Phonon dispersion of the bcc phase of group-IV metals. III. bcc hafnium

Abstract

The phonon dispersion of the high-temperature bcc phase of Hf has been measured. The dispersion resembles very much those of the other group-IV metals: bcc Ti and bcc Zr. It is dominated by the low-energy L 2/3(1,1,1) mode and by the low-energy ${\mathrm{T}}_{1}$ [\ensuremath{\xi}\ensuremath{\xi}0] phonon branch with transverse [11\ifmmode\bar\else\textasciimacron\fi{}0] polarization. These large-amplitude vibrations displace the lattice toward the stacking sequence of the high-pressure \ensuremath{\omega} structure and the low-temperature hcp structure, respectively, and are interpreted as dynamical precursor fluctuations toward these low-symmetry phases within the high-symmetry bcc phase.