Lattice dynamic of Ti, Co, Tc, and other hcp transition metals

New phonon-dispersion curves as determined by inelastic neutron scattering experiments are presented for the hcp metals, Ti, Co, and Tc, along with their theoretical analysis in terms of the phenomenological charge-fluctuation model. The model was also used to reanalyze the phonon data for some other hcp metals, Sc, Y, Zr, and Hf. For all the metals other than Sc and Y it was found that the data could be successfully analyzed only with a dipolar-charge-fluctuation model in contrast to Nb which required only monopolar terms. For Sc and Y the dispersion curves were satisfactorily analyzed in terms of a third-neighbor Born — von Kármán model without any charge-fluctuation terms. The softening of the longitudinal [001] mode near $\Gamma$ observed in some of the metals appears to be closely related to an incipient instability in the electronic system toward the formation of a dipolar charge-density wave. The temperature dependence of the large anomaly in Tc could be reproduced by extremely small changes in one of the parameters of the dipolar-charge-fluctuation model.