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Showing papers on "Gibbs–Duhem equation published in 1977"


Journal ArticleDOI
TL;DR: In this article, the authors investigated limiting Gibbs states with nearest neighbor ferromagnetic potentials on a (d+l)-tree and obtained several extremal Gibbs states by changing boundary conditions.
Abstract: In this paper we investigate limiting Gibbs states with nearest neighbour ferromagnetic potentials on a (d+l)-tree. Preston [1] has got a necessary and sufficient condition for the non-uniqueness of the Gibbs states for a given interaction (i.e. the necessary and sufficient condition for the phase transition to occur) in these models. The Gibbs states on a countable tree are studied in [1] and [2]. Our aim is to obtain several limiting Gibbs states by changing boundary conditions. Spitzer [2] has shown that (i) every extremal Gibbs state invariant under graph isomorphisms is a "Markov chain" in the sense of his definition (see Definition 1), and (ii) there are at most three "Markov chains" among the Gibbs states for any given nearest neighbour ferromagnetic potential. In section 4 we will prove that every "Markov chain" which is Gibbsian for the given interaction is obtained as a limiting Gibbs state for the same interaction with certain boundary conditions. In section 5 we will give examples of limiting Gibbs states such that the number of up-spins appearing in the corresponding boundary conditions is much smaller than that of down-spins on every boundary, while the probability for the spin at the origin to be up is larger than 1/2. In section 6 we will give several extremal Gibbs states using above examples.

62 citations


Journal ArticleDOI
TL;DR: In this article, a general equation for calculating excess Gibbs free energies from isothermal vapour-liquid equilibria is proposed and the relation between this equation and various other equations is established.

55 citations


Journal ArticleDOI
TL;DR: In this article, the experimental information on the solid state phase equilibria in the Fe−Mn−C system was analyzed in thermodynamic terms and the Gibbs free energy of each phase was described by a regular or subregular solution model and the numerical values of the parameters were determined.
Abstract: The experimental information on the solid state phase equilibria in the Fe−Mn−C system was analyzed in thermodynamic terms. Gibbs free energy of each phase was described by a regular or subregular solution model and the numerical values of the parameters were determined. The results were used to calculate isothermal sections between 873 and 1373 K. They show a reasonable agreement with all the experimental information available.

27 citations


Journal ArticleDOI
TL;DR: Gibbs energy and entropy data for aqueous Fe 2+, FeOH +, HFeO − 2 and FeO 2− 2 are critically reviewed in this paper, where the most reliable values are used in a Criss-Cobble extrapolation to calculate Gibbs energies to 300°C and, hence, the solubility of Fe 3 O 4 in H 2 O and D 2 O as a function of the pH or pD at 25°C.

25 citations





Journal ArticleDOI
TL;DR: In this paper, the Gibbs-Duhem equation for a non-stoichiometric compound with ionized atomic points defects was studied, and a more complete analysis of non-Stoichiometry was proposed, which takes account of the electronic band structure modifications.

Journal ArticleDOI
TL;DR: In this article, the kinematic viscosity of binary mixtures were measured at 40°C with an Ostwald viscometer, and the data were corrected for vapour phase nonideality, tested for thermodynamic consistency and correlated by Wilson equation.
Abstract: Molar excess enthalpies of mixing at 48.2°C, and molar excess volumes at 40°C were measured for acetonitrile-methyl cellosolve system using an isothermal phase change calorimeter and a glass dilatometer respectively. Molar excess Gibbs free energies were calculated from the isothermal vapour-liquid equilibrium data obtained in a circulation still at 70, 60 and 48.2°C. Complete isobaric vapour-liquid equilibrium data at 1 atm pressure are also reported. The kinematic viscosity of binary mixtures were measured at 40°C with an Ostwald viscometer. The VLE data are corrected for vapour phase nonideality, tested for thermodynamic consistency and correlated by Wilson equation. The viscosity data were correlated by McAllister and excess function models.