Tetrahedral honeycomb surface reconstructions of quartz, cristobalite and stishovite.

Crystalline silica (SiO2 ) is a major material used in many technologies, yet the exact surface structures of silica polymorphs are still mostly unknown. Here we perform a comprehensive study of surface reconstructions of α-cristobalite (001), α-quartz (001) and stishovite (110) and (100) using evolutionary algorithm USPEX in conjunction with ab initio calculations. We found the well-known "dense surface" to be among low-energy reconstructions of α-quartz (001), as well as its previously proposed distorted version, which we call "shifted surface". For cristobalite and stishovite we show the formation of reconstructions without dangling bonds which share common features with well-known "dense surface" of α-quartz (001). We call them "dense cristobalite" and "dense stishovite" - all of these have honeycomb arrangements of corner-sharing SiO4 -tetrahedra in the surface layers. These tetrahedral honeycombs have very low surface energies, and such tetrahedral surface pattern is observed even in stishovite (the bulk structure of which has SiO6 -octahedra, rather than SiO4 -tetrahedra).