A practical method of three-dimensional space-group analysis using convergent-beam electron diffraction

Symmetry rules are derived for relating the convergent-beam electron-diffraction pattern symmetries to the three-dimensional symmetry of the structure. These rules are applied to a study of 2M biotite. As a result the space group is determined as C2, or number 5 in International Tables for X-ray Crystallography, whereas it was previously held, in the absence of accurate data, to belong to C2/c or number 15. In addition, a method is described for uniquely determining the centrosymmetry of a crystal independently of space group, hence resolving the ambiguity between a centre of symmetry and a twofold axis present when approximations to dynamic electron scattering are used which take into accoufit only the symmetry of the projection.