Convergent-beam electron diffraction study of incommensurately modulated crystals. II. (3+1)-dimensional space groups

The convergent-beam electron diffraction (CBED) method for determining three-dimensional space groups is extended to the determination of the (3+1)-dimensional space groups for one-dimensional incommensurately modulated crystals. It is clarified than an approximate dynamical extinction line appears in the CBED discs of the reflections caused by an incommensurate modulation. The extinction enables the space-group determination of the (3+1)-dimensional crystals or the one-dimensional incommensurately modulated crystals. An example of the dynamical extinction line is shown using an incommensurately modulated crystal of Sr₂Nb₂O₇. Tables of the dynamical extinction lines appearing in CBED patterns are given for all the (3 + 1)-dimensional space groups of the incommensurately modulated crystal.