  Twinning is a common crystallographic phenomenon, which usually occurs in
crystals during symmetry-lowering phase transition. Once formed, twin domains
play an important role in defining physical properties: for example, twin
domains underpin the giant piezoelectric effect in ferroelectrics,
superelasticity in ferroelastics and the shape-memory effect in martensitic
alloys. Unfortunately, there is still a lack of experimental methods for
imaging and characterization of twin domain patterns. Here, we propose a
theoretical framework and an algorithm for the recognition of twinned pairs of
ferroelastic domains and the identification of the coherent twin relationship
using high-resolution reciprocal space mapping of X-ray diffraction intensity
around split Bragg peaks. Specifically, we adapt the geometrical theory of
twinned ferroelastic crystals (Fousek & Janovec, 1969) for the analysis of the
X-ray diffraction patterns. We derive the necessary equations and outline an
algorithm for calculation of the separation between the Bragg peaks, diffracted
from possible coherent twin domains, connected to one another via mismatch-free
interface. We demonstrate that such separation is always perpendicular to the
planar interface between mechanically matched domains. As examples, we present
the analysis of the separation between the peaks diffracted from tetragonal and
rhombohedral domains in the high-resolution reciprocal space maps of BaTiO3 and
PbZr1-xTixO3 crystals. The demonstrated method can be used to analyse the
response of multi-domain patterns to external perturbations such as electric
field, change of a temperature or pressure.
