关于自由能的一些讨论

给出了自由能函数的完整表达式,并说明了自由能展开式中各项的物理意义．指出了自由能展开式系数及自变量的共轭变量的意义,吉布斯自由能的一阶偏导数都是热力学变量;吉布斯自由能的二阶偏导数一律都是物性张量．讨论了相变过程中的自由能函数展开式应保留的项数等,还给出了相稳定性条件．     

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     

高压下Ni_3Al热力学性质的第一性原理研究北大核心CSCD

运用第一性原理方法结合准谐Debye-Grüneisen模型研究了高压下Ni3Al的热力学性质,拟合了Ni3Al的状态方程,计算了不同压强下Ni3Al的弹性模量及吉布斯自由能等热力学性质随温度的变化关系.计算结果表明:采用七阶Birch-Murnaghan方程拟合的晶格常数与实验测量结果吻合较好;零压下弹性模量、吉布斯自由能、焓、熵、热容和体膨胀系数随温度的变化与实验值符合较好;在特定压强下,Ni3Al的弹性模量和吉布斯自由能随温度升高而减小,焓、熵随温度升高而增加;预测的德拜温度约为500K,与实验值符合较好.     

高压下Ni3Al热力学性质的第一性原理研究

运用第一性原理方法结合准谐Debye-Grüneisen模型研究了高压下Ni3Al的热力学性质,拟合了Ni3Al的状态方程,计算了不同压强下Ni3Al的弹性模量及吉布斯自由能等热力学性质随温度的变化关系. 计算结果表明：采用七阶Birch-Murnaghan方程拟合的晶格常数与实验测量结果吻合较好;零压下弹性模量、吉布斯自由能、焓、熵、热容和体膨胀系数随温度的变化与实验值符合较好;在特定压强下,Ni3Al的弹性模量和吉布斯自由能随温度升高而减小,焓、熵随温度升高而增加;预测的德拜温度约为500K,与实验值符合较好.     

流体混合物热力学性质计算的混合法则新进展

回顾近期关于流体混合物热物性混合法则的研究新进展,特别是余吉布斯自由能(GE)和余亥姆霍兹自由能(AE)型混合法则的拓展及应用,重点介绍一种基于AE,仅通过偏微分方程便可计算混合物所有热力学性质的混合法则。可为发展未知流体混合物热物性计算方法以及各种常见混合物热物性的工程应用提供参考和依据。     

反钙钛矿结构RE_3AlC热物理性质理论研究

结合第一性原理和准谐德拜模型计算了RE_3AlC(RE=Sc、Y及镧系稀土)系列具有反钙钛矿结构碳化物的德拜温度、格律乃森常数、体积模量、自由能、比热容等热物理性质随着温度和压强变化的趋势。结果表明RE_3AlC碳化物的比热容、体积模量以及吉布斯自由能等随温度和压强变化的总趋势相似,其中RE_3AlC碳化物的体积弹性模量随着温度的升高而逐渐减小,同时随着压强的增加而增大;吉布斯自由能都随着温度的升高而降低,其中Sc_3AlC化合物的自由能最低,而Yb_3AlC化合物的自由能最高,表明Sc_3AlC化合物最稳定,而Yb_3AlC化合物稳定性最低;等容比热容随着温度和压强的变化在0-300 K温度段内变化较大,随后趋于平缓逐渐趋于杜隆.帕蒂极限值。     

统计力学的系综变换

一、引言 在统计力学中一般只研究三种统计系综,他们是微正则系综(适用于孤立体系)、吉布斯正则系综(适用于与热库有热相互作用的体系)和吉布斯巨正则系综(适用于与热库有热相互作用,又与物质库有粒子数交换的体系).体系处于平衡态,三种系综的分布函数为 ρ=cδ(E-E0)(1) 　ρ=e-ψ-E/kT(2) 　ρ=e-ζ-E/kT μN/kT(3)与这三种分布相应的热力学函数分别为式中(E,V,N)是由N个粒子组成、占有空间体积V的体系具有能量E的微观状态数;S、F和O分别是嫡、自由能和热力势.(4)一(6)式与(l)一(3)式等价,他们将热力学函数与配分函数联系起来,是三…     

