Distortions in the tetrahedral oxyanions of crystalline substances, with crystal structure refinements of slawsonite and celsian
Distortions in coordination polyhedra may be effected by (1) displacement of the central atom from a reference position within the polyhedron (bond-length distortion) and (2) displacement of the ligands from the apices of some reference polyhedron (edge-length distortion). For tetrahedral coordination the bond-length distortion parameter (BLDP) and edge-length distortion parameter (ELDP), which are linearly related to these two types of distortions, have been defined and compared with other distortion parameters currently in use.
Among tetrahedral oxyanions of non-transition elements, ELDP values of those exhibiting small bond-length distortions (e.g., LiO₄⁷⁻ and Ga₄⁵⁻) increase with the number of shared edges. For the oxyanions that show small edge-length distortions (e.g., Po₄³⁻ and SO₄²⁻) BLDP is related to the degree of tetrahedral polymerization. Although the relationships for oxyanions exhibiting fairly large ranges in both BLDP and ELDP (e.g., SiO₄⁴⁻) are not as straightforward, the same trends are recognized. For tetrahedral oxyanions of transition metals these structural trends are not well-developed.
For tetrahedral oxyanions of all but one non-transition element considered, bond angle variations are entirely or largely a function of O•••O variations; for SO₄²⁻, O-T-O variations are mainly a function of T-O bond length variations. With regard to transition metal oxyanions, those of V⁵⁺, Cr⁶⁺, and Mo⁶⁺ tend to have bond angles near 109.47°, while those of Fe³⁺ and Zn²⁺ behave much like oxyanions of non-transition elements. Baur's (1970) Rule 5 does not represent a generally adequate model for tetrahedral oxyanions.
Revised values for five of Shannon and Prewitt's (1971) effective tetrahedral ionic radii are presented, along with new values for the effective tetrahedral ionic radii of Ti⁴⁺ and Cu²⁺.
For tetrahedral oxyanions of non-transition elements the maximum value of bond-length distortion appears to be limited by a phenomenon analogous to the "rattling" of the hard-sphere model. The maximum edge-length distortions appear to be limited by coulombic repulsions between bonding electron concentrations, with non-bonded interactions becoming important at very small O•••O separations. For transition metal oxyanions it appears that the same factors may limit the maximum edge-length distortions. There is evidence for greater polarization of either the oxygen atoms or cations (or both) in the oxyanions of transition metals than in those of non-transition elements.
The crystal structure of slawsonite (SrA1₂Si₂O₈) has been refined to R = 0.048. Cell dimensions are positively correlated with both and and <>. Slawsonite appears to be fully ordered with = l.624Å and = l.748Å. Even where ordering is complete, apparently varies with structure type and cation combination.
The crystal structure of a celsian (Cn~₉₅Or~₅ ) has been refined to R = 0.034. Results are very similar to those of Newnham and Megaw (1960). In both celsians, bond lengths suggest that there is ~17 percent disorder in excess of that required by the deviation of the Al:Si ratio from 1:1. Considering similar synthetic materials which show partial disorder, it is concluded that the Al-avoidance principle is not operative for compounds with the celsian structure.