Framework structure crystalline materials and Rigid Unit Modes (RUMs). Introducing the new concept of MLRUMs and skeletions Authors

This article reviews Framework Structures (FWSs), defined as crystalline materials built of rigid AXn polyhedra sharing vertices (like perovskites, tungsten bronzes, Dion-Jacobson, Ruddlesden-Popper, and Aurivillius phases, quartz, silicates, and others), and their pecularities resulting from this linkage. The situation of rigid units linked by common vertices may allow the units to accomplish concordant rotations without deformation, which gives rise to soft phonon modes called “Rigid Unit Modes” (RUMs). The condensation of a RUM can trigger structural phase transitions to a structure of lower symmetry, with tilted polyhedra, at the origin of spontaneous ferroic or multiferroic properties. We overview results precedently obtained on RUMs in perovskites, tetragonal tungsten bronzes, and quartz, and detail new results on “maximally localized RUMs” (MLRUMs), a fundamental new concept in the physics of RUMs. We introduce also the related new concept of “skeletions” that allows to generate all ferroelastic phases found in these systems, and generalizes the Glazer's tilt-system approach.