Institute of Metals Division - A Simple Method of Estimating the Chemical Spinodal

It is shown that for systems having a miscibility gap the spinodal composition (c,) in the vicinity of the critical temperature (Tc) is related to the equilibrium composition (c,) by where cc is the critical composition. This expression is exart for the limit T — Tc and is a good approximation down to (T/Tc) - 0.9. If the miscibility gap meets the composition of the pure components THE recent theoretical treatment by cahn1,2 on spinodal decomposition of solid solutions has revived interest in methods of estimating the chemical spinodal, * i.e., the locus on a binary phase By use of the appropriate expression, the spinodal can be drawn on the Phase diagram almost by inspection with an accuracy comparable to that of lengthy calculations in which a free-energy function is fitted to the phase diagram. Satisfactory agveemenf is also obtained with spinodals comPuted from experimental free-energy curves. where G is the Gibbs free energy of the homogeneous solution and c the atomic fraction of component 2, the derivative being evaluated at constant temperature (T) and pressure (P). (These subscripts will hereafter be omitted from the partial derivatives.) If experimental measurements of G as a function of c and T are available in a single-phase region above the spinodal, then these can be extrapolated to obtain a series of metastable free-energy isotherms in the two-phase region, and from these isotherms a series of spinodal compositions can be calculated. Because the value of is very sensitive to experimental errors, an elaborate analytic procedure is required for