Dependence of pressure on elastic,electronic and optical properties of CeO2 and ThO2: A first principles study

The phase transformation of CeO₂ and ThO₂ from fluorite to cotunnite-type structure under pressure is predicted within the density functional theory implemented with the GGA-PW91 method, the pressure induced structural phase transition occurs at 28.9 GPa for CeO₂ and 29.8 GPa for ThO₂. These values are in excellent agreement with the experimentally measured data. The elastic, electronic and optical properties at normal as well as for high-pressure phase have been calculated, particular attention is devoted to the cotunnite phase. Further, the dependence of the elastic constants, the bulk modulus B, the energy band gaps and the dielectric function on the applied pressure are presented.     

Ab initio study of AlCu2M (M = Sc,Ti and Cr) ternary compounds under pressures

The structural, electronic and elastic properties of the AlCu₂M (M = Sc, Ti and Cr) compounds in the pressure range of 0–100 GPa was investigated based on density functional theory. The calculated lattice parameters of the AlCu₂M compounds at zero pressure and zero temperature are in very good agreement with the existing experimental data. The bulk modulus, shear modulus and Young’s modulus increases with the increase of pressure, which indicates that higher materials hardness may be obtained when increasing pressures. The bulk modulus and Young’s modulus of AlCu₂Cr is the greatest under pressure. The shear modulus of AlCu₂Ti is the highest above 30 GPa, while that of the AlCu₂Sc is the strongest below 30 GPa. The calculated B/G values at zero and higher pressure indicated that they are ductile materials. The electronic densities of states and bonding charge densities have been discussed in details, revealing these compounds exhibit half-metallic behavior. In addition, the pressure dependences of Debye temperatures of AlCu₂M compounds have also been calculated. The results indicate that Debye temperatures increase with increasing pressure.     

Effects of pressure on the elasticity and stability of zircon (ZrSiO4): First-principle investigations

We investigate the effects of pressure on the elasticity of zircon using the Local Density Approximation (LDA) within the density functional theory. Our LDA calculations predict the elastic constants (C_ij) with positive pressure derivatives, except C₆₆ whose pressure derivatives are nearly zero, showing small positive to negative departures with increasing pressure. We calculated Young’s moduli, E₁ and E₃ along the crystallographic axes a and c, respectively. At low pressures (<4 GPa) E₁ < E₃, but the relation reverses at pressures >4 GPa, implying a directional change of axial stiffness of zircon crystals. Our LDA calculated Hill’s average bulk (B) and shear (G) moduli show contrasting variations with pressure. B is more sensitive to pressure with positive derivatives varying from 2.25 to 5.63, as compared to much lower pressure derivatives (0.4) of G, which drops to negative values (?0.404) at pressures >7 GPa, and then take up positive values (1.3). The zircon to reidite phase transition, involving “bond switching mechanisms” [1] increases the magnitudes of both B and G, but shows relatively weak effects on their pressure derivatives. This study shows the effects of pressure on the degrees of shear and directional bulk modulus anisotropy of zircon. We also calculated its Debye temperature (708 K) from the elastic wave velocities, which fairly agrees to the available experimental data. Our study predicts that increasing pressure widens the electronic band gap of zircon, implying its greater insulation property at high pressures.     

Structural stabilities,elastic and thermodynamic properties of Scandium Chalcogenides via first-principles calculations

The high-pressure structural (B1–B2) phase transition and the elastic properties of ScS and ScSe are studied using the full-potential augmented plane wave plus local orbitals method (FP-APW + LO) with the generalized-gradient approximation (GGA) exchange-correlation functional. The elastic constants and their pressure dependence are calculated following the total energy variation with strain technique. The stability and the ductility mechanisms for these compounds are discussed via the electronic density of states (DOS) and the elastic constants C_ij. The thermodynamic properties of (B1) structure are predicted through the quasi-harmonic Debye model, in which the lattice vibrations are taken into account. The variation of bulk moduli, the thermal expansion coefficient, the heat capacities and the Debye temperature with pressure and temperature are successfully obtained. To our knowledge this is the first quantitative theoretical prediction of the elastic, high pressure and thermal properties for the investigated compounds and still awaits experimental confirmations.     

