ANALYTIC EQUATION OF STATE FOR GENERALIZED LENNARD-JONES SOLID INCLUDING LOWEST-ORDER ANHARMONIC AND CORRELATION CORRECTIONS

Based on the cell model, the general formula for the free energy of solids is derived analytically with the lowest order anharmonic modification and correlation effect taken into account. Combining a method of summing over lattice sites, the analytic equation of state for generalized Lennard-Jones solid is derived. The calculations show that the agreement between theory and computer simulation is quite good and is significantly improved as compared with the numerical results in literature. The comparison of different effects shows the theory including all neighbors but only considering the lowest anharmonic and correlation effects may be a good and convenient approximation for practical solids. The approximation can be easily extended to the quantum case and other generalized potentials.     

Quantum corrected cell model for an anharmonic generalized Lennard-Jones solid

A simple method is proposed to dispose the quantum effect and anharmonic effect at the same time. Considering the quantum effect is remarkable only at low temperature, and tends to zero at high temperature, the potential energy of an atom is expanded harmonically to consider the quantum effect of solids within the harmonic oscillator framework. The anharmonic effect is remarkable only at high temperature, and tends to zero at low temperature, it was disposed by using a classical approximation. The universal formalism is applied to the generalized Lennard-Jones solid. The comparison shows that the results with and without anharmonic effect are in agreement with each other at some low temperature, to which the Einstein model is applicable. The results without anharmonic effect become divergent at slightly higher temperatures; however, the results including anharmonic effect are in good agreement with the experimental data of solid xenon. The method proposed in this paper can be extended to other potentials to develop practical molecular thermodynamic equations of state for solids.     

推广的Lindemann熔化定律

本文将Lindemann理论应用于非谐振固体的情况,推广了Lindemann熔化定律,并且计算了Fe,Cu,Al的高压熔化曲线。计算结果与实验数据的符合是满意的。     

On the spin-phonon interaction in anharmonic crystals

In this paper, a theory is developed for examining the influence of the spin-phonon interaction on the phonon dynamics in anharmonic crystals. In contrast to a harmonic approximation such an approach allows for comparing the role of the direct interaction between lattice vibrations with that of the indirect interaction via spins in the propagation and attenuation of sound as well as in the behaviour of thermodynamic quantities. Explicit expressions are derived for the phonon self-energy using successively higher approximations obtained from a cumulant expansion of the density of interparticle distances. It is shown that even in the harmonic approximation the two-spin correlation function and the four-spin correlation function enter into the expression of the generalized dynamical matrix in deviation from previous results. The modification of this harmonic dynamical matrix due to the renormalization of the harmonic phonons and due to phonon-phonon scattering processes is given employing a “weak coupling” approximation between the localized spins and the interparticle-distance density of the crystal. The resemblance of the present approach to an earlier microscopic treatment of electronic contributions to phonon dynamics in anharmonic crystals is pointed out.     

Analytic Debye-Grüneisen equation of state for a generalized Lennard-Jones solids

The approximate method to treat the practical quantum anharmonic solids proposed by Hardy,Lacks and Shukla is reformulated with explicit physical meanings.It is shown that the quantum effect is important at low temperature,it can be treated in the harmonic framework.and the anharmonic effect is important at high temperature and tends to zero at low temperature,it can be treated by using a classical approximation.The alternative formulation is easier for various applications,and is applied to a Debye-Grueneisen solid with the generalized Lennard-Jones intermolecular interaction.The expressions for the Debys temperature and Grueneisen parameter as a function of volume are analytically derived.The analytic equation of state is applied to predict the thermodynamic properties of solid xenon at normal-pressure with the nearest-neighbour Lennard-Jones interaction,and is further applied to research the properties of solid xenon and krypton at high pressure by using an all-neighbour Lennard-Jones interaction.The theoretical results are in agreement with the experiments.     

A JWKB analysis of the sextic anharmonic oscillator in d dimensions

On the basis of a radial generalization of the JWKB quantization rule, which incorporates higher orders of the approximation, an explicit analytical formula is derived for the energy levels of the three-dimensional sextic anharmonic oscillator. The formula exhibits the scaling property of the exact eigenvalues, and is readily generalized to any dimension. The predicted results are in good agreement with known numerical values.     

An approximate scheme to determine the vibratory density of states in a quasi-harmonic solid

In a new and realistic conception of solids, an analytical approach is presented to find the phonon density of states in a quasi-harmonic one-dimensional solid by starting from the fact that a solid with strong interatomic forces can be regarded as an atomic array of quantum anharmonic oscillators under a Morse potential. In fact, our quasi-harmonic approximation is derived by assuming a large enough solid with an involved anharmonic parameter as a sufficiently small quantity. In this context, a mathematical relationship between the above parameter and the matrix element relative to oscillator’s strength is obtained.     

