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

Abstract

We present results of computer simulations of the time evolution of a model binary alloy following quenching. Our model system is a simple cubic lattice each site of which is occupied by either an $A$ or a $B$ atom. There is a nearest-neighbor interaction which favors segregation into an $A$-rich and a $B$-rich phase at a point inside the two-phase region. Starting from a random configuration the system is quenched to and evolves at a finite temperature $T$ as exchanges between atoms on nearest-neighbor sites are allowed to take place. In our present study, a lattice having a 20% concentration of $A$ atoms (${\overline{n}}_A=0.20\mathrm{}$), was quenched to temperatures $T=0.6\mathrm{}{T}_c$ and $T=0.9\mathrm{}{T}_c$, inside the two-phase region, and to $T=1.1\mathrm{}{T}_c$. We study the evolution of the spherically averaged structure function $S(k,t)\mathrm{}$, the energy, and various cluster properties, and compare our results with relevant theoretical predictions. We also compare the late time cluster distributions of small clusters for $T=0.6\mathrm{}{T}_c$ and $T=0.9\mathrm{}{T}_c$ with the equilibrium cluster distributions for corresponding temperatures on the coexistence curve (namely, ${\overline{n}}_A=0.0146\mathrm{}$ at $T=0.6\mathrm{}{T}_c$, and ${\overline{n}}_A=0.1272\mathrm{}$ at $T=0.9\mathrm{}{T}_c$). This shows that the phase segregation at $T=0.6\mathrm{}{T}_c$ takes 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. At $T=0.9\mathrm{}{T}_c$ (which is well inside the "classical" metastable region) such a segregation still seems to take place but at a slower rate.