Three-body Force Shell Model Research Articles

Phonon dynamics of orientationally disordered mixed crystals (RbCN) x(RbBr) 1− x

An extended three-body force shell model (ETSM) has been applied to investigate the phonon dynamics of (RbCN) x (RbBr) 1− x mixed crystals. The investigation is carried out for the composition range 0⩽ x⩽1 for temperature varying between 0 and 380 K. The phonon dispersion curves computed by us are in good agreement with the neutron scattering data at 300 K. The unusual feature of these curves is the upward curvature seen in some of the acoustic branches. This is a result of k-dependent softening of phonon due to translation–rotation coupling. The transverse acoustic branch is more soft near the zone center.

Lattice Dynamics of Transition Metal Oxides-An Application to FeO in the Paramagnetic Phase

The basic equations of three-body force shell model have been corrected for the ionic charge parameter Z . This correction also modifies the expressions for the shell and core charge parameters. Our model has been applied to study the phonon dispersion curves, Debye temperatures variation, combined density of states and two-phonon Raman scattering spectra of wustite. This approach has been found successful in interpreting the complete lattice dynamics of FeO only when both the ions are considered to be polarizable. There is good scope for the fresh determination of positive ion polarizability and Debye temperatures variation. It is concluded that the presence of magnetic and anharmonic interactions have no effect on the lattice dynamics of FeO in its paramagnetic phase.

Lattice Dynamics of the High Tc Superconductor ErBa2Cu3O7

The lattice dynamics of the high Tc superconductor ErBa2Cu307 have been investigated in detail with a modified three-body force shell model. The model accounts for the effect of many-body interactions in the lattice potential. The aim of the present work is to treat the various interactions between the ions in generalised way without making them numerically equal. The values of the phonon frequencies calculated at the zone centre by this new approach are in good agreement with the available Raman and infrared data.

Static and thermoelastic properties of alkali cyanide crystals

In the present paper an attempt has been made to analyse the thermoelastic properties of alkali cyanide crystals by estimating the values of their cohesive energy, bulk modulus and their pressure derivatives, Debye temperature and Gruneisen parameter. The modified form of the three-body force shell model used in the present study consists of long-range Coulomb and three-body interactions, short-range overlap repulsion of HZ-type, and van der Waals interactions. The van der Waals interaction coefficients are determined using the Kirkwood-Muller theory based on quantum mechanical considerations. Results obtained are compared with the available experimental data. A good agreement is found.

Phonon dispersion in mixed crystal K 0.5Rb 0.5Cl

In the present paper we have calculated the phonon dispersion curves of the mixed alkali halide k 0.5Rb 0.5Cl in all three symmetry directions (q, 0, 0), (q, q, 0) and (q, q, q). An extended three-body force shell model has been employed in the present study to calculate the phonon frequencies in symmetry directions (q, 0, 0), (q, q, 0) and (q, q, q). A concept of three body charge transfer has been taken into account to solve the dynamic matrix of the shell model. The results of phonon dispersion curves are found to agree reasonably well with the experimental results of Beg and Kobbelt. The experimental values of phonon frequencies have also been shown for the sake of comparison.

Phonon dispersion in mixed alkali halide crystal KCl 0.5Br 0.5

In the present paper we have calculated the phonon dispersion curves of the mixed crystal KCl 0.5Br 0.5 using the modified three-body force shell model. The modified force shell model consists of long-range three-body interactions and short-range overlap repulsion effective up to second neighbour ions. The repulsive parameters are determined from the expressions for elastic constants derived for NaCl structure solids. The results on phonon dispersion curves in symmetry directions ( q, 0, 0), ( q, q, 0) and ( q, q, q) are found to be in good agreement with the experimental curves of Beg and Kobbelt [ Phys.Rev. B26, 1893 (1982); Ref. (l)].

LATTICE DYNAMICS OF MgO USING THREE-BODY FORCE SHELL MODEL

A modified three-body force shell model is applied to evaluate the phonon dispersion values of MgO. The many-body interaction in the lattice potential is well accounted for by this theory. The values of the phonon frequencies evaluated by this method are in good confirmation with the neutron spectroscopic data.

Lattice mechanical and anharmonic properties of orientationally disordered caesium cyanide

An extended three-body force shell model (ETSM) has been developed for the description of lattice mechanical and anharmonic properties of orientationally disordered materials, like CsCN, by incorporating the effect of coupling between the translational modes and the orientations of cyanide (CN−) molecules in the framework of the original TSM. This ETSM is a more realistic model as it includes the three-body and van der Waals interactions which have quantum mechanical origin and play a vital role in the prediction of Cauchy discrepancy and associated properties of molecular and ionic crystals. We have applied this ETSM, for the first time, to caesium cyanide (CsCN) and successfully predicted its phonon-dispersion, anharmonic and dielectric properties.

Defect properties of divalent metal oxides

The Schottky defect formation energies in alkaline earth oxides have been calculated by using the modified polarizable point ion model and the three body force shell model (TSM). In these calculations the effect of long-range three-body interactions which arise due to deformation of the electron shells when the neighbouring ions overlap has been considered explicitly. The defect energies calculated from TSM reasonably agree with previously reported theoretical values. The three body forces, however, contribute about 5–10% to the defect energies.

