Structural phase transitions with little phonon softening and first-order character

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.