The Scanning for Layer Groups and Positional Dependence of Domain Wall Energy and Structure

Abstract

Linear orbits of sectional planes under the action of space groups are analyzed. It is shown that the sectional layer group is the same for all positions if the scanning group is polar. For other scanning groups, the orbits of special positions appear in alternating pairs and the layer symmetry of the plane of a general position along the scanning direction is the same for all such positions. This symmetry is the intersection of layer symmetries of special positions. From this follows a conjecture that one type of the special position corresponds to the maximum of the energy, the other to the minimum.

Keywords:

• Scanning group
• sectional layer groups
• orbits of planes

7. Acknowledgment

The author is indebted to prof. Janovec for countless discussions in which he proposed to check the conjecture. He also pointed out the importance of sectional layer groups to the author and thus inspired the preparation of the Scanning tables which also necessitated the standardization of subperiodic groups [8].