Phase-field modelling of rapid solidification in alloy systems: Spontaneous grain refinement effects

Phase-field modelling of rapid alloy solidification, in which the rejection of latent heat from the growing solid cannot be ignored, has lagged significantly behind the modelling of conventional casting practises which can be approximated as isothermal. This is in large part due to the fact that if realistic materials properties are adopted the ratio of the thermal to solute diffusivity (the Lewis number) is typically 103 - 104, leading to severe multi-scale problems. However, use of state-of-the-art numerical techniques such as local mesh adaptivity, implicit time-stepping and a non-linear multi-grid solver allow these difficulties to be overcome. Here we describe how the application of this model, formulated in the thin-interface limit, can help to explain the long-standing phenomenon of spontaneous grain refinement in deeply undercooled melts. We find that at intermediate undercoolings the operating point parameter, σ*, may collapse to zero, resulting in the growth of non-dendritic morphologies such as doublons and 'dendritic seaweed'. Further increases in undercooling then lead to the re-establishment of stable dendritic growth. We postulate that remelting of such seaweed structures gives rise to the low undercooling instance of grain refinement observed in alloys.