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• W2080756091 startingPage "4794" @default.
• W2080756091 abstract "In the late stages of phase separation in liquids or solids with negligible coherency stresses, the structure function S(k,t) is known to follow a scaling behavior in the form S(k,t)ensuremath{sim}${mathit{k}}_{mathit{m}}^{mathrm{ensuremath{-}}3}$(t)F(k/${mathit{k}}_{mathit{m}}$(t)), where ${mathit{k}}_{mathit{m}}$(t) is the value of k that maximizes S at a given t. Previous work has shown that, for many real systems and for three-dimensional computer models, the scaling function F(x) depends only on the volume fraction ensuremath{varphi} of the minority phase but not on the temperature T for a given ensuremath{varphi}. Results from a Monte Carlo simulation of the two-dimensional Ising model, and also from a recently published numerical solution of the two-dimensional Cahn-Hilliard equation, are shown here to give a scaling function that can be fitted, as in the three-dimensional case, by an analytical expression containing just one adjustable parameter ensuremath{gamma}ifmmode tilde{}else ~{}fi{}, independent of T but dependent on ensuremath{varphi}. We analyze and interpret some universal features of these scaling functions, including their behavior at small x and at large x, and their dependence on ensuremath{varphi}. Our discussion is based on a two-phase model, i.e., a mixture of two types of domains separated by thin interfaces, with kinetics based on the Cahn-Hilliard equation. We introduce an assumption of self-similar evolution (in the sense of self-similar probability ensembles) and show that it leads to the well-known ${mathit{t}}^{1/3}$ growth rate for the average domain size and to the above-mentioned universal properties of the scaling function. Simple geometric considerations also allow the calculation of the parameter ensuremath{gamma}ifmmode tilde{}else ~{}fi{}, so that the scaling function may be obtained without any adjustment of parameters. The influence of droplet-size distributions on the scaling function, the limit of very dilute alloys, and the temperature dependence of the coarsening rate are also considered." @default.
• W2080756091 created "2016-06-24" @default.
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• W2080756091 date "1991-09-01" @default.
• W2080756091 modified "2023-10-09" @default.
• W2080756091 title "Scaling functions, self-similarity, and the morphology of phase-separating systems" @default.
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• W2080756091 doi "https://doi.org/10.1103/physrevb.44.4794" @default.
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