Microscopic theory of lattice instability and incommensurate phase transition in NaNO2

The incommensurate (IC) phase transition in NaN${\mathrm{O}}_2$ is studied on the basis of a lattice dynamical model. At finite wave vector, molecular reorientations of the N${\mathrm{O}}_2$ groups around the crystallographic $\overrightarrow{\mathrm{c}}$ axis are coupled to acoustic lattice displacements. A modulation, along the $\overrightarrow{\mathrm{a}}$ axis, of nonequilibrium expectation values of the orientational order produces a modulation of expectation values of acoustic displacements with polarization in the $\overrightarrow{\mathrm{b}}$ direction. The IC transition corresponds to a freezing-in of both types of motion. Connection with phenomenological theories is made. The temperature and wave-number behavior of diffuse x-ray scattering peaks above the IC transition is explained.