Three-body Force Shell Model Research Articles

Lattice-mechanical properties of ammonium halides

A three-body force shell model (TSM) has been employed to describe several lattice-mechanical properties of ammonium halide crystals. The predictions achieved with this 8-parameter TSM for the phonon dispersion, cohesive and dielectric properties of these crystals are distinctly better than with various other multiparameter models. This success has been considered remarkable as the TSM has reproduced equally well the dispersion of phonons in the rocksalt and cesium chloridetype ammonium halides.

Dynamics and statics of sodium-halide crystals

A consistent and comprehensive calculation has been performed to describe the dynamics and statics of sodium-halide crystals using a well-known three-body-force shell model (TSM). The computed results on the phonon dispersion, two-phonon Raman and infrared spectra, Debye-temperature variations, dielectric and photoelastic behaviors, harmonic and anharmonic elastic constants, cohesive energy, relative stability, and phase-transition, have shown a reasonably good agreement with their accurately measured data. All these predictions have made use of the same set of TSM parameters throughout. The possible sources of improvements have also been indicated. In view of its overall success, TSM has been regarded as an adequate and appropriate model for the description of lattice-mechanical properties of ionic crystals.

Исследование статики и динамики решетки хлористого калия

A really consistent and comprehensive approach has been adopted to derive the framework of a three-body force shell model (TSM) which is capable to explain successfully the lattice statics and dynamics of ionic crystals. The model contains eleven parameters which have been determined from those physical constants whose prediction is not intended for. The application of this model to the case of potassium chloride crystal has reproduced fairly well the phonon dispersion, two-phonon Raman and infra-red spectra, cohesive energy, relative stability, phase transition pressure and volume, photoelastic constants and anharmonic elastic constants. The successful description of this series of various properties with the same set of model parameters may be considered as a remarkable feature of TSM. It may also be pointed out that the original TSM developed by Singh and Verma was formulated only to explain the lattice dynamics of ionic crystals.

A Critical Study of Dynamical Properties of Ionic Crystals

AbstractThe basic differences among the three most popular 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) are sought out by applying their nearest‐neighbour versions to some representative rocksalt type ionic crystals. The phonon dispersion curves are determined by each model for each of the crystals and compared with the experimental phonons which forms perhaps the best test for this purpose. The same number (eight) of parameters of each model are determined by using the same set of input data. The results and degrees of agreement obtained in each case show clearly the superiority of the “charge‐transfer mechanism” for representing the deformations of electron shells, used in the TSM, over the “breathing” and “deformation mechanism” used in the BSM and DSM, respectively, for the same purpose. The study also shows that the TSM, DSM, and BSM form a series of descending order according to their relative degrees of agreement, obtained in explaining the lattice dynamical behaviour of these crystals.

Lattice-dynamics of transition metal oxides MnO and NiO

Phonon dispersion curves for the transition metal oxides MnO and NiO have been calculated, for the first time, in the framework of modified three body force shell model (TSM). Both positive and negative ions are assumed highly polarizable. The results show a good agreement with recent neutron scattering measurements. Earlier calculations using one ion polarizable version of TSM are also criticized.

Analysis of the pressure derivatives of the second order elastic constants in alkaline earth oxides

The three body force shell model (TSM) has been applied to evaluate the magnitude of the pressure derivatives of second order elastic constants of alkaline earth oxides and a good agreement with the experimental values has been obtained. It is also pointed out that the calculated values of d C 44 ⧸d p show a smooth variation with ionicities. The theory has been modified by taking into account next nearest neighbour interaction.

On the three-body force shell model

On the three-body force shell model

Dispersion of phonons in metal carbides (UC)

AbstractAn attempt is made to formulate the theory of the dispersion of phonons in metal carbides. The three‐body‐force shell model (TSM) is used suitably extended to include the second neighbour short range interactions and the absence of LST splitting to study the dispersion curve of UC. The calculated frequencies of phonons are in good agreement with the experimental frequencies and are much better than those determined by the pseudo‐potential calculations.

