Computer modeling of the growth kinetics of ledged interphase boundaries—II. Finite train of steps

Abstract

The time-dependent growth characteristics of a train of steps was analysed numerically using a DuFort-Frankel finite difference method as in the preceding paper. The Lagrangian interpolation scheme was utilized to track the component steps moving at different speeds. The motion of a train of two steps may be classified into two cases: Case I, at large supersaturations and at large initial interledge spacings the leading step moves faster than the trailing step and the steps grow apart; Case II, when both are relatively small, the trailing step moves faster and finally coalesces into the leading step. The critical initial spacing at which a transition between these two cases occurs was determined. In a long train of ledges the characteristics are essentially similar, but coalescence occurs successively from the trailing end, not in a pairwise fashion as has been suggested by other authors. The thickening kinetics of a γ-plate in an Al-Ag alloy were analysed directly by applying the present scheme to the collective motion of 37 Schockley partial dislocations on a broad face of the precipitate plate.