Dynamics of Step Doubling: Simulations for a Simple Model and Comparison with Experiment

To interpret recent experiments on the dynamics of step doubling, we have studied a simple model of this phase transition. With Monte Carlo, we compute the time-dependence of the order parameter in the limit of rapid diffusion across terraces. Analysis of the data shows that the limiting step is the time for adjacent steps to touch each other; subsequent “zipping” together happens rapidly. From this vantage we develop an analytic expression for short times that changes into a phenomenological one for later times. Using data from two physical systems, we compare this function and another based on naive assumptions with a third based on chemical rate theory. For the more recent data, our expression describes the data best. Finally, in the opposite limit in which atoms can only move along step edges, we show characteristic configurations and compute the structure factor.