Unified study of lattice mechanics of alkali cyanides

An extended three-body force shell model (ETSM) for alkali cyanides has been developed by including the effects of coupling between the translational and rotational motions of cyanide (CN -) molecules in the framework of original TSM devised by Singh and Sanyal [Physica 132B (1985) 201]. This ETSM has been applied to describe the static, dynamic, anharmonic elastic and photoelastic properties of the alkali cyanide crystals. This model has satisfactorily reproduced their experimental phonon dispersion curves and cohesive energy values. However, the agreements between the experimental and our theoretical values on the third order elastic constants are not so good. These agreements have been found to improve significantly with the exclusion of three-body interaction (TBI) effects, which play a vital role in the prediction of harmonic and anharmonic elastic properties of alkali halides. This might be so due to the overestimated effects of TBI from the Cauchy violations ( C 12– C 44) which are much larger for alkali cyanides than those for alkali halides. It has been concluded that the ETSM, which has reproduced the lattice statics and dynamics of alkali cyanides so well, is incapable to explain their anharmonic elastic and thermal properties. However, this situation is expected to improve by using a more appropriate method for estimating TBI contributions and incorporating the effects of covalent and anharmonic interactions.

Dielectric and thermoelastic properties of alkaline-earth fluoride crystals

An extended three-body force shell model is developed and used to make an analysis of the volume dependence of low- and high-frequency dielectric constants and thermoelastic Gruneisen parameters for CaF2, SrF2, BaF2 and PbF2 crystals. Lorentz-Lorenz and Clausius-Mossotti relations are modified in view of three-body interactions (TBI). Calculated results yield better agreement with the experimental data as compared to those obtained by previous investigators.

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.

Unified study of lattice mechanics of alkaline earth oxides

Abstract A generalized three-body force shell model (GTSM) has been formulated by incorporating the effects of long-range Coulomb and three-body interactions and short-range Van der Waals and overlap repulsion in the framework of both ion polarizable shell model. This GTSM has been employed for a unified study of lattice statics and dynamics of alkaline earth oxides (AEOs) and found to take a coherent account of their diverse physical properties such as the lattice dynamic, thermodynamic, optic, static, dielectric, anharmonic and photoelastic properties with the same set of model potential and parameters.

Effect of three-body interactions on the electronic polarizabilities and photoelastic behaviour of ammonium halides

The effect of three-body interactions (TBI) on the electronic polarizabilities and photoelastic behaviour of ammonium halides has been studied in the framework of a three-body force shell model. This model takes proper account of Cauchy violation and gives and excellent description of various crystal properties of ionic solids. The strain derivatives of electronic polarizabilities have been evaluated through the influence of crystal potential on the polarizabilities of ions. The photoelastic behaviour has been studied by determining the strain derivatives of electronic dielectric constant. The strain derivatives of electronic polarizabilities and dielectric constants for ammonium halides are reported for the first time.

Analysis of effective compressibilities in PbS, PbSe, PbTe and SnTe

An analysis of effective compressibilities in ionic semiconductors PbS, PbSe, PbTe and SnTe has been performed within the framework of many-body lattice theory (MLT). The extended three-body force shell model (ETSM) has been employed to obtain the values of effective compressibilities in the solids under study. The model parameters have been calculated using the expressions for elastic and dielectric constants within the framework of the ETSM. It is found that the predicted values of β ∗/β agree fairly well with the results obtained from the Szigeti relation.

Crystal dynamics of magnesium oxide

Abstract Phonon dispersion curves, for MgO, have been calculated, for the first time, in the framework of the modified three body force shell model (TSM), assuming both the positive and negative ions to be polarizable. The results are in good agreement with the inelastic neutron scattering measurements and are somewhat better than our earlier one-ion polarizable TSM calculations. It has been possible to conclude that a revised set of values of the elastic constants which are relatively larger, is essentially responsible to lead to a better set of model parameters and hence of the phonon frequencies.

Crystal mechanics of some alkali halides

A three-body-force shell model (TSM) has been employed for a comprehensive and unified calculation of the crystal mechanics of some alkali halides. This includes the description of phonon dispersion, two-phonon Raman and infrared spectra, specific heats, cohesive energy, relative stability, phase-transition pressure and volume, dielectric constants, quasi- harmonic elastic and photoelastic properties of lithium fluoride, potassiumchloride and rubidium chloride. These predictions are reasonably good and have led to the conclusion that TSM is an appropriate model for lattice mechanical descriptions of ionic crystals.

Static, anharmonic and phonon properties of ND 4I

A detailed investigation of the phonon dispersion and static and anharmonic properties has been carried out for ND 4I using an extended three-body force shell model (ETSM) developed by Singh and Chandra. The ETSM results for phonon dispersion show better agreement with the experimental data than those obtained from the deformation dipole and rigid shell models. Calculated values have also been obtained for some other properties.

A Comparative Study of Dynamical Behaviour of Ionic Lattices

AbstractA critical study of all the three extensions of the shell model i.e. the breathing shell model (BSM), the deformable shell model (DSM), and the three‐body force shell model (TSM) is further carried out for cesium chloride type ionic crystals on the similar pattern as reported earlier. These models are applied to study comparatively the dynamical behaviour of cesium chloride (CsCI) and thallous bromide (TIBr). The results so obtained, again confirm the superiority of TSM over DSM and BSM, not only in explaining the phonon dispersion curves but also for interpreting the infrared (IR) and Raman spectral peaks and Debye temperature variations.

Lattice dynamics of thallous chloride

An extended three-body force shell model (ETSM) developed by Singh and Gupta has been applied to investigate the role of three-body forces in lattice-dynamical descriptions of thallous chloride. The results on phonon dispersion, Debye-temperature variations and two-phonon infra-red spectra for TICI have been computed and found to agree reasonably well with the available experimental data. Since the properties of this solid are less explored, therefore, the present results might be of academic interest to guide the experimental workers.