Phonon Dispersion in Equiatomic Li-Based Binary Alloys

The computations of the phonon dispersion curves （PDC） of four equiatomic Li-based binary alloys, namely Li0.5Na0.5, Li0.5K0.5, Li0.5Rb0.5 and Li0.5Cs0.5, to second order in the local model potential is discussed in terms of the real-space sum of Born von Karman central force constants. Instead of the concentration average of the force constants of metallic Li, Na, K, Rb and Cs, the pseudo-alloy atom （PAA） is adopted to compute directly the force constants of four equiatomic Li-based binary alloys. The exchange and correlation functions due to Hartree （H） and Ichimaru-Utsumi （IU） are used to investigate the influence of screening effects. The phonon frequencies of four equiatomic Li-based binary alloys in the longitudinal branch are more sensitive to the exchange and correlation effects in comparison with the transverse branches. However, the frequencies in the longitudinal branch are suppressed due to IU-screening function than the frequencies due to static H-screening function.     

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.     

Elasticity of single-crystal phase D (a dense hydrous magnesium silicate) by Brillouin spectroscopy

Phase D (MgSi₂O₆H₂) is the only hydrous magnesium silicate, where all Si atoms are octahedrally coordinated. The single-crystal elastic constants of phase D have been measured by Brillouin spectroscopy at ambient conditions. The elastic constants C₁₁, C₃₃, C₄₄, C₁₂, C₁₃ and C₁₄, based on a trigonal unit cell, are 284.4±3.0, 339.4±9.1, 120.7±1.9, 89.4±4.2, 126.6±3.1 and −4.7±1.4 GPa, respectively. The aggregate adiabatic bulk modulus, using the Voigt-Reuss-Hill (VRH) scheme, is 175.3±14.8 GPa and the shear modulus is 104.4±13.6 GPa. These data yield the compressional-wave velocity, V_p=9.70±0.51 km/s, and the shear-wave velocity, V_s=5.59±0.36 km/s, at ambient conditions. Thus, phase D is not only the most closely packed but the least compressible hydrous magnesium silicate known to date.     

Pressure dependence of elastic constants in zinc-blende GaN and InN and their influence on the pressure coefficients of the light emission in cubic InGaN/GaN quantum wells

We have studied the influence of nonlinear elastic effects on the pressure coefficients of light emission, dE_E/dP, in cubic InGaN/GaN quantum wells. By means of ab-initio calculations, we have determined the pressure dependences of the elastic constants, C₁₁, C₁₂ and C₄₄ in zinc-blende InN and GaN. Further, we show that the pressure dependence of the elastic constants results in significant reduction of dE_E/dP in cubic InGaN/GaN quantum wells and essentially improves the agreement between experimental and theoretical values.     

Lattice mechanical properties of alkaline earth metals in bcc and fcc phases

A model pseudopotential depending on an effective core radius treated as a parameter is used for alkaline earth metals in bcc and fcc phases to study the Binding energy, Interatomic interactions, phonon dispersion curves, Phonon density of states, Debye-Waller factor, mean square displacement, Debye-Waller temperature parameters, dynamical elastic constants (C₁₁, C₁₂ and C₄₄), bulk modulus (B), shear modulus (C′), deviation from Cauchy relation (C₁₂−C₄₄), Poisson's ratio (σ), Young's modulus (Y), behavior of phonon frequencies in the elastic limit independent of the direction (Y₁), limiting value in the [1 1 0] direction (Y₂), degree of elastic anisotropy (A) and propagation velocities of the elastic waves. The contribution of s-like electrons is incorporated through the second-order perturbation theory due to model potential. The theoretical results are compared with the existing experimental data. A good agreement between theoretical investigations and experimental findings has confirmed the ability of our potential to yield large numbers of lattice mechanical properties of certain alkaline earth metals.     

