The Inverse Phase Stability Problem as a Constraint Satisfaction Problem: Application to Materials Design

In general, the forward phase stability problem consists of mapping thermodynamic conditions (e.g., composition, temperature, pressure) to corresponding equilibrium states. In this paper, we instead focus on the generalized inverse phase stability problem (GIPSP) that deals with mapping a set of phase constitutions to a set of corresponding thermodynamic conditions. Specifically, we define the GIPSP as mapping of sets of phase constitution definitions in a multidimensional phase constitution search space to corresponding ranges of thermodynamic conditions. Mathematically, the solution to the GIPSP corresponds to all solutions to a continuous constraint satisfaction problem (CCSP). We present novel algorithms combining computational thermodynamics, evolutionary computation, and machine learning to approximate solution sets to the GIPSP as a CCSP. Some preliminary examples demonstrating the algorithms are presented. Moreover, the implications of the proposed framework for the larger problem of materials design are discussed, and future work is suggested.