The structure of the incommensurate modulated phase of NaNO₂

Abstract

The incommensurate phase of NaNO₂ is known to contain a transverse displacement modulation in addition to the modulated ferroelectric ordering, but the phase and sign of the displacement was left undetermined by the X-ray structural analysis. We discuss the phase, sign and magnitude of the displacement modulation from several points of view and build up a more detailed picture of its origin than previously. Rigorous group theoretical arguments fix the phase as zero, in contrast to the assumption of some workers, and indicate other possible aspects of the structure. The sign of the displacement is found to be positive due to the dominance of electrostatic forces and O−O repulsion over O−Na repulsion. The magnitude of the displacement seen in molecular dynamics simulations and estimated from simple atom packing agree reasonably with the X-ray value. The results confirm the displacement modulation as the essential ingredient responsible for the existence of the incommensurate phase.