Anomalous thermal expansion of cuprites: a combined high resolution pair distribution function and geometric analysis

The temperature-dependent local structures of cuprites (M ₂O for M = Cu ¹, Ag ¹) have been probed using variable-temperature (80-500 K) high-resolution pair distribution function (PDF) analysis of X-ray scattering data measured to very high values of momentum transfer (Q _max = 35 Å ^-1). These noble metal oxides exhibit negative thermal expansion (NTH) behavior; however, several unusual structural features and behaviors distinguish the cuprites from other NTE frameworks-the structure is inverted relative to conventional NTE frameworks and CU2O (but not Ag ₂0) shows an unusual transition from negative to positive thermal expansion behavior at higher temperature-thus motivating the present in-depth analysis of the particular thermal expansion mechanisms operating here. By coupling the local structural information from the PDFs with known geometric identities of the tetrahedra that form the framework, distortions contributing to NTE have been identified and the contrasting high temperature behaviors of the two isostructural analogues have been accounted for. Specifically, we demonstrate that thermal population of low-energy vibrational modes involving the dynamic distortion of the OM4 tetrahedra, away from the regular tetrahedral geometry (through M-O-M' bending), can induce a contraction of the average tetrahedral edge length (M-"M') and thus contribute to the NTE effect. This mechanism operates in combination with the transverse vibrational mechanism found in conventional NTE frameworks, where increasing transverse displacement of the bridging atom (O-M-O') draws corner-bridged polyhedra closer together.