Density-functional calculations of Esterel twinning in quartz

Abstract

Models for Esterel twin interfaces with mirror and rotation symmetry are presented that satisfy stoichiometry at the composition plane. The starting points are 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 are quite significant, as the initial unrelaxed interface energy is about $15\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ above the relaxed energy for our cells containing two twin interfaces. After relaxation, bond length and bond angles are close to bulk quartz values. It was found that reflection twins have lower interface energy than rotation twins.