Phase Field Modelling of Multiphase Alloy Solidification: A Review

The first phase field approaches to solidification of materials were limited to alloys with just two phases of matter: one liquid and one solid phase. A single phase field variable conventionally takes a value 1 in the liquid and 0 in the solid, where intermediate values indicate the boundary or solid surface. This prompts a natural generalisation whereby a vector of phase variables represents each possible phase of matter in an alloy where many phases of matter are possible. Beyond this, however, there is no consensus on the precise form this generalisation should take, save their equivalence to single phase formulations when the number of phases reduces to two. Broadly, the approaches to multiphase solidification fall into two camps: one, where the formulation is concerned only with binary interactions, and, two, where three phase junctions also contribute to the dynamics.