On the Equilibrium Solidification of Solid Solutions (68668456-9900-44e7-bb2f-ba0eb773d0fd)

This paper deals with the calculation of the composition of the infinitesimal trace of alloy that transfers from the liquid to the solid state at each temperature during the equilibrium solidification of a binary solid solution, and which thereby enables the compositions of the coexisting liquid and solid phases to follow along the liquidus and solidus lines respectively during the cooling. A general expression for the composition (d) of the liquid-to-solid transfer at each temperature has been derived: d = ZLXL(XL - P) + Zsxs(P- ZL(XL - P) + Zs(P - Xs) where ZL and Zs are the slopes of the liquidus and solidus lines at the given temperature, XL and xs are the composi-tions of the stable liquid and solid phases at the same temperature, and P is the composition of the alloy under considera-tion. The d equation is valid for the process of equilibrium heating as well as cooling, and may be applied to vapor-to-liquid, vapor-to-solid, liquid-to-liquid, and solid-to-solid transfers if the corresponding equilibrium diagrams are known. The d -versus-temperature curves for two alloys Pl and P2 are shown in Fig. I. In each case, the liquid-to-solid transfer has the same composition as the stable solid FIG. I.-GENERAL SOLID SOLUTION DIAGRAM SHOWING S CURVES FOR ALLOYS P1 AND P2. phase only at the temperature of the be-ginning of solidification, and has the same composition as the stable liquid phase only at the temperature of the completion of solidification. At each intermediate tem-perature, the composition of the liquid-to-solid transfer differs by a finite amount from those of the two coexisting phases. Therefore, during equilibrium cooling, the transfers must merge into the solid phase from the liquid without forming a transition phase; otherwise the condition of equilibrium would be violated. At any given temperature during solidification, the composition of the liquid-to-solid