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.     

Carbon nanostructures as an electromechanical bicontinuum

A two-field model provides a unifying framework for elasticity, lattice dynamics and electromechanical coupling in graphene and carbon nanotubes, describes optical phonons, nontrivial acoustic branches, strain-induced gap opening, gap-induced phonon softening, doping-induced deformations, and even the hexagonal graphenic Brillouin zone, and thus explains and extends a previously disparate accumulation of analytical and computational results.     

Lattice vibrations of armchair carbon nanotubes: phonons,soliton deformations and lattice discreteness effects

Small and large-amplitude elastic deformations of the armchair structure of single-walled carbon nanotubes are investigated with emphasis on the cylindrical geometry. As starting model, we consider a discrete one-dimensional lattice of atoms interacting via a Lennard-Jones type two-body potential. In an expansion scheme using cylindrical coordinates where radial displacements are assumed negligible compared to the angular motions, a sine-lattice Hamiltonian is derived. In the limit of small-amplitude angular displacements, the dispersion spectrum of acoustic phonons is derived and the associate characteristic frequency is given as a function of parameters of the model. In the large-amplitude regime, lattice vibrations give rise to kink-type deformations which move undergoing lattice dispersion and lattice discreteness effects. The dispersion law of the kink motion is obtained and shown to lower the effect of lattice discreteness, giving rise to a vanishing Peierls stress for kink sizes of the order of a few lattice spacings. Implications of the coupling of two armchair structures on the stability of vibrational modes of an individual armchair nanotube are also discussed. A gap of forbidden modes is predicted in the phonon spectrum while the energy needed to create a kink deformation in individual nanotubes is shifted in the presence of a wall-to-wall interaction.Received: 2 August 2004, Published online: 14 December 2004PACS: 81.07.De Nanotubes - 62.30. + d Mechanical and elastic waves-vibrations - 63.22. + m Phonons in low-dimensional nanoscale materials - 63.20.Ry Anharmonic lattices modes     

Effect of phonon scattering mechanisms on the lattice thermal conductivity of skutterudite-related compound

We have prepared the skutterudite-related compounds FeCo_3Sb_{12} and La_{0.75}Fe_3CoSb_{12} with different average grain sizes (about 0.8 and 3.9μm) by hot pressing. Samples were characterized by XRD, EPMA and SEM. The lattice thermal conductivity was investigated in the temperature range from room temperature to 200℃. Based on the Debye model, we analyse the change in lattice thermal conductivity due to various phonon scattering mechanisms by examining the relationship between the weighted phonon relaxation time τ(ω/ω_D)^2 and the reduced phonon frequency ω/ω_D. The effect of grain boundary scattering to phonon is negligible within the range of grain sizes considered in this study. The large reduction in lattice thermal conductivity of FeCo_3Sb_{12} compound contributes to the electron－phonon scattering. As for La_{0.75}Fe_3CoSb_{12} compound, the atoms of La filled into the large voids in the structure of the skutterudite produce more significant electron－phonon scattering as well as more substitute of Fe at Co site at the same time. Moreover, the point-defect scattering appears due to the difference between the atoms of La and the void. In addition, the scattering by the rattling of the rare-earth atoms in the void is another major contribution to the reduced lattice thermal conductivity. Introducing the coupling of the electron－phonon scattering with the point-defect scattering and the scattering by the rattling of the rare-earth atom is an effective method to reduce the lattice thermal conductivity of the skutterudite-related compounds by substitution of Fe for Co and the atoms of La filled in the large voids in the skutterudite structure.     

Vibrational properties of Re2N and Re3N compounds

Using first-principles calculations, we have studied the structural, lattice dynamical and thermodynamical properties of the recently synthesized Re₂N and Re₃N compounds. The generalized gradient approximation is used to model exchange-correlation effects. The phonon dispersion curves are derived using the direct method. The calculated equilibrium lattice parameters are in overall agreement with the available experimental and theoretical results. The present phonon dispersion results show that both compounds are dynamically stable for the structures considered. The temperature-dependent behavior of thermodynamical properties, such as free energy, entropy, heat capacity, and internal energy, is also presented.     

Ferroelectrics

A diatomic linear chain model is used to describe the dynamical properties of displacive type ferroelectric compounds. For these materials the non-bondingp-orbitals of the chalcogen ions play an essential role, which is taken into account by assuming a nonlinear fourth-order polarizability at the chalcogen-ion lattice site. Within the self-consistent phonon approximation soft modes, phonon dispersion curves, phonon anomalies and related quantities can be calculated for all temperatures. Going beyond the self-consistent phonon approximation, the model yields, in the continuum limit, interesting new solutions such as periodic non-linear waves, kinks, which describe the statics and dynamics of ferroelectric domain walls, and pulse solutions.Dedicated to Professor Harry Thomas on the occasion of his 60th birthday     

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.     

