A new type of partial diffraction enhancement of symmetry found in CdI2 polytype*

Abstract

Abstract A new trigonal polytype, 20 H7, of CdI2 was found to exhibit a peculiar type of partial diffraction enhancement of symmetry; the diffraction symmetry of hkl reflections with l ≢ 0 (mod 10) is 6/mmm, while that with l ≡ 0 (mod 10) is [unk]m. To explain this type of composite diffraction symmetry, the structure was assumed to be built up by superposition of two substructures: an idealized one-layer CdI2 polytype called the base, and a structure called the modifier and having in it, besides ordinary atoms, fictitious ‘negative’ Cd and I atoms so that it may convert appropriate layers in the base into those in the 20 H7 structure. Then, in view of the facts that twofold rotation symmetry appears in the vector set of the modifier which is governed by dichroic twofold rotation symmetry and that the base makes no contribution to hkl reflections with l ≢ 0 (mod 10), it was concluded that the diffraction symmetry of hkl reflections with l ≢ 0 (mod 10) is 6/mmm when Friedel's law holds. On the other hand, hk · 10 l′ reflections correspond to the hkl′ reflections from a new structure derived by the convolution of the original 20 H7 structure with a lattice with basis vectors a, b, and c/10, where a, b, and c represent the basis vectors for 20 H7. Consideration of this ‘convoluted’ structure led us to the conclusion that the symmetry of hkl reflections with l ≡ 0 (mod 10) is 6/mmm or [unk]m since the number of layers in the modifier is half the number of layers in the unit cell of the entire structure.