Theoretical investigations of structural, elastic and thermodynamic properties for PtN2 under high pressure

We have investigated structural and elastic properties of PtN₂ under high pressures using norm-conserving pseudopotentials within the local density approximation (LDA) in the frame of density-functional theory. Calculated results of PtN₂ are in agreement with experimental and available theoretical values. The a/a₀, V/V₀, ductility/brittleness, elastic constants C_ij, shear modulus C′, bulk modulus B, shear modulus G, Young's modulus E, Poisson's ratio σ and anisotropy factor A as a function of applied pressure are presented. Through the quasi-harmonic Debye model, we also study thermodynamic properties of PtN₂. The thermal expansion versus temperature and pressure, thermodynamic parameters X (X=Debye temperature or specific heat) with varying pressure P, and heat capacity of PtN₂ at various pressures and temperatures are estimated.     

Electronic structure and elastic constants of TiCxN1−x, ZrxNb1−xC and HfCxN1−x alloys: A first-principles study

The structural, electronic and elastic properties of TiC_xN_1−x, Zr_xNb_1−xC and HfC_xN_1−x alloys have been investigated by using the plane-wave pseudopotential method within the density-functional theory. The calculations indicate that the variations of the equilibrium lattice constants and bulk modulus with the composition are found to be linear. The calculated elastic constants C₄₄ and shear constants as a function of alloy concentration reveal the anisotropic hardness of these compounds. The partial and total density of states (DOS) for the binary and ternary compounds had been obtained, and the metallic behavior of these alloys had been confirmed by the analysis of DOS.     

Elasticity, band structure, and piezoelectricity of BexZn1−xO alloys

Lattice constants, elasticity, band structure and piezoelectricity of hexagonal wide band gap Be_xZn_1−xO ternary alloys are calculated using first-principles methods. The alloys' lattice constants obey Vegard's law well. As Be concentration increases, the bulk modulus and Young's modulus of the alloys increase, whereas the piezoelectricity decreases. We predict that Be_xZn_1−xO/GaN/substrate (x=0.022) multilayer structure can be suitable for high-frequency surface acoustic wave device applications. Our calculated results are in good agreement with experimental data and other theoretical calculations.     

Structural and elastic properties under pressure effect of the cubic antiperovskite compounds ANCa3 (A = P, As, Sb, and Bi)

Using first-principles density functional calculations, the effect of high pressures, up to 40 GPa, on the structural and elastic properties of ANCa₃, with A = P, As, Sb, and Bi, were studied by means of the pseudo-potential plane-waves method. Calculations were performed within the local density approximation and the generalized gradient approximation for exchange-correlation effects. The lattice constants are in good agreement with the available results. The elastic constants and their pressure dependence are calculated using the static finite strain technique. We derived the bulk and shear moduli, Young's modulus, Poisson's ratio and Lamé's constants for ideal polycrystalline ANCa₃ aggregates. By analysing the ratio between the bulk and shear moduli, we conclude that ANCa₃ compounds are brittle in nature. We estimated the Debye temperature of ANCa₃ from the average sound velocity. This is the first quantitative theoretical prediction of the elastic properties of PNCa₃, AsNCa₃, SbNCa₃, and BiNCa₃ compounds, and it still awaits experimental confirmation.     

Theoretical investigations on KClxBr1−x, KClxI1−x and KBrxI1−x: A first-principles study

Using first-principles total energy calculations within the full-potential linearized augmented plane wave (FP-LAPW) method, we have investigated the structural, electronic and thermodynamic properties of potassium halides (KCl_xBr_1−x, KCl_xI_1−x and KBr_xI_1−x), with x concentrations varying from 0% up to 100%. The effect of composition on lattice constants, bulk modulus, band gap and dielectric function was investigated. Deviations of the lattice constants from Vegard's law and the bulk modulus from linear concentration dependence (LCD) were observed for the three alloys. The microscopic origins of the gap bowing were explained by using the approach of Zunger and coworkers. On the other hand, the thermodynamic stability of these alloys was investigated by calculating the excess enthalpy of mixing ΔH_m as well as the phase diagram.     

