Third-order elastic constants of ZnS and ZnSe

The complete set of non-vanishing third-order elastic constants of the semiconductors ZnS and ZnSe is obtained theoretically. The strain energy density is estimated using finite strain elasticity theory by considering the interactions up to two nearest neighbours of each atom in the unit cell of these compounds. This energy density is compared with the strain dependent lattice energy density from the continuum model approximation. The second-order parameter of the potential function φ is obtained from the measured principal axis C_ij. The third-order potential parameter is estimated by assuming a Lennard-Jones type of interatomic potential. The interlattice displacements as well as the second-order elastic constants are evaluated along with the six third-order elastic constants of ZnS and ZnSe. Using these second- and third-order elastic constants of ZnS, the pressure derivatives of second-order elastic constants are evaluated. The second- and third-order elastic constants of ZnSe are compared with the available experimental values. The third-order elastic constants show anisotropy in different directions.     

Second order elastic anomalies in barium titanate from cubic to tetragonal phase transition

The anomalies of the second order elastic constants have been derived for barium titanate for the phase transition from cubic to tetragonal. The equilibrium values of the components of the order parameter and the strain variables have been obtained from the stability conditions. The fluctuations in the order parameter have been derived from the Landau-Khalatnikov equations. Expression for the shift in the zero point energy in the tetragonal phase is obtained and is shown to be proportional to (T −T _c)². The anomalies for all the second order elastic constants have been derived and relations among them reported. It is shown that the second order elastic anomalies suffer a discontinuity at the transition temperature.     

Ordering induced transformation from high-entropy to Heusler CrVTiAl alloy

The equimolar quaternary CrVTiAl is not only a potential spin filter, but also a light-weight high entropy alloy. The excellent performance strongly depends on the order degree. We use the ab initio calculation to investigate the structural, magnetic, elastic properties of CrVTiAl as a function of the order degree describing phase from full disorder A2 to DO₃, B2, and L2₁ to full order Y-type (LiMgPdSn-type) structure. The Cr-Al bonding plays a key role in the local magnetic moments, further induces the increasing lattice parameter and decreasing elastic constants. Furthermore, the effect of preferred sites on mechanical properties is discussed.     

Pressure-induced structural phase transition and elastic properties of rare earth Pr chalcogenides and pnictides

Pressure-induced structural aspects and elastic properties of NaCl-type (B1) to CsCl-type (B2) structure in praseodymium chalcogenides and pnictides are presented. Ground-state properties are numerically computed by considering long-range Coulomb interactions, Hafemeister and Flygare type short-range overlap repulsion, and van der Waals interaction in the interionic potential. From the elastic constants, Poisson's ratio ν, the ratio R_G/B of G (shear modulus) over B (bulk modulus), anisotropy parameter, shear and Young's moduli, Lamé's constant, Kleinman parameter, elastic wave velocity and thermodynamical property such as Debye temperature are calculated. Poisson's ratio ν and the ratio R_G/B indicate that PrX and PrY are brittle in B1 phase and ductile in B2 phase. To our knowledge, this is the first quantitative theoretical prediction of the ductile (brittle) nature of praseodymium chalcogenides and pnictides and still awaits experimental confirmation.     

Equation of state and elastic stiffness constants under pressure of noble metals

Using the total crystal energy expression with the overlap potential energy by Moriarty and with the model pseudopotential by Kulshrestha et al., the pressure-volume relations of noble metals are studied and the obtained results are in good agreement with the observed data. Then, the elastic stiffness constants B, C₄₄ and C′ under pressure are obtained by the homogeneous deformation method, and our calculated data will be useful to describe the typical pressure effect on the elastic constants of noble metals.     

BaTiO3晶体结构及弹性的分子动力学模拟

有效的势函数是分子动力学模拟的关键. 引入了一种势函数,该势函数的特点是运用参数r_eff计算原子间的静电作用. 通过分子动力学方法模拟得到了BaTiO₃晶体立方相、四方相结构的对关联函数和X射线衍射谱,计算得出了它们的晶格常数及弹性常数. 模拟结果与实验结果符合较好.该势函数可以有效地模拟BaTiO₃晶体的热学和力学性能. 关键词： 分子动力学模拟 势函数 3铁电晶体')" href="#">BaTiO₃铁电晶体     

Elastic behaviour under pressure of the cluster compound (Ag6Ge4P12)Ge6

The elastic stiffness constants of the cluster compound (Ag₆Ge₄P₁₂)Ge₆ have been measured by the ultrasonic pulse-echo overlap technique and are found to conform quite closely with those of zincblende structure compounds. The hydrostatic pressure dependences of the elastic constants and also the third-order elastic constants have been measured. It is found that, unlike the zincblende structure compounds, this compound does not show any tendency towards shear mode softening under pressure, all the long wavelength acoustic mode Grüneisen gammas being positive.     

