Classification of domain pairs and tensor distinction

The symmetries of domain states of a domain pair (S₁,S₂) can be determined from the symmetry group F₁ of the first domain state and a twinning operation g₁₂ which transforms this domain state into the second. A classification is introduced which classifies all possible domain pairs according to a classification of the pairs F₁ and g₁₂. One obtains 139 classes of which 43 correspond to non-ferroelastic domain pairs and 96 to ferroelastic domain pairs. The tensor distinction of domain states of a domain pair is determined by the group F₁ and g₁₂ and all domain pairs belonging to the same class have the same tensor distinction. The 139 classes of pairs F₁ and g₁₂ are tabulated along with their corresponding twinning group K₁₂ = < F₁, g₁₂ >, the group generated by F₁ and g₁₂. The tensor distinction of domain states of domain pairs of each class is given for a variety of material property tensors.