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.     

A variational approach to dynamics of simple ionic crystals at high temperatures

The variational theory of anharmonic lattice dynamics is applied to the sodium chloride structure. The Coulomb and the inverse-power repulsive pair potential between ions are used. The mean-square displacements (MSDs) at zero pressure for individual ions, i.e., cation and anion, are calculated as a function of temperature without use of any fit parameters. It is shown that the ratio of the MSDs for anion and cation depends strongly on the ionic-radius ratio. The average MSDs are in reasonably good agreement with the experimental data obtained by a Bragg diffraction technique. A discussion is given of the relation between the divergent behavior of the MSDs which we find at some critical temperature and the observed melting point.A Humboldt fellow on leave of absence from Department of Engineering Science, Hokkaido University, Sapporo 060, Japan     

Simple variational approach to the thermal properties of ionic crystals

The thermal properties of ionic crystals are analysed using the variational principle of classical statistical mechanics. The Einstein and Debye pictures of the lattice vibrations are adopted as trial Hamiltonians. No explicit calculation of the lattice spectrum is needed. The variational result for the thermal expansion in the Einstein picture is identical to that recently derived by Narayan and Ramaseshan by a physically motivated thermal force picture. The agreement with experimental values in the alkali halide family of crystals is surprisingly good, the root mean square error being about 14%. The parameters in the interionic potential used are obtained from the lattice spacings and compressibilities of the crystals and not from anharmonic properties. The Debye picture gives about equally good results for the thermal expansion, but better results for the thermal vibration amplitudes of the ions. It differs from the Einstein picture in incorporating correlated vibrations of atoms and in having an explicit Coulomb contribution to the thermal properties. It is suggested that the theory given in this paper has a useful role to play in studies of thermal expansion and phase stability for large families of ionic crystals when combined with semi-empirical theories.     

An experimental approach to the analysis of electric field gradients in ionic crystals

The spectrum of a partially oriented sample of ethanol has been analysed by making use of the simpler spectra obtained from the species CD₃CH₂OH and CH₃CD₂OH, together with ¹H?{²H} double resonance. With p-ethoxy-benzylidene-p-n-butylaniline (EBBA) as the nematic solvent the dipolar couplings of CH₃ and CH₂ protons with the OH proton can be observed, and their magnitudes are compared with values calculated assuming different models for C-O-H internal rotation. Information on the quadrupole coupling constant tensor elements for CD₃ and CD₂ deuterium nuclei is obtained.     

The Green function approach to the surface lattice dynamics of ionic crystals

The Green function approach to the surface dynamics of semiinfinite lattices is developed in detail and shown to be applicable to crystals with long-range interionic potentials. Such applicability stands on the use of an effective short range perturbation, uniquely defined by the imposition of the translational and rotational invariance conditions for the stress-free semiinfinite crystal. Numerical calculations of the surface dispersion curves and of the surface projected phonon densities of NaCl, LiF and NaI, based on the breathing shell model, are reported and discussed.     

A quantitative approach to ionic adsorption

Binding properties of multi-atomic systems with ionic bonds are calculated by using a recently developed method based on the density functional formalism. The charge density is obtained from a superposition of the respective atomic densities where the charge transfer between these atoms is chosen such that the total energy attains a minimum. The kinetic energy of the electrons can to a very good approximation be calculated by means of a modified Thomas-Fermi-v. Weizsäcker expression. The molecules NaCl and NaW and a NaW₄ cluster have been treated as model systems for ionic interaction. Moreover, we have computed the binding properties of a Na atom adsorbed on a W(100) surface. This particular problem is the primary subject of the present study. The calculations yield binding energies, binding distances, vibrational frequencies, and induced dipole moments.     

New approach to short range repulsion in pion condensation

We develop a new method, using static density correlation functions, to look at the effects of nucleon repulsion at short distances in a nuclear medium. The change in the critical density for pion condensation from the above effect is computed. Also, we investigate the behavior of the critical density on the inclusion of Δ-isobars and of S-wave pion-nucleon repulsion.     

A new expression for the Anderson-Grüneisen parameter δ for ionic crystals

The Anderson-Grüneisen parameter δ has been computed theoretically from a general expression developed by Sharma and Tripathi[6]. The δ-γ (Grüneisen parameter) curves have been plotted to find a relation for the best fitted yielding curves by the method of least squares. The relation developed can be put as δ = AγB and it can be inferred that chang's[3] relation is a particular case of this general equation.     

A point group approach to selection rules in crystals

The problem of generation of the selection rules for a transition between Bloch states at any point of the Brillouin zone in crystals is equivalent to the problem of the decomposition of Kronecker products of two representations (reps) of a space group into irreducible components (the full group method). This problem can be solved also by the subgroup method where small reps of little groups are used. In this article, we propose a third method of generation of the selection rules, which is formulated in terms of projective reps of crystal point groups. It is based on a well-known relation between small irreducible reps (irreps) of little space groups and projective irreps of the corresponding little cogroups. The proposed procedure is illustrated by calculations of the Kronecker products for different irreps at the W point of the Brillouin zone for the nonsymmorphic space group O _h ⁷ which is one of the most complicated space groups for the generation of selection rules. As an example, the general procedure suggested is applied to obtain the selection rules for direct and phonon-assisted electrical dipole transitions between certain states in crystals with the space group O _h ⁷ .     

