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.     

Effect of many body forces on the photoelastic constants of the alkali halides

A simple phenomenological lattice theory based on the Lundqvist potential of ionic cohesion (many body theory of elastic dielectric), to explain photoelastic behaviour of the solids with rock-salt structure, is presented and shown to apply within reasonable errors to the known experimental constants. The predicted values of the photoelastic constants of the alkali halides are very close to the experimental values and are better than obtained by all earlier workers.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Third-order elastic constants for 2:2 chalcide crystals possessing the sodium chloride structure

Third-order elastic constants of 45 chalcide crystals having the sodium chloride structure are reported using Born-Mayer potential model. We have considered repulsive interaction up to second nearest neighbours. The temperature coefficients of the third-order elastic constants have also been computed for these crystals. As is the case for NaCl-type alkali halides we find that C₁₁₁, C₁₁₂, C₁₆₆ are negative and C₁₄₄ are positive for 2:2 chalcide crystals possessing the NaCl-type structure. We have found that a₁₂₃, a₄₅₆ and a₁₄₄ are negative whereas a₁₁₂ and a₁₆₆ are positive, once again in agreement with the situation found for the alkali halides a₁₁₁ values are positive for alkali halides whereas they are both positive and negative depending upon the interionic distance for the chalcide crystals. We have found that the nature of the variation of C⁰_αβγ with interionic separation is similar for alkali halides and for the 2:2 chalcides having the NaCl-structure. We have also computed the values of the pressure derivatives of second-order elastic constants for MgO, CaO, and SrO which agree well with the experimental values indicating the satisfactory nature of our computed data for C_αβγ.     

Multiplication of anion and cation electronic excitations in luminescent wide-gap ionic crystals

The spectra of intrinsic luminescence excitation by synchrotron radiation (6–32 eV) at 8 K have been analyzed for NaCl, KCl, RbCl, KBr, RbBr, CsBr, MgO, CaO and YalO₃ crystals. In all crystalsv (except MgO and CaO) the process of multiplication of electronic excitations (MEE) causes a sharp increase of the intensity of self-trapped exciton emission, but leads (in KBr and NaCl) to the decrease of intra-band luminescence efficiency. The analysis of the intensity ratio spectra for two components of exciton emission allows us to separate the process of secondary exciton creation by hot photolectrons (NaCl, KBr, YAlO₃). The threshold energies of excitonic and electron-hole mechanisms of MEE are compared for a number of alkali halides.     

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.     

碱卤化合物和MgO的离子间距-压强关系分析

 给出了一种新的方法来决定固体的离子间距与压强的关系,并将这种方法应用到碱卤化合物和MgO晶体。这种新方法的理论基础是利用Hildebrand 近似、并运用Harrison的处理方法来考虑排斥能,即考虑离子间的相互作用直到次临近离子。还利用了更精确的方法来计算偶极子-偶极子和偶极子-四极子之间的相互作用。利用这种新方法得到的结果和实验结果吻合得很好。     

Application of three body force shell model to the lattice dynamics of transition metal oxides MnO,CoO and NiO

Lattice dynamics of some transition metal oxides has been studied using the three body force shell model. Reasonably good fits with the experimental phonon dispersion curves have been obtained by choosing values of molecular electronic polarisability substantially lower than those derived from the dielectric constant. This result is similar to those obtained in many other crystals which are not ideally ionic.     

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.     

Analysis of ionicity parameters and photoelastic behaviour of AB type crystals

Values of ionicity parameters have been obtained using the revised energy gap model due to Grimes and Cowley. We have used a power law as well as an exponential law for representing the dependences of homopolar energies on interatomic distances. Values of fractional ionic character of the chemical bond are calculated in 68 A^NB^8–N type diatomic solids. The heteropolar energy parameters have been found to exhibit systematic relationships with the interatomic separations for diatomic solids with the common cations in I–VII and II–VI crystals. The strain derivatives of electronic dielectric constant related to the photoelastic behaviour of solids have also been studied with the help of the ionicity parameters within the framework of Phillips–van Vechten dielectric theory. The results obtained from the power law and the exponential law are in close agreement with each other.     

A study of the optical absorption and the hyperfine constant of the F-centre in alkali halides by means of the multiple scattering Xα method

The F-centre in several alkali halides has been investigated by means of the multiple scattering Xα method. The calculated values of the first absorption peak and the hyperfine splitting constant are compared to experimental results and other theoretical work. It is found that the results agree quite well with experimental values.     

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.