Second order elastic anomalies in barium titanate from orthorhombic to rhombohedral phase transition

The anomalies in second order elastic constants have been derived for barium titanate for the phase transition from orthorhombic to rhombohedral state. The equilibrium values of order parameter, strain variables and fluctuations in order parameter have been derived using stability conditions and Landau-Khalatnikov equations respectively. Expression for shift in specific heat is obtained. All the anomalies in second order elastic constants have been derived and relations among them reported. The numerical values of anomalies in the individual constants are calculated and their variation is represented graphically. Changes in elastic constants occur over a range of temperature of the order 10⁻²K.     

A study of π states of H2 + in the one centre approach

The statistical theory of the elastic constants of nematic liquid crystals is applied to detailed calculations based on well-defined approximations for the direct correlation function of Ornstein and Zernike and for the singlet orientational distribution. The model of hard spherocylinders with superimposed r ^-6 attraction modulated by a Maier-Saupe P ₂(cos ?_{1 2}) term, is used. The dependence on temperature, on the order parameter and on the length to breadth ratio, of the reduced elastic constants K* _i (i=1, 2, 3), is discussed in some detail and comparison with experiment is included.     

Third order elastic constants of V3Si and V3Ge

General expressions have been derived for the second order elastic constants and third order elastic constants of the A-15 structure compounds with the nearest neighbour central interaction. The second order elastic constants, the third order elastic constants and the pressure derivatives of the second order elastic constants of V₃Si and V₃Ge are reported and compared with the available experimental measurements.     

Third-order elastic constants and pressure derivatives of the second-order elastic constants of β-tin

The second- and third-order elastic constants and pressure derivatives of second-order elastic constants of tetragonal β-tin have been obtained using the deformation theory. The strain energy density derived using the deformation theory is compared with the strain dependent lattice energy obtained from the elastic continuum model approximation to get the expressions for the second- and third-order elastic constants. Higher order elastic constants are a measure of the anharmonicity of a crystal lattice. The 12 non-vanishing third-order elastic constants and the six pressure derivatives of the second-order elastic constants in tetragonal β-tin are obtained in the present work and are compared with the available experimental values. The second-order elastic constant C₃₃ obtained in the present study is in reasonable agreement with the experimental values. The third-order elastic constants are generally one order of magnitude greater than the second-order elastic constants as expected of a crystalline solid. The third-order elastic constant C₃₃₃ is higher in magnitude than all other values. This shows a greater anharmonicity of β-tin along the c-axis direction of the crystal.     

A model analysis of the elastic constants of metals and alloy phases

A lattice energy function using a Mie inverse power interatomic potential and a quadrupole distortion term was fitted to the cohesive energy, lattice parameter, bulk modulus and C₄₄ of pure metals. Using this function and the fitted parameters, values were then predicted for C₄₄ and other elastic constants of alloy phases. It was found that the maximum discrepancy in C₄₄ for B2, C15, and L1₂ type phases was 40%, with the RMS value equal to 25%.It was found that the predicted nearest-neighbor bond angle dependent elastic constants were always smaller than the observed values. It is believed that this result is due to the formation of eovalent bonds in the alloy phases, a phenomenon that is not included in the model. An empirical procedure for correcting the elastic constants to account for eovalent bonding reduces the maximum discrepancy in both shear constants to less than 20%. Evidence is presented in support of this hypothesis. One of the consequences of this work is that ground state superstructures, of heteroelectronic type alloy components that are deduced on the basis of constancy of pair or many body interactions, need not necessarily correspond to the most stable superstructures.     

Fluctuation corrections at first order phase transitions: Application to C60

The temperature dependence of the elastic constants in C₆₀ is quite unusual in the vicinity of the order-disorder phase transition at 260 K, in sharp contrast to simple mean-field calculations. The observed deviations seem to be a combination of dynamical processes, the influence of defects and fluctuation effects. The latter are expected to be important, since the Landau free energy admits a third order term in the order parameter. We develop field theoretic perturbation theory for general models of this type. The formalism is applied to a simple scalar model of C₆₀ and the resulting temperature dependence of elastic constants is discussed.     

