Temperature-dependence of phonons,solid state properties and liquid structure of noble metals: A comparison of pair-potentials

Two groups of effective pair-potentials are studied from the viewpoint of their suitability in being able to describe solid state properties and liquid state structure of noble metals Cu, Ag and Au over a wide temperature range. Since the effective pair-potentials are usually empirical in nature, with parameters obtained by fitting to some reference state properties, the objective of the present study is to determine whether a particular parametrization scheme has any definite advantage over another. We consider Morse potentials with parameters determined by equilibrium lattice parameter, cohesive/sublimation energies as well as bulk modulus values of the solid at low/room temperatures. The other group of potentials considered is Erkoç potentials, where the parameters were determined first by studying dimers and further modified using bulk stability condition and bulk cohesive energy values. The potentials were then used to study the energetics of microclusters containing 3–7 atoms. Quasiharmonic results for the solid obtained at different temperatures and Monte Carlo simulation for the liquid state show that phonon spectra, thermal expansion, temperature-dependence of specific heats and liquid structure are much better described by the latter group. The first group of potentials may have an advantage in reproducing the temperature-dependence of elastic constants and bulk moduli, since they are based on room temperature values of these properties, which show only weak temperature-dependence in general for all metals. It is argued that potentials based on parameters fitted to the properties at a single volume are less versatile in capturing the temperature-dependence of various thermodynamic properties over a wide range. Potentials capable of reproducing the energetics of clusters of different co-ordination numbers and volumes per atom may fare better in this regard.     

Phase separation in Na–K liquid alloy

The quasi-chemical expression for weakly interacting binary alloy has been applied to obtain energy parameters and their temperature derivatives for Na–K liquid alloy at 384?K. These energy parameters have then been used to calculate thermodynamic functions, such as free energy of mixing, heat of mixing, entropy of mixing and microscopic functions, such as concentration fluctuation in long wavelength limit, Warren–Cowley short-range order parameter, ratio of mutual and self-diffusion coefficients. The analysis reveals that the energy parameters are temperature dependent and the Na–K liquid alloy at 384?K is a weakly interacting homocoordination system. The observed thermodynamic properties of Na–K alloy in molten state have successfully been explained by assuming Na₂K complex on the basis of the quasi-chemical formalism for a weakly interacting system.     

Approximate energies and thermal properties of a position-dependent mass charged particle under external magnetic fields

We solve the Schr?dinger equation with a position-dependent mass(PDM) charged particle interacted via the superposition of the Morse-plus-Coulomb potentials and is under the influence of external magnetic and Aharonov–Bohm(AB) flux fields. The nonrelativistic bound state energies together with their wave functions are calculated for two spatially-dependent mass distribution functions. We also study the thermal quantities of such a system. Further, the canonical formalism is used to compute various thermodynamic variables for second choosing mass by using the Gibbs formalism. We give plots for energy states as a function of various physical parameters. The behavior of the internal energy, specific heat, and entropy as functions of temperature and mass density parameter in the inverse-square mass case for different values of magnetic field are shown.     

LJ模型的热力学特性、相平衡及用于真实分子的研究

结合描述硬球固体Helmholtz自由能的自由体积方法与描述硬球固体径向分布函数的拟合的分析表达式与一阶热力学摄动理论,用于描述Lennard Jones(LJ)固体的Helmholtz自由能.按照一个修正的WCA方法将LJ势分为短程排斥部分与长程吸引部分,将文献中一个用于求取液相的等价的硬球直径的简单的迭代法扩展到固相,用于求取固相的等价的硬球直径.在固体Helmholtz自由能的计算中,使用200壳层,以便获得精确的结果.体相LJ液体的热力学特性由一个最近提出的状态方程求取.该方法很好地描述了LJ固体的过量Helmholtz自由能与状态方程,满意地描述了Lennard Jones模型的相平衡;通过选取合适的LJ势参数,能很好地描述了真实分子的融化曲线.     

Thermodynamics of a long-range triangle-well fluid

The long-range triangle-well fluid has been studied using three different approaches: firstly, by an analytical equation of state obtained by a perturbation theory, secondly via a self-consistent integral equation theory, the so-called self-consistent Ornstein–Zernike approach (SCOZA) which is presently one of the most accurate liquid-state theories, and finally by Monte Carlo simulations. We present vapour–liquid phase diagrams and thermodynamic properties such as the internal energy and the pressure as a function of the density at different temperatures and for several values of the potential range. We assess the accuracy of the theoretical approaches by comparison with Monte Carlo simulations: the SCOZA method accurately predicts the thermodynamics of these systems and the first-order perturbation theory reproduces the overall thermodynamic behaviour for ranges greater than two molecular diameters except that it overestimates the critical point. The simplicity of the equation of state and the fact that it is analytical in the potential range makes it a good candidate to be used for calculating other thermodynamic properties and as an ingredient in more complex theoretical approaches.     

