title: Incommensurate modulation in the microporous silica SSZ-24.
abstract: A detailed investigation of the structure of microporous silica, SSZ-24, is presented. It is shown by X-ray powder diffraction and (29)Si MAS NMR experiments that the structure deviates from the previously proposed AlPO(4)-5-type structure. At room temperature, electron diffraction (ED) patterns exhibit extra diffraction spots, which can be attributed to an incommensurate structural modulation along the c axis. This in turn results in a pleat pattern in real space with two different intervals arranged aperiodically along the c axis, as observed with high-resolution electron microscopy (HREM). The modulated structure may easily turn into a disordered one through excessive electron irradiation or heat-treatment. In order to understand the origin of the modulation, soft phonon-modes of the ideal premodulated structure were analyzed by the use of the rigid-unit-mode model. The distribution of soft modes in reciprocal space might correspond roughly to diffuse streaks that could be observed in the diffraction patterns at higher temperatures. It was found that several phonon branches soften at specific wave vectors, which are incommensurate with respect to the original period and might be responsible for the modulation. We present a simple analytic treatment to deduce the wave vectors and associated displacement eigenvectors for the incommensurate soft-modes.