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.     

Many body interactions in binary ionic solids

Recent developments in phonon models and microscopic theories of lattice mechanics have been reviewed, with particular emphasis on binary ionic solids. In doing so, we have traced the evolution of many body interactions from the electron-shell deformation and charge-transfer mechanisms and the approach of their incorporation in the framework of a dipolar model to describe the lattice static, dynamic, and anharmonic behaviours of these solids. The essential background and formalism of the sophisticated lattice dynamical models thus developed have been thoroughly treated in order to make them understandable and establish interrelationships between phonon and microscopic models and among themselves. An assessment of the relative merit of these models (e.g. breathing shell model, deformable shell model and three-body-force shell model) has been performed by making a critical comparison of theoretical results obtained from their comparative and unified lattice mechanical investigations with those measured from the experimental techniques and extensively surveyed in this article. Finally, we have outlined the future prospects and the scope of extension of various phonon models in view of the current trends in lattice dynamics and needs for a comprehensive study of the defect and anharmonic properties exhibited by the crystalline solids.     

Lattice dynamics and inelastic neutron scattering experiments on andalusite,Al2SiO5

We report coherent inelastic neutron scattering measurements of the phonon dispersion relations and lattice dynamics shell model calculations of several microscopic and macroscopic properties of andalusite, Al₂SiO₅. Andalusite has an orthorhombic structure with 32 atoms/unit cell. The inelastic neutron scattering measurements (up to energy transfers of 45 meV) were carried out using the triple axis spectrometer at Dhruva reactor, India using a single crystal of andalusite and the phonon dispersion relations along the [100] direction have been measured. The shell model calculations have been used to compute the crystal structure, elastic constants, phonon frequencies, dispersion relations, density of states and the specific heat. The calculated results are in good agreement with available experimental data. The computed one-phonon neutron scattering structure factors based on the shell model have been very useful in the planning and analysis of the inelastic neutron scattering experiments.     

Lattice dynamics of silver

The phonon dispersion curves of silver have been measured in the main symmetry directions at room temperature by coherent inelastic scattering of thermal neutrons using a correlation technique. The experimental results have been analyzed with parametrized expressions which have been derived from interatomic model potentials. With the Born-von Karman force constant model thermodynamic properties of silver could be calculated in good agreement with experimental results. Through the use of electron-ion model potentials the lattice dynamics of silver was correlated with its electronic properties. The results for some of those properties are compared with corresponding experimental values.     

Phonon anomalies in intermediate valence compounds

Phonon anomalies in the intermediate valence compounds SmS, TmSe and YS were studied extensively using a three-body force rigid shell model. Three-body interactions were used because, due to valence fluctuations, the radii of rare-earth ions change significantly and, therefore, the amount of overlap with neighboring chalcogen ions also changes. Change in the radii of the rare-earth ions results in the deformation of the rare-earth ions, whereas change in the amount of overlap with the neighboring chalcogen ion gives rise to long-range three-body interactions between the transferred charges of the lattice. Both of these changes strongly influence the phonon dispersion curves, particularly along the zone boundary. Results obtained from the model are in agreement with the measured data for phonon dispersion as compared to the results obtained using a three-body rigid ion model. Results for Debye temperature variations and two-phonon IR/Raman spectra for these crystals have also been presented, probably for the first time, but could not be compared with experimental data due to their non-availability.     

Lattice dynamical study of body-centred tetragonal indium

The phonon dispersion curves, phonon frequency distribution function as well as the lattice specific heat of body-centred tetragonal indium have been deduced using a lattice dynamical model which includes central, angular and volume forces. Six elastic constants, four zone boundary frequencies and an equilibrium condition were used in the evaluation of the force constants. It is shown that this model is elastically consistent and satisfies the symmetry requirements of the lattice, the phonon frequencies of indium deduced from it are in very good agreement with the experimental values of Reichardt and Smith and the theoretical values of Garrett and Swihart, and theθ _D values compare well with the experimental values over a wide temperature range. The apparent discrepancies in the phonon dispersion curves and theθ _D-T curves obtained from deficient models, importance of umklapp processes and the significance of angular forces in the lattice dynamical models are discussed.     

Coherent X-ray scattering by phonons

Interference effects arising from coherently coupled X-ray beams inelastically scattered from phonons have been used to determine phonon eigenvectors in Si and GaAs crystals. An outline of the method, experimental requirements, and theoretical background is presented. The experimental results are analyzed with the help of different lattice dynamical model calculations. Best overall agreement is found with phonon eigendata based on the bond charge model.     

Temperature and pressure dependence of some thermal characteristics of magnesium

The theoretical values of the Debye-Waller factor, specific heat and the phonon dispersion relations as functions of temperature for magnesium are derived from a simple model of lattice dynamics proposed by Czachor for hexagonal crystals.. The pressure dependence of the dispersion curves is also derived. The theoretical results have been found to be in very good agreement with experimental data available.     

Lattice dynamics of alkali cyanide crystals

The recent microscopic model of Michel and Naudts for the interaction of ionic vibrational displacements and molecular rotational displacements is combined with the lattice dynamical shell model to calculate phonon dispersion curves of KCN and NaCN. Very good agreement with the existing experimental data is obtained. In particular, the upward dispersion of the TA phonon branches, characteristic of the alkali cyanide crystals, is well reproduced.     

