Modelling Materials Microstructure Across Scales using Phase Field Methods

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Phase field crystal models and their recent extension will be summarized. Their application to non-equilibrium kinetics and phase transformations in materials will be reviewed. In particular, we review new results from applications of this modeling paradigm to solute trapping during rapid solidification of alloys, defect-mediated solid-state precipitation, and magneto-crystalline interactions. We close with a discussion of new complex amplitude representations of PFC models and how these can be used for multi-scale simulations using adaptive mesh refinement methods.