Abstract
Phonons have been measured in \ensuremath{\beta}-Ti and \ensuremath{\beta}-Zr over the whole range of existence of the high-temperature bcc phase. Low-frequency and strongly damped longitudinal phonons at q=(2/3(111) produce the necessary displacements for the martensitic \ensuremath{\beta}-\ensuremath{\omega} transition. The displacements needed for the martensitic \ensuremath{\beta}-\ensuremath{\alpha} transition are produced by low-frequency and damped transverse phonons at q=(1/2(110), which on approaching the phase transition soften further but not completely. The low-frequency and strongly damped phonons are precursor fluctuations of the \ensuremath{\alpha} or \ensuremath{\omega} phase within the \ensuremath{\beta} phase.
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