Phase transition in liquid crystal elastomers—A Monte Carlo study employing non-Boltzmann sampling

We investigate nematic-isotropic transition in liquid crystal elastomers employing a variant of Wang-Landau sampling. This technique facilitates calculation of the density of states from which other thermodynamic properties can be obtained. We consider a lattice model of a liquid crystal elastomer and a Hamiltonian which accounts for interactions among liquid crystalline units and interaction of local nematics with global strain. We investigate the effect of varying the strength of coupling between nematic and orientational degrees of freedom. When the local director is coupled strongly to the global strain, the transition is strongly first order. When the strength of the coupling decreases the transition becomes weakly first order. The transition temperature decreases when the coupling becomes weaker. We also report for the first time results on variation of free energy as a function of average energy at different temperatures and coupling constants.     

最近邻强交换相互作用对spin-1纳米管热力学性质的影响

利用有效场理论研究了纳米管上最近邻强交换相互作用下Blume-Capel模型的内能、比热和自由能,得到了系统的内能、比热和自由能与最近邻强交换相互作用、晶场强度和温度的关系.结果表明:最近邻强交换相互作用、晶场强度和温度等诸多因素相互竞争,使系统表现出比J_1=J_2=J=1时的BC模型更为丰富的热力学性质;系统内能随温度的变化曲线表现出不连续性;比热随温度的变化出现奇异性;一定条件下,基态时的自由能会发生突变.     

Temperature and density extrapolations in canonical ensemble monte carlo simulations

We show how to use the multiple histogram method to combine canonical ensemble Monte Carlo simulations made at different temperatures and densities. The method can be applied to study systems of particles with arbitrary interaction potential and to compute the thermodynamic properties over a range of temperatures and densities. The calculation of the Helmholtz free energy relative to some thermodynamic reference state enables us to study phase coexistence properties. We test the method on the Lennard-Jones fluids for which many results are available.     

NpT-ensemble Monte Carlo calculations for binary liquid mixtures

A Monte Carlo method for the calculation of thermodynamic properties in the isothermal-isobaric ensemble is described. Application is made to the calculation of excess thermodynamic properties (enthalpy, volume and Gibbs free energy) of binary mixtures of Lennard-Jones 12-6 liquids. Comparison is made with the predictions of a number of theories of liquid mixtures; the so-called van der Waals one-fluid model and the variational theory of Mansoori and Leland are both found to give excellent results. The accuracy attainable in estimates of the excess properties is discussed in terms of statistical fluctuations in various calculated quantities and the advantages and disadvantages of the method are examined in relation to calculations by the more familiar constant-volume method.     

纳米尺度下Sm-Co合金体系中相组成与相稳定性的研究

建立了纳米晶合金相的热力学模型,可定量描述纳米尺度下合金体系中化合物相的热力学性质,并预测合金相的稳定性及其转变规律.利用该模型全面计算了纳米晶Sm-Co合金体系中各化合物相在不同晶粒尺寸下的摩尔吉布斯自由能随温度的变化关系,预测了纳米尺度下Sm-Co合金体系中各物相的相对稳定性及转变规律.模型预测结果示出,在室温附近,随着纳米晶粒尺寸的减小,某些纳米晶合金相的摩尔吉布斯自由能将由负值变为正值,预示着将向其他更稳定的纳米晶合金相转变,这是与传统粗晶材料中合金相的稳定性仅依赖于温度条件而完全不同的纳米晶合金 关键词： 纳米晶材料热力学 Sm-Co合金 相稳定性 相变     

向列型液晶理论评述

本文评述了向列型液晶的唯象理论和微观理论。由简单的关于对称性的讨论,推得了以序参数张量为变量的唯象的Landau自由能密度展开式。然后在下列三方面阐明了Landau-deGennes理论的应用:计算了向列型—各向同性型相变的热力学性质,研究了大块向列型液晶对于外界干扰的响应,并描述了涨落和界面效应。关于向列型液晶微观理论的讨论又分为两部分,一是讨论基于位致排斥相互作用而给出的理论,另一是讨论基于分子间的吸引相互作用而给出的理论。本文将表明,虽然每一类型的理论都能阐明向列序存在的物理基础的某些方面,但没有一个理论能够全面地说明向列型液晶的状态和它向各向同性相的转变。最后,本文指出了某些尚未解决的问题及其可能的解决途径。     

Nonlocal fluid density distribution in the vicinity of the critical point

The differential equation for the component local density of a binary fluid was obtained as a result of an isoperimetric problem of the system free energy minimization under condition of particle number stability. The obtained expression can be used in the calculation of liquid's profiles as well as in the investigation of thermodynamic properties in the vicinity of the critical point. An isoperimetric problem solution for the model binary fluid of the system free energy minimization under condition of particle number stability was obtained in different cases: fluid within flat parallel layer under a gravitational field, under a gravitational field and wall potential as well as under a wall potential for another equation of state.     

