LATE-TIME THEORY FOR THE EFFECTS OF A CONSERVED FIELD ON THE KINETICS OF AN ORDER-DISORDER TRANSITION

The dynamics of an order-disorder transition is investigated through a nonlinear Langevin model known as model C. This model describes the dynamics of an ordering nonconserved field (e.g., sublattice concentration), phi, coupled to a nonordering conserved field (e.g., absolute concentration), c. An approximate asymptotic time-dependent solution is presented for both fields through a singular perturbative solution of the coupled nonlinear-dynamical system. In particular, analytic expressions for the dynamic structure factors [i.e., S-phi(k,t) = <phi-(k,t)-phi*(k,t)>, and S(c)(k,t) = <c(k,t)c*(k,t)>, where k is the wave vector and t is time] of both fields are presented. In the late-time regime these expressions reduce to the scaling forms S-phi-(k,t) almost-equal-to t(d/2)f-phi-(Q) and S(c)(k,t) almost-equal-to t(d/2-1)f(c)(Q), where Q = kt1/2. Furthermore it is shown that f-phi-(Q) is-proportional-to Q(-d-1), f(c)(Q) is-proportional-to Q(-d + 1) for Q >> 1 and f(c)(Q) is-proportional-to Q4 for Q << 1. Intermediate-time corrections, due to a finite interfacial width, to the asymptotic solutions of both fields are also obtained. Many of these predictions are experimentally accessible.