Lattice mechanical properties of noble and transition metals

A model pseudopotential depending on an effective core radius but otherwise parameter free is used to study the interatomic interactions, phonon dispersion curves (inq and r-space analysis), phonon density of states, mode Grüneisen parameters, dynamical elastic constants (C ₁₁,C ₁₂ andC ₄₄), bulk modulus (B), shear modulus (C′), deviation from Cauchy relation (C ₁₂–C ₄₄), Poisson’s ratio (σ), Young’s modulus (Y), behavior of phonon frequencies in the elastic limit independent of the direction (Y ₁), limiting value in the [110] direction (Y ₂), degree of elastic anisotropy (A), maximum frequencyω _max, mean frequency 〈ω〉, 〈ω ²〉^1/2=(〈ω〉/〈ω ⁻¹〉)^1/2, fundamental frequency 〈ω ²〉, and propagation velocities of the elastic constants in Cu, Ag, Au, Ni, Pd, and Pt. The contribution of s-like electrons is calculated in the second-order perturbation theory for the model potential while that of d-like electrons is taken into account by introducing repulsive short-range Born-Mayer like term. Very recently proposed screening function due to Sarkar et al. has been used to obtain the screened form factor. The theoretical results are compared with experimental findings wherever possible. A good agreement between theoretical investigations and experimental findings has proved the ability of our model potential for predicting a large number of physical properties of transition metals.     

Monocrystal elastic constants in the ultrasonic study of welds

For studying welds ultrasonically, the importance of knowing the material's single-crystal elastic constants, the C_ijs, is explained. Where these constants are not known, some guidelines are given for estimating them from polycrystalline elastic constants such as Young's modulus and the shear modulus.The important case of [001] fibre texture is considered. Being transversely isotropic, this case exhibits five macroscopic elastic constants, which are related to the three cubic elastic constants: C₁₁, C₁₂, C₄₄. From these five constants the angular variations of Young's modulus, the torsional modulus, and the sound velocities can be computed. For the same [001] fibre texture, results are given for a standard well-characterized material — copper, where the C_ijs are well known.     

High pressure X-ray diffraction study of Fe2B

We report the results of a synchrotron based X-ray diffraction study of bct-Fe₂B under quasi-hydrostatic conditions from 0 to 50 GPa. Over this pressure range, no phase change or disproportionation has been observed. A weighted fit of the data to the Birch-Murnaghan equation of state yields a value of the bulk modulus, K, of 164±14 GPa and the first pressure derivative of the bulk modulus, K′, of 4.4±0.5. The compression is found to be anisotropic, with the a-axis being more incompressible than the c-axis.     

A first principles study of cubic IrO<Subscript>2</Subscript> polymorph

We have studied structural, thermodynamic, elastic, and electronic properties of cubic IrO₂ polymorph via ab initio calculations within the LDA and GGA approximations. Basic physical properties, such as lattice constant, bulk modulus, second-order elastic constants (C_ij), and the electronic band structures are calculated, and compared with available experimental values. We have, also, predicted the Young's modulus, Poison's ratio (ν), Anisotropy factor (A), sound velocities, and Debye temperature.     

Screening dependence superconducting state parameters of La100−CGaC binary metallic glasses

The screening dependence theoretical investigations of the superconducting state parameters (SSP) viz. electron-phonon coupling strength λ, Coulomb pseudopotential μ^*, transition temperature T_C, isotope effect exponent α and effective interaction strength N₀V of six binary La_100−CGa_C (C=16, 20, 22, 24, 26 and 28 at.%) metallic glasses have been reported using Ashcroft's empty core (EMC) model potential for the first time. Five local field correction functions proposed by Hartree (H), Taylor (T), Ichimaru-Utsumi (IU), Farid et al. (F) and Sarkar et al. (S) are used in the present investigation to study the screening influence on the aforesaid properties. The T_C obtained from H-local field correction function is found in qualitative agreement with available experimental data and show almost linear nature with the concentration (C) of ‘Ga’ element. A linear T_C equation is proposed by fitting the present outcomes for H-local field correction function, which is in conformity with other results for the experimental data. Also, the present results are found in qualitative agreement with other such earlier reported data, which confirms the superconducting phase in the metallic glasses.     

