Phase diagrams-why they matter and how to predict them

Understanding the thermodynamic stability and metastability of materials can help us to gauge for example whether crystalline polymorphs in pharmaceutical formulations are likely to be durable. It can also help us to design experimental routes to novel phases with potentially interesting properties. In this article, we provide an overview of how thermodynamic phase behaviour can be quantified both in computer simulations and using machine-learning approaches to determining phase diagrams, as well as combinations of the two. We review the basic workflow of free-energy computations for condensed phases, including some practical implementation advice, ranging from the Frenkel-Ladd approach to thermodynamic integration and to direct-coexistence simulations. We illustrate the applications of such methods on a range of systems from materials chemistry to biological phase separation. Finally, we outline some challenges, questions and practical applications of phase-diagram determination which we believe are likely to be possible to address in the near future using such state-of-the-art free-energy calculations, which may provide fundamental insight into separation processes using multicomponent solvents.