Interionic Forces Research Articles

Binding of tetrahedral halocomplexes of polyvalent metal ions in an ionic model

Long-lived tetrahedral coordination of polyvalent metal ions by halogen ions is known to be stable in a number of liquid halide mixtures. We evaluate the binding of isolated tetrahedral halocomplexes for the alkaline earth metals and for Al, with the main aim of assessing their stability and their bond length. An appropriate interionic force model is available for the halides of Mg, Ca, Sr and Ba from analyses of cohesion in their crystalline state and in dihalide molecules. The model is extended to the halides of Be and Al with the adjustment of a parameter to the measured Be-F and Al-Cl bond lengths in liquid mixtures. The semi-quantitative usefulness of the model is confirmed by comparisons with bond lengths for other Al halides and with extensive information on local vibrational frequencies from Raman scattering and infrared emission experiments on liquid halides.

Acoustic Mode Vibrational Anharmonicity in the Intermediate Valent Compound Samarium Sulfide

AbstractAnharmonic elastic properties of SmS in its semiconducting form are analysed in terms of third order elastic constants and pressure derivatives of second order elastic constants calculated using an interionic force model. This potential model consists of long‐range Coulomb and three‐body interactions and short‐range overlap repulsion, effective up to second neighbour ions. Repulsive parameters (b, ϱij) are determined using the equation of equilibrium condition and overlap integrals. The results reported are compared with experimental values and fairly good agreement is obtained.

Elastic constants and Debye temperature of polycrystalline Y1Ba2Cu3O7−x

Using ultrasonic methods, the quasi-isotropic elastic stiffnesses of void-containing Y1Ba2Cu3O7−x were determined By a composite-material model, these were corrected to the void-free state. From these, the Debye characteristic temperature was calculated. All the elastic stiffnesses fall well below those of polycrystalline BaTiO3, an approximate crystalstructural building block of Y1Ba2Cu3O7−x. The low apparent stiffness may result from oxygen vacancies, which soften interionic forces. Also, it may result from microcracks, which reduce elastic stiffness without lowering mass density.

Inelastic neutron scattering investigation of the lattice dynamics of ThO2 and CeO2

The phonon dispersion relations of ThO2 and CeO2 have been measured in the three principal crystallographic directions at 293 K using inelastic neutron scattering. After correction for instrumental resolution effects, the data were fitted by rigid ion and shell models of the interionic forces, and the corresponding parameters determined. The results indicate a general similarity between the lattice dynamics of the two compounds.

Pair structure and interionic forces in molten zinc chloride

The structure of glass-forming liquid ZnCl 2 as observed in diffraction experiments presents a number of distinctive features that computer simulation in standard ionic models seems unable to describe globally. We examine several qualitatively different models for 2:1 molten salts, solving them in the hypernetted chain approximation. These models are basically of the charged-hard-sphere type, supplemented by distance-dependent dielectric screening and by non-additivity of excluded volumes. In agreement with the simulation results, a local structure consisting of first-neighbour tetrahedral coordination for zinc ions inside a chlorine network is simply related to suitable values for the ionic radii. The nature of the zinc-zinc correlations is shown to reflect more directly the character of the bonding, which appears to involve microscopic distortions of the electronic shells of the ions and an appreciable angular dependence of the interionic forces. Qualitative features of effective pair potentials which would be consistent with the gross topology of ZnCl 2 in liquid and vitreous states are assessed from our analysis.

Lattice dynamical study on polytypism and phase transition in K 3Co(CN) 6

Lattice dynamical calculations for the one-layer monoclinic (1M) and two-layer orthorhombic (2Or) polytypes of K 3Co(CN) 6 were carried out assuming a simple interionic force field. There are similarities in the vibrational character between the translational mode with a wavevector k = a*/2 in 1M and Raman active translational modes in 2Or. The soft mode in 2Or can be regarded as the zone center mode which arises from the folding-back of the zone boundary soft mode in 1M and has a character of the rigid layer mode in terms of the theory of the layered crystals.

Dynamical properties of copper halides. I. Interionic forces, charges, and phonon dispersion curves.

