Computer Simulation Studies of the Temperature Dependence of Domain Growth Kinetics
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COMPUTER SIMULATION STUDIES OF THE TEMPERATURE DEPENDENCE OF DOMAIN GROWTH KINETICS Kristen A. Fichthorn* and W.Henry Weinberg *Department of Chemical Engineering, Pennsylvania State University, University Park, PA 16802
**Department of Chemical Engineering, University of California, Santa Barbara, CA 93106 ABSTRACT
Understanding the kinetics of domain growth in quenched systems is a significant fundamental problem with particular relevance to materials science. The temperature dependence of domain growth has interesting manifestations which lie outside current theoretical developments. In a series of Monte Carlo studies, we have investigated and obtained a detailed resolution of the temperature dependencies of domain growth in a model of a two-dimensional, quenched, chemisorbed overlayer with a nonconserved order parameter. We discuss our findings. INTRODUCTION In thermally quenched systems, the development of long-range order is accomplished by the growth of ordered domains. When the order parameter of the system is nonconserved, the Lifschitz-Allen-Cahn (LAC) [1,2] theory provides the salient features of growth. Ordering kinetics in this theory are described by a power-law expression J(t) - (At) 1/2 , where f (t) is a characteristic length of a domain at time t and A is a proportionality factor. Although there is considerable evidence that LAC scaling holds over a wide range of temperatures in systems with a nonconserved order parameter, this theory cannot provide a complete description of domain growth. This is due, in part, to its implicit neglect of various temperature dependencies of domain growth. In the LAC theory, domain growth is temperature dependent through the proportionality factor, which contains an Arrhenius-type "kinetic coefficient". This description is not strictly valid at temperatures approaching the order-disorder phase transition temperature (Tc). As the final temperature of a quench is increased towards Tc, thermal fluctuations slow and, eventually, prevent system self-organization above Tc. Theories [3-5] of domain growth which include thermal fluctuations predict a LAC-type scaling in which the slowing down of domain growth arises through the temperature dependence of the proportionality factor. The proportionality factor can be expressed as A =waf
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Mat. Res. Soc. Symp. Proc. Vol. 237. @1992 Materials Research Society
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Here, a is a function of the surface tension and models the effect of thermal fluctuations, F is the rate of adatom hopping, and K is a constant. Although there has apparently been a successful corroboration of these theories with Monte Carlo simulations of shrinking circular domains [3,4], it is unclear whether, in all cases, theoretical developments including the surface tension provide an adequate description of domain growth at temperatures approaching zero. As the temperature of a quenched system approaches zero, the system may evolve to metastable states. At a temperature of 0 K, a freezing of domain growth will occur when these metastable states are r
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