) and Debye temperature (θ_D) with pressure was also presented.     

Cu_3N弹性和热力学性质的第一性原理研究

利用基于密度泛函理论的第一性原理全势线性缀加平面波方法,研究了立方反ReO3结构Cu3N在零温(0K)零压下的平衡晶格常数、体弹模量及其对压强的一阶导数,计算结果与其他实验及理论结果基本相符.同时得出Cu3N的弹性常数,Poisson比等,并分析出Cu3N在零温零压下是稳定的.通过准谐Debye模型计算Cu3N的热力学性质,得到了Cu3N的晶格常数、等压比热容、等容比热容、热胀系数与温度和压强之间的关系,同时计算出不同温度不同压强下其体弹模量及Debye温度的值。     

Elastic and thermodynamic properties of CaB6 under pressure from first principles

The elastic and thermodynamic properties of CsCl-type structure CaB₆ under high pressure are investigated by first-principles calculations based on plane-wave pseudopotential density functional theory method within the generalized gradient approximation (GGA). The calculated lattice parameters of CaB₆ under zero pressure and zero temperature are in good agreement with the existing experimental data and other theoretical data. The pressure dependences of the elastic constants, bulk modulus B (GPa), and its pressure derivative B′, shear modulus G, Young's modulus E, elastic Debye temperature Θ_B, Zener's anisotropy parameter A, Poisson ratios σ, and Kleinmann parameter ζ are also presented. An analysis for the calculated elastic constants has been made to reveal the mechanical stability of CaB₆ up to 100 GPa. The thermodynamic properties of the CsCl-type structure CaB₆ are predicted using the quasi-harmonic Debye model. The pressure-volume-temperature (P-V-T) relationship, the variations of the heat capacity C_V, Debye temperature Θ_D, and the thermal expansion α with pressure P and temperature T, as well as the Grüneisen parameters γ are obtained systematically in the ranges of 0-100 GPa and 0-2000 K.     

Theoretical study of the structural, elastic, electronic and thermal properties of the MAX phase Nb2SiC

Structural, elastic, electronic and thermal properties of the MAX phase Nb₂SiC are studied by means of a pseudo-potential plane-wave method based on the density functional theory. The optimized zero pressure geometrical parameters are in good agreement with the available theoretical data. The effect of high pressure, up to 40 GPa, on the lattice constants shows that the contractions along the c-axis were higher than those along the a-axis. The elastic constants C_ij and elastic wave velocities are calculated for monocrystal Nb₂SiC. Numerical estimations of the bulk modulus, shear modulus, Young’s modulus, Poisson’s ratio, average sound velocity and Debye temperature for ideal polycrystalline Nb₂SiC aggregates are performed in the framework of the Voigt-Reuss-Hill approximation. The band structure shows that Nb₂SiC is an electrical conductor. The analysis of the atomic site projected densities and the charge density distribution shows that the bonding is of covalent-ionic nature with the presence of metallic character. The density of states at Fermi level is dictated by the niobium d states; Si element has a little effect. Thermal effects on some macroscopic properties of Nb₂SiC are predicted using the quasi-harmonic Debye model, in which the lattice vibrations are taken into account. The variations of the primitive cell volume, volume expansion coefficient, bulk modulus, heat capacity and Debye temperature with pressure and temperature in the ranges of 0-40 GPa and 0-2000 K are obtained successfully.     

Structural,elastic, electronic,optical and thermal properties of c-SiGe<Subscript>2</Subscript>N<Subscript>4</Subscript>

We have investigated the structural, elastic, electronic, optical and thermal properties of c-SiGe₂N₄ by using the ultrasoft pseudopotential density functional method within the generalized gradient approximation. The calculated structural parameters, including the lattice constant, the internal free parameter, the bulk modulus and its pressure derivative are in agreement with the available data. The independent elastic constants and their pressure dependence, calculated using the static finite strain technique, satisfy the requirement of mechanical stability, indicating that c-SiGe₂N₄ compound could be stable. We derive the shear modulus, Young’s modulus, Poisson’s ratio and Lamé’s coefficients for ideal polycrystalline c-SiGe₂N₄ aggregate in the framework of the Voigt-Reuss-Hill approximation. We estimate the Debye temperature of this compound from the average sound velocity. Band structure, density of states, Mulliken charge populations and pressure coefficients of energy band gaps are investigated. Furthermore, in order to understand the optical properties of c-SiGe₂N₄, the dielectric function, refractive index, extinction coefficient, optical reflectivity and electron energy loss are calculated for radiation up to 40 eV. Thermal effects on some macroscopic properties of c-SiGe₂N₄ are predicted using the quasi-harmonic Debye model in which the lattice vibrations are taken into account. We have obtained successfully the variations of the primitive cell volume, volume expansion coefficient, heat capacities and Debye temperature with pressure and temperature in the ranges of 0–40 GPa and 0–2000 K. For the first time, the numerical estimates of the elastic constants and related parameters, and the thermal properties are performed for c-SiGe₂N₄.     

First principles lattice dynamical study of the cubic antiperovskite compounds AsNBa3 and SbNBa3

An ab initio pseudopotential plane wave method using linear response approach has been employed to study the lattice dynamics of two cubic antiperovskites AsNBa₃ and SbNBa₃. The bulk properties, elastic constants, phonon dispersion curves, phonon density of states and temperature dependent thermodynamic quantities of both antiperovskites are obtained. The calculated lattice constants, elastic and bulk properties are compared with the available theoretical data. This is the first systematic and quantitative prediction of phonon and thermodynamical properties of these antiperovskite compounds.     

Analysis of anharmonic and thermoelastic properties of non-centrosymmetric crystals

In the present paper an analytical potential form is used for overlap repulsive energy, derived by Harrison from quantum mechanical considerations, along with the composite effect of three-body forces and intersublattice displacement. The short-range overlap parameters in Harrison's potential form have direct correlation with the valence state energies for outermost electrons. The potential model is applied to calculate the third and fourth order elastic constants, first and second pressure derivatives of second order elastic constants, Grüneisen parameter and its volume dependence, Anderson parameter, and thermal expansion coefficient for three non-centrosymmetric crystals, viz. CaF₂, SrF₂ and BaF₂. The calculated values of various physical quantities are found to be in good agreement with experimental data.The authors are grateful to Dr. Mansour Khalef, the Head of Physics Department, TNRC, Tajura (Tripoli) for the facilities and encouragements.     

Structural and thermodynamic properties of the cubic perovskite BiAlO3

The structural and elastic properties of the cubic perovskite-type BiAlO₃ are studied using the pseudopotential plane wave method within the local density approximation. The calculated structural parameters are in good agreement with previous calculations. The elastic constants are calculated using the static finite strain technique. Thermal effects on some macroscopic properties of BiAlO₃ are predicted using the quasi-harmonic Debye model, in which the lattice vibrations are taken in account. We have obtained successfully the variations of the lattice constant, volume expansion coefficient, heat capacities and Debye temperature with pressure and temperature in the ranges of 0-30 GPa and 0-1000 K.