Data for 66 refined crystal structures of micas were used to obtain several functions representing the octahedral sheet that served as variables in a statistical analysis: metal–anion bond lengths, two ratios of anion–anion octahedral edges, 1MEFIR (mean Active ionic radius), octahedral angle ψ, and counter-rotation of top and bottom anion triads.

All octahedra are flattened, those around larger cations usually more than those around smaller ones. Flattening dominates over counter-rotation in octahedra with large cations and vice versa, as required by the sheet’s uniform thickness. Mean counter-rotation in a sheet increases as cation–anion bond lengths are less uniform, suggesting that it results from interactions in the whole sheet. Consequently, both counter-rotation and octahedral angle ψ for individual octahedra can be predicted by regression equations from cation–anion bond lengths or 1MEFIR for all octahedra in the 1M subcell. Thus the octahedral geometry can be checked or predicted from chemistry and an anticipated cation ordering.

Multiple linear regressions yielded a set of cation–anion bond lengths and effective ionic radii for octahedral cations and the vacancy.

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