A rigorous data-driven approach to the nucleation of defects in metals exploiting the link between kinetic properties and (dis)order parameters

Nucleation processes, through which a new structure progressively forms within a pre-existing homogeneous phase, are fundamental in materials science, but are also typically non-trivial to elucidate. Cases in which to nucleate are defects (or disorder) in an initially ordered structure make no exception. A prominent example is the nucleation of dislocations in metals, which critically govern their mechanical, electronic, thermal, and chemical properties. While atomic-level insights can be attained using, \textit{e.g.}, molecular dynamics simulations, systematically characterizing nucleation mechanisms and accurately quantifying kinetic rates remain challenging tasks. In this work, we demonstrate how the choice of the order parameter used to track the transition has a very strong effect on the accuracy of the kinetic rate predicted from the corresponding free-energy barrier and diffusion coefficient, a fact that has been often overlooked in the past. By exploiting this systematic error to our advantage, we demonstrate that it is possible to rigorously characterize the nucleation process using a data-driven scheme based on a variational principle, leading to optimal order parameters and a faithful mechanistic description. We apply this method to characterize, as a representative case study, the nucleation of dislocations in crystalline $fcc$ copper by analyzing replica molecular dynamics simulations at the elastic-plastic limit. By means of committor analysis and Langevin modeling, our approach allows to systematically rank candidate (dis)order parameters, identify the critical nuclei (transition states), and infer the free-energy landscapes. Given its general foundations, this method can be extended to nucleation phenomena in a broad class of materials.