Phonon dispersion relations of tetrahedrally-bonded crystals

The lattice dynamics of the tetrahedrally-bonded compounds is formulated from first principle by using a model of binding force proposed by us, which mainly includes covalent interactions in the perturbational treatment based on the pseudopotential formalism and also partly on ionic interactions. Numerical calculations are performed for GaP and ZnS. In spite of our introducing no adjustable parameter except the optical phonon-frequency splitting in the long-wavelength limit, the resulting phonon dispersion curves are qualitatively in good agreement with the observed data. We show that ionic contributions are important for the optical phonon frequencies of these compounds.     

Lattice dynamics in mixed valent Rare Earth compounds

In the frame of a single coherent picture for the electron lattice interactions in mixed valent Rare Earth compounds, the phase diagrams and phonon dispersions are studied. Our model is introduced on a microscopic level and discussed in detail. The mechanism of the phase transition and the role of the lattice is illuminated and various properties are considered in a model calculation. Anomalies in the phonon dispersions of Sm_1–x Y _x S, which have recently been found, find a satisfying explanation.     

Variable charges at govalent bonds and phonon dispersion in silicon

A model of variable charges at covalent bonds is proposed to describe the effective atomic interaction in a crystal lattice. It is shown that, in the region of elastic deformations, it is sufficient to take account only of the linear term in the expansion of the charge with respect to the relative deformation of the bond. Expressions are obtained for the dynamic matrix on the basis of the pseudopotential model and the model of variable charges at the bonds. The results of calculating the phonon spectrum of silicon are in good agreement with experimental data and reflect the characteristic features of the spectrum.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 95–98, July, 1988.     

Effect of normal processes on thermal conductivity of germanium,silicon and diamond

The effect of normal scattering processes is considered to redistribute the phonon momentum in (a) the same phonon branch — KK-S model and (b) between different phonon branches — KK-H model. Simplified thermal conductivity relations are used to estimate the thermal conductivity of germanium, silicon and diamond with natural isotopes and highly enriched isotopes. It is observed that the consideration of the normal scattering processes involving different phonon branches gives better results for the temperature dependence of the thermal conductivity of germanium, silicon and diamond with natural and highly enriched isotopes. Also, the estimation of the lattice thermal conductivity of germanium and silicon for these models with the consideration of quadratic form of frequency dependences of phonon wave vector leads to the conclusion that the splitting of longitudinal and transverse phonon modes, as suggested by Holland, is not an essential requirement to explain the entire temperature dependence of lattice thermal conductivity whereas KK-H model gives a better estimation of the thermal conductivity without the splitting of the acoustic phonon modes due to the dispersive nature of the phonon dispersion curves.      

Phonon-mediated heat dissipation in a monatomic lattice: case study on Ni

The recently introduced analytical model for the heat current autocorrelation function of a crystal with a monatomic lattice [Evteev et al., Phil. Mag. 94 (2014) p. 731 and 94 (2014) p. 3992] is employed in conjunction with the Green–Kubo formalism to investigate in detail the results of an equilibrium molecular dynamics calculations of the temperature dependence of the lattice thermal conductivity and phonon dynamics in f.c.c. Ni. Only the contribution to the lattice thermal conductivity determined by the phonon–phonon scattering processes is considered, while the contribution due to phonon–electron scattering processes is intentionally ignored. Nonetheless, during comparison of our data with experiment an estimation of the second contribution is made. Furthermore, by comparing the results obtained for f.c.c. Ni model to those for other models of elemental crystals with the f.c.c. lattice, we give an estimation of the scaling relations of the lattice thermal conductivity with other lattice properties such as the coefficient of thermal expansion and the bulk modulus. Moreover, within the framework of linear response theory and the fluctuation-dissipation theorem, we extend our analysis in this paper into the frequency domain to predict the power spectra of equilibrium fluctuations associated with the phonon-mediated heat dissipation in a monatomic lattice. The practical importance of the analytical treatment lies in the fact that it has the potential to be used in the future to efficiently decode the generic information on the lattice thermal conductivity and phonon dynamics from a power spectrum of the acoustic excitations in a monatomic crystal measured by a spectroscopic technique in the frequency range of about 1–20 THz.     

