Engulfment of a Particle by a Growing Crystal in Binary Alloys

Under quasi-steady particle pushing conditions in an alloy, fresh liquid has to flow to the gap separating a particle and an advancing solid–liquid interface of a crystal to feed the volume change associated with the liquid–solid phase transformation. In the meantime, solute rejected by the growing crystal has to diffuse out of the gap against the physical feeding flow. An inequality equation was derived to estimate the pushing-to-engulfment transition (PET) velocity of the crystal under which the particle is pushed by the growing crystal. Experiments were performed in an Al-4.5 wt.%Cu-2 wt.% TiB₂ composite under isothermal coarsening conditions. TiB₂ particles were indeed engulfed by the growing aluminum dendrites as predicted using the inequality equation. Predictions of the inequality equation also agreed reasonably well with literature data from the solidification of distilled water containing particles obtained under minimal convection conditions. The inequality equation suggests that the PET velocity is much smaller in a binary alloy than that in a pure material. Without the influence of fluid flow or other factors that put a particle in motion in the liquid, the particle should be engulfed by the growing crystal in alloys solidified under normal cooling rates associated with convectional casting conditions.