  We present a framework to segregate the roles of elastic and non-elastic
deformations in the examination of real-space experiments of solid-solid
Martensitic transitions. The Martensitic transformation of a
body-centred-tetragonal(BCT) to a body-centred-orthorhombic(BCO) crystal
structure has been studied in a model system of micron-scale ionic microgel
colloids. Non-affine fluctuations, i.e., displacement fluctuations that do not
arise from purely elastic(affine) deformations, are detected in particle
configurations acquired from the experiment. Tracking these fluctuations serves
as a highly sensitive tool in signaling the onset of the Martensitic transition
and precisely locating particle rearrangements occurring at length scales of a
few particle diameters. Particle rearrangements associated with non-affine
displacement modes become increasingly favorable during the transformation
process. The nature of the displacement fluctuation modes that govern the
transformation are shown to be different from those predominant in an
equilibrium crystal. We show that BCO crystallites formed through shear may,
remarkably, co-exist with those resulting from local rearrangements within the
same sample.
