Diffusive first-order phase transition: nucleation, growth and coarsening in solids

The phenomena of nucleation and growth, which fall into the category of first-order phase transitions, are of great importance. They are present everywhere in our daily lives. They enable us to understand and model a vast number of phenomena, from the formation of raindrops, to the gelling of polymers, the evolution of a virus population and the formation of galaxies. Surprisingly, this whole range of phenomena can be described by two seemingly antagonistic approaches: classical nucleation theory, which highlights the atomistic approach of the diffusion process, and the phase-field (PF) approach, which erases the discrete nature of the diffusion process. Although there is an huge quantity of articles and review papers dealing with the problem of first-order phase transition, the subject is so important and vast that it is very difficult to provide nowadays exhaustive syntheses on the subject. The revival over the past 20 years in the condensed matter world of PF approaches such as PF crystal, or the recent development of optimization methods such as gentle ascend dynamics, as well as the emergence of atom probe tomography, have enabled us to better understand the links between these antagonistic approaches, and above all to provide new experimental results to test the limits of both. This renewal has motivated the writing of this review, both to take stock of current knowledge on these two approaches. This review has two distinct objectives: summarizing generic previous models applies to discuss the nucleation, the growth and the coarsening processes. Despite some reviews already exist on these different subject, few of them present the different logical links between these models and their limitations, unifying them within the framework of the theory of macroscopic fluctuations, which has been developed over the last 20 years. In particular, we present the extension of the Cahn-Hilliard formalism to model the nucleation and growth process and we discuss the relevance of the notion of pseudo-spinodal and discuss. Such an extension allows interpreting experiments performed fat from the solubility limit and the spinodal line. Finally, this work proposes some clues to make this unified approach more predictive.