Unified study of lattice dynamics of NiO

A unified study of lattice dynamics of paramagnetic NiO has been studied by correcting the basic equations of the three-body force shell model for the valency of the cations and anions. The shell charge and core charge parameters are also modified. This approach explains the complete lattice dynamics of NiO successfully only when both the ions are taken to be polarizable. There is good scope for fresh determination of positive ion polarizability and Debye temperature variation.     

First-principles study of the high pressure phase transition and lattice dynamics of cerium

We present a first-principles study of the phase transition and lattice dynamics of Ce within the framework of the density functional theory using the GGA+U method. Our calculated results denote that under pressure the transition path is α-Ce (fcc)→α″-Ce (monoclinic, with two atoms per unit cell)→bct-Ce (body centered tetragonal), and the transition pressures are located at 5.36 and 14.37 GPa, respectively. The equation of state in a wide range of pressure is consistent with the experimental data. During the γ-α phase transition, the magnetic moment disappears gradually, which is mainly due to the strong interaction between the 4f and 5d electrons. By calculating the free energies from phonon dispersions including electronic contribution, the obtained γ-α transition temperature at zero pressure is 148 K. From the Blackman diagram of dimensionless elastic constant ratios, we can find that both γ- and α-Ce show negative Cauchy pressure—C₄₄>C₁₂.     

Phase transition of hard hexagons on a triangular lattice

Systems of hard hexagons on a triangular lattice are investigated. The orientation of the hexagons is kept fixed, while the size of the hexagons is varied. The existence of a phase transition is proved for all sizes by means of the Peierls'argument. The proof does not imply a phase transition in the continuous limit.Work supported by the U. S. Air Force under Contract No. F 44620-71-C-0013.     

The interaction of nonlinear waves in two-dimensional lattice

This paper investigates the collision between two nonlinear waves with arbitrary angle in two-dimensional nonlinear lattice. By using the extended Poincarge-Lighthill-Kuo perturbation method, it obtains two Korteweg-de Vries equations for nonlinear waves in both the ζ and η directions, respectively, and derives the analytical phase shifts after the collision of two nonlinear waves. Finally, the solution of u（υ） up to O（ε^3） order is given.     

Phase transition in a two-dimensional Ising ferromagnet based on the generalized zero-temperature Glauber dynamics

At zero temperature, based on the Ising model, the phase transition in a two-dimensional square lattice is studied using the generalized zero-temperature Glauber dynamics. Using Monte Carlo （MC） renormalization group methods, the static critical exponents and the dynamic exponent are studied; the type of phase transition is found to be of the first order.     

Computer simulation study of a two-dimensional dipolar lattice

Summary The present work reports Monte Carlo calculations on a classical square lattice, consisting of purely dipolar plane rotators with identical dipole moments. Dipolar interactions are known not be essential for nematic ordering, but they can play a significant role in some specific cases; along the lines of the lattice model approximation already used in simulation work on liquid crystals, our system can be considered as an extreme case of nematogenic potential model. The system possesses an antiferroelectric ground state and, at higher temperature, it undergoes a transition to an orientationally disordered phase; comparison with the mean-field treatment of the transition is also reported. The structural properties were investigated by calculating orientational correlation functions, and found to exhibit some qualitative differences with respect to other potential models previously investigated for nematics. Simulation results indicate a close qualitative similarity with a three-dimensional analogue investigated in our previous work.

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Riassunto Il presente lavoro riporta calcoli Monte Carlo per un reticolo classico quadrato, costituito da rotatori piani puramente dipolari, con identici momenti. è noto che le interazioni dipolari non sono essenziali per l'ordinamento nematico, ma esse possono avere un ruolo significativo in alcuni casi specifici; lungo le linee dell'approssimazione a modello reticolare già applicata in lavori di simulazione per cristalli liquidi, il nostro sistema può pertanto venire considerato come un caso estremo di modello di potenziale nematogenico. Il sistema possiede stato fondamentale antiferroelettrico ed, a temperatura piú elevata, transisce ad una fase orientazionalmente disordinata; si riportano per confronto i risultati della trattazione a campo medio per tale transizione. Le proprietà strutturali furono investigate calcolando funzioni di correlazione orientazionale, e si è trovato che esse mostrano qualche differenza qualitativa rispetto ad altri modelli di potenziale previamente studiati per nematici. I risultati di simulazione indicano una stretta somiglianza qualitativa con un analogo tridimensionale investigato in nostri precedenti lavori.

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Резюме В этой работе предлагаются вычисления по методу Монте-Карло для классической квадратичной решетки, состоящей нз чнсто дипольных плоских ротаторов с тождественными дипольными моментами. Известно, что дипольные взаимодействия не являются существенными для нематического упорядочения, но они могут играть существенную роль в некоторых специфических случаях: в частности, в приближении модельной решетки, уже использованном при моделировании на жидких кристаллах, наша система может рассматриваться как предельный случай модели немтическочо потенциала. Рассмотренная система обладает антиферромагнитным основным состоянием и при высоких температурах она претерпевает переход в ориентационно разупорядоченную фазу; также проводится сравнение с рассмотрением этого перехода с помощью среднего поля. Исследуются структурные свойства, вычисляя ориентационные корреляционные функции. Обнаружено существование некоторых качественных различий по сравнению с моделями потенциалов, ранее использованных для нематиков. Результаты моделирования обнаруживают качественное подобие с трехмерным аналогом, исследованным в нашей предыдущей работе.

