固体氩的晶格热导率的非简谐晶格动力学计算

用一种非简谐晶格动力学方法, 使用相互作用势作为惟一的输入参数, 准确地计算了固体氩的各个声子的频率和弛豫时间. 并将这些结果进一步和玻尔兹曼输运方程相结合, 预测了固体氩从10 K 到80 K 区间的热导率, 并得到了与实验值非常符合的结果. 分析了运用非简谐晶格动力学方法进行数值计算过程中的各个相关的计算参数, 包括布里渊区中倒格子矢量的选取, δ 函数的展宽的选择等对热导率和声子弛豫时间预测结果的影响. 通过对各个声子模式对热导率贡献的分析, 发现随着温度升高, 高频声子对于热导率的贡献率也逐渐变大, 结果和理论预测完全一致. 关键词： 热导率 固体氩 非简谐晶格动力学 声子     

Gap solitons in an anharmonic diatomic lattice

Localized stationary modes with frequency in the forbidden region of the elastic vibrations of a diatomic anharmonic lattice are studied by the coupled-wave method. The mechanisms responsible for the brightening of the lattice in the cases of narrow and wide forbidden frequency bands are determined and an analytical expression is found for the stationary gap solitons. Fiz. Tverd. Tela (St. Petersburg) 39, 158–162 (January 1997)     

Characteristic features of anharmonic effects in the lattice dynamics of fcc metals

The dispersion in the entire Brillouin zone and the temperature dependence (right up to the melting temperature) of the anharmonic frequency shift and phonon damping in a number of fcc metals is investigated on the basis of microscopic calculations. It is found that the anharmonic effects depend sharply on the wave vector in the directions Г-X, X-W, and Г-L and, in contrast to bcc metals, the magnitude of the effects is not due to the softness of the initial phonon spectrum. It is shown that the relative frequency shifts and the phonon damping near melting do not exceed 10–20%. The relative role of various anharmonic processes is examined, and the relation between the results obtained and existing experimental data is discussed. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 9, 649–652 (10 May 1999)     

The bogolyubov variational principle in the theory of an anharmonic crystal

The Bogolyubov variational principle for classical systems is used to obtain the variation equation for a self-consistent field. With the help of this equation, various approximations of the self-consistent field method in the theory of a crystal with a multiparticle interaction are studied. The free energy of the crystal is calculated.     

First order phase transition in an anharmonic ising lattice

Criteria are derived for the existence of a first order phase transition in a compressible anharmonic Ising lattice. The analysis is based on a variational calculation and on the assumption that a compressible harmonic Ising lattice does not show a first order transition. A first order transition can occure only if the lattice and magnetic Grüneisen constants have the same sign and if the pressure is below some critical value. At this pressure the transition changes from first to second order. The results are applied to ammonium cloride exhibiting an order disorder transition of this type.     

Lattice dynamics of an anharmonic crystal: evidence for interactions between atomic vibrations at high temperatures

In studying the lattice dynamics of a strongly anharmonic crystal, we solve a set of nonlinear Langevin equations for interacting oscillators while a multiwell potential is calculated in the displacive limit from the first principles. The model applied to the peculiar vibrations of beta-Zr along [111] allows us to analyze all contributions to the spectral density and their influence on each other. We predict the effect of induced anharmonicity for quick vibrations due to their interaction with intrinsically anharmonic slow vibrations. This effect results in the broadband distribution in energy of inelastic neutron scattering known as the symmetry-forbidden phonon-branch splitting.     

On the microscopic theory of electronic contributions to lattice dynamics of anharmonic crystals

A formalism is set up to study the electronic contribution to the phonon dynamics in an arbitrary crystal, conducting or insulating, without assuming small ionic oscillations. Therefore, in contrast to a harmonic Born-Oppenheimer approximation, such an approach allows for renormalization effects due to phonon-phonon interaction over the complete temperature range of the solid phase. The “weak coupling” approximation between nuclei and electrons is shown to be sufficient in order to obtain the dynamical matrix microscopically in terms of the complete inverse dielectric function of the electrons.     

Dynamics of quantum fluctuations in an anharmonic crystal model

For a model given previously by the authors describing a structural phase transition we compute theq-mode critical fluctuations of momentum and displacement as a function of the critical temperatures, the wave vectorq, and a fading-out external field. An explicit dependence on the rates of fading out is obtained. In order to define the critical fluctuation operators we prove a reconstruction theorem, which is of model-independent value. Finally we study the critical spectrum and get rigorous results on the soft modes and the central peak.     

A statistical theory of the surface of an anharmonic crystal

We perform a linearization of the transcendental equations for the moments of the single-particle atomic distribution functions of an anharmonic crystal with a surface. The transcendental equations can be derived from the nonlinear integral equations of the nonsymmetrized self-consistent field method. With the help of these equations we consider the relaxation of the lattice of an fcc crystal near its three surfaces and the mean square displacement of the atoms, assuming nearest-neighbor interactions. We discuss effects which result when interactions between nonnearest-neighbors are taken into account and also the application of the method to small cyrstalline particles.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 44–49, January, 1986.     

