Droplet Fluctuations in the Morphology and Kinetics of Martensites

We derive a coarse grained, free-energy functional which describes droplet configurations arising on nucleation of a product crystal within a parent. This involves a new `slow' vacancy mode that lives at the parent-product interface. A mode-coupling theory suggests that a {\it slow} quench from the parent phase produces an equilibrium product, while a {\it fast} quench produces a metastable martensite. In two dimensions, the martensite nuclei grow as `lens-shaped' strips having alternating twin domains, with well-defined front velocities. Several empirically known structural and kinetic relations drop out naturally from our theory.