Common origin of exotic properties in ceramic and hybrid negative thermal expansion materials

Many ceramic and hybrid metal-organic framework materials show negative thermal expansion (NTE): they \textit{contract} instead of expanding on heating \cite{Barrera_Miller_Lind_Romao 2005}. Their structures are invariably characterised as a network of polyhedral groups of atoms that are connected through sharing of corner atoms or by shared ligands. Empirically, NTE materials tend to show pressure-induced softening, pressure enhancement of NTE, and the reduction of NTE on heating. But such effects have only been investigated in a small number of materials \cite{Pantea 2006,Chapman 2005,Chapman 2007,Fangexp 2013}, and as yet there is no general framework for understanding the whole suite of properties together. By studying models with Hamiltonians chosen to reflect the physical picture generally accepted as responsible for NTE in framework materials, we demonstrate that NTE, pressure-enhanced NTE, and pressure-induced softening naturally emerge together. We then show how anharmonic interactions lead to structural warm hardening---something that has only previously been seen in laser-excited warm-dense matter \cite{Ernstorfer 2009}---as well as to the transition from NTE to positive thermal expansion and the disappearing of the pressure-induced softening at high temperatures.