Thermodynamic consistency of the interaction parameter formalism

The apparent contradiction between the exact nature of the interaction parameter formalism as presented by Lupis and Elliott and the inconsistencies discussed recently by Pelton and Bale arise from the truncation of the Maclaurin series in the latter treatment. The truncation removes the exactness of the expression for the logarithm of the activity coefficient of a solute in a multi-component system. The integrals are therefore path dependent. Formulae for integration along paths of constant X_i,or X _i/X_j are presented. The expression for In γ_solvent given by Pelton and Bale is valid only in the limit that the mole fraction of solvent tends to one. The truncation also destroys the general relations between interaction parameters derived by Lupis and Elliott. For each specific choice of parameters special relationships are obtained between interaction parameters.     

Thermodynamic consistency of the interaction parameter formalism

The apparent contradiction between the exact nature of the interaction parameter formalism as presented by Lupis and Elliott and the inconsistencies discussed recently by Pelton and Bale arise from the truncation of the Maclaurin series in the latter treatment. The truncation removes the exactness of the expression for the logarithm of the activity coefficient of a solute in a multi-component system. The integrals are therefore path dependent. Formulae for integration along paths of constant X_i,or X _i/X_j are presented. The expression for In γ_solvent given by Pelton and Bale is valid only in the limit that the mole fraction of solvent tends to one. The truncation also destroys the general relations between interaction parameters derived by Lupis and Elliott. For each specific choice of parameters special relationships are obtained between interaction parameters.     

The unified interaction parameter formalism: Thermodynamic consistency and applications

In a recent article, we proposed modifications to the standard interaction parameter formalism. The modified formalism, known as the “Unified Interaction Parameter Formalism,” is discussed in the present article with respect to thermodynamic consistency at finite concentrations in binary, ternary, and multicomponent systems. A new method, which is independent of integration paths, is proposed to derive the equations of the formalism by differentiation of the integral Gibbs energy expression. It is shown that the formalism is thermodynamically exact in both dilute and nondilute composition regions. It is also shown that the formalism reduces to Wagner’s formalism at infinite dilution and to Darken’s quadratic formalism in dilute solutions. Examples are presented and methods are discussed for determining the parameters of the formalism from thermodynamic data.     

The correlation of the thermodynamic properties of wustite by a gaussian based formalism

A Gaussian-based formalism is used to correlate precisely the data of Darken and Gurry¹ for the wustite phase of the industrially important system Fe-0 within and at the boundaries of this phase. Equations are also given for the free energy and heats of formation of metastable FeO, wustite in equilibrium with γ-Fe, and Fe₃O₄ from y-Fe and oxygen at 1 atm.     

Thermodynamic properties and diffusion thermodynamic factors in B2-NiAl

The vaporization of Ni-Al alloys has been investigated in the temperature range 1178 to 1574 K by Knudsen effusion mass spectrometry (KEMS). Thirteen different compositions have been examined in the composition range 38 to 57 at. pct Al. The partial pressures and thermodynamic activities of both Ni and Al have been evaluated both directly from the measured ion intensities for a component in both the alloy and the pure element, I _M ⁺ /I _M ⁺ °, and also from the ion intensity ratios of the alloy components, I _Al ⁺ /I _Ni ⁺ , by means of a Gibbs-Duhem integration. Reliable partial molar enthalpies and entropies for both components have been obtained by mass spectrometry for this system for the first time. Both properties are found to be nearly temperature independent over the wide temperature range investigated. Two separate component diffusion thermodynamic factors have also been evaluated for the first time by taking into account the large vacancy concentrations in these alloys. The enthalpy and Gibbs energy of mixing of stoichiometric Ni_0.5Al_0.5 at 1400 K, evaluated using the Gibbs-Duhem ion intensity ratio (GD-IIR) method, are −78.4±1.2 and −49.0 kJ/mol, respectively, with Al(liquid) and completely paramagnetic Ni(fcc, cpm) as reference states.