Models of environmental effects on anion polarizability

This paper deals with three different approaches to the representation of environmental effects on anion polarizability in cubic crystals of the stoichiometry MX, where M is an alkali metal and X is a halogen. Ab initio embedded cluster calculations of the variation in anion polarizability with pressure in a fixed crystal type are presented and compared with experiment. The results are then used in a scaled ab initio model used to predict further values for the pressure dependence of the in-crystal anion polarizability. This scaled model is compared with a fully empirical ‘universal’ model due to Batana et al. based on polarizability change with ionic radius [1997, Molec. Phys., 92, 1029]. The assumptions of the two models differ substantially and the central purpose of this paper is to contrast these differences and highlight their consequences for prediction. Although the empirical model typically overestimates the experimental pressure derivatives, and the ab initio calculations somewhat underestimate them, it is shown that the assumption of incompressible cations in the scaled ab initio-derived model has a firmer physical basis than the empirical picture in which all ions are compressible.     

Crystal radii of ions in alkaline earth chalcogenides

The crystal radii of ions in alkaline earth chalcogenides have been calculated from the effective nuclear charges of isoelectronic ions. The ionic radii thus calculated are found to follow the polarizability—radius cubed relation, according to which the ratio of the electronic polarizability of an ion to the cube of its radius in the free state is nearly equal to that in the crystalline state. The interionic separations in alkaline earth chalcogenides and also AB₂ and A₂B type crystals obtained from the ionic radii reported in the present paper agree closely with the experimental values.     

Vacuum ultraviolet and X-ray emission spectroscopy of anion and cation excitons in oxide crystals

The results of a combined experimental investigation into the radiative relaxation of anion and cation excitons during selective vacuum ultraviolet-(up edge) and soft X-ray (core) excitation of berylliumcontaining BeO, Be₂SiO₄ and La₂Be₂O₅ crystals are presented. They indicate that the relaxation of anion and cation excitons in multi-component oxides occurs in the same local fragments of the crystal lattice, due to their higher predisposition (in comparison with other fragments) to short-lived distortions. It has been found that in La₂Be₂O₅ crystals characterized by a considerable difference in the ionic radii of cations (beryllium and lanthanum), the beryllium-oxygen tetrahedra do not participate in exciton relaxation processes.     

Ion diffusion-controlled thermally stimulated processes in x-ray irradiated halide crystals

The ionic and ion diffusion-controlled thermally stimulated relaxation (TSR) processes in CaF₂, BaF₂, LiBaF₃ and KBr crystals were investigated above 290 K by means of the ionic conductivity, ionic thermally stimulated depolarisation current (TSDC) and thermal bleaching techniques. Under a DC field the halide crystals store large ionic space charge. We were able to detect in CaF₂, BaF₂, LiBaF₃ and KBr in the extrinsic ionic conductivity region a series of the ionic defect (the interstitial anion and/or anion vacancies - in fluorides; the cation vacancies - in KBr) release stages: 3-6 wide and overlapping ionic TSDC peaks. The correlated data of the ionic TSDC and the F band thermal show that above 290 K the TSR processes are initiated and controlled by the ionic defect thermal detrapping, migration and interaction with the localised electronic and ionic charges and colour centres. The ion diffusion-controlled TSR processes take place in the above halide crystals.     

Inter-relationship between optical dielectric constant and interatomic separation of mixed crystals in ionic and covalent binary compound families

An ion dependent dielectric model is developed for mixed binary crystals. The interatomic separation (R) and optical dielectric constant (ε_∞) of the mixed crystals are computed from the measured values of R and ε_∞ of pure crystals. An empirical relation between ε_∞ and R is therefore found for mixed crystals by using the computed values. It is found that the dielectric behaviour of ionic mixed crystals is cation dependent while that of covalent mixed crystals is anion dependent. The prescribed theory can therefore be used to form different mixed crystals with particular values of ε_∞ required in any specific opto-electronic devices.     

Temperature dependence of dielectric constant of crystals with fluorite structure

The experimental data on the temperature variation of dielectric constant of six crystals with fluorite structure are analysed using an approach proposed by Havinga and Bosman for ionic crystals. The temperature variation of dielectric constant is resolved in three components related to the thermal expansion, the pressure dependence of dielectric constant and the temperature variation of polarizability (theA, B, C terms). In the present work, theB term is calculated semiempirically, such that the analysis can be extended to crystals like EuF₂ for which high pressure dielectric constant data are not available. For the first time, such calculations have been made for EuF₂ and PbF₂ at elevated temperatures. TheC term, which is related to the temperature variation ofir polarizability is seen to play a dominant role in determining the temperature variation of dielectric constant.     

