关于二元混合物体系的偏摩尔吉布斯自由能的表达式

利用Gibbs-Duhem方程证明了偏摩尔自由能的一个计算公式.     

Application of the Sherman-Morisson formula to scattering problems by multi-component systems

The scattering matrix for multi-component systems is recalculated using the extended form of the Sherman-Morisson formula. The matrix elements are given explicitly in closed form. The Gibbs-Duhem relation separates the density and composition contributions. Received 5 April 2002     

Thermodynamics of a general ideal gas under shear

The integrated form of the Gibbs-Duhem relation is obtained for a general ideal gas subjected to a shear flow.     

On the thermodynamics of surfaces

Isotropic macroscopic thermodynamics is used to treat a classical model of surfaces. An equation of the Gibbs-Duhem type is derived from which the relation between surface stress and specific surface free energy follows. This derivation specifically considers the pressure dependence on size of a spherical particle bounded by an isotropic surface and hence is not restricted to the usual constant pressure assumptions. It follows from the conditions of thermodynamic equilibrium and the above Gibbs-Duhem relation that surface stress is the fundamental parameter controlling the internal hydrostatic pressure of isotropic particles as well as equilibrium vapor pressure and other phenomena dependent on internal pressure.     

Geometrical formulation of equilibrium phenomenological thermodynamics

An abstract geometric formulation of equilibrium phenomenological thermodynamics which generalizes and unifies that of Gibbs, Carathéodory, and others is given. As done by Hermann, one adapts here a contact manifold as the basic mathematical structure. Such a manifold for a thermodynamic system is constructed. The empirical laws of thermodynamics have been reformulated in terms of this manifold and by means of exterior differential forms. Such concepts as Gibbs phase rule, Gibbs-Duhem equation and thermodynamic potentials have been reexamined within such a general scheme.     

THERMOSTATIC PROPERTIES OF ASYMMETRIC NUCLEAR MATTER AT LOW TEMPERATURE

The Küpper, Wegmnn, and Hilf's theory on the thermostatic properties of symmetric nuclear matter is extended to the asymmetric nuclear matter at low temperature less than 10 MeV. The numerical result shows that the entropy per nucleon s depends on the asymmetry δ weakly while the compressibility coefficient K depends on δ very strongly. At the neutron drip point the nucleon density n decreases while the asym-, metry ^δND increases linearly with T² at low temperature. The thermodynamic stability of the asymmetric nuclear matter is studied by means of the Gibbs-Duhem inequality.     

The thermodynamic factors for cation diffusion in AO,p-type oxides doped with a trivalent impurity

The thermodynamic factors for cation diffusion in p-type semiconducting oxides of the formula AO doped with a trivalent impurity are evaluated, assuming a known structure of defects of the base oxide. It is shown that these parameters are not only functions of the oxygen activity and of the dopant concentration, but also strongly depend on the ratio between the gradients of these two variables. Limiting expressions corresponding to the presence of only one of these gradients are derived and evaluated by means of suitable approximations under conditions of very small or very large impurity concentrations. A general relationship between the two thermodynamic factors is obtained by means of the Gibbs-Duhem equation as applied to the relevant ternary system. Finally, the thermodynamic factors for cation diffusion are evaluated numerically for the case of NiO doped with a trivalent impurity at 1000°C, using a convenient detailed model to represent its defect structure.     

On the development of a general force field for the molecular simulation of perfluoroethers

We report the development of a transferable force field for the accurate modelling of perfluoroethers. The potential model takes the general form in which separate bond bending and torsional terms describe the intramolecular interactions, with the addition of van der Waals and electrostatic terms to describe the non-bonded interactions. Ab initio quantum mechanical calculations were carried out to obtain the partial charges and intramolecular torsional and bending potentials. The van der Waals interactions are described by Lennard-Jones potentials, the parameters of which are optimized to reproduce the available experimental vapour-liquid equilibrium data. An extension of the Gibbs-Duhem method was used to speed up the optimization.     

Thermodynamics and defect structures of silver sulfide

Published measurements of sulfur vapor pressure and silver electromotive force were used to determine thermodynamic properties of silver sulfide above 379 K. They were Gibbs-Duhem integrated to estimate the formation properties of stoichiometric Ag₂S of fcc, bcc, and monoclinic crystal structures. Statistical thermodynamics was applied to estimate free energies and find possible atom arrangements in off-stoichiometric silver sulfide. Theoretical calculations show that silver vacancies and atoms may be in quasi-chemical equilibrium between tetrahedral and octahedral sites in the fcc structure and between two states of atoms within tetrahedral sites in the bcc structure and within octahedral sites in the monoclinic structure. A strong indication is that vacancy clusters should predominate, each containing four-atom vacancies in the fcc phase and three-atom vacancies in the bcc phase.     