     

Inhomogeneous Glauber dynamics and the process of crystallization of a lattice gas

The model under consideration is a hard-core lattice gas in an external potential on a Bethe lattice with nonequilibrium time evolution governed by Glauber dynamics. A hierarchical decoupling of nonequilibrium correlations, motivated by and asymptotically providing the exact form of equilibrium multisite correlations in the inhomogeneous potential regime, is proposed. Application is made to the process of lattice gas crystallization, at high activity, from a spatially homogeneous fluid phase to an equilibrium crystal phase with unequal sublattice densities. The first few levels of the hierarchical decoupling give a consistent picture of two kinds of nonequilibrium instabilities—one leading to a sublattice density bifurcation, the other associated with an abrupt increase in densities and correlations in time.     

Analyticity of a hard-core multicomponent lattice gas

A multicomponent anti-Widom-Rowlinson lattice gas is introduced. An arbitrary numberM of particle types is permitted, all having the same activity. The only interactions are nearest-neighbor exclusions oflike particles (analogous to map-coloring problems). For any lattice it is shown that there is a finite numberM ₀ (depending only on the coordination number of the lattice) such that for allMM ₀ the infinite volume correlation functions exist and are analytic functions of the activity, for all positive values of the common activity.Research supported in part by NSF Grant No. GP-33535X, AFOSR Grant No. 73-2430B, and NSF Grant No. MPS75-20638.     

Inelastic neutron scattering and lattice dynamics studies in complex solids

At Trombay, lattice dynamics studies employing coherent inelastic neutron scattering (INS) experiments have been carried out at the two research reactors, CIRUS and Dhruva. While the early work at CIRUS involved many elemental solids and ionic molecular solids, recent experiments at Dhruva have focussed on certain superconductors (cuprates and intermetallics), geophysically important minerals (Al₂SiO₅, ZrSiO₄, MnCO₃) and layered halides (BaFCl, ZnCl₂). In most of the studies, theoretical modelling of lattice dynamics has played a significant role in the interpretation and analysis of the results from experiments. This talk summarises the developments and current activities in the field of inelastic neutron scattering and lattice dynamics at Trombay.     

Structure and phase transition of a two—dimensional dusty plasma

The structure and phase transition of a two-dimensional (2D) dusty plasma have been investigated in detail bymolecular dynamics simulation. Pair correlation function, static structure factor, mean square displacement, and bondangle correlation function have been calculated to characterize the structural properties. The variation of internalenergy, shear modulus, particle trajectories and structural properties with temperature has been monitored to studythe phase transition of the 2D dusty plasma system. The simulation results are in favour of a two-step continuoustransition for this kind of plasma.     

Nonlinear low-frequency electrostatic wave dynamics in a two-dimensional quantum plasma

The problem of two-dimensional arbitrary amplitude low-frequency electrostatic oscillation in a quasi-neutral quantum plasma is solved exactly by elementary means. In such quantum plasmas we have treated electrons quantum mechanically and ions classically. The exact analytical solution of the nonlinear system exhibits the formation of dark and black solitons. Numerical simulation also predicts the possible periodic solution of the nonlinear system. Nonlinear analysis reveals that the system does have a bifurcation at a critical Mach number that depends on the angle of propagation of the wave. The small-amplitude limit leads to the formation of weakly nonlinear Kadomstev–Petviashvili solitons.     

Inelastic neutron scattering and lattice dynamics of ZrO2, Y2O3 and ThSiO4

Zirconia (ZrO₂), yttria (Y₂O₃) and thorite (ThSiO₄) are ceramic materials used for a wide range of industrial applications. The dynamical properties of these materials are of interest as they exhibit numerous interesting phase transitions at high temperature and pressure. Using a combination of inelastic neutron scattering and theoretical lattice dynamics we have studied the phonon spectra and thermodynamic properties of these compounds. The experimental data validate the theoretical model, while the model enables microscopic interpretations of the observed data. The calculated thermodynamic properties are in good agreement with the experimental data.      

Ab initio study of lattice dynamics and thermal equation of state of Ni

Lattice dynamics and thermal equation of state of fcc nickel have been studied in the framework of density functional perturbation theory. The influence of the GGA+U on the structure is considered. The calculated phonon dispersion curve accords excellently with the experimental data. Within the quasi-harmonic approximation, the thermal equation of state, thermal expansion coefficient, thermal pressure, bulk moduli and Debye temperature are well reproduced. The thermal properties confirm the available experimental data and are extended to a wider pressure and temperature range.     

Lattice dynamics of cubic PbTiO3 by inelastic neutron scattering

High-temperature dispersion relations of the phonon modes in a cubic PbTiO₃ single crystal have been investigated along the [ξ 0 0] and [ξ ξ 0] directions by inelastic neutron scattering. Above T _c, the phonon dispersions are only temperature-dependent close to the Brillouin zone centre where the mode softening comes through. The measurements indicate large cubic anisotropy of the elastic tensor and relatively low anisotropy of the soft mode dispersion. The differences from an earlier inelastic neutron scattering study are discussed.     