Prediction of cell variations with pressure of ionic layered crystal Application to the matlockite family

Compounds belonging to the matlockite family are ionic layered crystals. Some previous experimental studies on these compounds demonstrated the correlation between the difference in bond strength translating the layered properties and the anisotropic coordination of the highly polarizable halogen anion. In the present paper, we present a model to estimate the anisotropic compressibilities of matlockites which could be generalized to other ionic layered compounds. The compressibilities of each individual polyhedron which built the sheet of an ionic layered crystal are determined from a simple relation based on a semi-empirical relation obtained by Hazen et al., involving the electrical charge of the ions and the interatomic distances. The electrical charge of the anions are taken to be direction-dependent and are modulated by the anion polarizability value. Finally, to validate the model, the calculated compressibilities are compared with previously published data, but also with new high pressure experimental data obtained by X-ray absorption spectroscopy up to 20 GPa on SrFCl and SrFBr at the K edge of the strontium and by X-ray diffraction up to 30 GPa on SrFBr and PbFBr. Present estimations give results which differ from the experimental values by less than 15%. Received 26 October 1998     

On the application of the theory of the brownian movement in a periodic potential to the study of inertial effects and dipole coupling

For a series of ten electron molecules (HF, H₂O, NH₃, CH₄) the molecular polarizability tensor and the derivatives with respect to the symmetry coordinates have been calculated from ab initio SCF wavefunctions using the finite field method as well as perturbation theory approaches. Raman intensities and degrees of depolarization derived from the finite field results agree well with the available experimental data.

The zeroth order bond polarizability model and the atom dipole interaction model have been analysed. Both models can be used to describe the computed static polarizabilities and the derivatives with respect to bond stretching, but fail for the derivatives with respect to the bending coordinates.     

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.     

Relationships between lattice energy and electronic polarizability of AB crystals

The correlations between the electronic polarizability, determined from Clausius-Mosotti equation based on dielectric constant ε, and the lattice energy density u have been established for A^NB^8-N crystals, such as the systems of rock salt crystals (group I-VII, II-VI) and tetrahedral coordinated crystals (group II-VI, III-V). For the A^NB^8-N crystals systems, our present conclusions suggest that lattice energy density u decreases exponentially with increasing electronic polarizability, and the normal mathematical expression between lattice energy density u and electronic polarizability is u = pα^q, p and q depend on the type of crystals. For the same cation binary A^NB^8-N crystals systems, curve fitting equations have been obtained, and the relevant squares of the correlation coefficient R² are larger than 0.99, which show all lattice energy density u are in good exponential relation with electronic polarizability. These empirical equations will give more information on calculating lattice energy or electronic polarizability. New data of lattice energy have been calculated on the above equation u = pα^q, and a good linear trend in the calculating values along with the Zhang’s values has been obtained.     

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.     

Molecular simulation of LiCl aqueous solutions

Non-primitive LiCl aqueous electrolyte solutions were studied at 1.0, 5.0 and 10.0 M concentrations by molecular dynamics simulations. It was observed that the ion hydration structure is progressively lost with increasing concentration. The ions are aggregated in small clusters at C = 1.0 M. However, at this concentration, two large clusters were detected that are an initial step in an aggregation process. At C = 5.0 M, the highly unstable ion clustering seems to correspond to an intermediary state between low concentration states with poor aggregation and states where the ions are highly aggregated, as observed at C = 10.0 M where almost all the ions are clustered in one cluster. This cluster does not present a crystal-like structure. The high solubility of LiCl in aqueous solutions can consequently be explained as a result of the large radii difference between the anion and the cation that results in the instability of the ionic aggregates, which makes the formation of crystal seeds difficult.     

Two-dimensional analysis of Bose-Einstein correlationsin hadronic Z decays at LEP

Bose-Einstein correlations are studied in pairs of charged pions from hadronic Z decays, collected by the ALEPH detector. The correlation function, measured using either the unlike-sign or the mixed reference sample, is studied in terms of the Lorentz-invariant four-momentum difference and its transverse, Q _T, and longitudinal, Q _L, components with respect to the longitudinal centre-of-mass system. Values for the correlation radii, R _T and R _L, are obtained from the fit of the Goldhaber parametrisation. The results indicate that the correlation radii values depend on the chosen kind of reference sample and on the two-jet purity.Received: 23 April 2004, Revised: 11 May 2004, Published online: 9 July 2004     

Structural and electronic properties of PbTe (rocksalt)/CdTe (zinc-blende) interfaces

We study interfaces between highly ionic crystals with different crystal structure by first-principles total-energy calculations in the repeated-slab approximation and compare the results with experimental data extracted from high-resolution transmission electron micrographs. The non-polar (1 1 0) interface between PbTe (rocksalt) and CdTe (zinc-blende) crystals gives rise to a lateral spatial offset between the two crystal halves. At the polar (1 0 0) interfaces a strong variation of the interface extent with respect to the cation or anion termination is observed. Furthermore, we calculate band offsets and projected interface band-structures for PbTe/CdTe interfaces. The results are discussed versus the interface orientation.     

