Refinement of the incommensurate crystal structure of NaNO2in (3+1)-dimensional space groups

Abstract

Two basic models of the incommensurate (IC) structure of NaNO2, one with purely occupational modulation and one with mixed modulation, have been tested using (3 + 1)-dimensional space groups. The refinements were performed in the two superspace groups PI m_{\bar 1} ms m1 and PI 2s ms m1. The main feature of this IC structure is the presence of the weak displacive waves superposed on the main modulating waves of the occupational type. The displacements of atoms take place only along the b axis. The amplitude of the displacive wave of the Na+ ion was found to be almost twice as large (0.077 A) as that of the NO-2 molecule (0.042 A) with the occupational amplitudes approximately the same. The best refinement yields an overall R factor of 0.063 in the PI 2s ms m1 group, revealing a small phase shift between individual waves of the Na+ ion and the NO-2 molecule. There are, however, practically no phase shifts between the two kinds of modulation waves involved. All waves were found to be harmonic.