What do crystals nucleate on? What is the microscopic mechanism? How can we model nucleation?

Crystallization is a key process in materials science, and most materials are made by processes that involve crystallization. Crystallization starts with nucleation, a process that is poorly understood for two reasons. First, nucleation occurs in contact with the typically uncharacterized surface of an impurity in the system. Second, we typically have little direct data on the microscopic mechanism of nucleation. We have a theory called classical nucleation, but when a simple application of the theory disagrees with experiment, it is unclear whether the theory is wrong, or if some feature of the surface is missing from the model. This article briefly reviews recent work on nucleation and its mechanisms. We are not alone in working with a stochastic process whose underlying mechanism is poorly understood. Engineers often have this problem and have developed powerful statistical models for stochastic processes. Surprisingly, even though they are sometimes used by materials scientists in different contexts, these are not used to model and predict nucleation behavior. We could advance the field with their use.