Extinction conditions in the dynamic theory of electron diffraction

Abstract

General conditions are given for the continued complete absence of kinematically space-group forbidden refiexions when the scattering is dynamic. It is shown that reflexions which are forbidden because of glide planes or twofold screw axes will remain forbidden under dynamic conditions if suitable restrictions are placed on the direction of the incident beam. These restrictions can be represented by a cross, one arm of which corresponds to the exact Bragg condition, the other arm being normal to the first and to the screw axis or glide direction. When only zero-layer interactions are taken into account the locus of zero intensity includes both arms. When higher-layer interactions are included the locus of zero intensity will be one or other arm of the cross depending on whether the incident beam is perpendicular to a screw axis or parallel to a glide plane. The case in which the incident beam is perpendicular to a glide plane, though trivial for zero-layer interactions, leads to a condition for zero intensity satisfied only at the intersection of the arms of the cross when higher layer interactions are included.

A retabulation of the 80 layer groups for electron diffraction usage

“…l(b), for which the crystal is rotated away from the [001] zone axis, shows that only those h00 reflexions very close to the Laue circle are extinguished; those near the 000 reflexion have strong intensity. This is an indication, according to the literal interpretation of the Gjg~nnes- Moodie (1965) rules (and later supported by the other zone-axis patterns of Fig. 2), that the horizontal screw axis 2~ parallel to a* is present in addition to the vertical glide planes.…”

Space-group determination by dynamic extinction in convergent-beam electron diffraction

“…We summarize the dynamic extinction rules for g, g' and 2', given by Gjonnes & Moodie (1965) in Table 1 using our notation. The symbols A and B indicate the GM lines as depicted in Fig.…”

Friedel's law and non-centrosymmetric space groups

“…212 (P4332) (Joubert, Berthet & Bertaut, 1970). SiO2 and Li2ZnTi308 exemplify the two major structural subdivisions for non-centrosymmetric structures (Moodie, 1965). The non-centrosymmetric character depends on the positions in the former and on weights in the latter.…”

“…There is no breakdown of Friedei's law, but the loci of zeros associated with glide lines establishes the symmetry of this projection as p4gm (Gjonnes & Moodie, 1965).…”