Theoretical investigation of new type of ternary magnesium alloys AMgNi4 (A=Y,La, Ce,Pr and Nd)

New ternary magnesium alloys AMgNi₄ (A=Y, La, Ce, Pr and Nd) have been studied by First-Principles calculations within the generalized gradient approximation. The optimized structural parameters were in good agreement with the available experimental data. The calculated cohesive energies and formation enthalpies showed that these alloys had strong structural stability. Then the elastic constants C_ij of these AMgNi₄ alloys were calculated, and the bulk modulus B, shear modulus G, Young's modulus E, Poisson's ratio ν and anisotropy value A of polycrystalline materials were derived from the elastic constants, the related mechanical properties were further discussed. The electronic structures were also calculated to reveal the underlying mechanism for the structural stability and the elastic property.     

Study of elastic properties of CeO2 by statistical moment method

The purpose of the present paper is to investigate the temperature and pressure dependences of the elastic properties of cerium dioxide using the statistical moment method (SMM). The equation of states of bulk CeO₂ is derived from the Helmholtz free energy, and the pressure dependences of the elastic moduli like the bulk modulus, B_T, shear modulus, G, Young’s modulus, E, and elastic constants (C11, C12, and C44) are presented taking into account the anharmonicity effects of the thermal lattice vibrations. In the present study, the influence of temperature and pressure on the elastic moduli and elastic constants of CeO₂ has also been studied, using three different interatomic potentials. We compare the results of the present calculations with those of the previous theoretical calculations as well as with the available experiments.     

Magneto-elastic properties of Tb<Subscript>3</Subscript>Ga<Subscript>5</Subscript>O<Subscript>12</Subscript> (TGG)

The temperature dependence of the elastic constants in Tb₃Ga₅O₁₂ was measured and analysed with a simple crystal field model. The magneto-elastic coupling constants have been deduced from this experiment. The coupling constant g_Γ5, related to the c₄₄ mode, is anomalously large. These coupling constants are important for the interpretation of the phonon Hall effect.     

Single-crystal elastic constants of magnesium difluoride (MgF2) to 7.4 GPa

The six independent elastic constants (C₁₁, C₁₂, C₁₃, C₃₃, C₄₄, and C₆₆) of single-crystal MgF₂ in the rutile structure have been measured by Brillouin spectroscopy at room temperature from ambient conditions to 7.4 GPa. Measurements were performed on two monocrystals with perpendicular faces, (001) and (100). A quasi-linear fit from finite strain theory was applied to the experimental data revealing the pressure dependence of the six elastic constants of MgF₂. The shear modulus C_S=1/2(C₁₁−C₁₂), and the aggregate shear (Voigt–Reuss–Hill) modulus G show a softening with increasing pressure, indicating the approach of the rutile-to-CaCl₂-type structural phase transition at P~9 GPa. The adiabatic bulk modulus (Reuss average) and its pressure derivative have been determined: K_0S=105.1±0.3 GPa, (∂K_0S/∂P)_T=4.14±0.05. The pressure–volume equation of state of MgF₂ was computed self-consistently from the Brillouin data. Our results are in good agreement with X-ray diffraction data. As the phase transition is approached, MgF₂ becomes strongly anisotropic and develops partially auxetic behavior (a negative Poisson's ratio in certain directions).     

Charge ordering and elastic anomalies in NaxCoO2

We report in-plane resistivity and elastic constant C₃₃ measurements on the Na_0.8CoO₂ and Na_0.5CoO₂ systems. An ordering transition is found at T₀=280 K for Na_0.8CoO₂. The temperature dependence of the elastic constant C₃₃ propagating perpendicular to the CoO₂ layers is interpreted, in a phenomenological approach, as being due to the anharmonicity of atomic vibrations. The effective Grüneisen parameter γ_eff deduced directly from the temperature dependence of C₃₃ exhibits important changes at the charge ordering, magnetic and metal-insulator phase transitions.