J. Shanker

On the evaluation of the van der Waals potentials in ionic crystals

An application of the Slater–Kirkwood variational method has been made to evaluate the van der Waals dipole–dipole and dipole–quadrupole energies in the four families of ionic crystals, viz., alkali halides, alkaline earth chalcogenides, alkali chalcogenides, and alkaline earth halides. The methods based on the perturbation theory adopted by previous investigators to evaluate the van der Waals potentials are critically discussed. In the present paper we have used an interpolation scheme and semiempirical formulas to estimate the dipole–dipole and the dipole–quadrupole coefficients between a number of different ions with electron configurations close to those of the rare gas atoms. An independent check of the approximate validity of the interpolation scheme has been provided by evaluating the dipole–dipole interaction coefficients between alkali metal atoms. The crystal energies of alkali halides, calculated using the new values of van der Waals potentials, agree closely with the experimental values.

Theory of thermal expansivity and bulk modulus for MgO and other minerals at high temperatures

Abstract The Gruneisen theory of thermal expansion as formulated by Born and Huang has been modified by including higher-order terms for the change in volume in the expansion of potential energy. New expressions are obtained for the thermal expansivity and bulk modulus, and used to estimate these quantities for MgO and other minerals in the temperature range 300–1800 K. The results are found to present close agreement with the experimental data.

Spectroscopic constants of alkali halides and hydrides using modified T‐Rittner model

The T‐Rittner model derived from quantum mechanical exchange perturbation theory is modified by incorporating (i) new values of molecular state polarizabilities, (ii) the recent values of van der Waals potentials estimated from the Kirkwood–Muller (KM) formula, and (iii) the repulsive hardness parameters evaluated from the overlap integrals using the exchange charge model (ECM). With the help of this modified potential model we calculate values of binding energy W, dipole moment μ, vibrational frequency ωe, vibrational anharmonicity constant ωeXe, and rotational constant αe for diatomic molecules of alkali halides and hydrides. The results obtained in the present study are compared with the experimental data. A good agreement between calculated and experimental values supports the validity of the modified T‐Rittner model used in the present study.

Equation of state and pressure derivatives of bulk modulus for NaCl crystal

A method has been developed to obtain an equation of state for ionic solids starting from the theory of interionic potentials and using analytical functions for the volume dependence of the short-range force constant. The expressions are also obtained for isothermal bulk modulus and its pressure derivatives. Numerical analysis is presented for a NaCl crystal up to 30 GPa. The results are compared with the available experimental data. The variation of the pressure derivative of bulk modulus with pressure has also been studied using the formulation recently developed by Stacey.

On the universality of phenomenological isothermal equations of state for solids

Abstract We present a test of universality for phenomenological isothermal equations of state by applying them in different types of solids. The pressure–volume relationship and the isothermal bulk modulus have been obtained using the Birch–Murnaghan third-order as well as fourth-order equation of state (EOS), the Vinet EOS and the Shanker EOS for rare gas solids (Ne, Ar), metals (Al, Cu) and diatomic solids (LiH, MgO) down to a compression of V / V 0 =0.2. It is found that the results obtained from the Shanker EOS compare well with the corresponding values obtained from the Vinet EOS for all the solids up to very large compressions. On the other hand, the Birch–Murnaghan EOS becomes less successful at high compressions in several cases. The variation of the pressure derivative of the isothermal bulk modulus for the entire range of compression has also been studied and used to discuss the suitability of the equations of state.

Theory of interionic forces in alkali halide molecules

A modified treatment of the interionic forces for alkali halide molecules is presented within the framework of Rittner’s model. The electronic polarizabilities of ions in the molecular state are calculated using an energy level analysis. The free ion polarizabilities used in Rittner’s model are replaced by the molecular state polarizabilities. The contributions arising from the van der Waals interactions and the mutual polarization of ions are recalculated. Values of the dipole moment, the binding energy, and the rotational and vibrational constants are estimated for twenty alkali halides using two alternative potential forms for the repulsion energy. The results are discussed in the light of experimental data.

Analysis of pressure - volume - temperature relationship for some alkali halide crystals

Abstract The Chopelas-Boehler approximation for the volume dependence of the Anderson-Gruneisen parameter and the Anderson formula for the temperature dependence of thermal expansivity have been used to study the pressure-volume-temperature relationship for LiF, NaF and CsCl crystals up to a pressure of 90 kbar and in the temperature range 298–1073 K. The results obtained are found to present close agreement with the available experimental data.

Analysis of the photoelastic effect in ionic crystals

Abstract An analysis of the photoelastic effect in ionic crystals has been presented within the framework of Clausius-Mossotti theory of the dielectric constant. The values of the strain derivative of the electronic dielectric constant have been calculated in alkali halides and MgO crystals by taking into account the variation of electronic polarizabilities with compressive stress. The results obtained are found closer to the experimental values. The photoelastic behaviour of MgO crystal is predicted to be of opposite nature to that of alkali halides, in conformity with the experimental observations.

Analysis of the repulsive softness parameter in alkali halides

Abstract An analysis of the repulsive softness parameter for alkali halides has been presented on the basis of the additivity rule. The softness parameters for individual ions have been obtained using data from three different sources viz. overlap data, molecular data and crystal data. The softness parameters so derived are used to evaluate the bulk modulus and its pressure dependence for 20 alkali halides with NaCl and CsCl structures adopting Smiths distortion model for repulsive interactions. Some attractive features of the present approach have been discussed in order to demonstrate its superiority over the previous work.

Additivity rule for the softness parameter in alkali halides

Abstract In the present communication we report an additivity rule for the repulsive potential softness parameter in alkali halides derived from the values of overlap integrals. This rule provides a new interpretation for the repulsive interactions between different ion pairs and reduces the number of parameters. The use of additivity rule eliminates the assumption that the anion-anion, anion-cation and cation-cation softness parameters are equal. Using the new model for repulsive interactions we have calculated the cohesive energy and compressibility of sixteen alkali halides with NaCl structure. The results obtained in the present study are in better agreement with experiment than those obtained earlier with the help of a traditional approach based on the Born model.