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.     

Characterisation of electric discharge in hollow electrode Z-pinch device by means of Rogowski coils

In this paper, the energy spectra of the general molecular potential are obtained using the asymptotic iteration method within the framework of non-relativistic quantum mechanics.With the energy spectrum obtained, the vibrational partition function is calculated in a closed form and is used to obtain an expression for other thermodynamic functions such as vibrational mean energy U, vibrational mean free energy F, vibrational entropy S and vibrational specific heat capacity C. These thermodynamic functions are studied for the electronic state \(\mathrm{X}^{1}\Sigma _g^+ \) of \(K_2\) diatomic molecules.     

NO分子宏观气体热力学性质的理论研究

采用量子统计系综理论,研究了基态NO分子宏观气体摩尔熵、摩尔内能、摩尔热容等热力学性质.首先应用课题组前期建立的变分代数法(variational algebraic method, VAM)计算获得了基态NO分子的完全振动能级,得到的VAM振动能级作为振动部分,结合欧拉-麦克劳林渐进展开公式的转动贡献,应用于经典的热力学与统计物理公式中,从而计算得到了1000-5000 K温度范围内NO宏观气体的摩尔内能、摩尔熵和摩尔热容.将不同方法计算得到的摩尔热容结果分别与实验值进行比较,结果表明基于VAM完全振动能级获得的结果优于其他方法获得的理论结果.振动部分采用谐振子模型对无限能级求和计算热力学性质的方法有一定的局限性,应当使用有限的完全振动能级进行统计求和.     

Ergodic Properties of Microcanonical Observables

The problem of the existence of a strong stochasticity threshold in the FPU- model is reconsidered, using suitable microcanonical observables of thermodynamic nature, like the temperature and the specific heat. Explicit expressions for these observables are obtained by exploiting rigorous methods of differential geometry. Measurements of the corresponding temporal autocorrelation functions locate the threshold at a finite value of the energy density, which is independent of the number of degrees of freedom.     

单势阱粒子溢流模型中热力学量的涨落效应

采用相空间积分方法严格导出了各态历经条件下单势阱粒子溢流模型中系统温度和阱内粒子数涨落的解析表达式,着重讨论了热力学量涨落与总粒子数和势阱体积之间的关系.研究表明,系统总粒子数越少以及势阱体积越小,热力学涨落越显著,并且热力学涨落与阱内粒子的溢出密切相关.粒子的溢出和系统负比热及热力学大幅涨落的发生存在一一对应的关系,这一对应关系的根源可以从表观能量逆均分来理解.     

Algebraic approach to thermodynamic properties of diatomic molecules

A simple model extending Lie algebraic techniques is applied to the analysis of thermodynamic vibrational properties of diatomic molecules. Local anharmonic effects are described by means of a Morse-like potential and the corresponding anharmonic bosons are associated with the SU(2) algebra. The total number of anharmonic bosons, fixed by the potential shape, is determined for a large number of diatomic molecules. A vibrational high-temperature partition function and the related thermodynamic functions are derived and studied in terms of the parameters of the model. The idea of a critical temperature is introduced in relation to the specific heat. A physical interpretation in terms of a quantum deformation associated with the model is given.     

Vibrations of Au?? and FeAu?? nanoparticles and the limits of the Debye temperature concept

We present first-principles calculations of the vibrational density of states (VDOS), the specific heat and the mean-squared displacement of the five lowest-energy isomers of Au(13) and of two low-energy FeAu(12) nanoparticles. We find that the vibrational contributions to the Helmholtz energy do not affect the energy ordering of the isomers. As expected, for nanoparticles the vibrational density of states differs dramatically from the function proposed by the Debye model. We demonstrate that, for the nanoclusters we studied, the alternative calculations of the 'Debye temperature' yield significantly inconsistent results. We conclude that T(D) obtained from a particular thermodynamic property is neither applicable for deriving conclusions about other thermodynamic properties nor correlated with atomic bond strengths. Instead, in order to describe the temperature dependence of a nanoparticle's mean-squared displacement and its specific-heat capacity, what is necessary is its discrete phonon spectrum.     

