Unusual Solutions of Twinning Equations in the X-ray Theory

Abstract

Typically, solutions of twinning equations for crystals require the interface to be a definite plane and are only applicable to a limited set of lattice vectors. To be presented are solutions for which the possible interfaces form an infinite set, any one being either a plane or of zigzag form, consisting of pieces of planes. Also, there are a few solutions valid for arbitrary lattice vectors. I complete the characterization of all of these. Further, I discuss solutions most likely to describe the twins involved in the “nearly 60°” crosses in staurolite.