Coarsening of self-stressed plates
by
W.C. Johnson and P.H. Leo
in
Scripta materialia, 43, pp. 1027 - 1032, 2000.
Category: Journal Article
Keywords: Phase transformations (spinodal decomposition); Theory and modeling (kinetics;
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Abstract:
In recent work [1], Cahn and Kobayashi (CK) examined one-dimensional spinodal decomposition in coherently self-stressed thin plates. In these systems, the lattice parameter is assumed to depend linearly on composition, so that diffusion through the thickness of the plate generates compositional strains which, in turn, affect the diffusional flux. CK observed that in the initial stages of decomposition, alternating layers of the two phases form consistent with spinodal decomposition. At later stages, the microstructure evolves by the rapid thickening of a single layer of a different phase from each of the two surfaces of the plate. Moreover, this thickening from the surfaces (termed coarsening by CK) is accompanied by bending of the plate to relieve a portion of the elastic energy. In this Letter, we employ a simple approximation to derive an expression for the time rate-of-change of the thickness of the surface phase, which we call the coarsening rate. We show that in the asymptotic limit of long times, the thickness of the end phase is linearly proportional to time, while the coarsening rate is proportional to the square of the compositional strain and inversely proportional to the film thickness. We present some results from numerical simulations for different compositional strains and film thicknesses which show good agreement with the analytic predictions.
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