  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.