Structural,electronic, elastic and thermodynamic properties of AlSi2RE (RE = La,Ce, Pr and Nd) from first-principle calculations

It is of academic interest to study the ternary intermetallic compounds of the Al–Si–RE system for the development of both structural and functional materials. In this work, the structural, electronic, elastic and thermodynamic properties of the AlSi₂RE (RE = La, Ce, Pr and Nd) compounds was investigated using first-principle calculations based on density functional theory. The calculated structural parameters of AlSi₂RE compounds are consistent with the experimental data. Due to the fact that there is strong Coulomb correlation among the partially filled 4f electron for RE atoms, we present a combination of the GGA and the LSDA + U approaches to investigate the electronic structures of Al₃RE compounds in order to obtain the appropriate results. The elastic constants were determined from a linear fit of the calculated stress–strain function according to Hooke’s law. The bulk modulus B, shear modulus G, Young’s modulus E, and Poisson’s ratio ν of polycrystalline AlSi₂RE compounds were determined using the Voigt–Reuss–Hill (VRH) averaging scheme. The Debye temperature of AlSi₂RE compounds can be obtained from elastic constants. The temperature dependence of the internal energy, free energy, entropy and heat capacity for AlSi₂RE compounds were also calculated by using the quasi-harmonic approximation.     

First-principles calculations of mechanical and thermodynamic properties of YAlO3

First-principles calculations are performed to investigate the crystal structure, electronic properties, the elastic properties, hardness and thermodynamic properties of YAlO₃. The calculated ground-state quantities such as lattice parameter, bulk modulus and its pressure derivative, the band structure and densities of states were in favorable agreement with previous works and the existing experimental data. The elastic constants C_ij, the aggregate elastic moduli (B, G, E), the Poisson’s ratio, and the elastic anisotropy have been investigated. YAlO₃ exhibits a slight elastic anisotropy according to the universal elastic anisotropy index A^U = 0.24. The estimated hardness for YAlO₃ is consistent with the experimental value, and Al–O bond in AlO₆ octahedra plays an important role in the high hardness. The Y–O bonds in YO₁₂ polyhedra exhibit different characteristic. Using the quasi-harmonic Debye model considering the phonon effects, the temperature and pressure dependencies of bulk modulus, heat capacity and thermal expansion coefficient are investigated systematically in the ranges of 0–20 GPa and 0–1300 K.     

First-principles investigations on structural,elastic and electronic properties of SnO2 under pressure

We investigate the structural, elastic, and electronic properties of rutile-type SnO₂ by plane-wave pseudopotential density functional theory method. The lattice constants, bulk modulus and its pressure derivative are all calculated. These properties at equilibrium phase are well consistent with the available experimental and theoretical data. Especially, we study the pressure dependence of elastic properties such as the elastic constants, elastic anisotropy, aggregate acoustic velocities and elastic Debye temperature Θ. It is concluded that this structure becomes more ductile with increasing pressure up to 28 GPa. Moreover, our compressional and shear wave velocities V_P = 7.02 km/s and V_S = 3.84 km/s, as well as elastic Debye temperature Θ = 563 K at 0 GPa compare favorably with the experimental values. The pressure dependences of band structures, energy gap and density of states are also investigated.     

Theoretical Investigation of the Phase Transition,Elastic and Superconductivity Properties of LaS Under Pressure

The first-principles method has been performed to investigate the phase transition, elastic, thermodynamic and superconductivity properties of lanthanum monosulphide (LaS) under pressure. A structural phase transition from the NaCl-type (B₁) to CsCl-type (B₂) structure is found to occur at around 16.8 GPa. The calculated ground state properties such as lattice constants, bulk modulus, and Debye temperatures are in good agreement with experimental data. Finally, the pressure dependence of the theoretical elastic constants and elastic modulus of LaS has been studied. The observations show that LaS is mechanically stable not only in B₁ phase below 8.77 GPa but also in B₂ phase under high pressure. LaS is ductile in B₁ phase while brittle in B₂ phase. The present observation of physical properties in B₂ phase of LaS needs validation by future experimental.     

Theoretical investigation on the transition-metal borides with Ta3B4-type structure: A class of hard and refractory materials

Based on density functional theory, we have systematically studied the structural stability, mechanical properties and chemical bonding of the transition-metal borides M₃B₄ (M = Ti, V, Cr, Zr, Nb, Mo, Hf, Ta, and W) for the first time. All the present studied M₃B₄ have been demonstrated to be thermodynamically and mechanically stable. The bulk modulus, shear modulus, Young’s modulus, Poisson’s ratio, microhardness, Debye temperature and anisotropy have been derived for ideal polycrystalline M₃B₄ aggregates. In addition, the relationship between Debye temperature and microhardness has been discussed for these isostructral M₃B₄. Furthermore, the results of the Cauchy pressure, the ratio of bulk modulus to shear modulus, and Poisson’s ratio suggest that the valence electrons of transition metals play an important role in the ductility of M₃B₄. The calculated total density of states for M₃B₄ indicates that all these borides display a metallic conductivity. By analyzing the electron localization function, we show that the improvement of the ductility in these M₃B₄ might attribute to the decrease of their angular bonding character.     

