Lattice vibrations in lithium nitride,Li3N

The phonon dispersion curves of the fast ionic conductor ${\mathrm{Li}}_3$N have been determined in the high-symmetry directions $\Sigma$, $\Delta$, and $T$ by coherent inelastic neutron scattering at room temperature. The elastic constants $c_{11}$, $c_{33}$, $c_{44}$, and $c_{66}$ have been determined from the slopes of the acoustic branches in the long-wavelength region. The measured dispersion curves are well reproduced by a shell model which takes into account long-range Coulomb interactions between ${\mathrm{N}}^{3-}$ and ${\mathrm{Li}}^{+}$ ions, short-range interactions between nearest-neighboring Li and N ions and an anisotropic electronic polarizability of the ${\mathrm{N}}^{3-}$ ions. The specific heat is calculated and found to be in good agreement with experiment. The two-phonon density of states is calculated and compared to the second-order Raman spectrum.