Finite temperature corrections to the Casimir effect in rectangular cavities with perfectly conducting walls

The thermodynamical properties of a quantized electromagnetic field inside a box with perfectly conducting walls are studied using a regularization scheme that permits to obtain finite expressions for the thermodynamic potentials. The source of ultraviolet divergences is directly isolated in the expression for the density of modes, and the logarithmic infrared divergences are regularized imposing the uniqueness of vacuum and, consequently, the vanishing of the entropy in the limit of zero temperature. We thus obtain corrections to the Casimir energy and pressures, and to the specific heat; these results suggest effects that could be tested experimentally.     

First-principles study of the elastic and thermodynamic properties of thorium hydrides at high pressure

The high pressure behaviors of Th_4H_(15) and ThH_2 are investigated by using the first-principles calculations based on the density functional theory(DFT). From the energy–volume relations, the bct phase of ThH_2 is more stable than the fcc phase at ambient conditions. At high pressure, the bct ThH_2 and bcc Th_4H(15) phases are more brittle than they are at ambient pressure from the calculated elastic constants and the Poisson ratio. The thermodynamic stability of the bct phase ThH_2 is determined from the calculated phonon dispersion. In the pressure domain of interest, the phonon dispersions of bcc Th_4H(15) and bct ThH_2 are positive, indicating the dynamical stability of these two phases, while the fcc ThH_2 is unstable. The thermodynamic properties including the lattice vibration energy, entropy, and specific heat are predicted for these stable phases. The vibrational free energy decreases with the increase of the temperature, and the entropy and the heat capacity are proportional to the temperature and inversely proportional to the pressure. As the pressure increases, the resistance to the external pressure is strengthened for Th_4H_(15) and ThH_2.     

Thermodynamical properties of graphene in noncommutative phase–space

We investigated the thermodynamic properties of graphene in a noncommutative phase–space in the presence of a constant magnetic field. In particular, we determined the behaviour of the main thermodynamical functions: the Helmholtz free energy, the mean energy, the entropy and the specific heat. The high temperature limit is worked out and the thermodynamic quantities, such as mean energy and specific heat, exhibit the same features as the commutative case. Possible connections with the results already established in the literature are discussed briefly.     

Thermodynamic properties of the XX model in a chain with a period two and three coupling

The exact solutions for the energy spectrum of the XX model with a periodic coupling and an external transverse magnetic field h are obtained. The diagonalization procedure is discussed, and analytical and numerical solutions are given. Using the solutions for period-two coupling, the free energy, entropy, and specific heat are calculated as functions of temperature and applied transverse external magnetic field. Their expressions show that below a particular value v and above a value u of the magnetic field |h|, the entropy and the specific heat vanish exponentially in the low temperature limit.     

Thermodynamic properties and the approximate solutions of the Schrödinger equation with the shifted Deng–Fan potential model

With the introduction of a new improved approximation scheme (Pekeris-type approximation) to deal with the centrifugal term, the energy eigenvalues and the wave functions of the Schrödinger equation of the shifted Deng–Fan molecular potential are obtained, via the asymptotic iteration method. Rotational–vibrational energy eigenvalues of some diatomic molecules are presented, these results are in good agreement with other results in the literature. For these selected diatomic molecules, energy eigenvalues obtained are in much better agreement with the results obtained from the rotating Morse potential model for moderate values of rotational and vibrational quantum numbers. Furthermore, thermodynamic properties such as the vibrational mean U, specific heat C, free energy F and entropy S for the pure vibrational state in the classical limit for these energy eigenvalues are studied.     

Thermodynamic quantities in a Bose-Einstein gas at the quantum limit in a strong magnetic field close to the critical temperature

We have determined the thermodynamic functions (the translational kinetic energy, the pressure, the chemical potential, and the specific heat jump) in a degenerate Boson gas, close to the temperature where a Bose-Einstein condensation takes place into the first Landau energy level in a strong magnetic field. It is shown that the rearrangement of the energy spectrum and the number density of the quantum states for charged particles in a quantizing magnetic field cause the thermodynamic functions for a degenerate Boson system to differ qualitatively and quantitatively from the analogous quantities in the absence of a field.Government Institute, Brest. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 51–55, January, 1993.     

