Ab Initio Evaluation of Solid-State Transformation Pathways from Ferrihydrite to Goethite

Phase transformations between iron (oxyhydr)oxide minerals can occur topotactically through the self-diffusion of ions in the solid state, particularly at high temperatures. However, under ambient conditions, the extent to which solid-state transformation pathways could be important, especially for nanoparticles where the associated diffusion path lengths are short, remains poorly known. Using density functional theory, here, we evaluated this prospect for ferrihydrite (Fh) transformation to goethite (Gt) by computing the energetic cost to displace the minimum set of iron cations needed to obtain Gt starting from model Fh structures by Michel et al. in 20071 and Manceau et al. in 2014.2 While transformation to Gt from the Manceau Fh model is straightforward and involves a moderate activation energy of 1.04 eV/unit cell, doing the same starting from the Michel model is more complex and could involve an energetically competitive intermediate orthorhombic phase structurally similar to Gt that converts to Gt through exchange of iron cations for protons. Two transition pathways yielding the orthorhombic intermediate were identified, with the fastest involving a rate-limiting atomic displacement having a large activation energy of 2.09 eV/unit cell. As a companion result, we also calculated the solid-state transformation energetics that interconnect the Michel and Manceau models of Fh, which are separated by an activation energy of approximately 1.82 eV/cell. We discuss and compare our calculated temperature-dependent iron self-diffusion coefficients in Fh models to those for hematite and magnetite derived from high-temperature measurements. The results show that although pH effects have not yet been treated explicitly, even for the nanoscale particle sizes of Fh it is unlikely that solid-state transformation pathways to Gt are accessible under ambient conditions, implicating other pathways as more important.