On the third order elastic constants of AgCl-AgBr mixed system

Lowdin's many body effect is accounted to explain the violation of Cauchy's relation (C₁₂=C₄₄) in silver halides. Lundqvists potential model with many body effect has been used to evaluate the third order elastic constants of AgCl and AgBr. A modified Lundqvist potential model is used to calculate the third order elastic constants for the simple AgCl- AgBr mixed system with varying concentration of AgCl and AgBr.     

Elastic properties of the RIV-RIII rotator phases of alkanes

A model free energy has been constructed to describe the R_IV-R_III rotator phase transition in alkanes in terms of the elastic strains and order parameter. The conditions for the R_IV-R_III phase transition are discussed. From the free energy, the order parameter and the elastic strains are determined. The model free energy describes the first or second order character of the R_IV-R_III transition depending on the strength of the coupling. The elastic properties in the vicinity of the R_IV-R_III transition are discussed on the basis of a free energy expansion. The temperature dependence of the elastic constants is calculated on both sides of the transition. The coupling between the order parameter and elastic stains is shown to have a crucial influence on the phase behavior and the order of the transition.     

High pressure effect on structural and mechanical properties of some LnO (Ln=Sm, Eu, Yb) compounds

The structural and mechanical properties of LnO (Ln=Sm, Eu, Yb) compounds have been investigated using a modified interionic potential theory, which includes the effect of Coulomb screening. We predicted a structural phase transition from NaCl (B₁)- to CsCl (B₂)-type structure and elastic properties in LnO compounds at very high pressure. The anomalous properties of these compounds have been correlated in terms of the hybridisation of f-electrons of the rare earth ion with conduction band and strong mixing of f-states of lanthanides with the p-orbital of neighbouring chalcogen ion. For EuO, the calculated transition pressure, bulk modulus and lattice parameter are close to the experimental data. The nature of bonds between the ions is predicted by simulating the ion-ion (Ln-Ln and Ln-O) distances at high pressure. The second order elastic constants along with shear modulus and Young's modulus, elastic anisotropy and Poisson's ratio are also presented for these oxides.     

Elastic constants of mixed ammonium halides

In the present communication a method based on the three body forces for the evaluation of second and third order elastic constants of mixed ammonium halides has been described. The Lundqvist three body potential is used along with long range Coulombian and short-range overlap repulsive potentials. The latter is taken of the Born-Mayer type and effective up to first neighbours only. It has been assumed that the charge transfer and short-range parameters depend linearly on the composition of solid solutions. Theoretical results obtained, for the entire range of compositions of mixed NH₄Cl and NH₄Br, have been compared with the recently measured experimental values and the theoretical results of other workers, whenever these are available.The authors are thankful to Dr. J. Shanker, Department of Physics, Agra University, Agra, for helpful discussions.     

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.     

First-principles study of the structural,elastic, mechanical,electronic, and optical properties of cubic Mg<Subscript>2</Subscript>TiO<Subscript>4</Subscript>

We have performed ab-initio total energy calculations using the plane-wave ultrasoft pseudopotential technique based on the first-principles density-functional theory (DFT) to study structural, elastic, mechanical, electronic, and optical properties of cubic Mg₂TiO₄. The calculated lattice parameter a is in good agreement with the experimental values. The independent elastic constants are calculated. The mechanical properties including bulk, shear and Young’s modulus, Poisson’s coefficient, compressibility and Lamé’s constants are obtained using the Voigt-Reuss-Hill method. Debye temperature is estimated using the Debye-Grüneisen model. Band structure, density of states and charge densities are shown and analyzed. In order to clarify the mechanism of optical transitions of cubic Mg₂TiO₄, the complex dielectric function, refractive index, extinction coefficient, reflectivity, absorption coefficient, loss function and complex conductivity function are calculated.     

Electronic and thermodynamic and elastic properties of pyrite RuO2

This paper calculates the elastic,thermodynamic and electronic properties of pyrite (P a3ˉ) RuO2 by the plane-wave pseudopotential density functional theory (DFT) method.The lattice parameters,normalized elastic constants,Cauchy pressure,brittle–ductile relations,heat capacity and Debye temperature are successfully obtained.The Murnaghan equation of state shows that pyrite RuO2 is a potential superhard material.Internal coordinate parameter increases with pressure,which disagrees with experimental data.An analysis based on electronic structure and the pseudogap reveals that the bonding nature in RuO2 is a combination of covalent,ionic and metallic bonding.A study of the elastic properties indicates that the pyrite phase is isotropic under usual conditions.The relationship between brittleness and ductility shows that pyrite RuO2 behaves in a ductile matter at zero pressure and the degree of ductility increases with pressure.