Calculation of phase equilibria in the Ga-Bi and Ga-P-Bi systems based on a theory of regular associated solutions

A new theory of regular associated solutions (RAS) has been formulated to provide a consistent representation of binary and ternary phase equilibria in the Ga-P-Bi system. The key postulate of the theory is that the major species in liquid alloys are Ga, P, and Bi atoms and Bi₂ dimers. At first, the gross component activities in the Ga-Bi binary system are approximated from the dimer dissociation constant,K, and the activity coefficients of the three species (identified here with the coefficients for a ternary regular solution). The accord observed between the form of the isothermal activity data and the theory permits the determination ofK and the Ga-Bi interchange energy. These parameters are then employed in the calculation of the enthalpy and entropy of mixing and the prediction of the liquidus curve and asymmetric miscibility gap for the Ga-Bi system, all of which are in good agreement with the experimental findings. Generalization of the enthalpy and entropy of mixing for a binary RAS facilitates the derivation of the activities in the ternary system. Knowledge of the activities leads to the evaluation of the ternary liquidus isotherms over the entire composition range, since the Bi-P interchange energy can be obtained from the GaP-Bi pseudobinary liquidus data. It is found that along the pseudobinary the standard error between calculated and experimental liquidus points is 7° C. Furthermore, in P-rich liquid solutions, at any temperature below ≈R 1380°C, an open miscibility gap intersects the primary liquidus isotherms of Bi-doped GaP. The predicted miscibility gap in the Bi-P system is consistent with the fragmentary evidence. Finally, the paper discusses extensions of the RAS model to other ternary systems involving compound semiconductors wherein association in the liquid is likely.