ReactCA: A Cellular Automaton for Predicting Phase Evolution in Solid-State Reactions

Abstract

New computational tools for solid-state synthesis recipe design are needed in order to accelerate the experimental realization of novel functional materials proposed by high-throughput materials discovery workflows. This work contributes a cellular automaton simulation framework (ReactCA) for predicting the time-dependent evolution of intermediate and product phases during solid-state reactions as a function of precursor choice and amount, reaction atmosphere, and heating profile. The simulation captures rudimentary kinetic effects, the effects of reactant particle spatial distribution, particle melting and reaction atmosphere. It achieves conservation of mass using a stochastic, asynchronous evolution rule and estimates reaction rates using density functional theory data from the Materials Project [1] and machine learning estimators for the the melting point [2] and the vibrational entropy component of the Gibbs free energy [3]. The resulting simulation framework allows for the prediction of the likely outcome of a reaction recipe before any experiments are performed. We analyze five experimental solid-state recipes for BaTiO$_3$, CaZrN$_2$ and YMnO$_3$ found in the literature to illustrate the performance of the model in capturing reaction pathways as a function of temperature, reaction selectivity and the effect of precursor choice. Our approach allows for straightforward comparison of predicted mass fractions of intermediates and products with experimental results. This simulation framework presents a step toward $\textit{in silico}$ synthesis recipe design and an easier way to optimize existing recipes, aid in the identification of intermediates and identify effective recipes for yet unrealized inorganic solids.