Theory of surface atom mean square displacements in chromium

The temperature dependence of the mean square displacements for atoms on the (100) and (110) surfaces of chromium has been studied theoretically using the harmonic approximation. Calculations were carried out for crystals with periodic boundary conditions in two directions and free boundary conditions in the third direction using a Born-van Karman model with central interactions up to third nearest neighbors and non-central angular stiffness interaction between nearest and next nearest neighbors. The values of the force constants were chosen to give good fits to the elastic constants and to the bulk phonon dispersion curves in the three major directions [100], [110] and [111]. The ratio of the mean-square displacements at a surface to that in the bulk was calculated as a function of temperature for both the (100) and (110) surfaces. The theoretical, results are compared with the available experimental data from low-energy electron diffraction.     

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.     

Interionic forces in AgF,AgCl and AgBr crystals

An interionic force model has been used in which the short range nearest neighbour and the next nearest neighbour repulsive interactions and the van der Waals’ interactions are balanced by the long range electrostatic forces. The nearest neighbour and the next nearest neighbour interactions are derived from the overlap integrals for outer shell electrons. The van der Waals’ interactions are estimated from the Slater-Kirkwood variational method. The cohesive energy, the bulk modulus and its pressure dependence for AgF, AgCl and AgBr crystals have been calculated and compared with experimental data.     

Photoelastic constants in silver and thallium halides

In the present communication the expressions for the photoelastic constants of the solids crystallizing in cesium chloride structure have been derived on the basis of lattice theory. These expressions have been utilized to predict the magnitudes of photoelastic constants in thallium halides. On the basis of these constants the validity of the Clausius-Mossotti model of electronic polarization in silver and thallium halides has been discussed.     

Two-fold interferometric measurements of piezo-optic constants: application to β-BaB2O4 crystals

We present the interferometric technique which allows to measure piezooptical and photoelastic characteristics of crystal materials of any symmetry. The offered two-fold interferometric method enables to determine all independent non-zero piezooptic and photoelastic constants by measuring pressure induced changes of optical path. As advantage to known acoustooptical techniques this method allows to measure both the absolute magnitude and sign of photoelastic constants. In general case the determination of 36 components of piezooptic tensor needs to carry out 57 measurements on 16 samples. The corresponding relationships are derived. As an example we apply here the interferometric technique to measure the piezooptic and photoelastic constants in trigonal β-BaB₂O₄ crystals.     

Photoelasticity in polycrystalline aggregates

A theory for the photoelastic behaviour of transparent polycrystalline aggregates consisting of randomly oriented anisotropic crystallites has been developed. Such an aggregate is isotropic but it becomes birefringent under the influence of a uniaxial load. The photoelastic constants of the aggregate are given by the components of the spatial average of the photoelastic tensor of the single crystal, and are worked out by assuming either the strain to be continuous (Voigt approximation) or the stress to be continuous (Reuss approximation). The components of the average photoelastic tensor are very different for these two limits. The elastic and the photoelastic constants of alkali halide aggregates have been evaluated for both the stress continuity and the strain continuity conditions. The maximum variation of the elastic constants in going from the Voigt to the Reuss condition is 50 per cent while the photoelastic birefringence can vary by as much as 300 per cent in alkali halides. In the case of KI and rubidium halides even the sign of the photoelastic birefringence is different for the two limits.     

Dynamic properties of graphene

The phonon spectrum of graphene has been studied with the minimum set of the nearest neighbors in the Born-von Kármán model taking into account the electron-electron and electron-phonon interactions. The widths, both natural and owing to interactions with defects, of phonons have been estimated. Symmetry constraints imposed on force constants are taken into account. For symmetry reasons, vibrations with the polarization normal to the plane of the layer are not related to in-plane vibrations. The phonon frequencies at symmetry points and elastic moduli are expressed in terms of force constants.     

Calculation of the components of the photoelastic effect in alkali-halide crystals

Calculations are made to determine the contribution of Lorentz-field and Coulomb-field anisotropy in alkali-halide crystals to the photoelastic coefficients p₁₁–p₁₂ and p₄₄ as well as to the piezopolarizability constants K, K, K_x, K_z, and K₀. These calculations are based on Mueller's theory of the photoelastic effect, with data on iron polarizability and photoelastic coefficients. The applicability of Mueller' s theory to the complete series of alkali-halide crystals is analyzed. Criteria are established for the ionicity of bonds in these crystals.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 28–34, December, 1975.     

Acoustooptical and elastic properties of laminated KY(MoO4)2 crystals

Data on acoustic (absorption and velocity of sound), optical (refractive index and optical absorption coefficient), and photoelastic (coefficients of acoustooptical quality and photoelastic constants) properties of KY(MoO₄)₂ crystals are obtained. It is shown that, not only does the anisotropy of binding forces lead to a significant anisotropy of acoustic and photoelastic properties, but it also determines anomalously high elastic nonlinearity in the direction of the Y-axis perpendicular to cleavage planes.     

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.     

Cohesive and elastic properties of alkaline earth chalcogenide crystals

In the present study an analysis of the cohesive and elastic properties has been performed in fourteen alkali chalcogenide crystals using the composite potential forms based on the Drude oscillator model. The short-range overlap repulsion has been considered up to the second nearest neighbour interactions. The van der Waals coefficients have been estimated from the Kirkwood-Muller formulae. Cohesive energies, bulk-modulus and its pressure derivatives calculated for the entire family of crystals under study are found to present a good agreement with available experimental data, better than those obtained by previous workers using the traditional Born potential model.On leave from theDepartment of Physics, G. B. Pant University, Pantnagar-263 145, India.Authors are thankful to Mr. Saleh O. Harraga for the computational help.     

