Polymorphism in the quasi-one-dimensional quantum magnet, [Ni(HF₂)(pyz)₂]PF₆

Abstract

Poster Sessions C703 edge-sharing MO 6 (M = octahedrally coordinated cations) octahedra forming parallel MO 4 chains.The crystal structures of all compounds in this family are derived from an aristotype structure in space group P4/mbm following a hierarchical scheme of subgroup relationships.Meanwhile, several compounds are added to this family, also extending the Bärnighausen tree representing all branches and cross-relationships of the symmetry derivations.Mullite itself is an aluminosilicate with an incommensurately modulated structure [3] reinvestigated here by single-crystal neutron-diffraction analysis of a high-quality 2:1 mullite.Its average crystal structure can be derived from the sillimanite structure by a disordered arrangement of (Al,Si)O 4 tetrahedra linking the octahedral chains according to the substitution scheme 2Si 4+ + O 2- 2Al 3+ + vacancy.The reaction involves removal of oxygen atoms from the structure and the formation of oxygen vacancies.Replacing Si by Al yields the oxygen vacancies and causes a migration of undersaturated Al to the so-called T* sites (red tetrahedra linking to bridging oxygen forming the T 3 O clusters.We have performed statistical calculations in a 2×2×2 and a 3×3×2 supercell to find the maximum number of symmetrically independent oxygen-vacancy configurations assuming one to four vacancies in the 2×2×2 case and up to seven vacancies in the 3×3×2 supercell.The total number of combinations is given just by the binomial coefficient with k representing the number of vacancies and n being the site multiplicity of the vacancy positions.As an example, the number of combinations for k = 2 vacancies distributed over n = 8 sites in the 2×2×2 supercell (corresponding to mullite with x = 0.25) is 28 as calculated from the binomial coefficient.Out of this number, only 20 combinations are crystal-chemically possible, and among these combinations, there are only 6 which are symmetrically independent.We are representing here the full ordering scheme of possible and independent oxygen vacancy distributions as a basis for the interpretation of the incommensurate modulation scheme of mullite.