The intermetallic compound Ni$_{3}\mathrm{Al}$ orders in the Cu$_{3}\mathrm{Au}$ structure, and it is generally believed to be a weak itinerant ferromagnet. However, the presence of any magnetic inhomogeneities, as suggested by specific-heat measurements, cannot be easily understood within the framework of an itinerant electron theory. In the present work inelastic neutron scattering techniques have been used to study the room-temperature phonon dispersion curves of Ni$_{3}\mathrm{Al}$. The force constants obtained by fitting the experimental data to a three-nearest-neighbor Born-von K\'arm\'an model were used to evaluate the phonon density of states and the lattice specific heat. We find that the electronic specific heat of Ni$_{3}\mathrm{Al}$ (obtained by subtracting the lattice contribution from the measured total specific heat) does not exhibit any anomalous features at low temperature. Thus, within experimental precision, we do not find any evidence for the presence of magnetic inhomogeneities in Ni$_{3}\mathrm{Al}$.

Inelastic neutron scattering techniques have been used to study the lattice dynamics of hcp Hf. The phonon dispersion curves along the [001], [100], and [110] symmetry directions were determined at 295 and 1300 K, and a selected number of phonon frequencies were measured also at 800 K. As the temperatures decreases we observe a rather large increase in the frequencies of all but the [001] LO branch. The zone-center mode of the [001] LO branch, on the other hand, softens appreciably, and at room temperature this branch exhibits a dip at the zone center. These features of the phonon dispersion curves of Hf are similar to those of hcp Zr and Ti. The data were used to evaluate the lattice specific heat at constant pressure as a function of temperature. The calculated total specific heat, obtained by taking into account the electronic contribution, was found to agree, to within experimental uncertainties, with the results of specific-heat measurements. We find that the phonon anomalies (and their temperature dependence) in the dispersion curves of the superconducting elements of the IV column of the Periodic Table can be understood qualitatively as originating from the splitting about the Fermi level of doubly degenerate bands by the lattice distortion corresponding to the [001] LO mode. We argue that this mechanism may also be responsible for the phonon anomalies observed in other superconducting elements (Tc) and compounds (La${\mathrm{Sn}}_{3}$).

We measured the phonon dispersion curves of hcp Hf at 295, 800, and 1300 K. We find that (unlike the other modes) the zone center [001]LO mode softens appreciably as the temperature decreases and at room temperature this branch exhibits a dip at the zone center. This anomalous behavior is similar to that observed in hcp Zr, Ti, and Tc and seems to be characteristic of the hcp superconducting elements.

Inelastic-neutron-scattering techniques have been used to study the lattice dynamics of hcp Ti. The phonon dispersion curves along the [001], [100], and [110] symmetry directions were determined at 295, 773, and 1054 K. As the temperature decreases, we observe a rather large increase in the frequencies of all but the [001]LO branch. The zone-center mode of the [001]LO branch softens appreciably and at room temperature this branch exhibits a dip at the zone center. These features of the phonon spectrum of hcp Ti bear a striking resemblance to those of hcp Zr and seem to be characteristic of the transition metals of column IV of the Periodic Table. The data were used to evaluate the lattice specific heat at constant pressure as a function of temperature. The calculated total specific heat, obtained by taking into account the electronic contribution, was found to agree, to within experimental uncertainties, with the results of direct specific-heat measurements.

Inelastic-neutron-scattering techniques have been used to study the temperature dependence of the normal vibrational modes of hcp Zr. The phonon spectra along the [001], [100], and [110] symmetry directions were determined at 295, 773, and 1007 K. The [001] LO branch and a selected number of phonons of other branches were determined also at 5.5 K. As the temperature decreases we observe a rather large increase in the frequencies of all but the [001] LO branch. The zone-center mode of the [001] LO branch softens appreciably and at 5.5 K this branch exhibits a dip at the zone center reminiscent of the anomalous dispersion of the corresponding branch of technetium at room temperature. The data were used to evaluate the lattice specific heat at constant pressure as a function of temperature. The calculated total specific heat at constant pressure, obtained by taking into account the electronic contribution, was found to be consistent, to within experimental uncertainties, with the results of specific-heat measurements. We propose an explanation for the softening of the zone-center mode of the [001] LO branch and the large increase in the frequencies of the other modes with decreasing temperature which is based on the electronic structure of Zr.