吉布斯自由能的农业应用和生物学意义

吉布斯自由能作为基本力学函数,在农业和生物学中有着重要的应用,在现代农业中,由吉布斯自由能的水势要概念,已成为判断农业系统水份动转的主要判据;在生物学中,吉布斯自由能作为生命体系赖以生存的能量,直接维持和驱动着生命体系的运转,本文讨论了吉布斯自由能的农业应用和生物学意义。     

环面黑洞的热力学函数

本文把宇宙学常数看成与压强相当的动力学变量,研究了环面黑洞的热力学函数.计算得到环面黑洞的状态方程,环面黑洞的Smarr关系.然后通过计算其欧氏作用量得到了吉布斯函数,并进一步求得环面黑洞的自由能、内能和热力学焓,以及环面黑洞的定压热容和定容热容.结果表明:环面黑洞没有范德瓦耳斯型的相变.环面黑洞的定压热容大于零,定容热容等于零,故是一个稳定的热力学系统.     

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.     

关于“平衡判据”的讨论

文章强调，当判断两个平衡态之间的过渡是否可逆时，用到的是平衡态的态函数；当考虑非平衡态向平衡态过渡及谈到平衡判据时，用到的是推广了的“广义”态函数．文章描述了由平衡态态函数推广到“广义”态函数，从而得到平衡判据的过程，解释了为什么一般文献中着重提熵判据、自由能判据及吉布斯函数判据，很少或不提焓判据及能量判据．     

Green函数及δ函数的三方向球函数展开式

将1/R及δ函数的积分表达式分离径向与角向变量得到了用三个分矢的球函数及冪级数表达的展开式。     

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     

量子引力的曲率两点真空相关

以平坦的Minkowski时空为背景，得到了任意坐标系和谐和坐标系中，n维GR引力和高导数引力的引力子自由传播子，求得了四种可能的曲率两点真空相关函数的首项.用微扰计算证明了曲率的两点真空相关函数在GR引力中为零，而在高导数引力中不为零.讨论了高导数引力与GR的引力子传播子、曲率相关函数的关系. 关键词： GR 高导数引力 引力子自由传播子 曲率真空相关函数 平移传播子     

论磁介质系统热力学函数的两种定义及其麦克斯韦关系

从磁介质系统四个热力学函数（内能、焓、自由能、吉布斯）的两种不同定义方式出发，导出了与之相应形式上并不完全相同的两组麦克斯韦关系，并对两组麦克斯韦关系彼此之间的等价性作了论证。     

δ函数的定义及其性质

对δ函数的传统定义及由此引起的奇性展开讨论,说明了在经典意义下δ函数可以被看成是弱收敛函数序列的弱极限以及阶跃函数Heaviside函数的导数;最后,借用泛函分析中广义函数的概念给出了δ函数的严格数学定义,并就其性质进行了讨论．     

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.     

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).     

A regular solution model for phases with several components and sublattices,suitable for computer applications

A thermodynamic model, based on the regular solution approximation is presented and a formalism, suitable for phases with an arbitrary number of sublattices, is developed. A new concept, the component array, is introduced in order to simplify the analytical expressions for the integral Gibbs energy. The definition of the component array allows a straightforward procedure for the derivation of expressions describing the Gibbs energy for any kind of phase. Expressions for the partial Gibbs energy are derived. The implementation of the model on a computer is discussed.     

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.     

Some aspects of the thermodynamic behaviour of ferroelastic and co-elastic phase transitions

Ferroelastic phase transitions and phase transitions involving coupling between the driving order parameter and elastic degrees of freedom (i.e. co-elastic phase transitions) follow empirically a Landau-type mean field behaviour over large temperature intervals. At temperatures close to the transition point the upper critical dimension is reduced to three if fluctuations are sufficiently constrained in reciprocal space. At low temperatures, the observed temperature independence of the order parameter in the saturation regime (S-regime) is correlated with the quantum limit of the dissipation-fluctuation theorem. The good agreement between experimental observations and the predictions of a Landau-type treatment of the excess Gibbs free energy even for large values of the order parameter leads to the conclusion that the convergency of the polynomial form of the Gibbs free energy is due to small energy coefficients rather than due to the order parameter being small.     

Surface induced mixed state of a superconducting film

Presented in this paper is a theoretical analysis of a planar surface induced mixed state for a superconducting film in parallel applied field. An analytical solution of the internal magnetic field is obtained based on Saint-James and de Gennes' order parameter in a film. An expression of Gibbs free energy per unit volume without restriction of a geometry is derived from non-linear Ginzburg-Landau (GL) equation in terms of a renormalized GL parameter and a modified geometric factor. Based on the Gibbs free energy, a phase diagram of distinguishing a first and second order phase transition for a type I superconducting film is calculated. The numerical results for exact solutions of spatial variation of order parameter, current density and internal magnetic field in the film geometry in parallel applied field case are presented. Near the upper critical field, the first entry of an applied field in the film exhibits a laminar structure.     

Thermodynamic approach to phase coexistence in ternary phospholipid-cholesterol mixtures

We introduce a simple and predictive model for determining the phase stability of ternary phospholipid-cholesterol mixtures. Assuming that competition between the liquid and gel order of the phospholipids is the main driving force behind lipid segregation, we derive a Gibbs free energy of mixing, based on the thermodynamic properties of the lipids main transition. A numerical approach was devised that enables the fast and efficient determination of the ternary diagrams associated with our Gibbs free energy. The computed phase coexistence diagram of DOPC/DPPC/cholesterol reproduces well-known features for this system at 10 °C, as well as its evolution with temperature.     

A Self-Consistent Ornstein–Zernike Approximation for the Edwards–Anderson Spin-Glass Model

We propose a self-consistent Ornstein–Zernike approximation for studying the Edwards–Anderson spin glass model. By performing two Legendre transforms in replica space, we introduce a Gibbs free energy depending on both the magnetizations and the overlap order parameters. The correlation functions and the thermodynamics are then obtained from the solution of a set of coupled partial differential equations. The approximation becomes exact in the limit of infinite dimension and it provides a potential route for studying the stability of the high-temperature phase against replica-symmetry breaking fluctuations in finite dimensions. As a first step, we present the predictions for the freezing temperature T _f and for the zero-field thermodynamic properties and correlation length above T _f as a function of dimensionality.     

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.     

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.