Hexagonal and tetragonal Symmetry in twinned crystals

Abstract

The authors studied the mechanism of twinning of calcite, chabazite and fluorite that occur as penetration twins. In the past, the interrelations of individual crystals of these twins were usually explained by the 180° rotation on the twin axis [0001] or [111]. Using an ideal form, in which the two individuals participating in the twin were develped into an equal size, the authors examined the symmetry axis which exists on the twin plane perpendicular to the two-fold rotation axis. It was ascertained that this plane had three two-fold symmetry axis intersecting each other at an angle of 120°, that is, the two-fold symmetry axes occur at an interval of 60°. Accordingly, the authors decided to describe these twins as the ones having six-fold symmetry axes as their principal axes, and proposed to call them hexagonal birhomb ohedron twin and hexagonal bicube twin, respectively.