Designing disorder into crystalline materials

Crystals are a state of matter characterized by periodic order. Yet, crystalline materials can harbour disorder in many guises, such as non-repeating variations in composition, atom displacements, bonding arrangements, molecular orientations, conformations, charge states, orbital occupancies or magnetic structure. Disorder can sometimes be random but, more usually, it is correlated. Frontier research into disordered crystals now seeks to control and exploit the unusual patterns that persist within these correlated disordered states in order to access functional responses inaccessible to conventional crystals. In this Review, we survey the core design principles that guide targeted control over correlated disorder. We show how these principles - often informed by long-studied statistical mechanical models - can be applied across an unexpectedly broad range of materials, including organics, supramolecular assemblies, oxide ceramics and metal-organic frameworks. We conclude with a forward-looking discussion of the exciting link between disorder and function in responsive media, thermoelectrics and topological phases.