THE EFFECTIVE SHAPES AND SIZES OF CU2+ AND MN3+ IONS IN OXIDES AND FLUORIDES

Structural data, retrieved from the Inorganic Crystal Structure Database, have been used to study the effective shape and sizes of six coordinated Cu2+ and Mn3+ ions in oxides and fluorides. The distortions of the coordination octahedra for these two metal ions, essentially due to the structural implications of the Jahn-Teller effect, are assumed to be interpretable in terms of a nonspherical (ellipsoidal) effective shape of the metal ions. For octahedra with approximate tetragonal D4h symmetry (rotational ellipsoid) a reasonable one-parameter correlation function is shown to be 2/r4(2) + 1/r2(2) = 3/r0(2), where r4 is the ionic size perpendicular to and r2 the size along the rotation axis. The single parameter r0 to be determined, estimated to 0.66(1) angstrom for CU2+ and 0.59(1) angstrom for Mn3+, represents the size of the spherical case. From the correlation function, possible estimates of the effective sizes for square planar four coordination (and linear two coordination) can be obtained by extrapolation, giving 0.54 angstrom and 0.48 angstrom for four coordinated Cu2+ and Mn3+, respectively. According to the correlation function the radii decrease with the square root of the coordination number. For ions with effective ellipsoidal shapes like Cu2+ and Mn3+, it is shown that i. a. not only the use of average bond distances but also the previously used linear relation between average distances and distortion-parameters are strongly dependent on the degree of non-sphericity. A modified linear relation, between average bond distance ana distortion, with improved linear correlation is suggested. As an alternative, the root harmonic mean square (rhms) value, 1/square-root 1/6SIGMA1/r(i)2, that gives an estimate of the parameter r0, is suggested to be used for judging the relevance of an observed bond length distribution (R1,...,R6 and r(i) estimated R(i) - r(ligand)) for six-coordinated ions.