Abstract
Basic symmetry properties of transformation twins and of ferroelectric or ferromagnetic domains are examined in terms of the abstract group theory. It is shown that the crystallographical relations between domains (twin components) and between domain pairs can be deduced from the decomposition of the symmetry group of the high symmetry phase into the left and double cosets of the group of the low symmetry phase. Expressions are derived for the numbers of proper and improper domains, for the number of crystallographically equivalent low symmetry phases, and for the number of crystallographically non-equivalent domain pairs. A classification of domain pairs according to their symmetry is proposed. The domain structure of the monoclinic phase in WO3 and the Dauphine twinning in quartz are analysed as illustrative examples.
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