Theoretical investigations on vibrational properties and thermal conductivities of ternary antimonides TiXSb,ZrXSb and HfXSb (X = Si,Ge)

We have performed density functional calculations of the vibrational and thermodynamic properties of the ternary antimonides TiXSb, ZrXSb and HfXSb (X = Si, Ge). The direct method is used to calculate the phonon dispersion relation and phonon density of states for these compounds as well as their infrared and Raman active mode frequencies for the first time. Their dynamical stability is confirmed by phonon spectra. The lattice thermal conductivities of these compounds have been calculated from third-order force constants and plotted as a function of temperature. We have also evaluated the high temperature thermal conductivity by means of the Clarke’s model and Cahill’s model. Some selected thermodynamical properties, e.g. Gibbs free energy, entropy and heat capacity at constant volume are predicted theoretically and discussed. We have showed the relationships between thermodynamical properties and temperature.     

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.     

The spin dynamics in distorted kagome lattices: a comparative Raman study

Despite the conceptional importance of realizing spin liquids in solid states only few compounds are known. On the other hand the effect of lattice distortions and anisotropies on the magnetic exchange topology and the fluctuation spectrum is an interesting problem. We compare the excitation spectra of the two s = 1/2 kagome lattice compounds, volborthite and vesignieite, using Raman scattering. We demonstrate that even small modifications of the crystal structure may have a huge effect on the phonon spectrum and low-temperature properties.     

Self-consistent treatment of superconducting hole systems and anharmonic lattices in oxides

An extention of Hirsch's Hamiltonian describing the hole system is proposed by including a coupling to the anharmonic lattice and a modulation of the hopping interaction due to lattice displacements. The model is discussed within the variational Bogoliubov's approach, assuming a BCS-like trial Hamiltonian for the hole-like subsystem and a self-consistent phonon approximation for the lattice. The model allows in general to discuss an interplay between superconductivity and ferroelectricity. The results for the critical temperature and the isotope effect coefficient in the superconducting paraelectric phase in one dimension are presented. In particular, the strong influence of the phonon softening on the superconducting transition is widely discussed.     

Lattice dynamics of strontium tungstate

We report here measurements of the phonon density of states and the lattice dynamics calculations of strontium tungstate (SrWO₄). At ambient conditions this compound crystallizes to a body-centred tetragonal unit cell (space group I4₁/a) called scheelite structure. We have developed transferable interatomic potentials to study the lattice dynamics of this class of compounds. The model parameters have been fitted with respect to the experimentally available Raman and infra-red frequencies and the equilibrium unit cell parameters. Inelastic neutron scattering measurements have been carried out in the triple-axis spectrometer at Dhruva reactor. The measured phonon density of states is in good agreement with the theoretical calculations, thus validating the interatomic potential developed.      

On the Model Pseudopotential Approach to Calculate the Lattice Mechanical Properties of Thorium

The applicability of model pseudopotential approach to investigate lattice mechanical properties of Thorium, a typical f-shell metal, has been examined in light of some recent experimental and theoretical studies. It is found that presently available model potentials do not account for s-d-f hybridization adequately. The equation of state is greatly affected by s-d-f hybridization. It is also observed that a model potential giving reasonably good phonon dispersion curves may not reproduce equally good density of phonon states and hence the related lattice mechanical properties. However, it is possible to have a model potential, which may give fairly good estimate of lattice dynamical properties.     

Calculation of Vacancy Induced Properties in FCC Metals Using an Alternative Lattice Dynamical Model

Combining the conventional Kanzaki's lattice statics method with an alternative lattice dynamical model called decoupling transformation, a new approach is proposed to calculate the vacancy induced properties in FCC metals. This approach has the advantage over the traditional least-square fit approach in the way that all the model parameters are linearly independent and so it can avoid the problem of non-uniqueness in dynamical model parameters when interactions with more distant atoms are taken into account by fitting to the experimental phonon frequencies only. Numerical results on the lattice dynamical properties such as phonon dispersion curves and interatomic interaction force constants and the vacancy induced properties such as the atomic displacements, lattice relaxation energy, divacancy interaction energy and relaxation volume are obtained specifically for two similar FCC metals, to wit, Cu and Ni and are compared with previous calculations. It is concluded that the interatomic interactions up to the fourth nearest neighbours are already good enough for describing both the lattice vibrational and vacancy induced properties for both metals.     

Lattice vibrational properties of TmTe

We have investigated the lattice dynamical properties of a TmTe compound by using a breathing shell model suitable for this compound. The calculated phonon dispersion curves (PDC) reveal that this compound does not show any anomaly in their phonon properties. Our results on PDC, phonon density of states and lattice specific heat reveal that the phonon properties of this compound are like the other rare earth chalcogenides, particularly Eu-chalcogenides. We emphasize the need of measurements of the complete PDC of TmTe to support the present results on the calculated phonon properties.