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.     

Electronic polarizabilities and sizes of ions in alkaline earth halides and alkali chalcogenides

An analysis of the electronic polarizabilities and sizes of ions in the crystals of alkaline earth halides and alkali chalcogenides has been performed using a relation between polarizability and ionic radius. The electronic polarizabilities and sizes of ions are calculated using the free state data reported by Pauling. The quantities obtained in the present study are found to vary from crystal and crystal, thus showing the deviations from the additivity rule. The results are discussed and compared with those obtained by other investigators.     

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.     

A new theory of compressible ions — structures of the alkali halides

Ions in ionic crystals are considered to exist in compressible space-filling polyhedral cells analogous to the Wigner-Seitz cell in metals. Repulsion arises from the compression energy of the ions written as a surface integral over the ionic cells. Two adjustable parameters are introduced per ion with the provision that the same parameters can be used in any crystal of any structure in which the ion occurs. The 18 parameters for the 5 alkali and 4 halogen ions have been determined from PV data on the 20 alkali halides. The important successes of the theory are: (i) All the twenty alkali halides are correctly predicted to occur in their observed structures (ii) The thermal transition in CsCl is explained (iii) The pressure transitions in the alkali halides are predicted well (iv) The calculated values of the variation of transition pressures with temperature agree well with experiment. These results are much better than those obtained by earlier theories.     

Correlation between electronic polarizabilities and ionic radii in alkali halides

An analysis of the electronic polarizabilities and sizes of ions in alkali halides has been carried out by considering a relationship according to which the electronic polarizability of an ion should vary as the n th power of its radius. The values of crystal radii, polarizabilities and the exponent “n”have been calculated using the free ion data reported by Pauling. The values of “n” are found to be nearly 3 in most of the crystals suggesting the validity of the polarizability radius cube relation. The polarizabilities and crystal radii calculated in the present study agree well with those estimated by earlier investigators.     

Analysis of crystal binding of ammonium halides

Electronic polarizabilities and sizes of ions in NH₄Cl, NH₄Br and NH₄I crystals are calculated using Ruffa's theory and an empirical relation between polarizability and radius. Using the electronic polarizabilities we have estimated the van der Waals dipole-dipole and dipole-quadrupole potentials following the Slater-Kirkwood varitional method. These potentials and ionic radii are then used to calculate the cohesive energies of ammonium halides. The results are discussed and compared with those of other investigators.     

Analysis of first and second order strain derivatives of the dielectric constants of alkali halides

Expressions for evaluating the first and second order strain derivatives of the electronic and static dielectric constants of alkali halides are derived. The strain derivatives of the electronic dielectric constant are calculated by taking account of the effect of the crystalline potential on the variation of electronic polarizabilities with volume. The strain derivatives of the static dielectric constant are evaluated adopting the exponential and the inverse power forms for the short range repulsive potential. Two sets of the Born repulsive parameters derived from ultrasonic data and dielectric data are used to evaluate the lattice contribution to the volume dependence of static dielectric constant of alkali halides.     

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 compressed-ion model of cohesion in alkali halides

First-principle local-density calculations of the total energy of ions confined within a sphere were performed The results for positive alkali and negative halogen ions are used to test the validity of the compressed-ion model for the cohesion of alkali halides recently proposed by Narayan and Ramaseshan It was found that the model is not realistic since the calculated ionic compression energies are by far too large to account for the observed equilibrium lattice constants and bulk moduli of alkali halides.     

A new approach to repulsion in ionic crystals

An empirical approach is attempted to make the repulsion potential of ions in an ionic crystal structure independent and crystal independent so that once the repulsion parameters for an ion are evaluated in one compound, in one structure, they could be used for that ion in any crystal. The repulsion between ions is postulated to be due to the increase in the internal energy of the ions arising from the distortion and the compression at the points of contact with their neighbours. Using an exponential form for the compression energy involving two parameters per ion, a repulsion potential for ionic crystals is proposed which includes the repulsion between nearest and next nearest neighbours. The repulsion parameters for the alkali and halogen ions have been determined to fit the behaviour of 20 alkali halides over the pressure range 0–45 kbars. The r.m.s. percentage deviations from experiment, of the calculated values of lattice spacing and compressibility are respectively 0.997% and 6.76%. The calculated radii of the ions in the various compounds compare well with the experimental values deduced from electron density maps. The advantages of the present form of the repulsion potential over earlier forms are discussed.     