Nonlinear Topological Effects in Optical Coupled Hexagonal Lattice

Topological physics in optical lattices have attracted much attention in recent years. The nonlinear effects on such optical systems remain well-explored and a large amount of progress has been achieved. In this paper, under the mean-field approximation for a nonlinearly optical coupled boson–hexagonal lattice system, we calculate the nonlinear Dirac cone and discuss its dependence on the parameters of the system. Due to the special structure of the cone, the Berry phase (two-dimensional Zak phase) acquired around these Dirac cones is quantized, and the critical value can be modulated by interactions between different lattices sites. We numerically calculate the overall Aharonov-Bohm (AB) phase and find that it is also quantized, which provides a possible topological number by which we can characterize the quantum phases. Furthermore, we find that topological phase transition occurs when the band gap closes at the nonlinear Dirac points. This is different from linear systems, in which the transition happens when the band gap closes and reopens at the Dirac points.     

Nonlinear travelling waves in φ6 polarizable model

We present a complete theoretical analysis of the periodic and non-periodic travelling waves in a diatomic chain model, in the continuum limit by incorporating nonlinear sixth order polarization potential (φ⁶) at the anion site. We have formulated a nonlinear lattice dynamical theory in which various energy curves are obtained for different types and magnitudes of the core-shell force constants. For periodic solutions, we have obtained two types of commensurate wave amplitudes which propagate in the opposite direction with respect to each other. For nonperiodic solutions, we have obtained various travelling excitations such as kink, antikink, excitons etc. for different values of the mass ratio and velocity parameter. The dipole moment per unit charge for SrTiO₃ has been calculated and it is found that the nonlinear excitations in this model carry large amount of energy as compared to those obtained from harmonic and anharmonic optical phonons in the φ⁴-polarizable model.     

High pressure lattice dynamics, dielectric and thermodynamic properties of SrO

Using density functional theory and density functional perturbation theory we have studied the effects of hydrostatic pressure on lattice dynamics, dielectric and thermodynamic properties of the rocksalt (NaCl) and CsCl phases of SrO. The stability of the NiAs type structure, experimentally confirmed to be stable in BaO, is also investigated. Studying the lattice dynamics of the NaCl and CsCl phases at various pressures, in the range of the phase stability, we have found the lattice dynamical instabilities which govern the phase transitions between NaCl and CsCl phases with increasing and decreasing pressure. By monitoring the behaviour of the found soft modes, we have calculated the transition pressures upon compression and decompression of SrO crystal. Lattice dynamics calculations reveal that the rocksalt and CsCl structures are unstable with respect to the soft transversal acoustic modes at single points of the Brillouin zone, which points to the fact that the transitions are of displacive type. Responses to electric fields and thermodynamic properties at high pressures are also given and discussed. All our results are in a good agreement with experimental data where applicable.     

Resistivity exponent of two-dimensional lattice animals

We calculate the average resistanceR(L) of lattice animals spanningL×L cells on the square lattice using exact and Monte Carlo methods. The dynamical resistivity exponent, defined asR(L) L , is found to be =1.36±0.07. This contradicts the Alexander-Orbach conjecture, which predicts 0.8. Our value for differs from earlier measurements of this quantity by other methods yielding =1.17±0.05 and 1.22±0.08 by Havlin et al.On leave from the Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing, China.     

A study of electronic structure and lattice dynamics of CoSb3 skutterudite

The novel filled skutterudite materials have attracted much interest in recent years and experimental studies have revealed that electrical properties (electrical conductivity and Seebeck coefficient) in these materials are dominated by their electronic structure while the effective suppression of thermal conductivity is mainly determined by their lattice dynamics. To clarify the relationship between microstructure and properties in further, we report a systematic study of electronic structures and lattice dynamics of CoSb₃ in this paper using linearized augmented plane waves based on the density functional theory of first principles. By calculating band structure and partial density of states (PDOS), effects of electronic structures of CoSb₃ on electrical properties were investigated. Based on the calculated results of phonon dispersions and phonon density of states of CoSb₃, lattice dynamics of CoSb₃ (heat capacity, Debye temperature, mean free path and lattice thermal conductivity) are discussed in detail. The calculated results are excellently consistent with other work and experimental data.     

Raman phonon spectra and lattice dynamics of 9,10-dinitroanthracene under pressure

Abstract

Raman phonon spectra of 9, 10-dinitroanthracene have been recorded in the pressure range 0-6GPa. No phase transition is detected up to the maximum pressure studied. Quasi Harmonic Lattice Dynamics calculations, based on an atom-atom potential previously modeled on homologous 9,10-disubstituted anthracenes, have been performed. The optimized potential was used to calculate the equilibrium geometry and the lattice phonon frequencies as a function of pressure. The calculated structure at ambient conditions closely resembles the experimental one. The calculated phonon frequencies show a good agreement with the experimental values at all pressures measured.