Computer modeling of the growth kinetics of ledged interphase boundaries—I. Single step and infinite train of steps

Abstract

A computer model of the DuFort-Frankel finite difference method was developed to simulate the motion of a single step and of an infinite train of steps. Volume diffusion of solute in the matrix to the riser of the step was assumed to control the growth rate. The results for a single step are fully consistent with the Atkinson analysis, based upon the steady state diffusion field equation, and in a limited range of supersaturation also with the Jones-Trivedi results reported earlier. At long reaction times the growth rate of an infinite train of equally spaced steps became nearly proportional to t −1 2 , the time dependence of the growth kinetics of a planar disordered boundary. The thickening by the former mechanism can be faster than that by the latter when the interledge spacings are smaller than about four times the step height. Scatter in the interledge spacing among precipitate plates formed in the same specimen can account fairly well for the variations in observed thickening rates. However, simulation of thickening by an infinite train of steps proves to be not always appropriate for analyzing the actual kinetics over long reaction times.