Development of a unified chain of phase field theories for multi--scale modelling of solidification microstructure evolution

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The properties of most materials are determined by their microstructure, a large part of which evolves during solidification. Modelling solidification is challenging because of the multiple length scales involved, from interface kinetics and solid-state defects at the atomic scale to diffusional processes that set the scale of microstructure patterning on the mesoscale. The emergence of rapid cooling processes in technology (e.g. 3D printing and laser welding) has driven a growing interest to understand such microstructure evolution processes on time scales of micro-milliseconds during rapid solidification. Here, strong non-equilibrium effects lead to meta-stable phases, thermal strain and plastic deformation, density heterogeneity and void formation near phase boundaries. There is presently no consistent modelling platform to study these inherently multi-scale phenomena. The vision of this research is to develop multi-scale chain of consistently connected theories that captures exotic microstructure phenomena that arise during solidification processes. The development of this modelling chain will be done in two stages. The first stage will have as its foundation the phenomenology of classical density functional theory for unary and binary materials based on multi-point correlation functions, duly simplified to render a PFC-like model for microstructure evolution that is tractable for use in simulations via high performance computing. This field theory will comprise a consistent fusion of successful elements of past phase field crystal (PFC) type models. The parameters of this new PFC type model will be systematically quantified against known experimental materials properties of pure material and alloys. The second stage of this modelling chain will comprise two parts. The first part will develop a coarse graining methodology to project a microscopic PFC model onto a traditional type of phase field (PF) model based on smooth fields representing order, orientation, local average density and concentration (for the case of alloy materials). The second part will expand the scope of this coarse graining methodology to further include local strain coupling to the aforementioned smooth fields. Both coarse graining methodologies will be applied to established PFC models for pure and alloy materials, and ultimately to the aforementioned new binary PFC model developed in this proposal. Phase field models so-obtained will retain the physics of several key microscopic properties of the generating PFC theory, and will be parametrically connected through coarse graining. The outcomes of this research will provide Canadian researchers in materials science and materials engineering a toolset for modelling the physics of non-traditional microstructure evolution processes in rapid solidification phenomena at different scales.