In the three papers in this series the anomalous dynamical properties of copper halides are analyzed. The present paper focuses on the interionic forces and phonons in these materials. It is shown that the partially ionic nature of these tetrahedrally coordinated semiconductors is best described by various valence-shell models which combine a valence-force-field approach with that of dipolar models (i.e., effective charge, polarizabilities, etc.). The trends of the interionic forces in the sequence CuCl\ensuremath{\rightarrow}CuBr\ensuremath{\rightarrow}CuI reflect the changes in the electronic band structure and the increasing tendency to superionic conductivity.

Evidence for Many-Body Interactions in the Structure of Molten Alkali Chlorides

Abstract An inversion of the measured partial structure factors of molten sodium chloride is attempted in order to assess some qualitative features of interionic forces in the melt. We start from a calculation of liquid structure and thermodynamic properties by means of a refined theory based on interionic pair potentials determined from properties of the solid phase. This yields very good agreement with the measured values of the internal energy and the compressibility of the liquid, whereas discrepancies with the observed structure are mainly localized in the region of interionic distances outside the minimum of the cation-anion potential. These discrepancies, when interpreted in terms of effective pair potentials in the melt through inversion of the structural data, strongly suggest the presence of many-body effects, insofar as such effective pair potentials oscillate with the local liquid structure and are inconsistent with the measured thermodynamic quantities. A similar analysis of data on molten rubidium and cesium chloride, though harder to carry out quantitatively, supports the above conclusion.

Higher order elastic constants and pressure derivatives of alkali halide crystals

In the present investigation the anharmonic elastic properties of NaCl, NaBr, NaI and NaF ionic crystals have been analysed by determining their six third order and eleven fourth order elastic constants. An interionic force model based on long-range and short-range crystal potentials has been considered for the evaluation of higher order elastic constants and the pressure derivatives of second order and third order elastic constant. Instead of traditional form of BM potential a different form of overlap short-range potential has been taken into account. The results achieved in the present study are compared with the experimental data and also with those results obtained by previous workers.

Conformation and binding of alkaline-earth dihalide molecules in an ionic model

The paper establishes a connection, in the framework of an ionic model, between the binding of alkaline-earth dihalides in the solid phase and in the molecular phase. The polarizabilities of the metal ion and the halogen radius are identified in the model as the parameters which determine the structure of these molecules as either linear or bent, as revealed in electrical deflection experiments on molecular beams. Calculations of the molecular angle, the bond length, the binding energy and the vibrational frequencies are carried out with interionic-force laws taken over from studies of the solid alkaline-earth halides, the results being compared with the available experimental data on molecules either in the free state or embedded in a solid-krypton matrix. The analysis provides a preliminary test of interionic force models for hot-solid and liquid-structure studies.

Interionic Forces and Elastic Properties of Na2S

AbstractAn interionic potential model is proposed for crystals with antifluorite structure which consists of long‐range Coulomb and three‐body interactions (TBI), and short‐range dispersive and repulsive interactions up to second‐neighbour ions. This potential is used to calculate the cohesive energy, second‐order elastic constants, and their pressure derivatives of Na2S. The calculated values of elastic constants and cohesive energy agree well with their measured data which shows that the TBI contribute significantly to these properties.

