Investigation of the vanadyl bond ordering and analysis of the spin exchange interactions in PD₂v₃O₉ and Pb ₂As₂VO₉

The structures of Pb₂V₃O₉ and Pb ₂As₂VO₉ were determined by X-ray diffraction to settle the issue concerning whether the arrangement of the V⁴⁺=O vanadyl bonds is ordered or disordered. The new crystal structure of Pb ₂V₃O₉ refined by using a twinned crystal differs from the previous structure, determined from a combined use of powder X-ray and neutron diffraction data, and suggests an ordered Ferro arrangement of the V⁴⁺=O vanadyl bonds as does the Antiferro crystal structure of the new Pb₂As₂VO₉. In Pb₂V ₃O₉, a triclinic → monoclinic transition is observed at 400°C, and the corresponding high temperature form was structurally characterized. The spin exchange interactions of Pb₂V ₃O₉ and Pb₂As₂VO₉ were evaluated by performing qualitative spin dimer analysis based on tight binding calculations, and those of Pb₂V₃O₉ were also examined by quantitative mapping analysis based on density functional theory calculations. To a first approximation, the spin-lattice of Pb₂V ₃O₉ is described by an alternating antiferromagnetic chain model, which is made up of the super-superexchange interactions mediated by VO₄ tetrahedra between adjacent chains of corner-sharing V ⁴⁺O₆ octahedra. The magnetic property of Pb ₂As₂VO₉ is predicted to be paramagnetic, in agreement with experiment.