What term describes the vibrational lattice mode that turns to 0 frequency at the change? [SEP] Likewise, group theory helps predict the changes in physical properties that occur when a material undergoes a phase transition, for example, from a cubic to a tetrahedral crystalline form.
entailment not_entailment entailment not_entailment entailment not_entailment not_entailment entailment not_entailment entailment entailment entailment entailment entailment not_entailment entailment entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment entailment not_entailment entailment entailment entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment entailment entailment not_entailment entailment entailment not_entailment entailment entailment not_entailment entailment not_entailment entailment not_entailment not_entailment not_entailment entailment entailment entailment not_entailment entailment entailment not_entailment entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment entailment not_entailment entailment not_entailment entailment not_entailment entailment entailment entailment not_entailment not_entailment not_entailment entailment entailment entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment not_entailment entailment entailment entailment entailment entailment entailment not_entailment entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment entailment not_entailment entailment entailment entailment entailment entailment entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment entailment entailment entailment entailment entailment not_entailment entailment entailment entailment not_entailment not_entailment entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment entailment not_entailment entailment entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment entailment entailment entailment entailment not_entailment not_entailment entailment not_entailment entailment not_entailment entailment not_entailment entailment not_entailment not_entailment not_entailment entailment not_entailment entailment entailment not_entailment not_entailment not_entailment entailment not_entailment entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment entailment entailment entailment entailment not_entailment entailment entailment entailment not_entailment entailment entailment not_entailment entailment not_entailment entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment not_entailment entailment entailment not_entailment not_entailment not_entailment entailment not_entailment entailment entailment entailment not_entailment entailment entailment not_entailment entailment not_entailment not_entailment entailment entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment entailment entailment entailment not_entailment not_entailment entailment not_entailment not_entailment entailment entailment entailment entailment entailment not_entailment not_entailment not_entailment entailment not_entailment not_entailment entailment entailment entailment not_entailment entailment entailment entailment not_entailment not_entailment not_entailment entailment entailment entailment not_entailment entailment not_entailment entailment entailment not_entailment not_entailment entailment entailment not_entailment entailment not_entailment entailment entailment not_entailment entailment entailment entailment not_entailment entailment entailment entailment entailment not_entailment entailment not_entailment entailment not_entailment entailment entailment not_entailment entailment entailment entailment not_entailment not_entailment entailment entailment entailment not_entailment not_entailment entailment not_entailment not_entailment entailment not_entailment not_entailment entailment entailment entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment entailment not_entailment not_entailment not_entailment entailment entailment entailment not_entailment entailment entailment entailment entailment entailment not_entailment not_entailment not_entailment entailment not_entailment entailment not_entailment entailment not_entailment not_entailment not_entailment entailment not_entailment entailment not_entailment not_entailment not_entailment entailment entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment entailment not_entailment entailment not_entailment entailment not_entailment entailment not_entailment not_entailment entailment entailment entailment entailment not_entailment entailment entailment not_entailment not_entailment not_entailment entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment entailment not_entailment not_entailment entailment entailment entailment entailment not_entailment not_entailment entailment entailment not_entailment entailment entailment entailment not_entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment entailment entailment not_entailment entailment entailment entailment not_entailment entailment not_entailment not_entailment entailment not_entailment not_entailment entailment entailment entailment not_entailment entailment not_entailment entailment entailment entailment not_entailment not_entailment entailment entailment entailment entailment not_entailment entailment not_entailment entailment not_entailment entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment entailment entailment not_entailment not_entailment not_entailment entailment entailment not_entailment entailment entailment entailment not_entailment entailment not_entailment not_entailment entailment not_entailment entailment entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment not_entailment entailment entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment entailment entailment not_entailment not_entailment not_entailment entailment not_entailment not_entailment entailment entailment entailment not_entailment not_entailment entailment entailment not_entailment entailment not_entailment not_entailment entailment entailment entailment entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment entailment entailment not_entailment not_entailment not_entailment not_entailment entailment entailment entailment not_entailment entailment entailment not_entailment entailment not_entailment entailment not_entailment not_entailment entailment entailment not_entailment entailment not_entailment not_entailment entailment not_entailment entailment entailment not_entailment entailment not_entailment entailment entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment entailment entailment not_entailment not_entailment not_entailment entailment entailment not_entailment entailment not_entailment entailment entailment not_entailment not_entailment not_entailment entailment entailment entailment entailment not_entailment entailment not_entailment entailment not_entailment entailment not_entailment entailment not_entailment entailment not_entailment entailment not_entailment entailment entailment entailment not_entailment not_entailment entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment entailment not_entailment not_entailment entailment entailment not_entailment