Models for Esterel twin interfaces with mirror and rotation symmetry were presented that satisfy stoichiometry at the composition plane. The starting points were unrelaxed models constructed from bulk quartz crystal and keeping the bulk volume per formula unit. The proposed unrelaxed models also maintain the fourfold coordination of all Si atoms and the twofold coordination of the O atoms, albeit with significant variation of bond length and bond angles at the composition plane. More realistic atomic positions were sought with density functional calculations. Relaxation energies were quite significant, as the initial unrelaxed interface energy was about 15eV above the relaxed energy for cells containing 2 twin interfaces. After relaxation, bond length and bond angles were close to bulk quartz values. It was found that reflection twins had a lower interface energy than rotation twins.

Density-Functional Calculations of Esterel Twinning in Quartz. B.Delley, H.Grimmer: Physical Review B, 2007, 76[22], 224106 (6pp)