Phase transformation and elastic behavior of MgX (X=S, Se, Te) alkaline earth chalcogenides

Pressure induced structural aspects of NaCl-type (B1) to CsCl-type (B2) structure in alkaline earth chalcogenides (AECs) magnesium chalcogenides (MgX; X=S, Se, and Te) are presented. An effective interionic interaction potential (EIoIP) with long-range Coulomb interactions and the Hafemeister and Flygare type short-range overlap repulsion extending up to the second neighbor ions and the van der Waals (vdW) interaction is developed. The vdW coefficients are evaluated following the Slater-Kirkwood variational method, as both the ions are polarizable. The present calculations have revealed reasonably good agreement with the available experimental data on structural transition (B1-B2 structure), the phase transition pressures P_t of 167 (MgS), 170 (MgSe), and 176 (MgTe) GPa as well the elastic properties. The calculated values of the volume collapses [ΔV(P)/V(0)] are also closer to their observed data. Further, the variations of the second and third order elastic constants with pressure have followed a systematic trend, which are almost identical to those exhibited by the observed data measured for other semiconducting compounds with rocksalt (B1) type crystal structure. The Born and relative stability criteria is valid in Mg monochalcogenides.     

Pressure induced B3-B1 structural phase transition and elastic properties of monopnictides InX (X = N,P, As)

An effective interionic interaction potential is developed to discuss the pressure induced structural phase transformation and mechanical properties of InX (X = N, P, As) semiconducting compounds. The effective interionic potential consists of the long-range Coulomb and three-body interactions and the Hafemeister and Flygare type short-range overlap repulsion extended upto the second neighbour ions and the van der Waals interaction. The present calculations have revealed reasonably good agreement with the available experimental data on the phase transition pressures (P_t = 11.5, 10, 7.5 GPa) and the elastic properties of InX (X = N, P, As). The equation of state curves (plotted between V (P)/V(0) and pressure) for both the structures zincblende (B3) and rocksalt (B1) structures obtained by us are in fairly good agreement with the experimental results. The calculated values of the volume collapses [ΔV(P)/V(0)] are also closer to their observed data.     

High pressure structural phase transition and elastic properties of Ga<Subscript>1-x</Subscript>In<Subscript>x</Subscript>As semiconducting compounds

The present paper addresses the high-pressure phase transformation and mechanical properties of Ga_1-xIn_xAs (x = 0.25, 0.5 and 0.75) by formulating an effective interionic interaction potential. This potential consists of the long-range Coulomb and charge transfer caused by the deformation of the electron shells of the overlapping ions and the Hafemeister and Flygare type short-range overlap repulsion extended upto the second neighbor ions and the van der Waals (vdW) interaction. The estimated values of phase transition pressure and the vast volume discontinuity in pressure-volume (PV) phase diagram indicate the structural phase transition from zinc blende (B3) to rock salt (B1). The equation of state curves plotted between V (P)/ V (0) and pressure are for both the zincblende (B3) and rocksalt (B1) structures. Further, the variations of the second and third order elastic constants with pressure have followed a systematic trend, which are almost identical to those exhibited by the observed data measured for other compounds of this family.     

Bond-stretching and bond-bending force constant of binary tetrahedral (AB and AB) semiconductors

In this Letter we present the two expressions relating the bond-stretching force constant (α in N/m) and bond-bending force constant (β in N/m) for the A^IIIB^V and A^IIB^VI semiconductors with the product of ionic charges (Z₁Z₂) and nearest neighbor distance d (Å). Interatomic force constants of these compounds exhibit a linear relationship when plotted on a log-log scale against the nearest neighbor distance d (Å), but fall on different straight lines according to the ionic charge product of the compounds. A fairly good agreement has been found between the observed and calculated values of the α and β for binary tetrahedral semiconductors.     

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.     

