  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
$l\propto\sqrt{W}$ 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.