not_entailment entailment entailment entailment entailment entailment entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment entailment not_entailment not_entailment entailment not_entailment entailment entailment entailment not_entailment entailment entailment not_entailment entailment not_entailment entailment not_entailment not_entailment entailment entailment not_entailment entailment not_entailment entailment entailment entailment entailment not_entailment entailment not_entailment not_entailment entailment entailment not_entailment entailment entailment entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment entailment entailment entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment entailment entailment entailment entailment not_entailment not_entailment not_entailment entailment entailment entailment entailment not_entailment entailment not_entailment entailment not_entailment not_entailment entailment not_entailment not_entailment entailment not_entailment entailment entailment not_entailment not_entailment not_entailment entailment entailment not_entailment not_entailment entailment entailment entailment entailment entailment entailment not_entailment not_entailment entailment not_entailment entailment entailment entailment entailment entailment entailment entailment not_entailment not_entailment entailment not_entailment entailment not_entailment entailment entailment entailment entailment entailment not_entailment not_entailment not_entailment entailment not_entailment entailment not_entailment entailment entailment entailment entailment not_entailment not_entailment entailment entailment not_entailment entailment entailment entailment not_entailment not_entailment entailment not_entailment entailment entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment entailment entailment not_entailment not_entailment not_entailment not_entailment entailment entailment entailment entailment entailment not_entailment entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment entailment not_entailment entailment not_entailment entailment not_entailment not_entailment not_entailment entailment entailment entailment entailment entailment not_entailment entailment not_entailment not_entailment entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment entailment not_entailment entailment entailment entailment entailment entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment entailment entailment not_entailment not_entailment not_entailment entailment not_entailment entailment entailment not_entailment not_entailment entailment not_entailment not_entailment entailment not_entailment not_entailment entailment entailment entailment not_entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment entailment entailment entailment entailment not_entailment entailment entailment not_entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment entailment entailment entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment entailment not_entailment not_entailment entailment not_entailment entailment entailment entailment not_entailment not_entailment entailment entailment not_entailment entailment entailment not_entailment entailment entailment entailment not_entailment not_entailment entailment entailment not_entailment not_entailment entailment not_entailment entailment not_entailment entailment not_entailment not_entailment entailment entailment not_entailment entailment entailment entailment entailment not_entailment not_entailment entailment entailment entailment entailment entailment not_entailment not_entailment entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment entailment entailment entailment entailment not_entailment not_entailment entailment entailment not_entailment entailment entailment entailment not_entailment not_entailment not_entailment entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment entailment not_entailment not_entailment entailment not_entailment entailment entailment not_entailment entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment not_entailment entailment entailment not_entailment entailment not_entailment not_entailment entailment entailment entailment entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment entailment not_entailment entailment entailment not_entailment entailment not_entailment not_entailment entailment entailment entailment entailment not_entailment entailment entailment entailment entailment entailment entailment not_entailment entailment entailment not_entailment entailment entailment entailment entailment entailment entailment entailment entailment not_entailment entailment entailment entailment entailment not_entailment entailment entailment not_entailment entailment not_entailment not_entailment not_entailment entailment entailment not_entailment entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment entailment entailment entailment entailment not_entailment not_entailment not_entailment entailment entailment not_entailment not_entailment not_entailment entailment not_entailment entailment entailment entailment entailment entailment not_entailment not_entailment entailment not_entailment entailment not_entailment entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment entailment entailment not_entailment not_entailment not_entailment entailment not_entailment entailment not_entailment entailment entailment not_entailment entailment entailment entailment not_entailment not_entailment entailment not_entailment entailment not_entailment not_entailment entailment entailment not_entailment entailment not_entailment entailment not_entailment entailment not_entailment not_entailment entailment entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment entailment entailment not_entailment entailment not_entailment entailment not_entailment entailment not_entailment not_entailment entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment entailment not_entailment not_entailment entailment entailment entailment not_entailment not_entailment not_entailment entailment not_entailment entailment entailment not_entailment not_entailment entailment entailment entailment not_entailment not_entailment not_entailment not_entailment entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment entailment not_entailment entailment not_entailment not_entailment not_entailment entailment not_entailment entailment entailment not_entailment not_entailment not_entailment entailment entailment not_entailment entailment entailment not_entailment entailment not_entailment entailment not_entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment entailment entailment entailment not_entailment entailment not_entailment not_entailment entailment not_entailment not_entailment entailment not_entailment entailment not_entailment entailment entailment entailment not_entailment entailment not_entailment not_entailment not_entailment entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment entailment not_entailment entailment not_entailment not_entailment entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment entailment