We review a number of features of diffusionless structural transformations in materials where phonon dispersion or elastic constants are highly anisotropic and have anomalously low values in a few directions. Though those may change with temperature, they neither soften significantly nor become harmonically unstable at a transition. Standard soft-mode theory is not applicable. Instead, a generic first-order Landau-model free energy describes most of the features found experimentally, including limited phonon softening and precursor fluctuations (e.g., ‘‘central peak’’). The microscopic basis of such models is demonstrated using anharmonic many-body phonon theory. The ideas are illustrated for ω phase transitions in zirconium.

• Received 14 September 1988

DOI:https://doi.org/10.1103/PhysRevB.39.3047