Finding stable $\alpha$-quartz (0001) surface structures via simulations

Reconstruction of $\alpha$-quartz (0001) surfaces is studied using combined classical molecular dynamics and density functional theory. Five reconstruction patterns are identified, including three (2 $\times$ 1) patterns and two (1 $\times$ 1) patterns. The energetically most stable surface structure is found to be a (2 $\times$ 1) reconstruction pattern, and several patterns can co-exist in a large scale surface. A combination of structures can explain the experimentally observed (2 $\times$ 2) diffraction pattern.