Effective elastic moduli under hydrostatic stress—I. quasi-harmonic theory

Fourth-order finite strain expressions for the effective elastic moduli of a solid under hydrostatic stress are derived from a general expression for effective elastic moduli. Expressions in terms of the strain tensors E and η are given. The expressions are then written in terms of the moduli and their pressure derivatives evaluated at an arbitrary reference state. The temperature dependence of these expressions is derived from the fourth-order quasi-harmonic expression for the lattice vibrational energy. Some general thermodynamic relations are derived between the parameters which specify the thermal effects and the pressure and temperature derivatives of the elastic moduli at the reference state. General relations between isothermal and isentropic elastic moduli and their pressure and temperature derivatives are also given. Much of the development is valid for materials of arbitrary symmetry, but the complete development is given only for materials of cubic symmetry.     

Gibbs free energy approach to calculate the thermodynamic properties of copper nanocrystals

Based on the thermodynamic and thermophysical properties of bulk materials, Gibbs free energy for nanocrystals is obtained and used to study the size-dependent melting point depression phenomenon. On the basis of size effects on the melting temperature of nanocrystals, thermodynamic properties of Cu nanocrystals, such as the specific heat capacity, the Debye temperature and the diffusion activation energy are investigated. Conversely, reliable predictions of these thermodynamic properties further verify the proposed approach.     

Modified 6-state and 8-state potts models in magnetic field

The exact solutions for the modified 6-state and 8-state Potts models in an external magnetic field are obtained within the framework of the Kramers-Wannier transfer matrix. The explicit analytical expressions for thermodynamic quantities such as magnetization, magnetic susceptibility and specific heat are derived and analyzed at length as functions of temperature and magnetic field.     

One-dimensional 3-state and 4-state standard Potts models in magnetic field

The exact solutions for 3-state and 4-state standard Potts models in external magnetic field are obtained within the framework of the Kramers-Wannier transfer matrix. The explicit analytical expressions for thermodynamic quantities such as magnetization, magnetic susceptibility and specific heat are derived and analysed at length as functions of temperature and magnetic field.     

One-dimensional ising model with next-nearest-neighbour interaction in magnetic field

The exact solution for the one-dimensional Ising model with nearest-neighbour and next-nearest-neighbour interactions in an external magnetic field is obtained within the framework of the Kramers-Wannier transfer matrix. The explicit analytical expressions for thermodynamic quantities such as magnetization, magnetic susceptibility and specific heat are derived and analyzed at length as functions of temperature, magnetic field, and the signs and values of the interaction parameters.     

Specific heat of a BCS superconductor

By expressing the free energy as an appropriate temperature integration over the square of the BCS energy gap function and by substituting simple but accurate analytic expressions for the latter, corresponding expressions are obtained for the specific heat in the superconducting state. In the upper portion of the temperature range, the ratio of the specific heats in the superconducting and normal states is 2.43 (1 + 0.936 in t), to better than one per cent accuracy, where t is the reduced temperature. Thus, the semilog plot of temperature versus the ratio of specific heat to temperature is a straight line over a large portion of one decade of specific heat. Corresponding expressions of similar simplicity and accuracy are obtained for the middle and low temperature ranges.     

混合气体声复合弛豫频谱的解析模型

为研究声传播和分子多模式振动能量弛豫的相互关系,本文提出了一种混合气体声 复合弛豫频谱的解析模型.该模型从振动模式微观能量转移及其耦合形成宏观弛豫过程两个角度, 分析了依赖于声频率的混合气体有效热容.并通过求解振动模式能量转移的通用弛豫方程, 最终得到可同时体现主副弛豫过程的声弛豫吸收和声频散的解析结果.仿真结果表明, 对于CO₂, CH₄, N₂和O₂组成的多种混合气体, 该模型的声吸收谱与实验数据相符,峰值误差在1%以内,且反映了多振动模式形成的 声复合弛豫吸收谱上通常仅会显现1-2个吸收波峰的物理现象.与已有模型相比, 本解析模型可直接求出混合气体声弛豫频谱上特征点的解析形式,并利于对其进行定性定量分析. 从而为研究声传播特性与气体分子弛豫特性的相互关系提供了一个有效理论模型.