Pressure induced phase transition in ZnS

The phase transition of ZnS from the zincblende (ZB) structure to the rocksalt (RS) structure is investigated by the ab initio plane-wave pseudopotential density functional theory method. It is found that the pressures for transition from the ZB structure to the RS structure are 17.5 GPa from total energy-volume data and 15.4 GPa from equal enthalpies, consistent with the experimental data. From the high pressure elastic constants obtained, we find that the ZB structure ZnS is unstable when the applied pressure is larger than 17 GPa. Moreover, the dependence of the normalized primitive cell volume V/V₀ on pressure P can also be successfully obtained.     

Structural, electronic and elastic properties of M2SC (M = Ti, Zr, Hf) compounds

Using ab initio calculations, we have studied the structural, electronic and elastic properties of M₂SC, with M = Ti, Zr and Hf. Geometrical optimization of the unit cell are in good agreement with the available experimental data. The band structures show that all three materials are conducting. The analysis of the site and momentum projected densities shows that the bonding is achieved through a hybridization of M-atom d states with S and C-atom p states. The Md-Sp bonds are lower in energy and are stiffer than Md-Cp bonds. The elastic constants are calculated using the static finite strain technique. We derived the bulk and shear moduli, Young's moduli and Poisson's ratio for ideal polycrystalline M₂SC aggregates. We estimated the Debye temperature of M₂SC from the average sound velocity. This is a quantitative theoretical prediction of the elastic properties of Ti₂SC, Zr₂SC, and Hf₂SC compounds, and it still awaits experimental confirmation.     

Ab initio study of Nb2SC and Nb2S2C: Differences in coupling between the S and Nb-C layers

Using ab initio calculations, we have studied the structurally related compounds Nb₂SC and Nb₂S₂C. In Nb₂S₂C (space group , prototype Bi₂Te₃), S atoms are nearest neighbours, while in Nb₂SC (space group P6₃/mmc, prototype Cr₂AlC) this is not the case. The calculated equilibrium volume for these two phases deviates by 1.6-3.7% to previously-published experimental data and the bulk modulus-to-c₄₄ ratios obtained are 1.5 and 5.9, respectively. These results indicate a resemblance of Nb₂S₂C to hexagonal BN and graphite. Furthermore, we have demonstrated that the uniform compression method is adequate for estimating the elastic properties of Nb₂SC, a so-called MAX phase. It is our ambition that these calculations will stimulate further experimental research on these compounds.     

Theoretical Study of Compressibility and Thermoelasticity of LaNi5-xAlx （x= 0.3, 0.5 and 1.0）

The compressibility, the temperature dependence of bulk modulus, the pressure dependence of normalized volume V/V0, thermal expansion coefficient and Debye temperature of LaNi5-xAlx compounds are successfully obtained using the first-principles plane-wave pseudopotential （PW-PP） method, the EOSFIT6.0 software and the quasiharmonic Debye model. The rapid decrease of relative lattice constant a/a0 shows that the deformation is easier in directions normal to the c-axis than that along it. The relationships between bulk modulus B and pressure at different temperatures are also analysed. It is found that the bulk modulus B increases monotonically with increasing pressure. Moreover, the pressure dependences of thermal expansion and Debye temperature are also successfully obtained. The calculated results are in agreement with the experimental data.     

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.     

First-Principles Calculations of Elastic Properties of Cubic Ni2MnGa

Dependence of bulk modulus on both pressure and temperature, the elastic constants Cij and the pressure and temperature dependence of normalized volume V/Vo of cubic Ni2MnGa alloy are successfully obtained using the first-principles plane-wave pseudopotential （PW-PP） method as well as the quasi-harmonic Debye model. We analyse the relationship between bulk modulus and temperature up to 800 K and obtain the relationships between bulk modulus B and pressures at different temperatures. It is found that the bulk modulus B increases monotonically with increasing pressure. Moreover, the temperature dependences of the Debye temperature are also analysed. The calculated results are in agreement with the available experimental data and the previous theoreticM results.     

