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Further improvements to the modified quasichemical model in the pair approximation for short-range ordering in liquid and solid solutions are presented. The energy of pair formation is expanded in terms of the pair fractions rather than the component fractions, and coordination numbers are permitted to vary with composition. A formalism is introduced whereby the quasichemical equations are shown to be equivalent to the equations of an associate model if the pairs are formally treated as fractional associates. The model is applied to the liquid phase in a new optimization of the KCl-MgCl 2 system.

The Fe-Zn-O phase diagram in air was studied over the temperature range from 900 ЊC to 1500 ЊC. The compositions of the phases in quenched samples were obtained by electron probe X-ray microanalysis (EPMA). This experimental technique is not affected by zinc losses resulting from vaporization of zinc at high temperatures. The model for the spinel solid solution was developed within the framework of the compound-energy formalism (CEF). The choice of parameters of the CEF and the sequence of their optimization can have a major influence on the predictions in multicomponent phases. These choices can only be made rationally by reference to the specific model being represented in the CEF. This is discussed for the case of the two-sublattice spinel model. In the limiting case, the proposed model reduces to the model by O'Neill and Navrotsky for spinels. When the CEF is used in combination with the equation of Hillert and Jarl to describe the magnetic contribution to thermodynamic functions of a solution, it is necessary to assign certain values of magnetic properties to all pseudocomponents and to magnetic interaction parameters to obtain the most reasonable approximation of the magnetic properties of a solution. It was shown how this can be done based on very limited experimental data. The same equations can be used when the Murnaghan or the Birch-Murnaghan equation is combined with the CEF to describe the pressure dependence of thermodynamic functions. The polynomial model was used to describe the properties of wustite and zincite, and the modified quasichemical model was used for the liquid slag. All thermodynamic and phase-equilibria data on the Fe-O and Fe-Zn-O systems were critically evaluated, and parameters of the models were optimized to give a selfconsistent set of thermodynamic functions of the phases in these systems. All experimental data are reproduced within experimental error limits. These include the thermodynamic properties of phases (such as specific heat, heat content, entropy, enthalpy, and Gibbs energy); the cation distribution between octahedral and tetrahedral sites in spinel; the oxygen partial pressure over single-phase, twophase, and three-phase regions; the phase boundaries (liquidus, solidus, and subsolidus); and the tie-lines.

Liquidus-phase equilibrium data of the present authors for the PbO-ZnO-SiO 2 system, combined with phase equilibrium and thermodynamic data from the literature, were optimized to obtain a selfconsistent set of parameters of thermodynamic models for all phases. The modified quasichemical model was used for the liquid slag phase. From these model parameters, the optimized ternary-phase diagram was back-calculated.

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