Is equilibrium always an entropy maximum?

A systematic development is given of the view that in the case of systems with long-range forces and which are therefore nonextensive (in some sense) some thermodynamic results do not hold. Among these is the relationU – TS + p = N and the Gibbs-Duhem equation. If a search for an equilibrium state is made by maximization of the entropy one may obtain misleading results because superadditivity may be violated. The considerations are worked out for a simple gas model, but they are relevant to black hole thermodynamics. Rather general conclusions can be drawn which transcend special systems.Based on a seminar given at the University of Florida, April 1983.On leave of absence from the Faculty of Mathematical Studies, University, Southampton S09 5NH, England.     

Ion-Exchange selectivity coefficients in the exchange of calcium,strontium, cobalt,nickel, zinc,and cadmium ions with hydrogen ion in variously cross-linked polystyrene sulfonate cation exchangers at 25°C

The ion-exchange selectivity parameters for the exchange of trace calcium, strontium, cobalt, nickel, zinc, and cadmium ions with hydrogen ion in cross-linked polystyrene-sulfonic acid cation exchangers have been determined from equilibrium ionic distribution measurements at 25°C in dilute solutions of perchloric acid and polystyrene-sulfonic acid. The selectivity behavior in perchloric acid solutions shows that the divalent ion is always preferred by the resin phase. The selectivity coefficients are a smooth function of resin phase concentration, increasing with concentration for Sr²⁺ more than for Ca²⁺ and Cd²⁺ and being practically independent of resin phase concentration for Co²⁺, Ni²⁺, and Zn²⁺. The selectivity coefficients measured in salt-free solutions of polystyrene-sulfonic acid show a marked dependence on the polyelectrolyte concentration, the divalent ion being preferred by the aqueous phase. This preference diminishes with the concentration of polyelectrolyte. These results are interpreted by resort to the Gibbs-Duhem equation. This thermodynamic analysis has been facilitated by the availability of osmotic coefficient data for the pure polyelectrolyte ion forms over a large concentration range. Ion-exchange selectivity predictions by using this approach accurately reflect the observed ion-exchange selectivity behavior.     

Pressure-dependent partition functions

It is shown that the partition functions relating to statistical ensembles can be classified as cumulative, distributive or differential with regard to any of the extensive thermodynamic variables. The Laplace transforms involved in the general formulation of transformed partition functions, when extensive parameters are replaced by their conjugate intensive variables, are two-sided and appear in different forms according to the classification mentioned.

The petit partition function at constant pressure can be defined for both classical and quantal systems as a Stieltjes integral or dimensionless Laplace transform over the volume-dependent partition function. This expression contains no arbitrary external parameters and satisfies all the conditions formulated by Münster; it can be interpreted as the ratio of two partition functions, the one relating jointly to the system and a macroscopic boundary, and the second to the boundary alone.

It is known that the constant pressure grand partition function as defined by Guggenheim diverges for all thermodynamically compatible values of its independent variables. It is shown that the Gibbs-Duhem relation, and hence all the statistical properties of the system, except its size, can be derived by differentiating the reciprocal of this, or a similarly defined, function, not its logarithm as with other partition functions.

The mathematical differences arising out of the various proposed definitions are illustrated in a number of simple examples.     

Raman spectra of GaAs-AlxGa1-xAs superlattices

Systematic theoretical studies of Raman spectra of GaAs-Al_xGa_1-xAs superlattices are presented. The electronic states are described by an envelope-function method and the phonon modes are described in a microscopic rigid-ion model. Both resonant and nonresonant Raman scattering processes are considered. For resonant Raman scattering, the effects of discrete exciton states plus the continuum and the valence-band mixing are included via a k-space sampling method. Both the Fröhlich and deformation-potential mechanisms for electron-phonon coupling are considered. These two mechanisms are responsible for principal features in the z(x, x)z̄ and z(x, y)z̄ geometries, respectively. We find that the effects of exciton continuum states are quite important and the resonant Raman spectra so obtained are in much better agreement with experiment compared to those without including the exciton continuum states.     

