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Calculations of the Rigid Unit Modes (RUMs) allowed in the nepheline structure are used to explain the diffuse scattering previously seen in electron diffraction experiments. The RUM calculations also show that the modulation wavelength for incommensurate nephelines is essentially determined by the framework topology. X-ray diffraction is used to measure the intensity of the diffuse scattering as a function of temperature. The diffuse intensity increases sharply at 308 K. This effect is interpreted as being due to the softening of a phonon mode, indicating a phase transition. Measurements of this phase transition below the transition temperature are made using hard mode infrared spectroscopy. [ABSTRACT FROM AUTHOR]

We consider the phase transitions in tridymite from the perspective of the rigid unit mode model. The rigid unit modes are the low-frequency phonons of a crystal structure that consists of an infinite framework of tetrahedra linked at corners, that can propagate without the tetrahedra distorting. Because they give distortions of the structure with a low energy cost they are the natural soft modes for displacive phase transitions. We consider the normal phase transition sequence in tridymite on cooling, HP LHP ..., as a successive condensation of rigid unit modes acting as soft modes. Some of the low-temperature phases (e.g. MX-1) arise as rigid unit mode distortions of the high-temperature structure and do not follow the sequence of phases found at higher temperatures. We are able to account for all the commensurate phases and some of the modulated phase within the framework of the rigid unit mode model. [ABSTRACT FROM AUTHOR]

The structure, symmetry and origin of the incommensurately modulated OS phase of tridymite (SiO2) and its lock-in to the OP three-fold superlattice structure are discussed in a computational study. The structure of the OS phase (which has not been determined experimentally) is deduced as the only geometrically possible structure derived from the parent OC phase by rotation and translation of the SiO4 tetrahedra without significant distortion of these units. It can be visualised conveniently in terms of the McConnell formalism of two component difference structures C1 and C2 whose space group symmetries are derived. The results are in accordance with the known lock-in structure at wave vector Q= a*. In the latter, the ±C1 regions expand and the structure can square up in a very general way to take advantage of the lost symmetries (lost compared with the OC phase). [ABSTRACT FROM AUTHOR]