Kinetics of an Order-Disorder Transition in the Presence of Elastic Energies

Abstract

AbstractAn approximate late time solution to the dynamics of phase separation for a nonconserved ordering order parameter (ø) coupled to a stable conserved field (c) is presented. In the Halperin Hohenberg(1) classification scheme this model is known as Model C with a symmetric coupling between nonconserved and conserved fields. The different time dependences of long (i.e., domain size lengths ∼ power law in time) and short wavelength (i.e., interfacial lengths ∼ exponential decay in time) fluctuations imply a simple relationship between the two fields. In essence ø controls the growth of the long wavelength fluctuations, and c modifies the interfacial profile. Asymptotically the dynamic structure factor (Sø(k,t)≡<Ø(k,t)Ø*(k,t)>) for the nonconserved field is shown to scale in the form Sø(k,t) = tdnfø(ktn), with n = 1/2. Similarly the structure factor for the conserved field (Sc(k,t)) is shown to obey the scaling law Sc(k,t) = tdn−1fc(ktn), with n = 1/2. Explicit expressions for the scaling functions fc(z) and fø(z) are presented for arbitrary dimension. These predictions can be tested through scattering experiments.