Mesoscopic kinetics of nonequilibrium solidification

Abstract

Disadvantages of Aziz interface partition model [J. Appl. Phys. 53, 1158 (1982)] are summarized in this article. Using transition state theory and Maxwell–Boltzmann distribution law, a mesoscopic solute partition model (MPM) including multilayer interface for dilute solution is put forward. It is shown that the static interface structure and roughening behavior have significant effects on solute partitioning. Both the partition processes of semiconductors and metals can be explained by MPM rationally. The Aziz model is just a particular case of MPM for monolayer interface without roughening before complete trapping occurs. Comparisons of MPM with experimental results in Si (As, Ge, Bi, Sn) and Al(Cu, Sn, Ge, In) show pretty good agreement, provided an educated speculation of interface roughening behavior is given. Also in MPM, it is pointed out that interface diffusivity Di correlates with the interface scale. For semiconductors with an atomic sharp solid/liquid interface, Di is close to DL, the diffusivity of bulk liquid. On the other hand, for metals with a diffuse interface, Di can be orders of magnitude lower than DL, to some extent estimated by DSDL, the geometric mean of the diffusivity of bulk solid and liquid.