Phonon instabilities in bcc Sc, Ti, La, and Hf

The lattice dynamics of the elements Sc, Ti, La, and Hf in the bcc structure is studied using the densityfunctional linear-response theory. The elements exhibit similar phonon instabilities which cover large parts of the Brillouin zone. In particular, the entire T[11¯0]@jj0# branch, where the zone-boundary phonon is responsible for the bcc→hcp transition, and the L@ 2 3 2 3 2 3 # mode (bcc→omega) are unstable. However, the T@jjj# branch is unstable for all elements except Sc, and Ti and Sc exhibit distorted bcc energy minima not seen in the other elements.