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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.
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