Heterogeneous nucleation on potent spherical substrates during solidification

For a spherical-cap nucleus to become a “transformation nucleus”, the linear dimension (d) of the flat substrate must exceed the critical nucleus size (2r*). This Turnbull criterion (d greater-or-equal, slanted 2r*) defines a minimum undercooling for grain formation on, and effective inoculation with, flat nucleating substrates. However, for nucleation on potent substrates the spherical-cap model is no longer tenable. The free growth model has in general considered the growth of a two-dimensional nucleus on a potent flat substrate. Inspired by the particle-core structures observed in magnesium alloys after inoculation with nearly spherical zirconium particles, a model has been proposed, on the basis of an adsorption and surface diffusion mechanism, for heterogeneous nucleation and grain formation on potent spherical substrates of d greater-or-equal, slanted 2r*. The critical undercooling required is found to be approximately the same as that defined by Turnbull’s patch nucleation theory. The model shows excellent agreement with experiments compared from different perspectives.