Calculation of anomalous phonons and the hcp-bcc phase transition in zirconium

Using molecular dynamics with a many-body potential fitted to properties of zirconium we study the behavior of phonons at high temperature in the bcc lattice; in particular, the T1N mode which according to the Nishiyama-Wassermann mechanism is the cause of the martensitic transition to hcp in group-IV transition metals. This phonon frequency softens towards the transition but does not tend to zero frequency. In contrast to the fast kinetics of the bcc→hcp transition, the reverse process, i.e., hcp→bcc, is not observed in standard molecular dynamics: it can be induced if the T1N phonon is perturbatively excited in the martensitic phase. The sluggishness of the reverse process is attributed to the fact that in the low-temperature hcp phase, the equivalent oscillation to T1N involves two modes with different frequency. The bcc to hcp transition is a first-order transition and occurs in such a way that most of the reversed bcc atoms obey Nishiyama-Wassermann rules, i.e., the path of transformation is reversible. However, there is some plastic damage which is not recovered.