The application of eigensymmetries of face forms to X-ray diffraction intensities of crystals twinned by `reticular merohedry'

Klapper, H.; Hahn, Th.

doi:10.1107/S0108767311032454

Figure 9
Hexagonal lattices (a-b planes, common c axis pointing upwards) of twin domain I (start domain, lattice points small circles, right-handed green unit cell a₁, b₁, c₁), of the [Sigma]

7 twin-related domain II (small crosses, left-handed blue unit cell a₂, b₂, c₂) and of the [Sigma]

7 coincidence lattice (large black points, right-handed red unit cell a_T, b_T, c_T). The six alternative twin reflection planes m'(12 $[\bar 3]$ 0), m'( $[\overline 3]$ 120), m'(2 $[\overline 3]$ 10), m'( $[\overline 5]$ 410), m'(1 $[\overline 5]$ 40) and m'(41 $[\overline 5]$ 0) are indicated by dashed lines. The coordinate axes a₂, b₂, c₂ of domain II (blue) are defined by the reflection plane m'(12 $[\overline 3]$ 0). The right-handed yellow unit cell a₃, b₃, c₃ of domain II is obtained from a₁, b₁, c₁ by a clockwise rotation of [varphi]

= 120° + 2 arcsin [(1/2)(3/7)^1/2] = 120° + 38.2° = 158.2° around the hexagonal axis (cf. Appendix C

). This cell is commonly used in structure determinations.