Effects of intrinsic anharmonicity in the Mie–Grüneisen equation of state and higher order corrections

The usual quasiharmonic Mie–Grüneisen (MG) equation of state is modified by the inclusion of ‘intrinsic anharmonicities’, which have been considered up to now primarily in the high temperature limit. A comparison with experimental data for the rare gas solids, Ar, Kr and Xe and for MgO reveals that the anharmonic contributions cannot be represented perfectly within the MG approximation. A small but significant modification of the MG approach is presented to estimate intrinsic anharmonic contributions within a mean-field approximation for the thermal part of the internal energy. This estimate results in reasonable interpolations to low temperatures, where quantum effects are dominant. The present approach is also compared with more restricted recent theoretical results.     

Many-body effects in molecular solids

The effects of many-body interactions in the molecular (rare-gas) solids have been investigated, on the basis of Axilrod-Teller approximation, by a rigid-atom model. It is found that the 3-body interaction is the most dominant of all and the rest may be safely ignored. The discrepancy seen in the phonon dispersion curves is expected to be removed by the inclusion of appropriate anharmonic effects.     

Transport theory for quantum crystals

A correlation function approach is developed to treat non-equilibrium phenomena of quantum crystals at low frequency and long wavelength within the renormalized harmonic approximation (RHA). The derivation of the transport equations is carried out by studying the hierarchy of equations of motion for the retarded Green's functions of a pure, nonprimitive, nonionic, anharmonic lattice. Using a factorization technique to take into account the most important terms due to the particle fluctuations and the leading contributions to the hydrodynamic singularities of the phonon self-energy, we find a differential equation for the displacement field and a generalized transport equation for the phonon gas. The microscopic RHA expressions for the local temperature, the local heat density and the energy current are derived; the quasiparticle parameters (elastic constants, generalized Grüneisen parameters, quasiparticle interaction) entering the equations of motion are shown to be consistent with the RHA. In the hydrodynamic regime the general equations are reduced to two coupled differential equations for the lattice deformations and for the local temperature. Then only the displacement-displacement, the displacement-energy density and the energy density-energy density correlation functions show macroscopic fluctuations; for these functions thermodynamical sum-rules are derived.     

Anharmonic effects and the lattice dynamics of insulators

Anharmonic effects manifest themselves in everyday properties of solids. Two of the more obvious examples are thermal expansion and heat conductivity. More sophisticated examples anharmonicity are provided by the direct measurement of the lifetimes and of the pressure and temperature dependence of modes of vibration solids by infrared, Raman, Brillouin, or neutron spectroscopy. The present article reviews current status of the theory of anharmonic effects in insulators. We will draw our examples almost exclusively from the simplest insulators, namely the fcc rare gas solids (RGS) and alkali-halides (AH) mostly of the rocksalt structure. Much what we have to say is applicable to other kinds solids also, but we shall not dwell on this aspect. We shall arbitrarily exclude perhaps the two most interesting classes of anharmonic solids, that ferroelectrics and quantum solids. These subjects are sufficiently developed as to warrant reviews their own and it would be impossible to do them justice in the space avdable here. No mention will be made of the vast subject of impurity modes which especially in the case of alkali-halides has developed into an autonomous branch of solidstate physics. For similar reasons we have chosen to exclude thermal conductivity attenuation sound and second sound. We are then left with what we feel to be a more manageable task reviewing the basic anharmonic properties of the simplest classes of perfect insulators. Our selection of material reflects our own biased and peculiar interests. Examples wdl be illustrative rather than exhaustive. Previous reviews and basic articles dealing with anharmonic effects are listed separately in the references at the end of this article.     

Vibrational and electronic spectral analysis of 2,3-pyrazinedicarboxylic acid: A combined experimental and theoretical study

Fourier transform infrared and Raman spectra of 2,3-pyrazinedicarboxylic acid were recorded and analyzed using density functional theory. The complete assignments of the anharmonic vibrational modes have been performed based on potential energy distribution. The anharmonic frequencies were computed using vibrational second-order perturbation theory as well as vibrational self-consistent field and correlation corrected vibrational self-consistent field methods. Mode–mode coupling strength is also estimated using two-mode representation of quartic force field approximation. The intra- and intermolecular interactions were also studied in the dimer and trimer forms of the title molecule. The ultraviolet–visible absorption spectra in ethanol, methanol, and acetonitrile solvents were recorded and analyzed using time-dependent density functional theory involving the polarization continuum model. The observed and calculated results are well comparable. Molecular electrostatic potential and the highest occupied and the lowest unoccupied molecular orbital analyses are also reported.     

