Non-affine fields in solid-solid transformations: the structure and stability of a product droplet.

We describe the microstructure, morphology, and dynamics of growth of a droplet of martensite nucleating in a parent austenite during a solid-solid transformation, using a Landau theory written in terms of both conventional affine elastic deformations and non-affine deformations. Non-affineness, φ, serves as a source of strain incompatibility and screens long-ranged elastic interactions. It is produced wherever the local stress exceeds a threshold and anneals diffusively thereafter. Using a variational calculation, we find three types of stable solution (labeled I, II, and III) for the structure of the product droplet, depending on the stress threshold and the scaled mobilities of φ parallel and perpendicular to the parent-product interface. The profile of the non-affine field φ is different in these three solutions: I is characterized by a vanishingly small φ, II admits large values of φ localized in regions of high stress within the parent-product interface, and III is a structure in which φ completely wets the parent-product interface. The width l and size W of the twins follow the relation l is proportional to √W in solution I; this relation does not hold for II or III. We obtain a dynamical phase diagram featuring these solutions, and argue that they represent specific solid-state microstructures.