Electronic polarizabilities and sizes of ions in AN B10−N type semiconductors

Electronic polarizabilities and sizes of ions in A^N B^10?N type semiconductors (PbS, PbSe, PbTe and SnTe) have been deduced in the present study. The free ion polarizabilities of Sn²⁺ and Pb²⁺ ions are estimated approximately following the procedure of Pauling. The effect of crystalline potential is then estimated on free cation polarizabilities. An empirical relation between ionic radii and polarizabilities has been applied to deduce the ionic sizes and anion polarizabilities. The calculated molecular electronic polarizabilities agree well with the experimental values. The variation of dielectric constant with strain has also been estimated in each crystal and the results are explained in terms of the optical anisotropy parameter.     

Studies on the opto-electronic properties of alkali halides from optical electronegativities

A simple method of evaluating refractive indices from Duffy's optical electronegativity values is proposed. In the proposed empirical relations the optical electronegativity for the anion as well as the cation are taken into consideration in order to obtain refractive indices in alkali halides. The refractive indices so obtained are used in the evaluation of electronic polarizabilities in these compounds and the results are found to be in good agreement with the standard values.     

Electronic polarizabilities of ions in transition metal oxides

A method for evaluating the electronic polarizabilities from ionic radii in transition metal oxides has been suggested. The ionic radii used in the present calculations are those deduced from the electron density measurements. The calculated polarizabilities agree closely with the experimental values obtained from the electronic dielectric constant.     

Electronic polarizabilities of ions in transition metal oxides

A method for evaluating the electronic polarizabilities from ionic radii in transition metal oxides has been suggested. The ionic radii used in the present calculations are those deduced from the electron density measurements. The calculated polarizabilities agree closely with the experimental values obtained from the electronic dielectric constant.     

Improved van der Waals potentials for alkali halide crystals

Improved values of the van der Waals energy coefficients are presented for 16 alkali halides using more recent electronic polarizabilities and, for each ion, three alternative values of the effective number of electrons. The statistical method of calculating interionic potentials is used to obtain the correlation energy at small interionic separations and the values are scaled to fit the van der Waals energy at large separation. The resultant correlation energy as a function of interionic separation is fitted to both a cubic polynomial and a cr^?6 analytic form. The extent to which the van der Waals interactions are quenched by ionic overlap is derived and contrasted with Catlow et al. work on this effect.     

Recent developments in the theory of ionic melts

Summary A brief review is given of the present state of the art in the theory and numerical simulation of ionic melts, and in particular of molten alkali halides. Some recent developments concerning the theoretical evaluation of the static pair structure, the phase diagram and the microscopic dynamics in these melts are discussed. The importance of ionic polarizabilities is stressed. Some perspectives for future work are pointed out in the conclusion. Unité de Recherche Associée 1325 du CNRS.     

On the formation of silver specks in silver halide crystals

This theoretical study summarizes ionic and electronic processes in AgBr crystals and the influence of its results on photographic process. It deals with the importance of surface generated interstitials which Gurney and Mott left untouched because of the non-availability of sufficient data at that time. The magnitude of various parameters,e.g., mean intra-electron-ion distance in a latent image site, the rate of neutralization of Ag⁺ ion with trapped electron and capture cross-section for combination of Ag⁺ ion with the trapped electron, etc. (as desired for understanding the theory of photographic process) are calculated at different temperatures. The results when used in our earlier papers (Singh and Sharma, 1974 and 1975, and Singh 1975) for calculating charged particle track characteristics theoretically were found to give good agreement with the published experimental data (Della Corteet al 1953 and Dyer and Hechman 1967). A model for the mechanism of latent image formation (silver speck) is discussed.     

Sizes and electronic polarizabilities of divalent ions in crystals

The Pauling’s form for the overlap repulsive energy is used to calculate the sizes of isoelectronic divalent ions in MgO, CaS, SrSe and BaTe crystals by minimising the next nearest neighbour repulsive interaction. The radii calculated by this method differ significantly from the conventional sets of ionic radii in a consistent way, being larger for cations and smaller for anions. The polarizability-radius cube relation is also utilized to calculate the electronic polarizabilities of ions. The electronic polarizabilities, thus obtained agree with the values determined from the refractivity measurements.     

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.