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

Published online by Cambridge University Press:  26 February 2011

K. R. Elder ,
B. Morin ,
M. Grant  and
R. C. Desai
K. R. Elder
Affiliation:
Centre for the Physics of Materials and Physics Department, McGill University, Rutherford Building, 3600 University Street, Montréal, Quebec, Canada H3A 2T8
B. Morin
Affiliation:
Centre for the Physics of Materials and Physics Department, McGill University, Rutherford Building, 3600 University Street, Montréal, Quebec, Canada H3A 2T8
M. Grant
Affiliation:
Centre for the Physics of Materials and Physics Department, McGill University, Rutherford Building, 3600 University Street, Montréal, Quebec, Canada H3A 2T8
R. C. Desai
Affiliation:
Department of Physics, University of Toronto, Toronto, Ontario, Canada M5S 1A7
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Abstract

An 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.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 205: Symposium F – Kinetics of Phase Transformations , 1990 , 357
Copyright
Copyright © Materials Research Society 1992

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