Growth of a coherent precipitate from a supersaturated solution
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P.W. Voorhees Metallurgy Division, National Bureau ofStandards, Gaithersburg, Maryland 20899 (Received 26 May 1987; accepted 2 November 1987) 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 super saturation. 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.
I. INTRODUCTION Elastic deformation can influence the kinetics of precipitate growth in at least two important ways. First, the stress field alters the magnitude and symmetry of the local value of the transport or mobility tensor, B. This tensor couples the thermodynamic driving force for diffusion to the local flux of solute. Expressions relating the local stress field to changes in the magnitude and symmetry of B are well known.1 Second, the chemical or diffusion potential at a point is a function of the local state of stress. If solute fluxes are assumed proportional to gradients in the diffusion potential, the flux becomes a function of both gradients in concentration and stress. This result has significant and fundamental repurcusions in the form and nature of the governing equations for diffusion. Larche and Cahn2 have shown that if elastic self-stresses owing to compositional inhomogeneities are present, Fick's law is often invalid and the local flux becomes a functional of the composition field, i.e., the flux at a point depends implicitly on the concentration field everywhere in the system. Changes in the mobility tensor owing to elastic stress are usually small and can often be neglected in studying the kinetics of a phase transformation. However, changes in the governing field equations for diffusion owing to stress can give rise to unexpected behavior including diffusion in directions of increasing concentration.2 The coupling of stress and diffusion in singlephase media has been considered by a number of investigators.2"6 These authors show that stresses induced by compositional inhomogeneity can affect the kinetics of diffusion, the effects of which can sometimes be expressed in terms of an effective diffusion coefficient.216 J. Mater. Res. 3 (2), Mar/Apr 1988
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In addition, it has been demonstrated that elastic anisotropy can affect the symmetry of the diffusion fields in the pres
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