Calculation of elastic and thermal properties of alkali metals by the pseudopotential method

The elastic and thermal properties of alkali metals are analyzed from the viewpoint of effective ion-ion interaction in rectilinear space. Consideration is given to the approximation of pair interaction between ions. The atomic-interaction potential is calculated on the basis of the pseudopotential method. Numerical calculations are made of the elastic constants, the second and fourth moments of the frequency spectrum, the temperature dependence of the Debye temperature, the specific heat, and the vibrational free energy of Na, K, Rb, and Cs. The calculations are in good agreement with the experimental values. The influence of exchange-correlation effects on the given properties is discussed. The results obtained indicate that the pseudopotential method may be successfully used for the calculation of the thermodynamic properties of metals by a traditional scheme, restricting consideration to the first two coordination spheres.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 25–33, February, 1979.     

Phase transition and thermodynamic properties of ThO2：Quasi-harmonic approximation calculations and anharmonic effects

The thermodynamic properties and the phase transition of ThO2 from the cubic structure to the orthorhombic structure are investigated using the first-principles projector-augmented wave method. The vibrational contribution to Helmholtz free energy is evaluated from the first-principles phonon calculations. The anharmonic contribution to quasi-harmonic free energy is accounted for by using an effective method(2010 Phys. Rev. B 81 172301). The results reveal that at ambient temperature, the phase transition from the cubic phase to the orthorhombic phase occurs at 26.45 GPa, which is consistent with the experimental and theoretical data. With increasing temperature, the transition pressure decreases almost linearly. By comparing the experimental results with the calculation results, it is shown that the thermodynamic properties of ThO2 at high temperature improve substantially after including the anharmonic correction to quasi-harmonic free energy.     

Thermodynamics and elastic properties of Ta from first-principles calculations

<正>Within the framework of the quasiharmonic approximation,the thermodynamics and elastic properties of Ta, including phonon density of states(DOS),equation of state,linear thermal expansion coefficient,entropy,enthalpy, heat capacity,elastic constants,bulk modulus,shear modulus,Young’s modulus,microhardness,and sound velocity, are studied using the first-principles projector-augmented wave method.The vibrational contribution to Helmholtz free energy is evaluated from the first-principles phonon DOS and the Debye model.The thermal electronic contribution to Helmholtz free energy is estimated from the integration over the electronic DOS.By comparing the experimental results with the calculation results from the first-principles and the Debye model,it is found that the thermodynamic properties of Ta are depicted well by the first-principles.The elastic properties of Ta from the first-principles are consistent with the available experimental data.     

Hard-thermal-loop QED thermodynamics

The weak-coupling expansion for thermodynamic quantities in thermal field theories is poorly convergent unless the coupling constant is tiny.We discuss the calculation of the free energy for a hot gas of electrons and photons to three-loop order using hard-thermal-loop perturbation theory (HTLpt).We show that the hard-thermal-loop perturbation reorganization improves the convergence of the successive approximations to the QED free energy at large coupling,e ～ 2.The reorganization is gauge invariant by construction,and due to the cancellations among various contributions,we obtain a completely analytic result for the resummed thermodynamic potential at three loops.     

An improved way of minimizing free energy in the variational method with the square well reference system

For the variational method of the thermodynamic perturbation theory with the square well reference system to which the semianalytical way of solving the mean spherical approximation is applied, a new way of minimizing the free energy is proposed. The approach is applied to liquid sodium and potassium, the effective pair interaction in which is described within the framework of the pseudopotential theory. For each of the metals under study, the global minimum of the free energy was found as a function of two independent variables (the hard core diameter and the mean atomic volume). In this minimum, a better agreement between the calculation results and the experimental data is obtained than when using the hard sphere reference system.     

Free energy of a long-range gauge theory on a triangular lattice

We discuss some properties of a model approximating a spin glass on a triangular lattice in two dimensions and present an exact calculation of the free energy of the corresponding “gauge field” model in the long-range interaction limit. The results are compared to a mean field approximation.     

