Lattice dynamics of LaSn3

Inelastic neutron scattering techniques have been used to measure the phonon dispersion curves of La${\mathrm{Sn}}_3$ at room temperature and the frequencies of a selected number of phonons at 750 and 1200 K. We find that the frequencies of the optical modes in the vicinity of the first ${\Gamma }_{15}$ point are lower than those of the corresponding modes in the isostructural compound Ce${\mathrm{Sn}}_3$ and decrease with decreasing temperature. The similarity of these results to those obtained in the superconducting elements Zr, Ti, Hf, and Tc suggests that these anomalies are due to the splitting of the flat doubly degenerate ${\Delta }_5$ electronic bands just below $E_F$ by the lattice distortions corresponding to these modes. The force constants obtained by fitting the experimental data to a three-nearest-neighbor Born—von Kármán model were used to evaluate the phonon density of states, the lattice specific heat, and the atomic temperature factors of Ce and Sn in this compound.