Prediction study of structural and elastic properties under pressure effect of M2SnC (M=Ti, Zr, Nb, Hf)

Using first-principles calculations, we have studied the structural and elastic properties of M₂SnC, with M=Ti, Zr, Nb and Hf. Geometrical optimization of the unit cell is in good agreement with the available experimental data. The effect of high pressures, up to 20 GPa, on the lattice constants shows that the contractions along the a-axis were higher than those along the c-axis. We have observed a quadratic dependence of the lattice parameters versus the applied pressure. The elastic constants and their pressure dependence are calculated using the static finite strain technique. A linear dependence of the elastic stiffnesses on the pressure is found. We derived the bulk and shear moduli, Young's moduli and Poisson's ratio for ideal polycrystalline M₂SnC aggregates. We estimated the Debye temperature of M₂SnC from the average sound velocity. This is the first quantitative theoretical prediction of the elastic properties of Ti₂SnC, Zr₂SnC, Nb₂SnC, and Hf₂SnC compounds.     

Full potential calculation of structural, elastic properties and high-pressure phase of binary noble metal carbide: ruthenium carbide

We present in this paper the results of an ab initio theoretical study within the local density approximation (LDA) to determine in rock-salt (B1), cesium chloride (B2), zinc-blende (B3), and tungsten carbide (WC) type structures, the structural, elastic constants, hardness properties and high-pressure phase of the noble metal carbide of ruthenium carbide (RuC).The ground state properties such as the equilibrium lattice constant, elastic constant, the bulk modulus, its pressure derivative, and the hardness in the four phases are determined and compared with available theoretical data. Only for the three phases B1, B3, and WC, is the RuC mechanically stable, while in the B2 phase it is unstable, but in B3 RuC is the most energetically favourable phase with the bulk modulus 263 GPa, and at sufficiently high pressure (P_t=19.2 GPa) the tungsten carbide (WC) structure would be favoured, where ReC-WC is meta-stable.The highest bulk modulus values in the B3, B2, and WC structures and the hardnesses of H(B3)=36.94 GPa, H(B1)=25.21 GPa, and H(WC)=25.30 GPa indicate that the RuC compound is a superhard material in B3, and is not superhard in B1 and WC structures compared with the H(diamond)=96 GPa.     

Velocity dependence of total Penning ionization cross sections

The velocity dependence of the total Penning ionization cross sections,σ(v), is measured in the thermal relative velocity region, using a time of flight method.σ(v) curves are reported for the collision systems He(2¹ S)/Ar, Kr, Xe, N₂, Hg, He(2³ S)/Ar, Kr, Xe, N₂, Hg, Ne(³ P _{2, 0})/Kr, Hg, and Ar(³ P _{2, 0})/Hg. In a qualitative discussion it is shown that all features of the measuredσ(v) curves may be explained within the frame of the theory of Penning ionization, allowing to extract information on the physical quantities governing the process: on the interaction potentialV(R) and on the transition probabilityW(R). A theoretical calculation for the He(2³ S)/Ar system shows good agreement with our experimentalσ(v) curve. On the basis of the present results earlier data onσ(v), and on absolute cross sections and rate constants obtained at certain relative velocity distributions are discussed.     

First-Principles Calculations of Elastic Properties of LaNi5 Compound

The equilibrium lattice constants, temperature dependence of bulk modulus, the pressure dependence of the normalized volume V/V0, elastic constants Cij and bulk modulus of LaNi5 crystal are obtained using the firstprincipies piane-wave pseudopotential method in the GGA-PBE generalized gradient approximation as well as the quasi-harmonic Debye model. We analyse the relationship between bulk modulus and temperature up to 2000 K and obtain the relationship between bulk modulus B and pressure at diFFerent temperatures. It is found that the bulk modulus B increases monotonously with increasing pressure. Moreover, the pressure dependences of Debye temperatures and the pressure derivatives of lattice constants are also successfully obtained. The calculated results are in agreement with the experimental data and the other theoretical results.     

