Phase-field model of stoichiometric compounds and solution phases

The ability to predict the microstructures of a multiphase solid is critical to manipulating their physical properties. One of the main challenges is the fact most of the multiphase solids contain a mixture of ordered stoichiometric compounds with fixed compositions and disordered solid solutions with variable chemical compositions. Although phase-field method has been extensively employed to predict mesoscale structural evolution, all existing phase-field models treat ordered stoichiometric compounds as disordered solid solutions by approximating their mathematically delta-function dependences on composition with parabolas assuming a rather arbitrary curvature, leading to possibly orders of exaggerated non-stoichiometries, thermodynamic inconsistencies, and numerical instabilities. Here we develop a phase-field model for predicting microstructure patterns involving simultaneous solid stoichiometric and solution phases. We demonstrate its application using a well-known example of precipitation of stoichiometric θ ′ precipitates in a solid solution matrix in which the elastic strain contribution also plays an important role in the resulting microstructure. The proposed framework should be applicable to other common processes such as crystallization of stoichiometric compounds, vapor-phase deposition of stoichiometric thin films or two-dimensional materials, oxidation of alloys, electrochemical deposition, interfacial reactions, etc.