Structural rationale for the occurrence of the elbow twins in cassiterite and rutile

Elbow twins are a distinct feature of cassiterite and rutile. Their occurrence is justified by the reticular theory of twinning because of the existence of a common sublattice- the twin lattice - formed by the overlap of a large fraction of the lattice nodes of the individuals. Yet, the atomic basis for the existence of twins falls outside the possibilities of the reticular theory. We present here the analysis of the pseudo-eigensymmetry of the crystallographic orbits building the structure of the elbow twins and show that their occurrence is justified by the complete restoration of the structure near the composition surface, with a deviation of less than 0.7 angstrom.