The Born repulsive parameters and dielectric behaviour of alkali halides

The dependence of the Born repulsive parameters of alkali halides on elastic and dielectric data has been discussed. The values of hardness parameter in alkali halides have been recalculated using the revised values of van der Waals energies. It is observed that the two sets of hardness parameter corresponding to elastic and dielectric data differ from each other but become compatible if an effective charge parameter for the ions is introduced. Its usefulness has been demonstrated by calculating the strain derivative of static dielectric constant of alkali halides.     

Evaluation of the second order strain derivatives of the electronic dielectric constant of alkali halides

We have evaluated the second order strain derivatives of the electronic dielectric constant of alkali halides employing two different theories viz. the Clausius—Mossotti theory of polarizability and the Penn model of energy gap. The results obtained from the two theories are in fair agreement with each other. It has been emphasised that the present calculations can be used to separate the electronic and ionic contributions to the second order strain derivative of the static dielectric constant.     

Dielectric behaviour and optic mode Gruneisen parameters of the halides of silver,caesium and thallium

The optic mode Gruneisen parameters in silver, caesium and thallium halides are calculated using the Born model for interionic forces and the Szigeti theory of dielectric constants. The strain derivatives of the electronic and static dielectric constants are also evaluated and compared with experimental data. The strain derivative of static dielectric constant reveals the inadequacy of the Born model for the crystals under study. Possible modifications have been suggested to improve the situation. The theoretical values of the optic mode Gruneisen parameters closely agree with recent experimental data. An appropriate process has been adopted to evaluate the average values for the Gruneisen parameter.     

Theory of strain derivative of electronic dielectric constant of ionic crysts

A theoretical method for evaluating the strain derivative of the electronic dielectric constant of ionic crystals has been developed. The analysis presented here is based on the shell model and takes account of the exchange charge polarizations. Values of strain derivative of the electronic constant dielectric calculated for 6 alkali halides and MgO show a remarkable agreement with experimental data on photoelastic constants.     

Analysis of the photoelastic effect in ionic crystals

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.     

Study of strain optical constants of mixed lithium halides

The theory of photo-elasticity of mixed alkali halides has been used to analyse the strain optical constants and volume derivative of the electronic dielectric constant of the mixed crystal, LiF_0.5Cl_0.5.     

Temperature derivatives at constant volume of the elastic constants of alkali halide crystals

A new method has been developed for calculating the temperature derivatives at constant volume of the elastic constants of the alkali halides using the concept of phonon pressure. Calculated values of temperature derivatives of elastic constants are compared with the corresponding values recently derived from ultrasonic experimental data.     

Analysis of polarizabilities of alkali halides using Narayan-Ramaseshan repulsive potential

The repulsive potential in ionic crystals recently proposed by Narayan and Ramaseshan (NR) can be expressed as the sum of the contributions from the individual ions. In the present paper we show that using this repulsive potential it is possible to divide the polarizability arising from the relative displacement of ions into its ionic constituents. NR have also derived the ionic radii in alkali halides which we have used to estimate the electronic polarizabilities of ions with the help of polarizability-radius cube relation. The electronic polarizabilities of alkali and halogen ions thus evaluated show a good agreement with those deduced from the experimental refraction data.     

Transverse optic mode Gruneisen parameter and dielectric properties of alkali halides

The well known Szigeti relations for the dielectric theory of ionic crystals have been critically examined by investigating the volume dependence of dielectric behaviour of alkali halides. It has been predicted that the strain derivative of effective ionic charge parameter should be nearly equal to zero. Values of transverse optic mode Gruneisen parameter for NaCl structure alkali halides have been estimated.     

Analysis of the repulsive softness parameter in alkali halides

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 Smith's 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.     