Structure of a high temperature phase of potassium dideuteriophosphate (DKDP)

We previously determined the crystal structures of the high temperature phases of KH₂PO₄ [J.A. Subramony, S. Lovell, B. Kahr, Chem. Mater. 10 (1998) 2053. [6]]. These triclinic and monoclinic phases were obtained by heating the room temperature tetragonal form until new crystal phases were identified by polarization microscopy. These samples were subsequently cooled to room temperature thereby preserving the metastable high temperature phases for analysis. KD₂PO₄ is distinct from KH₂PO₄ in that it crystallizes at room temperature in a monoclinic phase unknown for its isotopomer, therefore the question as to whether it would support the corresponding high temperature phases remained open until our report here of the transformation of monoclinic KD₂PO₄ to an isomorphous triclinic high temperature phase: space group P with a=7.475(1) Å, b=7.440(1) Å, c=7.184(1) Å, α=88.53(1) Å, β=86.81(1)°, γ=88.09(1)°, V=398.58 Å³. This is the first known high temperature phase of DKDP, a material coveted at room temperature for its optical properties.     

Structural phase transition and elastic properties of ZnSe at high pressure

We have evolved an effective interionic interaction potential to investigate the pressure-induced phase transitions from zinc blende (B3) to rock salt (B1) structure in II-VI [ZnSe] semiconductors. The elastic constants, including the long-range Coulomb and van der Waals (vdW) interactions and the short-range repulsive interaction of up to second-neighbor ions within the Hafemeister and Flygare approach, are deduced. Keeping in mind that both of the ions are polarisable, we employed the Slater-Kirkwood variational method to estimate the vdW coefficients. The estimated value of the phase transition pressure (P _t ) is higher than in the reported data, and the magnitude of the discontinuity in volume at the transition pressure is consistent with that data. The major volume discontinuity in the pressure-volume phase diagram identifies the structural phase transition from zinc blende to rock salt structure.

The variation of second-order elastic constants with pressure resembles that observed in some binary semiconductors. It is inferred that the vdW interaction is effective in obtaining the thermodynamic parameters such as the Debye temperature, the Gruneisen parameter, the thermal expansion coefficient and the compressibility. However, the inconsistency between the thermodynamic parameters as obtained from present model calculations and their experimental values is attributed to the fact that we have derived our expressions by assuming the overlap repulsion to be significant only up to the nearest second-neighbor ions, as well as neglecting thermal effects. It is thus argued that full analysis of the many physical interactions that are essential to binary semiconductors will lead to a consistent explanation of the structural and elastic properties of II–VI semiconductors.     

Equation of state of cubic hafnium(IV) nitride having Th3P4 -type structure

Pressure dependence of the specific volume, V(P), of the recently discovered high-pressure compound Hf₃N₄ having cubic Th₃P₄-type structure (c- Hf₃N₄) has been measured at room temperature up to 43.9 GPa in a diamond anvil cell using energy-dispersive X-ray powder diffraction combined with synchrotron radiation. A least-square fit of the Birch-Murnaghan equation of state to the experimental V(P)-data yielded for c- Hf₃N₄ the bulk modulus of and its first pressure derivative of . For fixed at 4 the bulk modulus of c- Hf₃N₄ was determined to be . The obtained B₀-value is only insignificantly below that estimated in preliminary measurements. Existing theoretical predictions for B₀ scatter around the present experimental data. The observation of a high bulk modulus of c- Hf₃N₄ supports the suggestion that this compound could have high hardness.     

Elastic properties of tantalum carbide (TaC)

Elastic properties of TaC have been investigated experimentally and by model calculations. The elastic stiffness coefficients c₁₁=597(11) GPa and c₄₄=153(2) GPa were determined on a (100)-oriented disc-shaped monocrystal at room temperature using a plane-wave ultrasound method. The corresponding theoretical values (c₁₁=621(3), c₄₄=166.8(3) GPa) agree within 4 and 8%, respectively. Therefore, we are confident that the predicted value for c₁₂ is equally accurate, and this allows the prediction of the Bulk and Young's moduli and the Poisson ratio. Data published earlier are critically reviewed and predictions concerning the possibility to synthesize extremely incompressible carbides are made.     

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.