Structural relationships in (Mn_1−xZn_x)Mn₂O₄ (0 ≤ x ≤ 0.26): The “dragging effect” of the tetrahedron on the octahedron

Ten hausmannite crystals (from Ilfeld and Friedrichrode, Harz, Germany), belonging to the (Mn_1−xZn_x)Mn₂O₄ (0 ≤ x ≤ 0.26) system (I4₁/amd hausmannite structure type), were characterized by chemical (electron microprobe) and structural (single-crystal X-ray diffractometer) analysis. The prevailing trivalent cation is Mn³⁺, with very minor Al (not higher than 0.005 apfu). Among divalent cations, the main substitution involves Zn → Mn²⁺. Cation distribution was obtained by comparing chemical and structural data, and results confirm normal distribution, with Mn³⁺ ordered on the octahedral site. A specific bond distance of 2.030 Å was refined for ^VIMn³⁺-O.

Unit-cell parameters a and c range from 5.752 to 5.763 Å and from 9.408 to 9.461 Å, respectively. The smallest values are characteristic of the sample with the highest hetaerolite content. T-O bond distance (2.027–2.041 Å) shows a strong positive correlation with unit-cell constants, while the O-T-O angle (103.3–103.7°) is related only to the oxygen coordinate, z. The two octahedral bond distances show limited variations: the shorter one, M-O_S, ranges from 1.927 to 1.930 Å, and is not significantly correlated with unit-cell parameters. The longer one, M-O_L, shows a larger variation, from 2.281 to 2.290 Å, and is positively correlated with c. Regularization of the octahedron with increasing hetaerolite content coincides with an increase in the oxygen coordinate y and a decrease in c and c/a. Of particular interest is the positive linear relation between octahedral elongation and V_T. As the octahedral content of all samples is almost constant, given the closeness of Mn³⁺ to stoichiometry, all structural distortions are linked to ^IVZn → ^IVMn²⁺ that reduces the T-O bond distance and causes movement of the structure toward cubic symmetry. This interaction is due to the “dragging effect” of the tetrahedron on the octahedron.

In hausmannite-type structures, besides the main structural distortion produced by the Jahn-Teller effect, a secondary one, without symmetry modification, is determined by the geometrical effects of the tetrahedron on the octahedron.