Structural relationships in close-packed AB2O4 oxides involving spinel,olivine, and hexagonal LiFeSnO4 structures

Close-packed structures with formula AB₂O₄ were studied in terms of polyhedra arrangement. The junction between octahedral layers (kagome) and mixed (octahedral and tetrahedral) layers were analyzed; this association allows one to determine two types of double layers whose packing leads to three closely related structural types: spinel, double-hexagonal LiFeSnO₄, and a hypothetical hexagonal structure. Olivine structure shows a polyhedral arrangement closely related to those of these three structures and can be described alike in terms of mixed layers and double layers. AB₂O₄ close-packed oxides can exhibit polymorphism; from this analysis a mechanism, involving geometrical operations applied to the double layers, is proposed for the different transitions, really observed as (DH) LiFeSnO₄ spinel and olivine-spinel or theoretical as (DH) LiFeSnO₄—hypothetical hexagonal and olivine—hypothetical hexagonal.