The elastic constants and their temperature and pressure derivatives of AgBr-AgCl mixed crystals

The three independent second-order elastic constants and their temperature and pressure derivatives have been measured for four AgBr-AgCl mixed crystals, with 19.5, 39.1, 56.6 and 78.7 mole % AgCl, using the ultrasonic pulse-echo technique at room temperature. The explicit temperature dependence of the elastic constants is calculated and is found to be much larger than that of other NaCl structure crystals. The violation of the Cauchy relation C₁₂ = C₄₄ is found to be significant and increases between AgBr and AgCl. The high temperature limit of the Gruneisen parameter is calculated from the elastic data. A comparison is made between the elastic properties of the silver halides and the alkali halides.     

The generalised Huggins-Mayer form of born repulsive potentials for NaCl-type alkali halides

The generalised Huggins-Mayer form of Born repulsive potentials for NaCl-type alkali halides have been re-evaluated using more reliable, recently published thermodynamic data and van der Waals energy coefficients. As with older versions of these potentials excellent agreement between model and experimental values of interionic distance and cohesive energy is achieved. Further, the earlier shortcomings in the failure of the stability condition and predicted elastic constants are significantly reduced. For the majority of salts the new short-range interactions have stronger van der Waals attractions and slider repulsions. The model gives average crystal radii for the alkali ions about ~0.3 Å larger than traditional free ion radii and ~0.08 Å larger than Tosi-Fumi crystal radii. The predicted halogen crystal radii are correspondingly smaller by the same amounts.     

Interionic potentials and force constant models for rocksalt structure crystals—II

A lattice dynamical model for rocksalt structure crystals is presented in which the interionic force constants are taken to be central and the departure from the Cauchy relations is accounted for by isotropic and anisotropic deformations of the anions. The model is applied to NaBr, NaI and KBr for which C₁₂ > C₄₄ and it is appropriate to consider only the anisotropic deformations. The model parameters are determined entirely from macroscopic data. By assuming an exponential form for the repulsive part of the interionic potential the cohesive energy of the crystals may be determined from the interionic force constants. The cohesive energies are in surprisingly good agreement with experiment although the potential parameters differ considerably from those of other workers. While the dispersion curves obtained from the model are in markedly worse agreement with experiment than those from the standard breathing shell model it is shown that the potentials(in addition to giving good cohesive energies) result in a reasonably consistent dynamical model.     

Interionic potentials and force constant models for rocksalt structure crystals

It is suggested that the observed departure from the Cauchy relation in alkali halide structure crystals is due to ionic deformations. Interionic forces may then be taken to be central and a comparison between lattice dynamical models and interionic potential models becomes possible. In this paper attention is restricted to MgO, NaCl, LiF and KI for all of which (i) an isotropic (breathing) deformation can account for the difference C₄₄–C₁₂ and (ii) only the negative ion need be considered deformable. The interionic potential is assumed to consist of Coulombic and van der Waals terms, which are taken as known, and short range repulsive terms with an exponential dependence on separation. The constants in these repulsive terms are determined from the force constants of the lattice dynamical models. Satisfactory agreement with measured cohesive energies can be achieved only if the charge on the ions is very close to the electronic charge (2e in the case of MgO). This leads to a sacrifice in accuracy of the lattice dynamical models but this is shown to be small so that reasonable compatibility between the two sets of models is thus demonstrated. The interionic potentials are compared with those of other workers.     

A theoretical study of structural, elastic and thermal properties of heavy lanthanide monoantimonides

The structural, elastic and thermal properties of three heavy monoantimonides of holmium, erbium and thulium (LnSb, Ln=Ho, Er and Tm) have been investigated theoretically by using an interionic potential theory consisting of long-range Coulomb, short-range repulsive and van der Waal’s (vdW) interactions. These compounds exhibit first-order crystallographic phase transition from their initial NaCl-type structure to CsCl-type structure at pressures 27, 33.2 and 29.8 GPa for HoSb, ErSb and TmSb, respectively. The values of elastic constants and Debye temperatures as a function of pressure are also reported. The elastic properties such as Young modulus (E), Shear modulus (G), Poisson ratio (υ) and anisotropic ratio (A) in an NaCl-type structure are also predicted.     

