Dynamics of a two-dimensional order-disorder transition

Abstract

We present results of a Monte Carlo study of the time development of a two-dimensional order-disorder model binary alloy following a quench to low temperature from a disordered, high-temperature state. The behavior is qualitatively quite similar to that seen in a recent study of a three-dimensional system. The structure function exhibits a scaling of the form ${K}^{2}(t)S(k,T)=G(\frac{k}{K}(t))$ where the moment $K(t)$ decreases with time approximately like ${t}^{\ensuremath{-}\frac{1}{2}}$. If one interprets this moment as being inversely proportional to the domain size, the characteristic domain growth rate is proportional to ${t}^{\ensuremath{-}\frac{1}{2}}$. Additional insight into this time evolution is obtained from studying the development of the short-range order, as well as from monitoring the growth of a compact ordered domain embedded in a region of opposite order. All these results are consistent with the picture of domain growth as proposed by Lifshitz and by Cahn and Allen.