Thermodynamic properties of gold–water nanolayer mixtures using molecular dynamics

The physical behavior of a fluid in contact with solid layers is still not fully understood. The present work focuses on the study and understanding of thermodynamic and structural properties of gold–water nanolayer mixtures using molecular dynamics simulations. Two different systems are considered, where approximately 1,700 water molecules are confined between gold nanolayers with separations of 7.4 and 6.2 nm, respectively. Novelties of the present work are in the use of accurate force fields for modeling the inter- and intra-molecular interactions of the components, and providing comprehensive thermodynamic properties of the mixtures. The results are validated by examination of the pure fluid and pure solid properties. Results indicate that the thermodynamics of the system does not behave as an ideal mixture. The structure of the pure fluid is also analyzed and compared against the structure of the confined fluid in the mixture. Anisotropicity is observed in the fluid structure close to the surface of the nanolayer. Higher ordering and higher flux are detected in the fluid molecules close to the fluid–solid interface. Unusual thermodynamic behavior, anisotropicity, liquid layering, and higher interfacial fluid flux could be just some of the factors leading to the enhanced energy transport observed in mixtures involving at least one nanoscale component, such as nanofluids.     

Unified low-parametrical equation used to calculate the viscosity coefficient of argon

Using the previously obtained dependence of excess viscosity on internal energy density and low-parametric unified equation of state for calculation of thermodynamic properties of liquid, gas, and fluid, the equation for the excess viscosity of argon in the range of the “mixed” mechanism of momentum transfer in the shear flow was derived. Different versions of approximation of excess viscosity dependence on the density of interaction energy were compared, and the optimal version of this dependence was determined. A simple unified low-parametric equation was obtained for describing the coefficient of argon viscosity in a wide range of state parameters. It is shown that the proposed low-parametric equation for calculating the viscosity coefficient of liquid and gas allows reliable extrapolation beyond the studied region.     

Simulation of fluid-solid coexistence via thermodynamic integration using a modified cell model

Despite recent advances, precise simulation of fluid-solid transitions still remains a challenging task. Thermodynamic integration techniques are the simplest methods to study fluid-solid coexistence. These methods are based on the calculation of the free energies of the fluid and the solid phases, starting from a state of known free energy which is usually an ideal-gas state. Despite their simplicity, the main drawback of thermodynamic integration techniques is the large number of states that must be simulated. In the present work, a thermodynamic integration technique, which reduces the number of simulated states, is proposed and tested on a system of particles interacting via an inverse twelfth-power potential energy function. The simulations are implemented at constant pressure and the solid phase is modeled according to the constrained cell model of Hoover and Ree. The fluid and the solid phases are linked together by performing constant-pressure simulations of a modified cell model. The modified cell model, which was originally proposed by Hoover and Ree, facilitates transitions between the fluid and the solid phase by tuning a homogeneous external field. This model is simulated on a constant-pressure path for a series of progressively increasing values of the field, thus allowing for direct determination of the free energy difference between the fluid and the solid phase via histogram reweighting. The size-dependent results are analyzed using histogram reweighting and finite-size scaling techniques. The scaling analysis is based on studying the size-dependent behavior of the second- and higher-order derivatives of the free energy as well as the dimensionless moment ratios of the order parameter. The results clearly demonstrate the importance of accounting for size effects in simulation studies of fluid-solid transitions.     

Nonlinear ultrasonic nature of organic liquid and organic liquid mixture

Based on Jacobson's molecular free length theory in liquids and the relationship between ultrasonic velocity and the molecular free length in organic liquids, this paper deduces the equations for pressure coefficient and temperature coefficient of ultrasonic velocity and nonlinear acoustic parameter B/A in both of organic liquid and organic liquid binary mixtures. These nonlinear acoustic parameters are evaluated against the measured results and data from other sources. The equations reveal the connections between the nonlinear acoustic parameters and some internal structural of the medium or mixtures e.g. the sizes of molecule, several thermodynamic physical parameters and outside status e.g. condition of pressure and temperature of the liquid or liquid mixture. With the equations the nonlinear acoustic parameter B/A of organic liquid binary mixtures, which is impossible to know without the nonlinear acoustic parameter B/A of the tow components before, can be calculated based on the structural and physical parameters of organic liquid and organic liquid binary mixtures.     

Bianchi -V Space -Time with Anisotropic Dark Energy in General Relativity

In a spatially homogeneous and anisotropic Bianchi type-V space-time the consequences of the presence of dynamically anisotropic dark energy and perfect fluid with heat-conduction are studied. We assume that dark energy is minimally interacting with matter and has an equation of state which is modified in a consistent way with the conservation of energy momentum tensor. Exact solutions of Einstein field equations are obtained by taking constant value of deceleration parameter. We find that this assumption is reasonable for the observation of the present day universe. The physical and geometrical properties of the models, the behavior of the anisotropy of dark energy and the thermodynamical relations that govern such solutions are discussed in detail.     

