Overlooked problems in manifold twins: twin misfit in zero‐obliquity TLQS twinning and twin index calculation

It is shown that the twin index n calculated, according to Friedel, as a function of the indices ( hkl ) and [ uvw ] of the lattice plane and lattice direction defining the cell of the twin lattice applies only to twofold twins, i.e . twins where the twin element is of order 2. For manifold twins, where the twin operation is a three‐, four‐ or sixfold (direct or inverse) rotation, it is shown that the generalized formula becomes n = N Ξ/ξ, where N is the number of lattice planes of the ( hkl ) family passing within the cell of the twin lattice, Ξ the two‐dimensional coincidence index for a plane of the ( hkl ) family and ξ the number of planes out of N of that family that are partially restored by the twin operation. The existence of twin lattice quasi‐symmetry (TLQS) twins with zero‐obliquity in manifold twins leads to the introduction of a new parameter as a general measure of the pseudo‐symmetry of TLQS rotation twins: the twin misfit δ , defined as the distance between the first nodes along the two shortest directions in the plane of L T (quasi‐)perpendicular to the twin axes that are quasi‐restored by the twin operation. Taking the example of staurolite twins, several inconsistencies in the treatment of manifold twins are pointed out.