Density Functional Theory Study of Ferrihydrite and Related Fe-Oxyhydroxides

The atomic and magnetic structure and thermodynamic stability of ferrihydrite (Fe₅O₈H) are calculated based on the structure recently proposed by Michel et al. (Science 2007, 316, 1726). Ferrihydrite stability is compared with that of the Fe-oxyhydroxide polymorphs goethite (α-FeOOH) and lepidocrocite (γ-FeOOH) and the oxide hematite (α-Fe₂O₃). The GGA+U method is employed to correct known errors in treating correlated d-electrons in Fe atoms. GGA+U yields smaller errors in calculated thermodynamic quantities relative to experiment as compared with a standard GGA functional for all of the Fe-oxyhydroxides studied. Good agreement is obtained between the DFT-predicted and experimental ferrihydrite structure when the effects of varying crystallinity and particle size are taken into account. The magnetic properties of ferrihydrite are modeled using a Heisenberg model parametrized with DFT-based magnetic coupling constants. The groundstate magnetic ordering of bulk ferrihydrite is predicted to be ferrimagnetic, with the Fe-site spins ordering with alternating alignment in layers stacked along the c-direction in the crystallographic unit cell. The groundstate is predicted to disorder to a paramagnetic structure at T_N = 250 K, undergoing a Néel transition. The enthalpy and Gibbs free energy of reaction of bulk crystalline ferrihydrite at 298.15 K are predicted to be ΔH^298.15K_rxn (Fe₅O₈H) = 6.4 kJ/(mol-Fe) and ΔG^298.15K_rxn (Fe₅O₈H) = 6.9 kJ/(mol-Fe), respectively, relative to bulk hematite and liquid water. The values demonstrate that fully crystalline ferrihydrite is metastable with respect to the formation of both hematite and goethite at 298.15 K but may be stabilized at small particle sizes due to favorably low surface formation energy. A simple surface energy model is used to predict the formation energy of ferrihydrite nanoparticles of arbitrary size, yielding results consistent with the observed formation energies for nanoparticle samples.