Thermodynamic properties for the triangular-well fluid

The thermodynamic properties of the triangular-well fluid with a well range of up to twice the hard sphere diameter were studied by means of a new developed equation of state and molecular simulation. This EoS is based on the perturbation theory of Barker and Henderson with the first and second-order perturbation terms evaluated by molecular simulation and then a fit with a simple function based on the radial distribution function of the reference fluid. The thermodynamic properties for the triangular-well fluid were also obtained directly by Gibbs ensemble and NPT Monte Carlo simulations. Good agreement is observed between the proposed EoS and the molecular simulation results. A model for the triangular-well solid is also presented; this has been used to calculate the solid–liquid transition line. Very good agreement is obtained with previously report values for this line and for the triple point temperature and pressure.     

Equation of state for pure fluids at critical temperature

In this paper, we employ the concept of probability for creating a cavity with diameter d in fluid along with the perturbation and variation approach, and develop an equation of state (EOS) for a hard sphere (HS) and Lennard– Jones (LJ) fluids. A suitable axiomatic form for surface tension S(r) is assumed for the pure fluid, with r as a variable. The function S(r) has an arbitrary parameter m. S(r) = A + B(d/r)/[1 + m(d/r)]. We use the condition in terms of radial distribution function G(λd, η) containing the self-consistent parameter λ and the condition of continuity at r = d/2 to determine A and B. A different EOS can be obtained with a suitable choice of m and the EOS has a lower root-mean-square deviation than that of Barker–Henderson BH2 for LJ fluids.     

基于Gay-Berne势能模型的粗粒化动力学模拟研究正丁醇的玻璃态相变

通过基于Gay-Berne势能模型的粗粒化动力学模拟,研究液态正丁醇体系的冷却过程. 采用密度泛函计算,拟合出适合正丁醇体系的GB势能参数. 体系的密度、平均势能等性质随温度的降低(由290 K降至50 K,间隔为10 K)发生特殊变化,即体系发生玻璃态相变,相变温度为T_g=120±10 K,与实验值110±1 K符合很好.     

关于二级相变中热力学物理量突变的分析与自旋链模拟

理论上对二级相变中热容、体膨胀系数、等温压缩系数三个热力学物理量的变化进行了分析,进而使用自旋链模型的基态能量和von Neumann熵随模型参数变化的突变行为对二级相变中这三个物理量的变化所引起的系统序变进行模拟,得到二级相变中热容、体膨胀系数、等温压缩系数的变化是由于系统内部微观上发生关联序变的结果。     

非对易相空间中谐振子体系热力学性质的探讨

2000年以来, 有关非对易空间的各种物理问题一直是研究的热点, 并在量子力学、场论、凝聚态物理、天体物理等各领域中已被广泛地探讨. 采用统计物理方法讨论非对易效应对谐振子体系热力学性质的影响. 先以对易相空间中确定二维和三维谐振子的配分函数求出谐振子体系的热力学函数; 非对易相空间中的坐标和动量通过坐标-坐标和动量-动量之间的线性变换而以对易相空间中的坐标和动量来表示; 最终以非对易相空间中求出配分函数来讨论非对易效应对谐振子体系热力学性质的影响. 结果显示, 在非对易相空间中谐振子体系的配分函数和熵表达式均包含因非对易引起的修正项. 从分析结果得出如下结论: 非对易效应对谐振子的配分函数和熵函数等微观状态函数有一定的影响, 但对谐振子体系的内能、热容量等宏观热力学函数没有影响. 研究结果只是对应于满足玻尔兹曼统计的经典体系, 对于满足费米-狄拉克和玻色-爱因斯坦统计的量子体系需进一步推广研究.     

Readout of a weakly coupled qubit through the use of an auxiliary mode

The dispersive coupling between a qubit and a cavity mode is widely used for performing non-destructive readout of the qubit state. In this approach, it is typically required that the dispersive strong coupling regime is achieved. Here we show that the use of an auxiliary cavity mode reduces by orders of magnitude the required value of the dispersive coupling, for a given decay rate of the cavity mode. The analysis is performed within the input-output formalism, in terms of the photon scattering matrix elements and of the signal-to-noise ratio. We derive simple analytical expressions for the optimal parameters and recover the standard single-mode result as a limiting case. The present results can also be applied to the qubit readout based on longitudinal cavity-qubit interactions, and to any sensing scheme where the cavity frequency is used as a probe to estimate some physical parameter of interest.