Higher order elastic constants of alkali halides

The Coulomb, van der Waals and repulsive lattice sums occurring in the higher order elastic constants up to sixth order have been calculated for the rocksalt and cesium chloride structures. Numerical values of the static elastic constants up to sixth order based on a rigid ion model with van der Waals and Born-Mayer type central force interaction between first and second nearest neighbors are calculated for several alkali halides representing both structure types. Fair agreement with the available experimental third and fourth order elastic constant data is found.     

Use of Harrison's potential in ZnS,NaCl and CsCl-structure solids

Harrison's overlap repulsive potential has been used for evaluating cohesive energies, bulk modulus and its pressure derivatives, Gruneisen parameter, and the volume derivatives of Gruneisen parameter for cuprous halides, silver halides and thallous halides. This potential has replaced the old and widely used Born-Mayer potential in ionic crystals. The Harrison repulsive potential has been represented by a quantum mechanical analytical potential form derived from the tight binding theory. The parameters involved in this potential form have been determined in terms of valence state energies of outermost d-electrons of Cu⁺, Ag⁺ and Tl⁺ ions. The results calculated in the present study have been found in good agreement with experimental data and better than those predicted from the Born potential model.On leave fromDepartment of Physics, G. B. Pant University, Pant Nagar, U. P., India.     

Additivity rule for the softness parameter in alkali halides

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.     

Effect of three-body interactions on electronic polarizabilities and photoelastic behaviour of partially covalent crystals

Summary We have investigated the effect of three-body interactions on the photoelastic behaviour and the electronic polarization of silver, thallium and copper halides, which are partially covalent in character and possess three different crystall structures. The cation, anion and molecular polarizabilities calculated in their crystalline state seem to be reliable as they follow a systematic trend. Our calculated values of the strain derivatives of the electronic dielectric constants are much closer to their experimental data than those obtained by earlier workers. To speed up publication, the authors of this paper have agreed to not rceive the proofs for correction.     

On the Mott-Littleton dielectric theory for alkali halides

It has been demonstrated that the Mott-Littleton theory of dielectric constant is consistent with the recent experimental data on the pressure dependence of dielectric constant of alkali halides. On the other hand, the Clausius-Mossotti and Drude models yield large deviations from the observed data.     

Evaluation of strain polarizability parameter in alkali halides

The strain polarizability parameter λ for alkali halides under the effect of hydrostatic pressure has been evaluated. The correlations of λ with fractional ionic character, effective ionic charge and the overlap repulsive energy have been pointed out.     

Dielectric and anharmonic behaviour of mixed alkali halides

Summary In the present paper an analysis of the dielectric behaviour and anharmonic contribution to the dielectric constants has been made of KCl−KBr mixed ionic crystals. The temperature and volume derivatives of static (ε₀), electronic (ε_∞) dielectric constants and energy gap parameter (E _g) have been calculated using the Szigeti and Havinga and Bosman dielectric theories. The anharmonic contributions have been estimated in terms of temperature derivatives of dielectric constants at constant volumes. The modified form of Clausius-Mossotti theory of dielectric polarization has been used for the mixed crystal under study. The calculated quantities have been compared with the available experimental data. A good agreement has been obtained. To speed up publication, the authors of this paper have agreed to not receive the proofs for correction.     

Strain derivatives of high and low frequency dielectric constants of cuprous halides

A phenomenological lattice theory is derived to study the strain derivatives of the high and low frequency dielectric constants of solids with the ZnS type structure. The theory is used to analyse the peculiar photo-elastic behaviour and the mechanism of polarisation in cuprous halides.     

Structural and dynamical properties of silicon in a «covalent» huggins-mayer scheme

Summary A rereading of the Fumi and Tosi paper on the ionic sizes and Born repulsive parameters in the alkali halides family led us to draw a parallelism with recent total-energy calculations for semiconductors, where the Coulombic interactions are substituted by a semi-empirical tight-binding estimation of the covalent attraction and the repulsive term is still of Huggins-Mayer form. We find that for crystalline silicon the hardness parameter ρ is surpirisingly the same as for the alkali halides. In honour of Prof. Fausto Fumi on the occasion of his retirement from teaching.