- © The Mineralogical Society Of America
The theoretical construction of the “Rigid Unit Mode” model arose from asking a few simple questions about displacive phase transitions in silicates (Dove 1997a,b). The simplest of these was why displacive phase transitions are so common? Another was why Landau theory should seemingly be so successful in describing these phase transitions? As the construction developed, it became clear that the model is able to describe a wide range of properties of silicates, in spite of the gross over-simplifications that appear so early in the development of the approach. In this review, we will outline the basic principles of the Rigid Unit Mode model, the experimental evidence in support of the model, and some of the applications of the model.
The Rigid Unit Mode (RUM) model was developed to describe the behavior of materials with crystal structures that can be described as frameworks of linked polyhedra. In aluminosilicates, the polyhedra are the SiO4 or AlO4 tetrahedra, and in perovskites, these may be the TiO6 octahedra. At the heart of the RUM model is the observation that the SiO4 or AlO4 tetrahedra are very stiff. One measure of the stiffness of the tetrahedra might be that the vibrations involving significant distortions of the tetrahedra have squared frequency values above 1000 THz2 (Strauch and Dorner 1993), whereas vibrations in which there are only minimal distortions of the tetrahedra and a buckling of the framework have squared frequency values of around 1 THz2 (see later). The values of the squared frequency directly reflect the force constants associated with the motions of a vibration, so clearly the stiffness of a tetrahedron is 2–3 orders of magnitude larger than the stiffness of the framework against motions in which the tetrahedra can move without distorting. This large range …