碱金属封装到氧化锌纳米笼的第一原理研究

利用密度泛函理论研究了碱金属(Li、Na、K、Ru)封装到Zn₁₂O₁₂纳米笼的过程. 在298 K和100 kPa,Li和Na原子的封装在热力学上是有利的, 吉布斯自由能为负值, 分别为约-130.12和-68.43 kJ/mol. 随着封装原子大小的增加,封装过程变得不那么有利,封装K和Rb过程的吉布斯自由是正值. 结果表明,LUMO、费米能级、尤其是HOMO向更高的能量转移,以至于HOMO-LUMO能隙明显变窄. 封装后的碱金属簇的功函数由于费米能级转移到     

关于Young—Laplace公式的吉布斯自由能证明

对于为论证球形液滴附加压强的Young-Laplace公式而设计的一个理想实验,有文献试图借助吉布斯自由能函数进行证明,本文给出符合这一条件的证明方法.     

“热-化学能-功”转换的理想热力循环研究

近年来,运用电化学方法实现中低温热能高效利用的方法受到学界的广泛关注,但目前尚缺乏以一般性的热力学原理研究多种"热-化学能-功"转换系统的方法论。本文着眼于能量转换机制,在T-S图中引入表征化学能的吉布斯自由能作为图像表达的第三维坐标,将化学能定量化。进而基于卡诺循环,通过循环过程量在T-S-G图中的几何移动得到了"热-化学能-功"转换的理想循环。该研究方法有望应用于多种涉及化学能的热功转换系统的研究。     

The phase diagrams of a spin-1 transverse Ising model

The phase diagrams of the spin-1 transverse Ising model with the presence of a crystal field is investigated by using an effective-field theory (EFT). We give a method to calculate the Gibbs free energy numerically at finite temperature within the EFT. The first-order transition lines are obtained by comparing the Gibbs free energy. The phase diagrams and the Gibbs free energy are also compared with those given using the mean-field theory (MFT).     

Surface free energy of platinum nanoparticles at zero pressure: A molecular dynamic study

Metallic nanoparticles are interesting because of their use in catalysis and sensors. The surface energy of the FCC platinum nanoparticles are investigated via molecular dynamics simulation using Quantum Sutton–Chen (QSC) potential. We have calculated the Gibbs free energy for the FCC platinum bulk and also for its nanoparticle. All calculations have been carried out at zero pressure. We have used the thermodynamic integration method to obtain the Gibbs free energy. The total Gibbs free energy is taken as the sum of its central bulk and its surface free energy. We have calculated the free energy of a platinum nanoparticle as a function of temperature.     

On the energy of formation of defects

We present a formulation of the Gibbs free energy of defect formation in crystals which is formally based on a quasi-classical thermodynamical cluster expansion of the Gibbs free energy of the defect crystal. Thus a microscopic formulation of the Gibbs free energy of formation is achieved. The related quantities like formation volume per defect and defect susceptibility functions are then derived from the formation energy. The resulting expressions depend only on the defect concentration and the bulk properties of the crystal. Finally we discuss an approximate form of the formation energy which was introduced intuitively by Varotsos and Alexopoulos. As an example for the applicability of this formulation we present an explanation of the anomaly in the conductivity and diffusion of AgBr.     

Hydrogen bonds between water molecules: thermal expansivity of ice and water

The free energy components of two low pressure crystalline ices and an amorphous form of water are calculated over a wide range of temperatures. The Gibbs free energy at a given temperature is minimized with respect to volume of a system. This enables us to evaluate a thermal expansivity at fixed temperature and pressure from only intermolecular interaction potential. The negative thermal expansivity at low temperature is obtained for both crystalline ices and an amorphous form, which arises from the bending motion of hydrogen bonded molecules.     

