The rigid unit mode model: review of ideas and applications

We review a set of ideas concerning the flexibility of network materials, broadly defined as structures in which atoms form small polyhedral units that are connected at corners. One clear example is represented by the family of silica polymorphs, with structures composed of corner-linked SiO₄tetrahedra. The rigid unit mode (RUM) is defined as any normal mode in which the structural polyhedra can translate and/or rotate without distortion, and since forces associated with changing the size and shape of the polyhedra are much stronger than those associated with rotations of two polyhedra around a shared vertex, the RUMs might be expected to have low frequencies compared to all other phonon modes. In this paper we discuss the flexibility of network structures, and how RUMs can arise in such structures, both in principle and in a number of specific examples of real systems. We also discuss applications of the RUM model, particularly for our understanding of phenomena such as displacive phase transitions and negative thermal expansion in network materials.