Theory of surface force-constant changes in body-centered cubic lattices

A calculation has been made of force-constant changes at the (100) and (110) surfaces of body-centered cubic crystals. A model consisting of first, second and third-neighbor Lennard-Jones interactions together with harmonic angle-bending interactions is employed. The parameters characterizing the interactions are chosen to fit the equilibrium lattice spacing, the elastic constants, and certain phonon frequencies at high symmetry points in the Brillouin zone. The procedure consists of first calculating the static displacements produced by the creation of the surface and then calculating the change in force constants produced by the cubic and quartic anharmonic terms in the potential energy. Specific results have been obtained for chromium, iron, tungsten, and molybdenum.     

Theory of the photoelastic effect in ZnO,ZnS and CdS crystals

It has been a general opinion that the Clausius-Mossotti dielectric theory is not capable of explaining the observed photoelastic behaviour of partially ionic crystals.However in the present communication we show that by making account of the variation of polarizabilities under compressive stress within the framework of the Clausius-Mossotti theory it is possible to obtain a reasonable agreement with experimental data on the photoelastic behaviour of ZnO, ZnS and CdS crystals.     

A three-body force shell model calculation of Schottky defect formation energies of ionic crystals with CsCl structure

A three-body force shell model (TSM) for the calculation of Schottky defect formation energies in solids with cesium chloride structure has been developed by incorporating the effects of long-range three-body interactions (TBI) in the shell model. These TBI in the defect lattice arise from the deformation of electron shells when the nearest neighbour ions get relaxed from their equilibrium position. This model has been used to calculate the cation and anion extraction and Schottky defect formation energies of CsCl, CsBr, CsI, TlCl, TlBr and NH₄Cl crystals. The calculated values of these defect properties agree reasonably well with their measured values.     

Defect modes due to substitutional impurities in FCC lattice: Green's function approach

Lattice dynamical study of monoatomic fcc crystals containing substitutional impurities has been made by the Green's function technique, using group theory. The impurity and its 12 nearest neighbors constitute an XY₁₂ impurity space having O_h symmetry. The phonon Green function matrix is analyzed according to the irreducible representations of the point group pertaining to the substitutional impurity in the fcc lattice. The effects due to change in mass at the impurity site and the change in nearest neighbor force constants for the impurity-host atom interactions are taken into account. Analytical expressions for the various modes of vibrations pertaining to the defect space have been obtained. Local mode frequencies due to various substitutional impurities, corresponding to F_1u mode (defect atom moving) have been computed. A special model is chosen for the defecthost force and it is assumed that there are no distortions of the lattice structure due to the defect. A Kihara hardcore potential with parameters fitted to neutron data has been used to compute lattice dynamics and Green functions of the host lattices. Our theoretical results have been compared with available experimental and theoretical results. Our results show reasonably good agreement with experimental results.     

Elastic characteristics of 2D carbon supracrystals as compared to graphene

The constants of the central and noncentral interactions between carbon atoms in 2D supracrystals, i.e., generalized two-dimensional crystals in which the sites of the lattice contain, instead of individual atoms, their symmetric complexes, have been calculated. It has been shown that these constants essentially depend on the symmetry of the 2D supracrystal and can significantly differ from the corresponding constants for graphene.     

Static and thermophysical properties of chalcogenide crystals with NaCl structure

In the present communication an analysis of interionic potentials in fourteen chalcogenide crystals has been performed. This interionic potential has been used to predict the values of cohesive energy, isothermal bulk modulus and the pressure derivatives of bulk modulus in the solids under study. The many body interaction (MBI) effects have been taken into account within the framework of Hafemeister Zarht potential. Instead of using BM potential the Hafemeister-Zarht (HZ) type short range overlap potential has been considered between nearest as well as between next nearest neighbour ions. The short-range interactions, effective up to second neighbours are treated by considering the hardness parameter as an ionic property. The hardness parameter ρ_ij is evaluated using the data on overlap integrals. The results achieved in the present study are generally in good agreement with available experimental data. Values of cohesive energy, bulk modulus and its pressure derivatives calculated by previous investigators have also been shown for the sake of comparison.     

Rectangular lattice gas model with competing interactions and the two-dimensional ANNNI model in a field

A lattice gas model with short range competing interactions for adsorption on (110) surfaces of fcc crystals, in particular for O/Pd(110), as well as its Ising analog, the two-dimensional ANNNI model with antiferromagnetic axial nearest and next-nearest neighbour interactions in a field, are studied using the free fermion approximation and Monte Carlo techniques. The phase diagrams display different commensurate phases and incommensurate regions. Static and dynamic aspects of topological defects (walls and dislocations) characterising the incommensurate structures are investigated.     

Contributions from the indirect ionic interactions to the elastic constants in the rock-salt structure crystals

Under the harmonic approximation, the contributions from the indirect ionic interactions to the elastic constants are calculated for the alkali halide and silver halide crystals with the rock-salt structure. The coupling constants of the indirect ionic interactions are calculated by the self-consistent field treatment of the local density approximation and the spherical solid model. The calculated values of the coupling constants are large for the silver ion. The indirect ionic interaction significantly affects the elastic constants. It quantitatively explains the deviation from the Cauchy relation in alkali halide crystals. Moreover, it provides a clear account for the large values of the deviation from the Cauchy relation in AgCl and AgBr.     

Relaxation of static photoelasticity in triglycine fluoroberyllate crystals

The relaxation of the static photoelasticity in triglycine fluoroberyllate crystals has been studied. The anisotropy of the relaxation amplitudes and their anomalies near the phase transition have been revealed. The photoelastic relaxations and peculiarities of their temperature behavior have been explained in terms of the piezocaloric mechanism.