Crystal Growth and Solute Trapping

Abstract

A simple model for solute trapping during rapid solidification is presented in terms of a single unknown parameters, the interfacial diffusivity D_i. A transition from equilibrium segregation to complete solute trapping occurs over roughly an order of magnitude in growth speed, as the interface speed surpasses the maximum speed with which solute atoms can diffuse across the interface to remain ahead of the growing crystal. This diffusive speed is given by D_i/Lambda, where Lambda is the interatomic spacing, and is typically of the order 10 meters per second. Comparison is made with experiment. The steady-state speed of a planar interface is predicted by calculating the free energy dissipated by irreversible processes at the interface and equating it to the available driving free energy. Steady-state solutions are presented for Bi-doped Si during pulsed laser annealing.