Phonon Theory of Martensitic Transformation Precursors

A phonon theory of precursor phenomena in martensitic phase transformations is developed. Extending Gr\"uneisen theory of thermal expansion, this theory addresses the effects of deformation-dependent low-energy phonons on the structural, thermal, and elastic behaviors of pre-martensitic cubic crystals that undergo incomplete phonon softening. It reveals spontaneous symmetry breaking, pre-martensitic transformation, phonon domains, and tweed structure. The theory naturally explains the ubiquitous pre-transitional anomalies that are difficult to explain from conventional phase transition theories.