Concepts and applications of rigidity in non-crystalline solids: a review on new developments and directions

Abstract

We present the most recent developments and applications of Rigidity Theory in atomic-scale disordered materials such as glasses, liquids or amorphous solids. While the framework of rigidity, elastic phase transitions and topological constraint counting has been extensively used in glass science, its potentially wide applicability has remained difficult because of some inherent limitations of the theory. Here, we review promising methods that have been recently introduced, and which allow to overcome such limitations, and to extend these methods to the case of densified liquids or partially ordered solids, and also to the non-mean-field case. We introduce and describe a several methods based on an explicit account of temperature effects. In addition, the calculation of bond length and bond angle standard deviations is presented, accessed from molecular simulations, which allows to estimate atomic stretching and bending topological constraints as a function of pressure or temperature. These new methods are illustrated through a set of applications ranging from several archetypal glass-forming liquids (SiO2, GexSe1−x, …) to semiconductors (Si-C:H), phase change materials (Ge-Te) and cement, while also emphasizing the role of isostatic composition for the design of stable glasses with reduced ageing. Results furthermore reveal that in certain situations, adaptive isostatic phases appear, and these lead to remarkable physical properties over a finite interval in composition defining an intermediate phase. These features do not seem to be restricted to glasses, and, instead, connect to universal features found in disordered networks.