First-principles study on the structural stabilities,electronic and elastic properties for zirconium under pressure

Using the first-principles calculation based on density-functional theory (DFT), we investigate the pressure-induced phase transitions, electronic and elastic properties of Zr at 0 K. The metal is shown to exhibit a crystal structure sequence of hcp → ω → bcc with increasing pressure. And the transitions happen at 0.14 GPa and 27.01 GPa, respectively. This is in good agreement with the experimental observation. The density of state (DOS) reveals the basic reason for the stability sequence of Zr. The shear moduli c′, c₄₄ and bulk modulus B of bcc Zr all increase with pressure. It is found that bcc Zr satisfies the mechanical stability at pressure beyond 9 GPa. Furthermore, the high-pressure limit of 360 GPa for a stable bcc Zr is deduced for the first time from the cohesive energy calculations. The Mulliken population analysis shows that both s and p electrons transfer to the d orbital with increasing pressure, however, the number of s electrons starts to increase when the pressure exceeds about 100 GPa.     

Ultrasonic investigation of the relaxor behaviour of ferroelectric ceramics (Pb1−xCax)TiO3 for x = 0.475, 0.50 and 0.55

Three samples of calcium modified lead titanate (Pb_1?xCa_x)TiO₃ with x = 0.475, 0.50 and 0.55 were studied in terms of their ultrasonic properties. The samples were prepared using the solid state reaction technique. Ultrasonic attenuation and velocity were measured as a function of the temperature at 5 MHz and 10 MHz with X-cut quartz transducers, using the ultrasonic pulse-echo technique and Papadakis method for accuracy determination of the transit time of ultrasonic RF pulses. An equation regarding elastic–electric coupling between strain and spontaneous polarization was used in order to fit the elastic modulus. The nature of the phase transition was characterized through the diffusivity exponent obtained from this fit. Our results show that, as calcium concentration increases from 0.475 to 0.55, the behaviour of ferroelectric phase transition changes from normal to relaxor. This process is accompanied by a systematic decrease of the critical temperature.     

Structural,elastic, and lattice dynamical properties of Germanium diiodide (GeI2)

To investigate the structural, elastic, and lattice dynamical properties of the germanium diiodide, we have performed the first-principles calculations by using the local density approximation method based on density-functional theory. Some basic physical parameters such as lattice constant, bulk modulus and its first derivatives, elastic constants, shear modulus, Young’s modulus, and Poisson’s ratio are calculated. The phonon dispersion curves, electronic band-structures, and total and partial density of states have also been calculated for ground state C6 phase of GeI₂. Our results show that this structure has got 1.72 eV direct band gap. Our secondary results on the temperature-dependent behavior of thermodynamical properties such as entropy, heat capacity, internal energy, and free energy are also presented for the same compounds. The obtained results are in good agreement with the available experimental and other theoretical data.     

First-principles calculations of the structural and elastic properties of OsSi2 at high pressure

We investigated the pressure dependence of the structural and elastic properties of OsSi₂ in the range 0–60 GPa using first-principles calculations based on density functional theory. Calculations were performed within the local density approximation as well as the generalized gradient approximation to the exchange correlation potential. The calculated lattice constants and atomic fractional coordinates are in good agreement with previous experimental results. The pressure dependence of nine independent elastic constants, c₁₁, c₂₂, c₃₃, c₄₄, c₅₅, c₆₆, c₁₂, c₁₃, and c₂₃, of orthorhombic OsSi₂ has been evaluated. The isotropic bulk modulus, shear modulus, Young’s modulus, Poisson’s ratio, elastic anisotropy, and Debye temperature of polycrystalline OsSi₂ under pressure are also presented.     

