The existence of the spinodal, an incompletely solved problem in the thermodynamics of solids

Abstract

AbstractA thermodynamic investigation of the concept of the spinodal, usually considered to be a curve within the coexistence curve of an alloy with a miscibility gap, demonstrates that no thermodynamic meaning can be ascribed to the concept unless additional constraints and thermodynamic variables are assigned to the system. Such constraints are usually applied implicitly in solid solution models like the Bragg‐Williams model, but it is difficult to characterize such poorly defined constraints in terms of the new thermodynamic variables which should be associated with them. A method of constraining the solution out of its unstable state, inside the spinodal. is introduced which can be characterized in terms of simple thermodynamic variables. The relation of the spinodal, thereby induced. to the rate process of spinodal decomposition is discussed.As an important byproduct of this work, it is demonstrated that the traditional stability criterion, requiring the positiveness of the second derivative of free energy with respect to composition, is really invalid, except that it is asymptotically valid for fluctuations of macroscopic extent. Also, critical discussions concerning the differences, if any, between stable and metastable equilibria are presented.It is concluded that the existing theories of spinodal decomposition are, in mechanistic form, valid and essentially correct, even if a completely unambiguous definition of the spinodal cannot be given.