Unmixing of binary alloys by a vacancy mechanism of diffusion: a computer simulation

Abstract

The initial stages of phase separation are studied for a model binary alloy (AB) with pairwise interactions ε _AA , ε _AB , ε _BB between nearest neighbors, assuming that there is no direct interchange of neighboring atoms possible, but only an indirect one mediated by vacancies (V) occurring in the system at a concentrationc _v and which are strictly conserved, as are the concentrationsc _A andc _B of the two species.A-atoms may jump to vacant sites with jump rateГ _A , B-atoms with jump rateГ _B (in the absence of interactions). Particular attention is paid to the question to what extent nonuniform distribution of vacancies affects the unmixing kinetics. Our study focuses on the special caseГ _A =Г _B on a square lattice, considering three different choices of interactions with the same ε=ε _AB − (ε _AA +ε _BB )/2: (i) ε _AB =ε, ε _AA = ε _BB = 0; (ii) ε _AA = 0, ε _AA = ε _BB ; = ∓ ε; (iii) ε _AB = ε _BB = 0, ε _AA = −2ε. We obtain both the time evolution of the structure factorS(k,t) following a quench from infinite temperature to the considered temperature, and the timedependence of the mean cluster size and the various neighborhood probabilities of a vacancy. While in case (i) forc _V ≦0.16 the distribution of vacancies in the system stays nearly random, in case (ii) the vacancies cluster in theA-B interfacial region, and in case (iii) they get nearly completely expelled from theA-rich regions. While phase separation proceeds in case (i) only slightly faster than in case (ii), a significant slowing down of the relaxation is observed for case (iii), which shows up in a strong reduction of the effective exponents describing the growth.