Twin domains and antiphase domains

Displacive phase transitions and phase transitions of the type disorder-order usually result in symmetry changes such that the space groups of both structures are related as group and subgroup. The subgroups of a space group always belong to one of the following three types: they have either the same primitive cell as the original space group (they are translationengleich), or they belong to the same crystal class (klassengleich), or they are general (allgemein), i.e. they do not belong to either one of the previous categories exclusively and thus have lost translations as well as other symmetry operations with respect to their higher-symmetry (parent) space group. Twin domains are expected whenever the derived structure belongs to a lower-symmetry crystal class. Antiphase domains are possible whenever the derived structure has lost translational symmetry operations. The usefulness of these considerations is demonstrated and discussed for several materials with derivative structures.