An extended three-body force shell model for the lattice-dynamics of ionic crystals

An extended three-body force shell model (e. t. s. m.) for the dynamics of ionic crystals of cesium chloride structure has been developed by reformulating the original t. s. m. The dynamical matrix of the model consists of the long-range Coulomb and three-body interactions and short-range overlap repulsions effective up to the second-neighbours. The off-diagonal elements of this matrix along symmetry directions contain a completely new term having significant contribution for unequal shell charges. The long-wave aspects of e. t. s. m. have been explored to describe the elastic and dielectric behaviour of the crystals. The adequacy of e. t. s. m. to describe the lattice dynamics has been investigated by applying it to the case of thallous bromide (TIBr). The overall agreement between theoretical and experimental results seems to be encouraging and gives some confidence to regard it as an appropriate model for the dynamical description of ionic crystals.

Lattice dynamics of CsF by extended three-body force shell model

Detailed calculations are presented for the phonon dispersion curves and two-phonon Raman spectra of cesium fluoride. The model applied for the purpose is the extended three-body force shell model which takes account of three-body and second-neighbour interactions. Theoretical predictions and experimental data are in almost exact agreement.

Three-body-force shell-model study of phonon dispersion in the transition-metal carbides TaC and HfC

Phonon dispersion curves of two transition-metal carbides TaC and HfC have been derived from the three-body-force shell model (TSM). To account for the absence of the Lyddane-Sachs-Teller splitting between the long-wave optic-mode frequencies the model has to be so set as to give a zero value to the Lundqvist effective charge. The TSM results are found to agree well with the experimental curves of Smith and Glaser and are in this regard much better than the pseudopotential calculations of Mostoller and almost as good as the double-shell-model and the simple-screened-shell-model results of Weber for TaC and HfC, respectively.

The lattice dynamics of alkaline earth oxides

A theoretical investigation of the lattice vibrations in alkaline earth oxides (CaO and SrO) has been carried out by means of a three-body force shell model which considers the ionic charge Z as an independent parameter and both the ions polarizable. A satisfactory description of the dispersion of phonons, Debye temperature variations and second-order Raman and i.r. spectra is obtained. Analysis of these descriptions has revealed that the alkaline earth oxides are ionic crystals with simple interionic interactions.

Lattice dynamics of some lithium salts

The lattice dynamics of LiD, LiBr and LiI has been investigated in terms of a modified three-body force shell model which was developed by Verma and Singh (see abstr. A9196 of 1971) by incorporating the effect of net charge transfer in the framework of their original model. The successful interpretation of the observed data on dispersion of phonons in LiD has led to the conclusion that the effect of charge transfer is important.

Shell model lattice dynamics of transition metal oxides

The lattice dynamics of transition metal oxides has been investigated in detail with threebody force shell model which is a successful extension of the shell model and includes the effect of electron shell displacements as well as deformations. The phonon dispersion relations along three principal symmetry directions obtained from this model have been compared with neutron data and found to give better agreement as compared to other models. The complete phonon spectra have also been computed and used to derive the temperature dependence of Debye temperature, and the second-order Raman and infrared spectra. The derived data agree fairly well with the observed ones wherever available.

Three-body force shell model — An application to CaO

A three-body force shell model has been applied to compute the dispersion of phonons in calcium oxide along principal symmetry directions. The results show much better agreement with the measured phonon dispersion data as compared to the other variations of the shell model.

Dispersion of phonons in lithium deuteride

The study of dispersion of phonons of lithium deuteride (LiD) has been presented on the basis of the three-body force shell model which includes the effect of charge transfer of about 0.88 electrons. The results show an excellent agreement with extensively measured phonon dispersion data.

Dispersion properties of manganous oxide

The dispersion properties of manganous oxide have been studied using three-body force shell model. The results give reasonable agreement with measured phonon dispersion data. The applicability of the shell models and the requirement of more accurate measurements of the dispersion of phonons in MnO has also been discussed.

Phonon spectra of paramagnetic cobaltous oxide

The phonon dispersion relations in paramagnetic cobaltous oxide have been computed from a three-body force shell model and compared with extensively measured data. The results show excellent agreement between theory and experiment. The results for antiferromagnetic CoO have also been discussed for academic interest.