Time evolution of a quenched binary alloy. III. Computer simulation of a two-dimensional model system

We present new results of computer simulations of the time evolution of a model binary alloy following quenching. Our model system is a square lattice the sites of which are occupied by one of two species of atoms, say $A$ and $B$. There is a nearest-neighbor interaction favoring segregation into an $A$-rich and a $B$-rich phase at low temperatures, $T<\mathrm{}{T}_c$. Starting with a random configuration (corresponding to an "infinite" temperature) and a 50 or 20% concentration of $A$ atoms the system is quenched to a temperature $T=0.59\mathrm{}{T}_c$ and we observe (using Monte-Carlo simulations of a nearest-neighbor exchange dynamics) the segregation into the two phases. We study the evolution of the structure function $S(k,t)\mathrm{}$ and the energy and compare their observed asymptotic behavior with theoretical power-law predictions. We also study, when there is a 20% concentration of $A$ atoms, the cluster distribution and other characteristic parameters of the $A$ droplets such as average cluster size $\overline{l}$, average cluster energy $\overline{\epsilon }$, etc. The phase segregation appears to take place in two distinct stages: (i) a "rapid" condensation of the $A$ atoms into "liquid" drops and a "gas" phase consisting of monomers, dimers, etc., and (ii) a "slow" growth of the droplets by coagulation through diffusion of large droplets and by evaporation of monomers, etc., from one droplet and their condensation on other droplets. By marking and following the clusters, a diffusion constant $D_l$ for the center of mass of clusters of size $l$ is obtained and its dependence on $l$ is studied.