Stability conditions for an anharmonic crystal in the mixed state

Stability conditions and the existence of metastable states for anharmonic crystals are examined within the framework of the theory of self-consistent phonons. Taking account of the self-consistent formation of liquid-like and crystal-like clusters in a crystal of fluid, the temperature nature of the behavior of the rms displacements and vibrations frequencies of atoms, the specific heat and the fraction of atoms in the liquid phase are investigated at the crystal-fluid transition. Expressions are obtained for the melting point and the absolute stability of the crystalline state, and domains of existence of crystal overheating and fluid supercooling are determined. The results of the computation are compared with experimental data for inert gases and with results obtained within the framework of a single-phase theory of consistent phonons.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 15–19, December, 1990.     

纳米晶体线的晶格动力学格林函数及晶格振动

通过求解差分方程,推导了纳米晶体线的晶格动力学格林函数,分析了其晶格振动,并推导了声子数表象中的原子位移及晶格振动哈密顿公式.研究结果表明,纳米晶体线的晶格振动能带分裂为一系列的子带,格波只能沿纳米晶体线的纵向传播,沿纳米晶体线的横截面只存在驻波.     

Specific heat and lattice dynamics of layered TiS2 crystal

The specific heatC of the layered 1T-CdI₂ type TiS₂ crystal has been measured over the temperature range 20–300 K using a thermal relaxation method. Based on the available information about lattice dynamics for acoustic and optical phonon modes in TiS₂, the dispersion curve and the density of states for each mode are evaluated using a simplified phonon Brillouin zone of a cylindrical form. The calculatedC-T curve is in good agreement with the observation.     

Angular forces in the lattice dynamics of diamond crystal lattices

The lattice dynamics of the diamond lattice has been investigated using a model in which the interatomic forces include, in addition to central forces, the angular forces of the type employed by de Launay and Clark, Gazis and Wallis. The 2 models have been applied to silicon and germanium to investigate the phonon dispersion curves in the three symmetry directions of the Brillioun zone. The results are found to be qualitatively in good agreement with experiments.     

Collective excitations in the anharmonic crystal

We consider a lattice model of an anharmonic crystal and compute the isothermal (χ_T) and adiabatics (χ_S) susceptibilities for the lattice displacement below T_c. A detailed analysis is given in terms of the dimension of the lattice and a decay parameter of the harmonic force. It turns out that there is a phase-space region for which 0 < χ_T/χ_S < 1, indicating breaking of ergodicity, and a region for which χ_T is finite, indicating the presence of a plasmon frequency due to the anharmonicity.     

Heat conduction in a three-dimensional momentum-conserving anharmonic lattice

Heat conduction in three-dimensional anharmonic lattices was numerically studied by the Green-Kubo theory. For a given lattice width W, a dimensional crossover is generally observed to occur at a W-dependent threshold of the lattice length. Lattices shorter than W will display a 3D behavior while lattices longer than W will display a 1D behavior. In the 3D regime, the heat current autocorrelation function was found to show a power-law decay as a function of the time lag τ as τ^{β} with β=-1.2. This indicates normal heat conduction. However, the decay exponent deviates significantly from the conventional theoretical value of β=-1.5. A flat power spectrum S(ω) of the global heat current in the low-frequency limit was also observed in the 3D regime. This provides not only an alternative verification of normal heat conduction but also a clear physical insight into its origin.     

Frequency shift and damping in Ford's anharmonic lattice

Mori's general theory of Brownian motion is used to calculate the secular part of the frequency shift and the resonance-frequency part of the damping in Ford's anharmonic lattice.     

Fluorine dynamics in BaF2 crystal lattice as an example of complex motion in a simple system

Fluorine relaxation profiles for a BaF₂ single crystal collected at several temperatures have been analyzed in terms of essentially different motional models: free rotational and free translational diffusion. The analysis has been performed to critically review the sensitivity of field dependent relaxation studies to mechanisms of molecular motions. The tested motional models do not realistically describe the fluorine dynamics within the crystal lattice. They have been chosen to attempt to answer quite fundamental questions regarding the feasibility of the field dependent nuclear spin relaxation studies to provide unique information on dynamic processes: 1. Is it possible to get information about the motional mechanisms by analyzing relaxation profiles collected in a broad frequency range? 2. To what extent is it possible to reasonably reproduce relaxation profiles in terms of unrealistic motional models?It has been concluded from the analysis that the rotational model leading to a single exponential correlation function explains the experimental data much better than the translational one. Validity regimes of the second order perturbation theory have been discussed in the context of the investigated system and the applied models.