Growth of a coherent precipitate from a supersaturated solution

Abstract

A treatment of diffusion limited growth of a coherent spherical precipitate into supersaturated solution is presented. It is found that the growth kinetics are affected by dilatational coherency strains and by compositionally induced strains in the matrix phase. Numerical solutions to the time-dependent problem are obtained and are compared to the quasistationary solution. The parabolic growth coefficient is a function of the transformation strain, partial molar volumes of the components, elastic constants in each phase, interfacial compositions and far-field composition while, in contrast, the growth coefficient in the absence of stress is a function only of the reduced supersaturation. Elastic effects shift the interfacial concentration of the matrix in the direction of the far-field concentration, reducing the effective driving force for growth. At the same time, compositionally induced strains increase the diffusive flux, increasing the growth rate.

Competition between surface energy and elastic anisotropies in the growth of coherent solid-state dendrites

“…Many of these studies have focused on the interaction of elastic fields on growth and coarsening rates of solid state particles [16,33]. These studies have shown that elas-tic effects play an important role in controlling growth rates and morphology, consistent with previous analytical predictions of Laraia et al [14] and Voorhees et al [35]. Energy minimization techniques also showed that the elastic free energy drives the interface to become unstable for mismatched elastic coefficients under both applied and self strain [18,19].…”

“…ǫ ele is calculated by consideration of the anisotropy in the strain field by substituting Equation 14 for ǫ xx + ǫ yy , giving…”

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“…In this section we calculate (following Laraia et al [125,113]) the rate of growth of a spherical inclusion of radius R in an infinite elastically isotropic matrix,…”

A coarsening model for coherent precipitates

“…The rectangle that forms initially, at D = 6.8r 0 , has edge lengths, band c, such that its aspect ratio, 1C = b/c, is 2. 25. As D increases further, the equilibrium rectangle monotonically increases in aspect ratio, steadily decreasing its elastic energy.…”