The determination of rigid-body translation vectors of twins with nearly common reflections

Abstract

A method has previously been reported in the literature for determining the rigid body translation vector of a twin boundary using diffraction contrast. The technique relies on imaging the twin boundary with a reflection which is common to the two crystals on either side of the boundary. In order to completely define the rigid body translation vector, at least three such common reflections must be used. This procedure can become extremely difficult, however, in the case of crystals which have an element of pseudo-symmetry. These are crystals which have a Bravais lattice which is slightly distorted from a different Bravais lattice of higher symmetry. An example of this kind of crystal is the high temperature superconductor, Y1Ba2Cu3O7-δ. This material has a unit cell which is orthogonal, but which is only slightly different from tetragonal, with a=3.82 Å and b=3.89 Å. Crystals of this type often exhibit transformation twins which are formed when the crystal is transformed from the higher to the lower symmetry structure during cooling.