Time evolution of a quenched binary alloy. II. Computer simulation of a three-dimensional model system

Abstract

We present results of the computer simulation of the time evolution of a model binary alloy following quenching. Our model system is a simple cubical lattice the sites of which are occupied either by $A$ or $B$ particles. There is a nearest-neighbor interaction favoring segregation into an $A$-rich and a $B$-rich phase at low temperatures, $T<{T}_{c}$. Starting from a random configuration, $T=\ensuremath{\infty}$, the system is quenched to and evolves at a temperature ${({k}_{B}\ensuremath{\beta})}^{\ensuremath{-}1}$ where the probability of an exchange between an $A$ and $B$ atom on nearest-neighbor sites is assumed proportional to ${e}^{\ensuremath{-}\ensuremath{\beta}\ensuremath{\Delta}U}{(1+{e}^{\ensuremath{-}\ensuremath{\beta}\ensuremath{\Delta}U})}^{\ensuremath{-}1}$. $\ensuremath{\Delta}U$ is the change in energy resulting from the exchange. This depends on the configuration of the ten sites neighboring the pair of sites on which the exchange would take place. In the work reported here we used a 30\ifmmode\times\else\texttimes\fi{}30\ifmmode\times\else\texttimes\fi{}30 lattice with half the sites occupied by $A$ particles. The system was quenched to temperatures $\frac{T}{{T}_{c}}=0.6,0.8,0.9,\mathrm{and} 1.1$. Results are presented for the evolution of the Fourier transform of the spherically averaged structure function $S(k,t)$ and of the energy. Comparison is made with various theories of this process and with some experiments.