Predicting continuous and discontinuous phase decompositions using steepest-entropy-ascent quantum thermodynamics

The decomposition kinetics of a solid solution into separate phases are analyzed with an equation of motion initially developed to account for dissipative processes in quantum systems. This equation and the steepest-entropy-ascent quantum thermodynamic framework of which it is a part make it possible to track kinetic processes in systems at nonequilibrium while retaining the framework of classical equilibrium thermodynamics. The general equation of motion is particularized for the case of the decomposition of a binary alloy, and a solution model is used to build an approximate energy eigenstructure, or pseudoeigenstructure, for the alloy system. This equation is then solved with the pseudoeigenstructure to obtain a unique reaction path and the decomposition kinetics of the alloy. For a hypothetical solid solution with a miscibility gap at low temperatures, the conditions under which this framework predicts a continuous transformation path (spinodal decomposition) or a discontinuous one (nucleation and growth) are demonstrated.