The effect of the heat capacity of the liquid phase on the heat of fusion liquidus equation of compound semiconductors

We have critically examined the assumptions involved in the derivation of Vieland's widely used heat of fusion liquidus equation for binary compounds and conclude that the thermodynamic form of this equation ignores the relative partial molar heat capacity of the liquid solution. Taking into account this quantity, we obtain the generalized heat of fusion equation which is exact and show its complete equivalence to its alternative, the heat of formation equation. The generalized result provides a correction term to Vieland's equation which can be expressed as a function of the activity coefficients at the compound composition. Applying the correction term to the activity coefficients derived for a number of useful solution models, we find that the regular solution form of Vieland's equation is exact, as shown previously, if α (interchange energy) is a constant or a linear function of temperature. But when α is expanded as an nth order polynomial in temperature (simple solution), Vieland's equation is inexact for n ? 2. In addition, it is demonstrated that for a regular associated solution and for Darken's quadratic representation, Vieland's thermodynamic equation is exact only with certain restrictions, while for a quasi-chemical solution it is invalid.