Volume-change phase transition in solids at valence instability

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Abstract
Volume changes at the valence phase transition occur as a macroscopic mechanical instability, where only a single mode representing homogeneous expansion becomes unstable without critical phonon enhancement. As a consequence, the Landau theory of phase transitions holds exactly at the critical point in describing the transition phenomenologically. However, there is a new possibility: If crystals are allowed to change their shapes in only one direction, the acoustic mode in that direction can become critical at the transition. We examine macroscopic dynamics near the transition and point out the resemblance between the valence transition and the swelling transition in gels. The frequency-dependent specific heat is also proposed.