Cellular approximation of the method of the model electron density functional. Alloys of alkali metals

The expression obtained in Part 1 of this work for the total energy of a disordered binary substitution alloy is employed to calculate the thermodynamic characteristics of alloys of the systems Na-Rb, Na-Cs, Li-Na, Li-K, k-Rb, Rb-Cs, K-Cs, Na-K. A model expression, whose parameters are calculated starting from the equilibrium characteristics of the metals studied, is employed to describe the energy of interaction of ions with conduction electrons. In order to calculate the properties of alloys no additional parameters are introduced into the theory, but rather the values of the parameters of the pure components are employed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 77–83, May, 1991.     

Modelling in relation to cation ordering

We review the methodology of using computer models to obtain quantitative information about cation ordering. Empirical interatomic potentials or ab initio electronic structure calculations are used to generate the energies for many configurations containing disordered arrangements of cations, and the parameters in model Hamiltonians can be determined from these energies. Monte Carlo simulations are then used to generate ensemble averages as functions of temperature or chemical composition. Analysis of the Monte Carlo ensembles directly yields the temperature dependence of long-range and short-range order, and thermodynamic quantities such as energy and heat capacity. Use of thermodynamic integration allows for the calculation of entropy and free energy. The methods are illustrated by examples showing long-range order/disorder phase transitions (feldspars), short-range order in solid solutions (pyrope-grossular), and non-convergent ordering (magnesium aluminate spinel); where comparisons with experimental data are possible, the model calculations are seen to give results that are reasonably accurate. The example in which ab initio electronic structure calculations are used show that it is now possible to extract accurate thermodynamic data for ordering processes using models that require no prior experimental data.     

Quasi-lattice model for the thermodynamic properties and microscopic structure of molten Fe-Si alloy

The quasi-lattice model has been used to study the concentration dependant thermodynamic properties and microscopic structure of Fe-Si alloys in molten state. We have determined the free energy of mixing, excess entropy of mixing, the concentration-concentration structure factor in long wavelength limit [S_CC(0)] and the Warren-Cowley short range order parameter (α₁) of Fe-Si liquid alloy at 1873 K. The observed asymmetry in the properties of mixing of Fe-Si alloy in molten state is successfully explained on the basis of the quasi-lattice model. The analysis suggests that the Fe₂Si complexes are most likely to exist in the liquid state and are strongly interacting in nature. The theoretical analysis suggests that the pairwise interaction energies between the species depend considerably on temperature and the alloy is more ordered towards Fe rich region.     

The Mean Field Ising Model trough Interpolating Techniques

Aim of this paper is to illustrate how some recent techniques developed within the framework of spin glasses do work on simpler model, focusing on the method and not on the analyzed system. To fulfill our will the candidate model turns out to be the paradigmatic mean field Ising model. The model is introduced and investigated with the interpolation techniques. We show the existence of the thermodynamic limit, bounds for the free energy density, the explicit expression for the free energy with its suitable expansion via the order parameter, the self-consistency relation, the phase transition, the critical behavior and the self-averaging properties. At the end a formulation of a Parisi-like theory is tried and discussed.     

Effect of Transverse Correlation Function on the Thermodynamic Quantities of Ferromagnetic Systems

The effect of transverse correlation between spins on the thermodynamic properties of ferromagnetic systems is investigated in details. Qualitatively, at finite temperature the transverse correlation reflects the short-range interaction between spins, so that lowers the internal energy and consequently raises the free energy. It also means the introduction of some ordering, and hence lowers the entropy. It is depressed by the field which forces the spins to turn to the field direction, so that it decreases with the field when temperature is fixed. The low-temperature expansion of the energy shows that the inclusion of the transverse correlation at least partly considers the interaction between spin waves.     

Interaction mean free path in the emulsion and interaction radius of the nucleus

The interaction mean free path of the high energy nucleus in the emulsion is studied with the Glauber model and Hartree-Fock type variational calculation for the nuclear structure. It is found that the experimentally observed interaction mean free paths are well reproducible. It is also found that the interaction radius of the projectile nucleus can be determined with the emulsion experiment.     

Thermodynamic assessment of the K-Na and Cr-V system

The assessment of the thermodynamic properties of K-Na and Cr-V molten alloys has been theoretically examined using a simple statistical mechanical model based on pairwise interaction to obtain higher-order conditional probabilities that describe the occupation of the neighbouring atoms in molten binary alloys. The optimised values of order energy ω obtained are used to describe a number of thermodynamic quantities computed for different concentrations in the alloys at 384 and 1550 K, respectively. The study shows that there is a tendency for homocoordination (like atoms pairing as nearest neighbour) in K-Na and the existence of heterocoordination in Cr-V at all concentrations. Thus, the consistency between calculated and reported experimental thermodynamic values enforces the legitimacy of the findings.