The thermal conductivities of crystals and glasses vary strongly and with opposite trends upon heating, decreasing in crystals and increasing in glasses. Here, we show---with first-principles predictions based on the Wigner transport equation and thermoreflectance experiments---that the dominant transport mechanisms of crystals (particle-like propagation) and glasses (wave-like tunnelling) can coexist and compensate in materials with crystalline bond order and nearly glassy bond geometry. We demonstrate that ideal compensation emerges in silica tridymite, carved from a meteorite found in Steinbach (Germany) in 1724, and yields a ‘Propagation-Tunneling-Invariant’ (PTI) conductivity that is independent of temperature and intermediate between the opposite trends of α-quartz crystal and silica glass. We show how such PTI conductivity occurs in the quantum regime below the Debye temperature, and can largely persist at high temperatures in a geometrically amorphous tridymite phase found in refractory bricks fired for years in furnaces for steel smelting. Overall, we elucidate how disorder in the bond geometry determines the macroscopic conductivity, providing guidance to design materials for heat management, electronics, and phononics. We discuss implications to heat transfer in solids exposed to extreme temperature variations, ranging from planetary cooling to heating protocols to reduce the carbon footprint of industrial furnaces.

This record contains the atomic structures studied of α-quartz crystal, average (AV) tridymite, monoclinic (MC) meteoritic tridymite, Topologically Ordered and Geometrically Amorphous (TOGA) HP tridymite, and silica glass.