Dynamic scaling in vacancy-mediated disordering

Abstract

We consider the disordering dynamics of an interacting binary alloy with a small admixture of vacancies which mediate atom-atom exchanges. Starting from a perfectly phase-segregated state, the system is rapidly heated to a temperature in the disordered phase. A suitable disorder parameter, namely, the number of broken bonds, is monitored as a function of time. Using Monte Carlo simulations and a coarse-grained field theory, we show that the late stages of this process exhibit dynamic scaling, characterized by a set of scaling functions and exponents. We discuss the universality of these exponents and comment on some subtleties in the early stages of the disordering process.Comment: 15 pages, 6 figure

Universal aspects of vacancy-mediated disordering dynamics: The effect of external fields

“…Anticipating inhomogeneities along the y-direction only, due to the bias, we seek steady-state solutions of the form φ(r, t) = φ o (y) and ψ(r, t) = ψ o (y). Eqn (5) can now be integrated once, and the reflecting boundary conditions force the integration constant, i.e., the hole current, to zero. We can immediately integrate again, whence φ o (y) = C exp(Ey) .…”

“…Vacancy concentrations are typically extremely small (of the order of 10 −5 ). As a first step towards a deeper understanding of disordering dynamics, we will neglect any asymmetries in the microscopics of the two atom species, leaving them for consideration at a later stage [5]. Thus, our study will be based on an Ising model with a very small admixture of empty sites, namely a single vacancy, undergoing an "upquench" from zero to infinite temperature.…”