Elastic behaviour of mixed manganese-magnesium ferrites

of the interatomic and interionic forces in them. Further, a detailed investigation of the dependence of elastic moduli on magnetic field or AE effect is interesting from the stand point of explaining the domain process occurring in the ferrite material. Thus, a study of the dependence of the elastic behaviour of Mn-Mg ferrites on composition and magnetic field at room temperature has been undertaken. The results are presented in this paper. Young's modulus (E) and the rigidity modulus (g) of polycrystalline Mn-Mg ferrites were measured by using the composite oscillator [3]. Mixed Mn-Mg ferrites having the chemical formula Mnl_xMgxFe20 4 (x = 0 to 1) are prepared by the double sintering method. X-ray diffraction patterns for these mixed ferrites have been obtained using CuKa radiation. The lattice constants for ferrites were calculated and it is observed that the variation of lattice constants with composition is linear (Table I). Bulk densities of samples are determined from volume and weight measurements in air at room temperature (30 ° C) are found to be 95% of the corresponding X-ray densities in all the cases. The experimental values of the elastic moduli obtained on porous specimens at room temperature are corrected to theoretical density using the method of Mackenzie [4]. The corrected values of Young's modulus (E) and rigidity modulus (/.t), together with calculated values of the bulk modulus (k), compressibility (fl) and Poisson's ratio (o) are presented in Table I. Following Wooster's work [5] the experimental data are interpreted in terms of the binding forces between the atoms. It can be observed from Table I that an addition of 0.25 tool magnesium ferrite to manganese ferrite has increased the value of the E by about 15%. Similarly an addition of 0.1 mol manganese ferrite to magnesium ferrite has resulted in an increase in E of about 5%. The value of the rigidity modulus is increased by about 15% and 9%, respectively, Further addition of magnesium ferrite to manganese ferrite has also resulted in an increase of the values of E and g. This shows that an addition of a small quantity of magnesium ferrite to manganese ferrite or manganese ferrite to magnesium ferrite has resulted in an increase in the binding forces between the atoms. It can also be observed from the table that the values of k and tr are smaller for mixed magnesium-manganese ferrites of various compositions than for magnesium ferrite.

Elastic behaviour and internal friction of polycrystalline magnesium ferrite

The magnetic, dielectric and electrical properties of ferrites have been investigated in great detail. The magnetic properties [1] have been studied thoroughly in the neighbourhood of the Curie point and these studies established that the magnetic behaviour of ferrites is similar to that of metallic ferromagnetic substances. However, there is meagre information available on the various "non-magnetic" properties such as thermal expansion, specific heat, elasticity, etc., in the neighbourhood of the Curie point in the case of ferrimagnetic materials. A detailed study of the elastic behaviour is of particular significance in the theory of solids in understanding the nature of the interatomic and interionic forces in them. It is thus a matter of great interest to study the elastic behaviour of ferrites in the neighbourhood of the Curie point, where the energy of the spontaneous magnetization disappears. As such we have undertaken a study of the dependence of the elastic moduli of polycrystaUine magnesium ferrite on temperature and magnetic field in the neighbourhood of Curie temperature. Internal friction is another important property, which is closely related to the elastic behaviour. As such the internal friction of the ferrites is also studied. The specimens of magnesium ferrite were prepared by the double sintering method. The final sintering was done between 1250 and 1350 ° C in an air atmosphere. The ferrite specimens were analysed from the results of X-ray diffraction studies and are found to be monophasic. The bulk densities of the samples were found to be about 90% to 95% of the corresponding X-ray densities. The natural longitudinal and transverse frequencies of the specimens as a function of temperature and magnetic field have been determined by the three-component oscillator method [2]. The internal friction measurements were also carried out using the same composite oscillator method, as was used for the elastic moduti measurements. The internal friction values are calculated after noting the width of the resonance curve, when the specimen vibrates in resonance with transducer. The length and density of the ferrite specimens at different temperatures (t) have been calculated using the thermal expansion (a) determined in this laboratory. The relevant equation used for magnesium ferrite is,

Force constants between interstitial hydrogen atoms and host atoms in a FCC aluminium crystal

The hydrogen-aluminium atomic force constants and the interionic force constants between aluminium ions are determined by means of the pseudopotential. The inclusion of a proton within a homogeneous electron gas produces a large change in the electron density, so that the electron density around hydrogen cannot be described correctly by the linear screening theory. In obtaining the hydrogen-aluminium atomic force constants, the authors have taken account of the non-linear screening effect by means of the Kohn-Sham formalism. The coupling between interstitial hydrogen and aluminium atoms is found to be fairly weak, and the hydrogen behaves as a free particle in the small region around its site.

