Structure, charge distribution, and electron hopping dynamics in magnetite (Fe3O4) (1 0 0) surfaces from first principles

For the purpose of improving fundamental understanding of the redox reactivity of magnetite, quantum-mechanical calculations were applied to predict Fe²⁺ availability and electron hopping rates at magnetite (1 0 0) surfaces, with and without the presence of adsorbed water. Using a low free energy surface reconstruction (½-Fe_tet layer relaxed into the Fe_oct (1 0 0) plane), the relaxed outermost layer of both the hydrated and vacuum-terminated surfaces were found to be predominantly enriched in Fe²⁺ within the octahedral sublattice, irrespective of the presence of adsorbed water. At room temperature, mobile electrons move through the octahedral sublattice by Fe²⁺-Fe³⁺ valence interchange small polaron hopping, calculated at 10¹⁰-10¹² hops/s for bulk and bulk-like (i.e., near-surface) environments. This process is envisioned to control sustainable overall rates of interfacial redox reactions. These rates decrease by up to three orders of magnitude (10⁹ hops/s) at the (1 0 0) surface, and no significant difference is observed for vacuum-terminated versus hydrated cases. Slower hopping rates at the surface appear to arise primarily from larger reorganization energies associated with octahedral Fe²⁺-Fe³⁺ valence interchange in relaxed surface configurations, and secondarily on local charge distribution patterns surrounding Fe²⁺-Fe³⁺ valence interchange pairs. These results suggest that, with respect to the possibility that the rate and extent of surface redox reactions depend on Fe²⁺ availability and its replenishment rate, bulk electron hopping mobility is an upper-limit for magnetite and slower surface rates may need to be considered as potentially rate-limiting. They also suggest that slower hopping mobilities calculated for surface environments may be amenable to Fe²⁺-Fe³⁺ site discrimination by conventional spectroscopic probes.