The C-M2O3 sesquioxide structure as a subgroup of fluorite type crystals

The connection between the C-M2O3 compounds (example Y2O3) and a CaF2-type structure is studied. The space group (SG) of Y2O3 is Th7, that of CaF2 is Oh5, the first being a subgroup of the latter (index 32). The distortion mode is single and belongs to a point on the Σ-lineΣ-line in the first BZ of Oh5. This same mode occurs in yellow InCl (SG T4, heavily distorted NaCl-structure). Although the space groups of the parent structures are the same, these differ in the cation–anion ratio, so that the resemblance is restricted to cations on a threefold axis. We observed previously in InCl an invariant connected to this mode. This same invariant, also occurs in Y2O3. It is a ferri-distortive scalar of symmetry A2g (with respect to Oh) and invariant for the point group of the crystal (Th).There appear two types of Y3+-ions. Y1, with site-symmetry S6, and Y2 (C2). In the surroundings of the latter, screws and twists are observed. These lead to antiferro-ordered expressions of A1u and A2u-type.