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Diffusional Phase Transformations in Elastic Solids

Diffusional transformations occur when the temperature of a uniform mixture of materials is lowered into a regime where the uniform mixture is unstable. The system responds by nucleating second phase precipitates (e.g. crystals) that then evolve diffusionally until the process either reaches equilibrium or is quenched by further reducing the temperature. The diffusional evolution consists of two phasesgrowth and coarsening. Growth occurs in response to a local supersaturation in the primary (matrix) phase and a local mass balance relation is satisfied at each precipitate interface. Coarsening occurs when a global mass balance is achieved and involves a dynamic rearrangement of the fixed total mass in the system so as to minimize a global energy. Typically, the global energy consists of the surface energy. If the transformation occurs between components in the solid state, there is also an elastic energy that arises due to the presence of a misfit stress between the precipitates and the matrix as their crystal structures are often slightly different.

Diffusional phase transformations are responsible for producing the material microstructure, i.e. the detailed arrangement of distinct constituents at the microscopic level. The details of the microstructure greatly influence the material properties of the alloy (i.e., stiffness, strength, and toughness). In many alloys, an in situ coarsening process can occur at high temperatures in which a dispersion of very small precipitates evolves to a system consisting of a few very large precipitates in order to decrease the surface energy of the system. This coarsening severely degrades the properties of the alloy and can lead to in service failures. The details of this coarsening process depend strongly on the elastic properties and crystal structure of the alloy components. Thus, one of the goals of this line of research is to use elastic stress to control the evolution process so as to achieve desirable microstructures.

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