Anomalous crystal growth of a binary chain.

Abstract

Crystal growth in a two-component chain is studied by Monte Carlo simulation. The mean displacement 〈n(t)〉 of the solid-liquid interface is found proportional to the time t in a one-phase region, and to ${\mathit{t}}_{1}^{\ensuremath{\nu}}$ in a two-phase coexistence region with an exponent ${\ensuremath{\nu}}_{1}$ being smaller than 1, and decreasing on leaving the phase boundary. The variance \ensuremath{\sigma}(t) deviates from the linearity in time at a lower concentration in the one-phase region. This dynamical transition is related to the change of the probability distribution P(n,t). In the one-phase region the peak of P shifts steadily, whereas in the two-phase region P is scaled only by the width. Even though the model has a finite backward jump probability, the obtained behaviors of 〈n(t)〉, \ensuremath{\sigma}(t), and P(n,t) agree with those of the one-dimensional random directed walk.