Lattice dynamics of cubicNaNbO3: An inelastic neutron scattering study

Abstract

The phonon-dispersion relations for cubic ${\text{NaNbO}}_{3}$ have been determined along the [100], [110], and [111] directions using inelastic neutron scattering. A simultaneous softening of transverse acoustic (TA) phonon modes occurs at the zone-boundary $M(0.5,0.5,0)$ and $R(0.5,0.5,0.5)$ points, indicating the instabilities of in-phase and out-of-phase rotations of the oxygen octahedra about the [001] direction. These zone-boundary modes exhibit an extremely gradual softening as the temperature is lowered toward ${T}_{c1}=913\text{ }\text{K}$. The inelastic diffuse scattering at the $M(0.5,0.5,0)$ point polarized along the $[1\overline{1}0]$ direction remains up to 9 meV, whereas the inelastic diffuse scattering at the $M$ point polarized along the [001] direction is suppressed. Polarization dependence shows that the inelastic diffuse scattering at the $M$ and $R$ points originates from the dynamical motion of oxygen octahedra. The transverse optic (TO) phonon modes along the [110] direction polarized with the [001] direction also soften around $\mathbf{q}=[0.15,0.15,0]$ and merge into the lower-energy TA phonon modes. This is basically similar to the waterfall phenomenon observed for Pb-based perovskite relaxor ferroelectrics. The extreme broad longitudinal acoustic (LA) and TA modes in ${\text{NaNbO}}_{3}$ contribute significantly to the inelastic diffuse scattering around Bragg points. The broadening of TA and TO modes are attributed to the anharmoic lattice potential in ${\text{NaNbO}}_{3}$. The coexistence of long-wavelength and zone-boundary phonon instabilities above ${T}_{c1}=913\text{ }\text{K}$ is closely related to the complex sequence of phase transitions in ${\text{NaNbO}}_{3}$.