The elastic behaviour of the ternary zincblende structure semiconductor CuGe2P3

A single crystal has been grown of CuGe₂P₃, a ternary semiconductor with a zincblende structure in which the copper and germanium atoms are randomly distributed on the cation sites. The second order elastic constants measured by the ultrasonic pulse echo overlap technique (C₁₁ = 13.66, C₁₂ = 6.17, C₄₄ = 6.66 and bulk modulus B = 8.67 in units of 10¹⁰Nm^?2 at 291 K) are closely similar to those of GaP and conform well to Keyes' correlation for zincblende structure crystals. The hydrostatic pressure derivatives of the second order elastic constants ($\text{?C}{}_{11}\text{?P}\text{= 4.40}$, $\text{?C}{}_{12}\text{?P}\text{= 3.9}$, $\text{?C}{}_{44}\text{?P}\text{= 0.93}$ and $\text{?B}\text{?P}\text{= 4.07}$) and the third order elastic constants (C₁₁₁ = ? 8.45, C₁₁₂ = ? 3.49, C₁₂₃ = ? 1.13, C₁₄₄ = ? 2.82, C₁₅₅ = ? 1.44 and C₄₅₆ = ? 0.69 in units of 10¹¹Nm^?2) also resemble those of GaP: even the anharmonicity of the long wavelength acoustic modes of this ternary semiconductor resembles that of its binary “parent” compound. The positive signs of the hydrostatic pressure derivatives and the negative signs of the third order elastic constants show that the acoustic modes at the long wavelength limit stiffen under pressure, an effect which is quantified here by computation of the mode Grüneisen parameters, which are all positive. The harmonic and anharmonic force constants, obtained in the valence force field model, fit well into the pattern shown by related zincblende structure compounds: the ratio ($\text{β}\text{α}$) for bond bending (β) to stretching (α) force constants is greater than 4:1; the dominating anharmonic force constant is γ: most of the anharmonicity is associated with nearest neighbour atoms. Analysis of the temperature dependence of the elastic constants on the basis of a simple anharmonic model again emphasises the similarity between the elastic behaviour of CuGe₂P₃ and GaP. The thermal expansion of CuGe₂P₃ varies almost linearly with temperature between 291 K and 1000 K, the linear coefficient of thermal expansion α being 8.21 ± 0.02 × 10^?6 °C^?1. The similar lattice parameters and elastic behaviour of CuGe₂P₃ and GaP indicate that semiconducting devices made of epitaxial deposits of CuGe₂P₃ on a GaP substrate should prove to be almost strain-free.     

Modes of vibrations due to (U-center + additive cation impurities) in alkali halides

Local and resonant modes due to hydride ions in various alkali halides containing additive cation impurities have been computed by the Green function technique. Local vibrations due to U-centers in alkali halides have O_h symmetry. When one of the six nearest neighbour cations is replaced by an additive impurity, the site symmetry of the system is lowered from O_h to C_4v. The phonon Green functions matríx is analysed according to the irreducible representation of the point group symmetry pertaining to the substitutional impurity. We have considered the vibrations of the hydride ion and all its six nearest neighbours. Analytical expressions have been derived for various modes of vibrations. Using group theory the 21 × 21 matrix has been block diagonalized into various irreducible representations. The effect of mass changes and the changes in short-range force constants have been taken into account. The computed results of the localized modes have been compared with the available experimental results. Good agreement has been found. Theoretical results on resonant modes are also displayed, which will be of use in future experiments on these systems.     

Compression curves of the cesium halides using murnaghan logarithmic equation

The pressure derivatives of the adiabatic bulk moduli of the cesium halides are evaluated from the pressure derivatives of their elastic constants C₁₁ and C₁₂. Murnaghan's logarithmic equation is then used to determine the compression curves of these solids. The agreement between the calculated and experimental compression-ratio values for these halides of cesium is good.     

Study of high pressure behavior and elastic properties of praseodymium monochalcogenides and monopnictides

The structural and elastic properties of praseodymium monochalcogenides (PrX: X = S, Se, Te) and monopnictides (PrY: Y = P, As, Sb, Bi) with NaCl-type structure have been investigated by using an interionic potential theory with necessary modification to include the effect of Coulomb screening due to the delocalized f-electrons of rare earth ion. The calculations are done at ambient as well as at high pressure. The structure of the high pressure phase of PrX compounds is CsCl-type while all the PrY compounds have been found to undergo from their initial NaCl-type structure to high pressure body centered tetragonal (BCT) structure, which can be seen as the distorted CsCl-type with c/a ratio ≈ 0.82–0.87. The calculated transition pressures are in good agreement with the experimental results. The elastic properties like second-order elastic constants for PrX, Y compounds are calculated for the first time. The nature of the bonding is also predicted by calculating the distance between the ions with the increasing pressure.     

First-principles calculations of structural stability and mechanical properties of tungsten carbide under high pressure

The structural stability and mechanical properties of WC in WC-, MoC- and NaCl-type structures under high pressure are investigated systematically by first-principles calculations. The calculated equilibrium lattice constants at zero pressure agree well with available experimental and theoretical results. The formation enthalpy indicates that the most stable WC is in WC-type, then MoC-type finally NaCl-type. By the elastic stability criteria, it is predicted that the three structures are all mechanically stable. The elastic constants C_ij, bulk modulus B, shear modulus G, Young?s modulus E and Poisson?s ratio ν of the three structures are studied in the pressure range from 0 to 100 GPa. Furthermore, by analyzing the B/G ratio, the brittle/ductile behavior under high pressure is assessed. Moreover, the elastic anisotropy of the three structures up to 100 GPa is also discussed in detail.     

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.     

