The crystal structure of highly stoichiometric magnetite (Fe3O4) below the Verwey transition has been refined from high-resolution neutron and synchrotron x-ray powder-diffraction data. The refined model has a monoclinic P2/c symmetry cell with orthorhombic Pmca pseudosymmetry constraints on the atomic positions, and contains four independent octahedral B site iron atoms. Charge ordering is evidenced by the presence of expanded and contracted BO6 octahedra, and by the distribution of B-B distances resulting from unequal Coulombic repulsions between the different B site charges. The B-B distances are inconsistent with dimer formation. Competition between the B-O and B-B interactions results in polar displacements of two of the B site cations. The charge ordering has a predominant [001] density modulation, which relieves a nesting instability in the electronic density of states, but a second [00 1/2] phase modulation also occurs. The monoclinic distortion at the Verwey transition is consistent with a macroscopic rhombohedral magnetostriction, driven by the localization of orbitally degenerate Fe2+, coincident with the microscopic charge ordering distortions that have an orthorhombic lattice symmetry.
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