SELF-SIMILAR REGIME OF THERMALLY CONTROLLED SOLIDIFICATION OF BINARY MELTS

When heat supply to a binary melt at its outer boundary is absent, macrokinetics of solidification are governed by progressive cooling of the melt rather than by withdrawal of an admixture. Because the former process is much faster than the latter one, a metastable region of concentrational supercooling arises and has time to expand before the ingot surface noticeably changes its position. This leads to bulk crystallization within such a region prior to solidification at the surface. If crystalline grains are forming and growing rapidly enough, the two-phase region is practically at the state of thermodynamic equilibrium. This case is considered under the assumptions that the melt phase diagram consists of straight liquidus and solidus lines with one eutectic point and that the physical parameters are constant. A simple self-similar solution of relevant equations is obtained which approximately describes unidirectional processes.