Multi-scale computational modelling of solidification phenomena

Abstract

Multi-scale modelling of phenomena in which a complete description requires the coupling of many processes at widely different length, time and energy scales offers a new and state-of-the-art strategy in computational condensed matter physics. This review is concerned with a multi-scale computational modelling of the solidification phase transition, as a highly complex and truly multi-scale process. The modelling integrates the initial nucleation processes unfolding at the nano-scale with a probabilistic micro-scale model of micro-structure formation. The resulting nano–micro model is then coupled with the macroscopic heat flow equation to provide an unified approach to the solidification phenomenon. Molecular dynamics (MD) simulation method provides the theoretical framework for modelling the formation of the initial atomic clusters at the nano-scale. Phase transitions are detected at this scale, and the all important material properties are also computed. Pertinent inter-atomic potentials that model the energetics and dynamics of the clusterisation process at the nano-scale are also given. The computed material properties form the input into a cellular automata (CA)-based model of the micro-structure formation at the micro-scale, as well as the input to the macroscopic heat flow equation. Solid fractions generated from the micro-scale model also form part of the input to the macro-scale model whose temperature field distribution is, in turn, fed back into both the micro-scale and the nano-scale models. There is thus a close interplay between the different levels of the multi-scale model. As well as providing a nano-scale basis for the CA-based model of micro-structure formation, an extension of that model, based on concepts from the Ito stochastic dynamics, is also discussed. A set of computer-based simulations of the solidification of the elemental and alloy systems are discussed for each component of the overall multi-scale model, with the full multi-scale model applied to the simulation of the solidification of some of the industrially important alloy systems.