A model for the structure of liquid Li 4Pb

We present the results of calculations of the partial structure factors and radial distribution functions of liquid Li 4Pb at different temperatures. Assuming that this alloy is partially ionic, we have modelled the interionic forces by pairwise potentials that are strongly repulsive at small separations r and electronically screened Coulombic at large r. This model was motivated by the fact that a r dependent ‘ordering potential’ which exhibits approximately screened Coulombic decay for a large r, can be extracted from the neutron diffraction data for S cc(q) in Li 4Pb. Our calculations, which are based on the mean-spherical and the hyper-netted-chain approximations, show that the wave number dependence of the measured concentration structure factor S cc(q) can be reasonably well accounted for by our model with effective electron charges of about 0.5 and −2.0 at the Li and Pb sites, respectively, and an inverse screening length of 1·1 Å −1. These parameters are consistent with values obtained from the ordering potential extracted from experiment. In order to explain the observed temperature dependence of S cc(q) it is necessary to assume that the charge transfer between species decreases with increasing temperature.

Low angle structure factors for expanded liquid rubidium

The observed structure factors of expanded liquid rubidium (up to a temperature of 1900K near saturation conditions) can be explained using first nearly free electron theory to describe the interionic forces and then approximate techniques (WCA, MDA) of classical liquid theory to calculate the structure. The WCA approximation confirms the hard sphere fittings of Franz et al. at high K and the MDA leads to a quantitative description of the low K Ornstein-Zernike behaviour.

A model for the structure of liquid Li4Pb

The authors present the results of calculations of the partial structure factors and radial distribution functions of liquid Li4Pb at different temperatures. Assuming that this alloy is partially ionic, they have modelled the interionic forces by pairwise potentials that are strongly repulsive at small separations r and electronically screened Coulombic at large r. This model was motivated by the fact that an r-dependent ordering potential, which exhibits approximately screened Coulombic decay for larger r, can be extracted from the neutron diffraction data for SCC(q) in Li4Pb. The calculations, which are based on the mean-spherical and the hyper-netted-chain approximations, show that the wavenumber dependence of the measured concentration structure factor SCC(q) can be reasonably well accounted for by the model with effective electron charges of about 0.5 and 4-2.0 at the Li and Pb sites, respectively, and an inverse screening length of 1.1 AA-1. These parameters are consistent with values obtained from the ordering potential extracted from experiment. In order to explain the observed temperature dependence of SCC(A) it is necessary to assume that the charge transfer between species decreases with increasing temperature.

Raman scattering from molten alkali halides

Measurements have been made of the quasi-elastic light scattering from molten Na, K and Cs chlorides and bromides. The salts were measured at about 35 degrees above the melting point in the frequency shift ( nu ) spectral range of 4-400 cm-1 (0.5-50 meV). In the quasi-elastic region the depolarisation ratios ( rho d) are large and decrease rapidly with nu up to 50 cm-1 whereas in the inelastic range there are regions where rho d is constant. It is noteworthy that both Cs salts show depolarisation greater than the relatively small values for Na and K salts. The reduced-intensity spectra show broad bands whose peak positions vary in a similar manner to those of the optical vibrational frequencies in the solids, i.e. with the inter-ionic force constants.

Orbital-moments analysis of ionic radii in silver and copper halides

We present a linear relation between traditional ionic radii and ab initio orbital moments for ${\mathrm{Ag}}^{+}$, ${\mathrm{Cu}}^{+}$, halide, and, for comparison, alkali ions. Based on the connection of first and second orbital moments with repulsive and attractive interionic forces, respectively, we introduce a quantity $q$ which indicates an ion's contribution to the dominant short-range interaction in a crystal. Some peculiar properties of silver and copper halides are interpreted in terms of strong van der Waals interaction.

Dielectric and anharmonic behaviour of alkali halide crystals

AbstractThe dielectric and anharmonic behaviour of alkali halide crystals is studied by determining the volume derivatives of low frequency dielectric constant and polarizability. An interionic force model which takes into account the contributions arising from the short range overlap repulsion and the van der Waals interactions is used in calculations. The implicit and explicit temperature derivatives of low frequency and high frequency dielectric constants are obtained separately for all the alkali halide crystals with NaCl and CsCl structures. The anharmonic contribution to the dielectric constant is calculated using theoretical models due to Szigeti and Havinga. The recent analysis of pressure dependence of effective charge parameter and dielectric constant of ionic crystals performed by Varotsos is shown to be invalid.