Morphology of coherent precipitates via a discrete atom method

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Morphological evolution of coherent precipitates is analyzed by means of a discrete atom method, which is based on classical statistical mechanics and linear elasticity. Precipitates having a dilatational misfit strain and elastic constants different from those of the matrix phase are treated in dislocation-free, anisotropic elastic systems. In the first part, precipitate shapes in a three-phase system are studied under a plane strain condition. It is found that envelopment of one phase by another phase can have its origin entirely in strain energy reduction, even if the competing interfacial energies are similar to each other. If a hard particle has a misfit strain and a soft particle is misfit-free, the soft particle envelopes the hard particle, producing a concentric double-ring equilibrium shape. This is also true when the signs of the misfit strains are opposite. If a soft particle has a misfit strain and a hard one is misfit-free, the soft particle migrates away from the hard particle due to the coherency-induced image force. If both phases have misfit strains of the same sign, the soft particle wets partially the hard particle, but its other end stretches away from the hard particle. Employing a face centered cubic as a basis lattice, the discrete atom method is then extended to the three-dimensional case. The features predicted by the previous, two-dimensional model are reproduced. In an isotropic system with a purely dilatational strain, a hard coherent particle takes on a spherical equilibrium shape, while a soft particle tends to have a plate-like equilibrium shape. In an anisotropic system with Zener's ratio, A = 2.33, a soft precipitate shows a series of shape transitions from a radial to four-fold, then to two-fold symmetry. The four-fold shape is concave cuboidal, and is of transient nature, as it is later replaced with a convex plate. The hard particle, however, maintains a convex, cuboidal equilibrium shape. Under an applied tensile stress, a soft particle with a positive misfit strain tends to become a plate perpendicular to the applied stress axis, while a hard particle elongates along the stress direction. If the elastic interaction between the applied stress and the coherency strain is strong enough, precipitates often split into smaller particles and then follow coarsening. © 1997 Elsevier Science S.A.

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Materials Science and Engineering A