Ion diffusion-controlled thermally stimulated processes in X-ray irradiated halide crystals

The ionic and ion diffusion-controlled thermally stimulated relaxation (TSR) processes in CaF 2 , BaF 2 , LiBaF 3 and KBr crystals were investigated above 290 v K by means of the ionic conductivity, ionic thermally stimulated depolarisation current (TSDC) and thermal bleaching techniques. Under a DC field the halide crystals store large ionic space charge. We were able to detect in CaF 2 , BaF 2 , LiBaF 3 and KBr in the extrinsic ionic conductivity region a series of the ionic defect (the interstitial anion and/or anion vacancies - in fluorides; the cation vacancies - in KBr) release stages: 3-6 wide and overlapping ionic TSDC peaks. The correlated data of the ionic TSDC and the F band thermal evidence that above 290 v K the TSR processes are initiated and controlled by the ionic defect thermal detrapping, migration and interaction with the localised electronic and ionic charges and colour centres. The ion diffusion-controlled TSR processes take place in the above halide crystals.     

Observation of ionic deformation and bonding from compton profiles

We describe a new method of interpreting Compton profile data using a function B(r) which is the autocorrelation function of the one-electron wave function Ψ(r). In any particular direction B(r) can be obtained by a one-dimensional Fourier transform of the corresponding directional Compton profile. The technique is applied to LiF and it provides a means of determining the ionic radii, as well as locating some inadequacies in the tight-binding overlap model for ionic crystals.     

Structure and M?ssbauer studies of manganese monosulfide solid solutions MxMn1 ? xS (M = Cr, Fe)

This paper reports on the results of the synthesis and study of the diffraction patterns and M?ssbauer spectra of single crystals of homogeneous M xMn_{1 − x} S solid solutions with a cubic NaCl structure prepared by the cation substitution of 3d elements for divalent manganese ions in manganese monosulfide. It has been shown that, similarly to the hydrostatic pressure, the substitution of 3d ions with a smaller ionic radius is accompanied by the contraction of the MnS cubic cell. The calculated lattice parameters agree with the experimental data. The homogeneous region of the formation of homogeneous solid solutions is limited in composition x, which depends on the choice of a substitutional cation.     

Lattice dynamics and superionic properties of Cd1−xPbxF2 crystals

Reflectivity in the infrared range, Raman scattering and ionic transport properties in Cd_1−xPb_xF₂ crystals have been investigated. A “one-mode” behaviour of these crystals has been found. The role of the PbF₂ cation sub-lattice in the anion disordering process has been discussed. A correlation has been found between the ionic transport properties and the fluorine-cation interaction coefficient for Cd_1−xPb_xF₂ crystals.     

Effect of quenching on the electrical conductivity of doped KCl crystals

Electrical conductivity and optical absorption of divalent cation and anion doped KCl crystals have been measured before and after quenching from 750 °C. The conductivity after quenching is found to decrease in undoped and cation doped crystals while it increases in the anion doped crystals. This is due to higher coagulation rate of cation impurities as compared to anion impurities. Since the divalent impurities diffuse in the form of impurity-vacancy complexs, the higher mobility of cation vacancies (which form dipoles with divalent cation impurities) accounts for the higher aggregation rate of the cation impurities. The aggregation rate, during annealing after quenching, has also been found to depend on concentration.The author is indebted to Prof. H. N.Bose for helpful discussions. Thanks are also due to Dr. M. L.Mukherjee for providing the crystals.     

Modeling of lattice constant and their relations with ionic radii and electronegativity of constituting ions of A2XY6 cubic crystals (A=K, Cs, Rb, Tl; X=tetravalent cation, Y=F, Cl, Br, I)

In the present paper a new empirical model is proposed to describe and predict the lattice constants for a series of cubic crystals, all of which have the A₂XY₆ composition (A=K, Cs, Rb, Tl; X=tetravalent cation, Y=F, Cl, Br, I). The model is based on a thorough analysis of structural properties of 85 representative crystals from this group. It was shown that the lattice constant is a linear function of the ionic radii and electronegativity of the constituting ions. A simple empirical equation was obtained as a result of the performed analysis. It gives very good agreement between the experimental and modeled values of the lattice parameters, with an average error of 1.05%. The developed approach can be efficiently used for a simple, fast, and reliable prediction of lattice constants and interionic distances in isostructural materials having a similar composition.