The magnetite structure was studied with synchrotron x-ray powder diffraction above and below the Verwey transition. A symmetry-mode analysis was performed to obtain the atomic displacements from the amplitudes of condensing modes. The main contributing modes that drive the structural phase transition at the Verwey temperature correspond to the irreducible representations ${\Delta }_5$, $X_1$, $X_4$, $W_1$, and $W_2$. The $W$ modes, neglected so far, must be taken into account so a reliable description of the low-temperature crystal structure can be obtained. This is refined in the nonpolar space group $C$2/$c$ with ten nonequivalent octahedral irons. The condensation of the mentioned modes leads to a wide distribution of local environments around the octahedral iron atoms, whose valences range between 2.53 and 2.84. This finding rules out any bimodal charge disproportionation of the octahedral iron atoms, i.e., an ${\mathrm{Fe}}^{2+}$-like/${\mathrm{Fe}}^{3+}$-like ordering.

• Received 25 January 2011

DOI:https://doi.org/10.1103/PhysRevB.83.104105