A Gibbs free energy formula for protein folding derived from quantum statistics

The fundamental law for protein folding is the thermodynamic principle. The amino acid sequence of a protein determines its native structure and the native structure has the minimum Gibbs free energy. Lacking of a Gibbs free energy formula is the reason that all ab initio protein structure prediction only empirical and various empirical energy surfaces or landscapes are introduced to fill the gap. We make a quantum mechanics derivation of the Gibbs free energy formula G(X) using quantum statistics for a single conformation X. For simplicity, only monomeric self folding globular proteins are considered.     

Explicit Gibbs free energy equation of state for solids

Semi-empirical equations of state (EOS) are used for interpolation and extrapolation of experimental data and/or electronic structure calculations. For calculation of phase equilibria, it is preferable to use an explicit Gibbs free energy EOS, that is, to express the Gibbs free energy directly as a function of the pressure and temperature. Existing explicit Gibbs free energy EOS formulations often give unphysical predictions at high pressures. The origins of these problems are internal inconsistencies and uncontrolled extrapolations. A set of conditions is put forward, that should be fulfilled by semi-empirical EOS formulations in order to constrain them to known physical behaviour, e.g., to the Thomas-Fermi and quasi-harmonic models at high pressures. A new alternative integration path is devised that eliminates the need for the problematic extrapolation of the heat capacity to high temperatures at low pressures. Based on these developments, a new explicit Gibbs free energy EOS is formulated which is suitable for computational applications. The new EOS may be fitted to represent the thermophysical properties of solids with a reasonably small number of adjustable parameters. A sample application for MgO is presented.     

Thermal consequences of a regular black hole with cosmological constant and Einstein–Aether black hole

We discuss the thermodynamics of regular black hole (RBH) with cosmological constant and Einstein–Aether black hole (BH) with coupling constant in the presence of thermal corrections. For these BHs, we develop various thermodynamical quantities such as entropy, pressure, specific heats, Gibbs free energy and Helmholtz free energy. Thermal stability is also being analyzed through γ factor, Gibbs free energy and Helmholtz free energy. It is found that RBH with cosmological constant and Einstein–Aether show stable behavior with the increase of the values of cosmological and coupling constants.     

Energy model for the Zr-based metallic glass alloy melt with clusters

An energy model for the melt of bulk metallic glass (BMG) with clusters was established, the Gibbs free energy and interfacial energy for the Zr-Al-Ni ternary alloy melt with Zr2Ni clusters were calculated, and the effects of the clusters on the Gibbs free energy, interfacial energy and nucleation rate were analyzed. The results showed that the existence of the clusters in the Zr-Al-Ni ternary alloy melt enables the Gibbs free energy to decrease in the composition range where bulk metallic glass forms easily, makes the interfacial energy increase and changes the distribution of the interfacial energy with the alloy composition. Because of the clusters in the melt, the Gibbs free energy of the Zr66Al8Ni26 alloy melt decreases about 0.3-1 kJ/mol and the interfacial energy between the melt and crystal nucleus increases about 0.016 J/m2. The nucleation rate of the undercooled Zr66Al8Ni26 alloy melt decreases evidently under the influence of the clusters on Gibbs free energy and the interfacial energy, and the maximum of the nucleation rate in the melt with the Zr2Ni clusters is only about 107 mol-1·s-1.     

Gibbs free energy and equilibrium states in the Si/Si oxide systems

In this paper, the equilibrium states in the Si/Si oxide systems formed as a result of the phase separation of nonstoichiometric silicon oxide films are studied. The expressions for the Gibbs free energy of Si oxide and Si/Si oxide systems are derived thermodynamically. The transformations of the Gibbs free energy in the amorphous Si/Si oxide and the crystalline Si/Si oxide systems with the change in the amount of separated silicon and the composition of the silicon oxide phase are analyzed. By minimizing the Gibbs free energy of these systems, the equilibrium stoichiometry indices of silicon oxide are calculated as functions of its initial stoichiometry and the temperature. The solubility limits of Si in SiO(2) in equilibrium with amorphous and crystalline Si are determined. The obtained results form the basis for the development of a complete thermodynamic theory of phase separation in nonstoichiometric silicon oxide films with the formation of Si nanoinclusions in the silicon oxide matrix.