not_entailment entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment entailment entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment entailment entailment entailment not_entailment entailment not_entailment entailment not_entailment entailment not_entailment not_entailment entailment not_entailment entailment entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment entailment entailment entailment entailment not_entailment entailment entailment not_entailment not_entailment not_entailment entailment entailment entailment not_entailment entailment not_entailment entailment not_entailment entailment entailment not_entailment entailment not_entailment entailment entailment entailment not_entailment entailment not_entailment not_entailment entailment not_entailment not_entailment entailment entailment entailment entailment not_entailment entailment entailment entailment not_entailment entailment entailment entailment not_entailment not_entailment entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment not_entailment entailment entailment entailment not_entailment not_entailment entailment entailment not_entailment entailment not_entailment entailment not_entailment not_entailment not_entailment entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment entailment entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment entailment not_entailment entailment entailment entailment entailment entailment entailment not_entailment not_entailment not_entailment entailment entailment not_entailment not_entailment entailment entailment entailment entailment not_entailment not_entailment not_entailment not_entailment entailment entailment not_entailment not_entailment entailment entailment not_entailment entailment entailment entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment entailment entailment entailment entailment entailment not_entailment not_entailment entailment not_entailment entailment not_entailment entailment entailment not_entailment entailment not_entailment entailment entailment not_entailment not_entailment entailment entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment entailment not_entailment entailment entailment not_entailment entailment not_entailment not_entailment entailment not_entailment entailment not_entailment entailment entailment not_entailment entailment not_entailment not_entailment entailment entailment entailment entailment entailment entailment not_entailment entailment entailment not_entailment entailment entailment not_entailment not_entailment not_entailment entailment entailment not_entailment entailment entailment entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment entailment entailment entailment entailment entailment not_entailment entailment entailment entailment not_entailment entailment not_entailment entailment not_entailment entailment entailment not_entailment entailment entailment entailment entailment entailment not_entailment not_entailment entailment not_entailment entailment entailment not_entailment entailment not_entailment entailment not_entailment entailment entailment not_entailment entailment entailment entailment entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment entailment not_entailment entailment not_entailment entailment entailment entailment entailment entailment entailment entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment not_entailment entailment entailment entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment not_entailment entailment entailment entailment not_entailment entailment not_entailment not_entailment not_entailment entailment not_entailment entailment entailment not_entailment entailment not_entailment not_entailment entailment entailment not_entailment not_entailment entailment entailment not_entailment entailment entailment not_entailment entailment entailment entailment entailment entailment entailment not_entailment not_entailment not_entailment entailment not_entailment entailment entailment entailment not_entailment entailment not_entailment entailment not_entailment not_entailment entailment entailment entailment not_entailment not_entailment entailment entailment entailment not_entailment entailment entailment not_entailment entailment entailment entailment entailment not_entailment entailment entailment not_entailment not_entailment not_entailment not_entailment entailment entailment not_entailment entailment not_entailment not_entailment entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment entailment not_entailment not_entailment entailment entailment entailment entailment not_entailment not_entailment entailment entailment entailment entailment not_entailment not_entailment not_entailment entailment not_entailment entailment not_entailment entailment entailment entailment entailment not_entailment entailment not_entailment entailment entailment entailment not_entailment entailment entailment not_entailment not_entailment entailment not_entailment not_entailment entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment entailment not_entailment not_entailment entailment entailment entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment entailment entailment not_entailment not_entailment not_entailment entailment entailment not_entailment entailment entailment not_entailment not_entailment not_entailment entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment entailment not_entailment not_entailment entailment not_entailment entailment entailment entailment entailment not_entailment not_entailment entailment entailment entailment entailment not_entailment not_entailment entailment entailment not_entailment not_entailment not_entailment entailment entailment entailment not_entailment entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment entailment entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment entailment entailment not_entailment not_entailment entailment entailment not_entailment entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment entailment not_entailment entailment entailment not_entailment not_entailment not_entailment entailment not_entailment entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment entailment not_entailment entailment not_entailment not_entailment not_entailment entailment not_entailment entailment entailment not_entailment not_entailment not_entailment entailment not_entailment entailment not_entailment not_entailment entailment entailment not_entailment not_entailment not_entailment entailment entailment not_entailment entailment entailment not_entailment entailment not_entailment not_entailment entailment entailment not_entailment not_entailment entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment entailment not_entailment not_entailment entailment entailment not_entailment not_entailment entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment entailment entailment not_entailment not_entailment entailment entailment not_entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment entailment entailment not_entailment not_entailment entailment not_entailment