Elastic and electronic properties of YNi2B2C under pressure from first principles

The elastic and electronic structure properties of YNi₂B₂C under pressure are investigated by performing the generalized gradient approximation (GGA) and local density approximation (LDA) correction scheme in the frame of density functional theory (DFT). The pressure dependences of the normalized lattice parameters a/a₀ and c/c₀, the ratio c/a, and the normalized primitive volume V/V₀ of YNi₂B₂C are also obtained. The lattice constants and bulk modulus obtained are in agreement with the available experimental and other theoretical data. We have also studied the pressure dependences of elastic properties. It is found that, as pressure increases, the elastic constants C₁₁, C₃₃, C₆₆, C₁₂, and C₁₃ increase, the variation of elastic constant C₄₄ is not obvious. Moreover, our compressional and shear wave velocities V_L=6.99 km/s and V_S=3.67 km/s as well as the Debye temperature Θ=549.7 K at 0 GPa compare favorably with the available experimental data. The pressure dependences of band structures, energy gap and density of states are also investigated.     

First-principles calculations of structural, electronic, optical and elastic properties of magnesite MgCO3 and calcite CaCO3

Detailed ab initio calculations of the structural, electronic, optical and elastic properties of two crystals - magnesite (MgCO₃) and calcite (CaCO₃) - are reported in the present paper. Both compounds are important natural minerals, playing an important role in the carbon dioxide cycling. The optimized crystal structures, band gaps, density of states diagrams, elastic constants, optical absorption spectra and refractive indexes dependence on the wavelength all have been calculated and compared, when available, with literature data. Both crystals are indirect band compounds, with calculated band gaps of 5.08 eV for MgCO₃ and 5.023 eV for CaCO₃. Both values are underestimated by approximately 1.0 eV with respect to the experimental data. Although both crystals have the same structure, substitution of Mg by Ca ions leads to certain differences, which manifest themselves in noticeable change in the electronic bands profiles and widths, shape of the calculated absorption spectra, and values of the elastic constants. Response of both crystals to the applied hydrostatic pressure was analyzed in the pressure range of phase stability, variations of the lattice parameters and characteristic interionic distances were considered. The obtained dependencies of lattice constants and calculated band gap on pressure can be used for prediction of properties of these two hosts at elevated pressures that occur in the Earth's mantle.     

Radiation-stimulated pulse conductivity of alkali halide crystals with a NaCl lattice

The temperature dependence of the pulse conductivity σ for crystals of alkali halides with the NaCl-type lattice is measured at different densities j of excitation with an electron beam of picosecond duration. It is demonstrated that an increase in j leads to a weakening of the σ(T) dependence. This effect is due to the overlap of the wave functions of recombination centers and a decrease in the activation energy of separation of genetic electron-hole pairs.     

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.     

Acoustic mode vibrational anharmonicity of hexahelometallate crystals

The vibrational anharmonicity and Grüneisen parameters of hexahelometallate A₂MX₆ single crystals have been determined theoretically by making use of phonon lattice theory. The potential model employed to calculate these properties consists of long range coulomb, three body interactions, short range overlap repulsion effective upto the nearest neighbour ions and phonon-lattice interactions. These antifluorite structure compounds contain large MX²⁻₆- ions and as the interionic spacings are much greater than those of the alkaline-earth fluorite structure halides, their elastic constants are correspondingly smaller. The hydrostatic pressure derivatives of the second order elastic constants (SOEC) calculated for K₂SnCl₆, K₂ReCl₆, (NH₄)₂SnCl₆, (NH₄)₂TeCl₆, (NH₄)₂SnBr₆, and (NH₄)₂TeBr₆, are found to be positive and close to the experimental values. The vibrational anharmonicities of the long-wavelength modes are explained in terms of the acoustic mode Grüneisen parameters.     

Microscopic theory of second-order and third-order elastic constants for an NaCl crystal

Relations between the second-order and third-order symmetry-independent elastic constants and the energy of interatomic interactions dependent on the mutual arrangement of pairs and triplets of atoms are obtained for crystals belonging to the crystal class O _h. The derived relations and experimental data on the elastic constants are used to calculate four third-order elastic constants and the temperature dependence of the elastic anisotropy factor a(T) for an NaCl crystal. The calculated dependence a(T) is in qualitative agreement with the experimental dependence a _exp(T).     

Effect of pressure on the elastic properties of silicon carbide

The pressure dependences of the second-order elastic constants C _ij and the velocity of sound in 3C-SiC and 2H-SiC crystals are calculated in the framework of the Keating model. The third-order elastic constants C _ijk for 3C-SiC are determined from the dependences of the second-order elastic constants C _ij on the pressure p.     

High pressure behavior and structural properties of transition metal carbides

A pressure induced structural phase transition from NaCl-type (B₁) to CsCl-type (B₂) structure has been predicted in transition metal carbides, namely TiC, ZrC, NbC, HfC, and TaC by using an interionic potential theory with modified ionic charge (Z_m ), which includes Coulomb screening effect due to d-electron. The phase transition pressure (P_T ) relies on large volume discontinuity in pressure–volume relationship, and identifies the structural phase transition from B₁ phase to B₂ phase. The variation of second-order elastic constants with pressure follows a systematic trend identical to that observed in other compounds of NaCl-type structure. The Born criterion for stability is found to be valid in transition metal carbides.