Phonon dispersion of the bcc phase of group-IV metals. II. bcc zirconium, a model case of dynamical precursors of martensitic transitions

Abstract

The phonon dispersion of the high-temperature bcc phase of Zr has been measured at several temperatures. The longitudinal L 2/3(1,1,1) mode and the transverse ${\mathrm{T}}_{1}$ 1/2(1,1,0) mode with [11\ifmmode\bar\else\textasciimacron\fi{}0] polarization are of very low energy (i.e., of large amplitude) and overdamped. These phonons achieve the displacements necessary for two martensitic phase transitions. The L 2/3(1,1,1) phonon displaces the lattice toward the high-pressure \ensuremath{\omega} phase and the ${\mathrm{T}}_{1}$ 1/2(1,1,0) phonon shifts the bcc planes into the stacking sequence of the low-temperature hcp phase. These fluctuations are interpreted as dynamical precursors of the low-symmetry phases within the bcc phase. Elastic precursors or central peaks were not found in pure bcc Zr. Furthermore, it is shown that the bcc phase is stabilized mainly by the excess vibrational entropy due to the low-energy phonons.