Phase-field modelling for metals and colloids and nucleation therein-an overview

Phase-field modelling, as it is understood today, is still a young discipline in condensed matter physics, which established itself for that class of systems in condensed matter physics, which can be characterized by domains of different phases separated by a distinct interface. Driven out of equilibrium, their dynamics results in the evolution of those interfaces, during which those might develop into well-defined structures with characteristic length scales at the nano-, micro- or mesoscale. Since the material properties of such systems are, to a large extent, determined by those small-scale structures, acquiring a precise understanding of the mechanisms that drive the interfacial dynamics is a great challenge for scientists in this field. Phase-field modelling is an approach that allows us to tackle this challenge simulation-based. This overview summarizes briefly the essentials of the conceptual background of the phase-field method, as well as recent issues the phase-field community is focusing on, as far as they are related to nucleation. To that end a brief introduction to the basic understanding underlying the diffuse interface description, which is the conceptual backbone of phase-field modelling, is given at the beginning, followed by a detailed picture of its achievements so far in applications to nucleation phenomena in metals and colloids. Within the most relevant fields of condensed matter physics, approached by phase-field modelling until now, applications to metallic systems are a traditional domain of phase-field modelling and nucleation phenomena therein have been addressed by several groups. This paper provides an overview of these. Advances in the field of colloidal systems, on the other hand, are only more recent and are addressed here in the context of contributions to soft matter physics in general.