Calculations for the transverseN-point phonons in bcc Zr, Nb, and Mo

Abstract

The frequencies of the transverse N-point phonons in Nb and Mo have been calculated using the first-principles frozen-phonon method. The ordering of the modes is reversed in these metals in agreement with experiment. Similar calculations for the L and $T_2$N-point phonons in the high-temperature bcc phase of Zr agree with recent measurements, while the results for the $T_1$ phonon of Zr indicate an instability toward the formation of the hcp phase.