One-Particle Distribution Functions and Thermodynamics of Crystals with Many-Body Forces. III. Perturbation Theory

The theory of crystalline state described in preceding papers is considered as a zeroth-order approximation. Statistical perturbation theory is used for the purpose of improving this approximation. The second-order corrections to the Helmholtz free energy and thermodynamic properties of strongly anharmonic crystals are derived. The properties of solid Ar, Kr, and Xe are calculated using various pair-potential functions in conjunction with the AXILROD -TELLER -MUTO three-body potential. The first quantum corrections are taken into account in the quasi-classical approximation. The result of computations are compared with the experimental data.     

Structural, electronic and optical properties of high pressure stable phases of ZnTe

We have performed full potential linear augmented plane wave calculations to investigate the pressure induced phase transition in ZnTe. Total energies of three phases (zinc-blende, cinnabar and Cmcm) are calculated using density functional theory formalism under generalized gradient approximation and Engel-Vosko generalized gradient approximation for the exchange correlation potential approximation. The pressure stability corresponding to zinc-blende, cinnabar and Cmcm phases of ZnTe are computed. We find that cinnabar phase could be formed as a metastable phase by releasing pressure from the high pressure Cmcm phase. The obtained structural, electronic and optical results are compared with previous calculations and available experimental data. Overall good agreement is found.     

Lattice dynamics of strongly anharmonic crystals with hard core interaction

The renormalized anharmonic phonon theory and especially the self-consistent harmonic approximation can not be used for hard core interaction in it's original form. Additional short-range correlations have to be incorporated into this theory. A method is proposed which allowes to do this in a systematic way and criteria are found which have to be obeyed by the short-range correlation function. Two examples valid at high and at zero temperature, respectively, are discussed.     

The shape of NMR absorption and cross-relaxation spectra in a heteronuclear spin system

A dynamic theory of heteronuclear spin systems in solids at high temperatures is developed. A system of nonlinear integral equations for the spin time correlation functions is derived in the self-consistent fluctuating local field approximation taking into account corrections for the correlated local field fluctuations in real crystal lattices. The theory is applied to interpretation of the experimental data available for a LiF crystal representing a system with the nuclei of two types. The signals of free precession for Li and F nuclei, as well as the spectra of harmonic cross-relaxation, cross-polarization of the ⁶Li isotope, and depolarization of the ⁸Li isotope, were calculated for the magnetic field oriented along the principal crystallographic axes of LiF. The results of calculations show good agreement with experiment.     

Vacancies in metals: from first-principles calculations to experimental data

We have revealed, and resolved, an apparent inability of density functional theory, within the local density and generalized gradient approximations, to describe vacancies in Al accurately and consistently. The shortcoming is due to electron correlation effects near electronic edges and we show how to correct for them. We find that the divacancy in Al is energetically unstable and we show that anharmonic atomic vibrations explain the non-Arrhenius temperature dependence of the vacancy concentration.     

Thermodynamics of impure anharmonic crystals

The vibrational thermodynamic properties of doped anharmonic solids are investigated using thermodynamic Green's functions. The study uses cubic and quartic anharmonic interactions, and different masses and force constants for the impurity and host lattice atoms. The explicit expressions so derived for the partition function, free energy, entropy, and lattice heat capacity for these solids in the low-impurity-concentration limit are discussed for various situations. Our results are modified due to the presence of interaction terms between the anharmonic and localized fields and reduce to those obtained by earlier workers as limiting cases.     

Anharmonic stabilization of the high-pressure simple cubic phase of calcium

The phonon spectrum of the high-pressure simple cubic phase of calcium, in the harmonic approximation, shows imaginary branches that make it mechanically unstable. In this Letter, the phonon spectrum is recalculated by using density-functional theory ab initio methods fully including anharmonic effects up to fourth order at 50 GPa. Considering that the perturbation theory cannot be employed with imaginary harmonic frequencies, a variational procedure based on the Gibbs-Bogoliubov inequality is used to estimate the renormalized phonon frequencies. The results show that strong quantum anharmonic effects make the imaginary phonons become positive even at zero temperature so that the simple cubic phase becomes mechanically stable, as experiments suggest. Moreover, our calculations find a superconducting T(c) in agreement with experiments and predict an anomalous behavior of the specific heat.     

Third Order Anharmonic Effects in Many-Body Nuclear Quantum Theory

JETP Letters - The quantum theory of third order anharmonic effects in the photon production amplitude developed by V.A. Khodel has been generalized for nuclei with pairing and for a more accurate...