Perception of structural complexity; fillowite revisited and α-iron related

All 23 cations in the asymmetric unit of fillowite, including two ordered vacancies, a = 15.28, c = 43.51 Å, R3, 18(Na₂CaMn₃)(Mn₄□₂P₆)O₂₄ can be related to the hexagonal (rhombohedral) cell of α-Fe, a(h)_α = 4.05, c(h)_α = 4.96 Å, R3c, 6Fe. This relation corresponds to 3a(h)_α and 6c(h)_α and has 3².6 = 54 unit cells of α-Fe in hexagonal setting or 54·6 = 324 metals in the expanded α-Fe cell. There is a 1:1 correspondence with the 324 cations (including 36 ordered vacancies) in fillowite. In c/a ratio, fillowite is dilated 14% along c relative to its α-Fe counterpart. This is believed due to insertion of many oxide anions in the (001) plane of fillowite. The largest difference between cation centroids of fillowite and corresponding invariant centroids of α-Fe is Δ = 1.34 Å for Na(3) compared with perpendicular bisection of t/2 = 1.47 Å in the (001) plane and t/2 = 1.81 Å parallel to c, the calculations based on the fillowite cell.

All cations fall within their respective Dirichlet domains in the projection on (001). It is believed that the two ordered vacancies, □(1) and □(2) in general positions, arise from near-eclipsing of terminal tetrahedral bases, in this case five beads of T-M-T-M-T. Such sections of rods are called stalks and appear in other structural colossi such as palmierite, cerite, and arrojadite-dickinsonite. These stalks may force a large number of atoms in a unit cell. Fillowite’s cell alone has 756 atoms as its contents. Yet only three distinct rods, each of 12 cation beads in the orepeat, occur in the unit cell: rod I (× 3), rod Ia (× 6), and rod II (× 18). The I and Ia correspond to pole points on (001) as (00) for (xy), and II corresponds to (⅔⅓) for the parent structures α-Fe(h), Ni₂In, and glaserite [(K₃NaS₂)O₈], respectively.