Based on our definitions of local and global stability, we can define metastable materials more generally as materials that are locally stable, but globally unstable at a given set of conditions. Metastable materials can, in principle, transform to a lower energy state, but in many cases, they have sufficient lifetimes for preparation, characterisation, or practical applications. Common examples are anatase TiO 2 and diamond. One case is the synthesis of wurtzite-derived β-CuGaO 2 , which usually adopts a delafossite structure, by ion exchange of NaGaO Figure illustrates competing phase stability as a function of an order parameter, which for simplicity can be imagined as an atomic displacement. In the left panel, two phases are locally stable at low temperature, and the phase at negative order parameter is globally stable, whereas the other phase is metastable. With increasing temperature, the phase at positive order parameter becomes globally stable. In this case, a first order phase transition with hysteresis is expected between the two phases, since each phase will remain metastable in (part of) the temperature region, where the competing phase becomes globally stable. In the right panel, a phase at zero order parameter is both locally and globally stable at high temperature, whereas the phase at finite order parameter becomes both locally and globally stable at low temperatures. This is expected to result in a secondorder phase transition between the phases with no hysteresis. Importantly, only in the case of the left figure, the high temperature phase can be retained to low temperature, since it remains locally stable.