Temperature dependence of second order Raman spectra of rubidium iodide crystal

The temperature variation of the second order Raman spectra of RbI has been theoretically studied in three basic symmetries on the basis of the modified Born and Bradburn theory. The phonon frequencies and corresponding eigenvectors have been determined at the room temperature by employing a three body force shell model. It has been assumed that the major factor which governs the temperature dependence of Raman intensity is the occupation number and the changes in the phonon eigen data and the polarizability parameters with temperature have been ignored. Calculations have been made at three temperatures namely, 300,90 and 23 K and the theoretical results have been compared to the experimental Raman spectra.     

Lattice dynamics of ferromagnetic superconductor UGe2

This paper reports the lattice dynamical study of the UGe₂ using a lattice dynamical model theory based on pairwise interactions under the framework of the shell model. The calculated phonon dispersion curves and phonon density of states are in good agreement with the measured data.      

Inelastic neutron scattering and lattice dynamics of GaPO<Subscript>4</Subscript>

We report here measurements of phonon spectrum and lattice dynamical calculations for GaPO₄. The measurements in low-cristobalite phase of GaPO₄ are carried out using high-resolution medium-energy chopper spectrometer at ANL, USA in the energy transfer range 0–160 meV. Semiempirical interatomic potential in GaPO₄, previously determined using ab-initio calculations have been widely used in studying the phase transitions among various polymorphs. The calculated phonon spectrum using the available potential show fair agreement with the experimental data. However, the agreement between the two is improved by including the polarisability of the oxygen atoms in the framework of the shell model. The lattice dynamical models are also exploited for calculations of various thermodynamic properties of GaPO₄.     

Static,anharmonic and phonon properties of ND4I

A detailed investigation of the phonon dispersion and static and anharmonic properties has been carried out for ND₄I 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.     

Harmonic dynamical behaviour of thallous halides

Harmonic dynamical behaviour of thallous halides (TlCl and TlBr) have been studied using the new van der Waals three-body force shell model (VTSM), which incorporates the effects of the van der Waals interaction along with long-range Coulomb interactions, three-body interactions and short-range second neighbour interactions in the framework of rigid shell model (RSM). Phonon dispersion curves (PDC), variations of Debye temperature with absolute temperature and phonon density of state (PDS) curves have been reported for thallous halides using VTSM. Comparison of experimental values with those of VTSM and TSM are also reported in the paper and a good agreement between experimental and VTSM values has been found, from which it may be inferred that the incorporation of van der Waals interactions is essential for the complete harmonic dynamical behaviour of thallous halides.     

The thermal expansion of rubidium chloride by the shell model

The equation of state and the thermal expansion of rubidium chloride have been studied by making use of shell model with both the ions polarisable. The lattice constants at different temperatures have been obtained from the isotherms, drawn between the temperature range 0° and 1000°K; and show good agreement with the experimental results.     

Lattice dynamics of II–VI and III–V compounds

To study the lattice dynamics of II–VI and III–V compounds having zinc-blende structure in a model which incorporates three types of interactions: (i) central ion-ion forces (ii) bond-bending forces and (iii) long range Coulombic forces, has been developed. The model involves in total eight disposable parameters. The use of six critical point phonon frequencies, two elastic constants and the lattice equilibrium condition has been made to evaluate the consistent values of the parameters. The application of the present model has been made to calculate the phonon dispersion relations of ZnSe and InSb compounds. The comparison of theoretical results with the available experimental data has been made along the three symmetry directions [100], [110] and [111]. A reasonably good agreement is observed between theory and experiments.     

Atomistic simulation of the motion of dislocations in metals under phonon drag conditions

The mobility of dislocations in the over-barrier motion in different metals (Al, Cu, Fe, Mo) has been investigated using the molecular dynamics method. The phonon drag coefficients have been calculated as a function of the pressure and temperature. The results obtained are in good agreement with the experimental data and theoretical estimates. For face-centered cubic metals, the main mechanism of dislocation drag is the phonon scattering. For body-centered cubic metals, the contribution of the radiation friction becomes significant at room temperature. It has been found that there is a correlation between the temperature dependences of the phonon drag coefficient and the lattice constant. The dependences of the phonon drag coefficient on the pressure have been calculated. In contrast to the other metals, iron is characterized by a sharp increase in the phonon drag coefficient with an increase in the pressure at low temperatures due to the α-∈ phase transition.     

Phonon dispersion in NiO

The phonon dispersion relations in NiO have been measured using coherent inelastic neutron diffraction. Good fits to the data were obtained using various shell models. The room temperature phonon density of states was calculated and used to determine the temperature dependence of the lattice specific heat and the Debye temperature.     

First-principles study of lattice dynamics and thermodynamics ofosmium under pressure

We have performed the first-principles linear response calculations of the lattice dynamics, thermal equation of state and thermodynamical properties of hcp Os metal by using the plane-wave pseudopotential method. The thermodynamical properties are deduced from the calculated Helmholtz free energy by taking into account the electronic contribution and lattice vibrational contribution. The phonon frequencies at Gamma point are consistent with experimental values and the dispersion curves at various pressures have been determined. The calculated volume, bulk modulus and their pressure derivatives as a function of temperature are in excellent agreement with the experimental results. The calculated specific heat indicates that the electronic contribution is important not only at very low temperatures but also at high temperatures due to the electronic thermal excitation. The calculated Debye temperature at a very low temperature is in good agreement with experimental values and drops to a constant until 100~K.