Density functional calculations of polysynthetic Brazil twinning in α-quartz

Polysynthetic Brazil twinning in α-quartz, which occurs commonly in amethyst, is interpreted in the literature as having its composition planes parallel to one of the faces of the major rhombohedron r. It is shown that, instead, the composition planes are parallel to one of the faces of the minor rhombohedron z. The proposed translation 0.4547a between neighbouring lamellae leads to binding distances and binding angles across the composition plane that differ less from their bulk values than for the translation 0.5a proposed in the literature. Density functional calculations show that the energy of the unrelaxed polysynthetic twin is lower for the proposed translation. They also show that relaxation increases the thickness of the polytwin by 4 pm per composition plane.