Finite-amplitude cellular solidification fronts are calculated for morphologically unstable rapidly solidifying metals and semiconductors. A two-dimensional directional solidification model is used which accounts for nonequilibrium segregation of dopant. Finite-element approximations of temperature, concentration, and melt-solid interface shape are used in conjunction with computer-implemented perturbation techniques and a fully implicit time integration scheme to analyze the dependence of melt-solid interface morphology on solidification rate and dopant concentration. A sequence of transitions between cellular interfaces with different spatial and temporal oscillation frequencies is found. Stable time-periodically oscillating families of cellular melt-solid interfaces are observed as Hopf bifurcations both off of the planar family and off of oscillatory families. The role of nonequilibrium dopant segregation in driving oscillatory interface morphologies is elucidated with use of calculations for rapidly solidified antimony-doped silicon.

• Received 21 March 1986

DOI:https://doi.org/10.1103/PhysRevB.34.1746