We describe the microstructure, shape 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 conventional affine, elastic deformations and {em non-affine} degrees of freedom. Non-affineness, $phi$, 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. A description in terms of $phi$ is inevitable when the separation between defect pairs, possibly generated during the course of the transformation, is small. Using a variational calculation, we find three types of stable solutions ({hv I}, {hv II} and {hv III}) for the structure of the product droplet depending on the scaled mobilities of $phi$ parallel and perpendicular to the parent-product interface and the stress threshold. In {hv I}, $phi$ is vanishingly small, {hv II} involves large $phi$ localized in regions of high stress within the parent-product interface and {hv III} where $phi$ completely wets the parent-product interface. While width $l$ and size $W$ of the twins follows $lproptosqrt{W}$ in solution {hv I}, this relation does not hold for {hv II} or {hv III}. We obtain a dynamical phase diagram featuring these solutions and argue that they represent specific microstructures such as twinned or dislocated martensites.
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