Positron-electron doublet in ionic crystals

The states of a positron-electron doublet in ideal ionic crystals are analyzed, taking into account the Coulomb interaction of the particles, with their localization both on the immediately nearest ions of different sign, and on the ions next after them. The exactly-solvable quasi-one-dimensional model of a crystal is considered in detail. The wave functions and the characteristic energies of the doublet are obtained. It is shown that states of two types are realized, one of which has a threshold nature, and arises only for definite magnitudes of the Coulomb integrals. For the ground state of the doublet, one can with good precision take the state corresponding to the computation of the Coulomb interaction for localization of the particles on the nearest ions. The role of the Coulomb interactions of higher order are discussed.Translated from Izvestiya Vysshikh Uchebnyk Zavedenii, Fizika, No. 12, pp. 56–61, December, 1989.     

Metal colloids in ionic crystals

Small metallic particles with diameters in the range 1–100 nm have interesting properties which can sometimes be very different from those of bulk metals. Such colloidal particles play an important part in fields which range from catalysis to radiation damage in compound solids, and also have an intrinsic interest since in some respects they can be regarded as a state of matter intermediate between that of a molecule and a solid. In ionic crystals colloids can be produced either by irradiation or by the introduction of a stoichiometric excess of the metal constituent. In either case the colloids form as a result of the aggregation of fundamental point defects, but it is only fairly recently that a reasonably coherent picture of these processes has emerged and the properties of the colloids have been related to those of small metallic particles studied for other reasons. This review discusses the progress which has been made through the use of a large number of different techniques to study the properties of colloids in ionic crystals and related media such as glasses. Particular emphasis is placed on the optical, magnetic resonance and kinetic properties of colloids, and on the discussion of results in the wider context of the physics of small particles.     

Positron thermalization in ionic crystals

The time required for the thermalization of positrons in ionic crystals is estimated. It is shown that the proton-thermalization time in an ionic crystal is much shorter than the shortest positron lifetime with respect to annihilation, so positron annihilation can be used to study the energy spectrum of valence electrons in ionic crystals.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 68–72, April, 1971.     

Positron annihilation in ionic crystals

Positron lifetime measurements were made on Ca²⁺ doped NaCl, Ba²⁺ doped NaCl and X-ray- and additively-coloured KCl crystals. In the NaCl(Ca) system a correlation which could be approximated by a power equation was found between the dopant concentration and the positron annihilation parameters. In the NaCl(Ba) system the decay parameters do not change significantly as expected and no significant difference in the decay parameters of the coloured and uncoloured crystals could be found. Paper C 4 presented at 3rd Internat'l Conf. Positron Annihilation, Otaniemi, Finland (August 1973).     

Charged dislocations in ionic crystals

Experiments and theories concerning charged dislocations in alkali halide crystals are reviewed in detail, with particular attention to the way in which the experiments should be interpreted and to the range of applicability of the sweep-up and various forms of thermal-equilibrium models. Possible effects on mechanical properties and internal friction are analysed. The transient and steady-state effects of plastic deformation on ionic conductivity are described and new interpretations involving charged dislocations are proposed. A survey of results on the scattering of light by alkali halide single crystals leads to the conclusion that charged dislocations do not play an important role.

Evidence about charges on surfaces and on dislocations in AgCl and AgBr is reviewed and compared with that for alkali halides. Comparisons are also made with MgO, the CsCl and CaF₂ structures, semiconductors and ice.     

Electrical breakdown in ionic crystals

A model of formation of an electrical discharge channel in alkali halide crystal is presented. Electrons are generated to the conduction band through cascade Auger transitions in the valence band of the dielectric. The breakdown channel consists of melt and charged layers. The model explains the crystallographic direction and velocity of the discharge channel, as well as generation of prebreakdown current, without resorting to the mechanism of impact ionization of the valence band of the crystal by electrons from the conduction band.     

Electrical breakdown in ionic crystals exposed to nanosecond pulses

Electrical breakdown in alkali halide crystals subjected to ∼10-ns-long electrical pulses is studied. Two, primary and basic, channels of the anodic discharge are noted. In the presence of the primary channel, the other arises at static breakdown voltages. Otherwise, the basic channel forms at voltages exceeding the static breakdown voltage by more than four times. The basic channel is assumed to form via a cascade of Auger transitions. The generation and migration of linear defects seem to play a significant role in the basic channel formation. The enhancement of the pulsed dielectric strength of the crystals is related to conditions of current passage through the metal-insulator interface.     

Localization of polaritons close to dislocations in ionic crystals

It is shown that two types of polaritons are localized at dislocations in ionic crystals. Dispersion equations are obtained for the localized polaritons; the dependence of the oscillation amplitude on the distance to the dislocation is determined. Saratovsk State Technical University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 45–50, October, 1996.