Theory of infra-red and optical spectra of antiferromagnets

The contributions of magnons to the optical properties of antiferromagnets having the rutile structure are discussed. The properties considered are electric-dipole active two-magnon absorption in the infra-red, and magnon sidebands on sharp-line exciton transitions in the visible. The discussion is based on a thorough treatment of the properties of excitons and magnons in the antiferromagnetically ordered state. The site-group and space-group symmetries of the magnetic excitations are derived and the selection rules for electric and magnetic dipole transitions are determined. The occurrence of magnetic Davydov splittings of the excitons is investigated, and their symmetry properties throughout the Brillouin zone are derived. The functional dependences of exciton energy on wave vector are calculated. Applications of the theory are made to experimental results on excitons and magnons in MnF₂, FeF₂ and CoF₂.

The possible mechanisms for two-magnon and magnon-sideband absorption are discussed, and the influence of crystal symmetry on these mechanisms is described. The two-magnon state responsible for electric-dipole absorption is identified and selection rules for electric-dipole activity are presented. A spin Hamiltonian for the two-magnon process is set up and used to derive expressions for absorption coefficients for electric vector parallel and perpendicular to the crystal c-axis. Comparison with experiment for MnF₂ yields numerical values for the parameters of the basic coupling mechanism. The exciton-magnon states which give rise to magnon-sideband absorption are explicitly constructed and electric-dipole selection rules are derived for all possible types of sideband. Spin Hamiltonians for the various magnonsideband absorption processes are presented and used to derive expressions for sideband shapes. The results are applied to the experimental spectra for MnF₂ and FeF₂ and the sideband shapes in MnF₂ are calculated numerically. The sideband shapes observable in emission spectra are also briefly discussed.     

<Emphasis Type="Italic">R</Emphasis> soliton in the Wess-Zumino model

The Wess-Zumino model involving a renormalizable interaction potential and possessing R symmetry is considered. It is shown that an R soliton, which is a nontopological soliton state, is present in this model. Characteristic properties of the R soliton are discussed. Problems associated with the stability of the R soliton are considered. The results obtained by numerically calculating the energy and the charge of the R soliton are presented for several values of the model parameters. The scalar field configurations in this supersymmetric model are characterized by the presence of fermionic zero modes. Expressions for the fermionic zero modes of the R soliton are obtained, and some of their properties are considered.     

Study of quark distribution amplitudes of 1<Emphasis Type="Italic">S</Emphasis> and 2<Emphasis Type="Italic">S</Emphasis> heavy quarkonium states

In this paper, the quark distribution amplitudes of 1S and 2S heavy quarkonium states are studied in terms of Gaussian-type wave functions. The transverse momenta p _⊥ integrals of the formulae for the decay constant are performed analytically. Then the quark distribution amplitudes are obtained. In addition, the ξ-moments are also calculated. After fixing the relevant parameters appearing in the quark distribution amplitude, the curves of the quark distribution amplitude for 1S and 2S heavy quarkonium states are plotted. Finally, the numerical results of this approach are compared with the other theoretical predictions.     

Mechanisms of formation of P-odd,P-even and T-odd asymmetries in the angular distributions of products of binary and ternary fission induced by cold polarized neutrons

The experimentally measured P-odd, T-even; P-even, T-even; and P-even, T-odd asymmetries in the angular distributions of products of binary and ternary fission induced by cold polarized neutrons are classified, and the mechanisms of their appearance are studied. Basic asymmetries in the angular distributions of binary-fission fragments are found theoretically and are used to construct induced asymmetries in the angular distributions of prescission and evaporated third particles emitted in true and delayed ternary fission. If effects associated with the collective rotation of the polarized fissile system are disregarded, P-odd, T-even; P-even, T-even; and P-even, T-odd asymmetries in the angular distributions of prescission and evaporated photons are proven to be absent, and the coefficients of the analogous asymmetries in the angular distributions of prescission and evaporated neutrons are calculated for this case. The features of the coefficients of induced P-even, T-odd asymmetries are studied for evaporated photons and neutrons associated with taking into account the quantum rotation of the polarized fissile system.     

The electronic structure,elastic and optical properties of Cu2ZnGe(SexS1 − x)4 alloys: density functional calculations

The electronic structure, elastic and optical properties of Cu₂ZnGe(Se_xS_{1 ? x})₄ alloys are systematically analysed using first-principles calculations. The lattice parameters agree well with the theoretical and experimental values which are searched as complete as possible indicating our calculations are reliable. The elastic properties are investigated first and are compared with the similar compounds CZTS and CZTSe due to the unavailable experimental data currently. The variation of the optical properties caused by the increase of Se/S ratio is discussed. The static optical constants are calculated and the corrected values are also predicted according to the available experimental data.