Structural phase transition,electronic and elastic properties in TlX (X = N,P, As) compounds: Pressure-induced effects

Using the first-principles plane-wave pesudopotential (PW-PP) method with the generalized gradient approximation (GGA) for the exchange-correlation potential, we have studied the structural, electronic and elastic properties of TlX (X = N, P, As) compounds under hydrostatic pressure. Our calculations show that TlN, TlP and TlAs undergo a phase transition from the zincblende (ZB) to the rocksalt (RS) structure at 19.05, 7.29 and 5.01 GPa, with a volume collapse of 14.96%, 17.45% and 18.03%, respectively. The influence of crystallographic structure and hydrostatic pressure on electronic band structures, elastic constants, and aggregate bulk moduli are investigated. Further, the elastic wave velocities, Debye temperatures and melting temperatures for zincblende TlN, TlP and TlAs compounds are obtained. Our calculated results are compared with the previously reported theoretical data.     

Ab-initio study of phase transitions in NaNO2 crystals based on band structure calculations

The present investigation is an ab-initio study using CRYSTAL’06 code of the thermally and pressure stimulated phase transitions in NaNO₂ crystal using band structure calculations. The paraelectric crystal structure has been represented by the double ferroelectric unit cell with opposite spatial orientations of the main molecular unit NaNO₂ in neighboring cells along the polar y-axis. The “total energy – unit cell volume” dependences E(V) for the ferroelectric and paraelectric structures have been found to possess two crossing points. The corresponding dependences of enthalpy H versus pressure P possess crossing points as well, that is in agreement with the pressure induced phase transition at 8.8 GPa and the temperature stimulated ferroelectric–paraelectric phase transition at 437–438 K. The sequence of principal components of the elastic compliance tensor, s₁₁ > s₂₂ > s₃₃, has been found to be the same as the corresponding sequence of thermal linear expansion coefficients, α₁ > α₂ > α₃, of the crystal.     

Crystal structure and thermal expansion of LaCr1−xMgxO3, 0 < x ≤ 0.25

Solid solution LaCr_1?xMg_xO₃, 0 < х ≤ 0.25 was prepared by heating stoichiometric amounts of appropriate oxides in air at 1400 °C, 48 h. At room temperature it crystallizes in orthorhombically distorted GdFeO₃-type structure (a ≈ √2 × a_per; b ≈ √2 × a_pe; c ≈ 2 × a_per, where a_per – perovskite subcell parameter). High-temperature X-ray powder diffraction (HT XRPD) and dilatometry revealed first order phase transition to rhombohedral perovskite phase (R-3c, a ≈ √2 × a_per, c ≈ 2√3 × a_per) at 260–311 °C (OR phase transition). Crystal structures of room-temperature orthorhombic and high-temperature rhombohedral phases for LaCr_0.75Mg_0.25O₃ were refined using HT XRPD data. Temperature of OR phase transition increases gradually with increasing of magnesium content. Low-temperature orthorhombic phase exhibits TEC lower in comparison with high-temperature rhombohedral one (e.g. for LaCr_0.85Mg_0.15O₃ TEC(O) = 8.8 ppm K^?1; TEC(R) = 11.6 ppm K^?1). TEC for rhombohedral phase increases with increasing magnesium content from 10.4 ppm K^?1 for LaCr_0.95Mg_0.05O₃ to 12.1 ppm K^?1 for LaCr_0.75Mg_0.25O₃.     

Elastic constants of AlB2-type compounds from first-principles calculations

Elastic constants (C_ij’s) of 24 compounds in the AlB₂-type diborides have been calculated by first-principles with the generalized gradient approximation and compared with the available experimental data. Values of all independent elastic constants as well as bulk modulus in a and c directions (B_a and B_c, respectively) were predicted. The elastic modulus of the AlB₂-type compounds were calculated according to the theoretical elastic constants by Voigt-Reuss-Hill averaging scheme. Ductility and anisotropy in these compounds were further analyzed based on their B/G ratio and elastic constants. It is founded that AlB₂ is more ductile while ScB₂ is more brittle, and AlB₂ has a highest elastic anisotropy in the 24 AlB₂-type compounds.     

Correlation between hardness and elastic moduli of the covalent crystals

From a statistical manner, we collected and correlated experimental bulk (B), shear (G), Young’s modulus (E), and ductility (G/B) with Vickers hardness (H_v) for a number of covalent materials and fitted quantitative and simple H_v–G and H_v–E relationships. Using these experimental formulas and our first-principles calculations, we further predicted the microhardness of some novel potential hard/superhard covalent compounds (BC₂N, AlMgB₁₄, TiO₂, ReC, and PtN₂). It was found that none of them are superhard materials (H_v ? 40 GPa) except BC₂N. The present empirical formula builds up a bridge between Vickers hardness and first-principles calculations that is useful to evaluate and design promising hard/superhard materials.