Despite the ubiquity of ferrihydrite in natural sediments and its importance as an industrial sorbent, the nanocrystallinity of this iron oxyhydroxide has hampered accurate structure determination by traditional methods that rely on long-range order. We uncovered the atomic arrangement by real-space modeling of the pair distribution function (PDF) derived from direct Fourier transformation of the total x-ray scattering. The PDF for ferrihydrite synthesized with the use of different routes is consistent with a single phase (hexagonal space group P6(3)mc; a = approximately 5.95 angstroms, c = approximately 9.06 angstroms). In its ideal form, this structure contains 20% tetrahedrally and 80% octahedrally coordinated iron and has a basic structural motif closely related to the Baker-Figgis delta-Keggin cluster. Real-space fitting indicates structural relaxation with decreasing particle size and also suggests that second-order effects such as internal strain, stacking faults, and particle shape contribute to the PDFs.

We show that intercalation of cations (Na+, Ca2+, Ni2+, and Co2+) into the interlayer region of 1T-MoS2 is an effective strategy to lower the overpotential for the hydrogen evolution reaction (HER). In acidic media the onset potential for 1T-MoS2 with intercalated ions is lowered by ∼60 mV relative to that for pristine 1T-MoS2 (onset of ∼180 mV). Density functional theory (DFT) calculations show a lowering in the Gibbs free energy for H-adsorption (ΔG H) on these intercalated structures relative to intercalant-free 1T-MoS2. The DFT calculations suggest that Na+ intercalation results in a ΔG H close to zero. Consistent with calculation, experiments show that the intercalation of Na+ ions into the interlayer region of 1T-MoS2 results in the lowest overpotential for the HER.

Periodic plane-wave density functional theory (DFT) and molecular cluster hybrid molecular orbital-DFT (MO-DFT) calculations were performed on models of phosphate surface complexes on the (100), (010), (001), (101), and (210) surfaces of α-FeOOH (goethite). Binding energies of monodentate and bidentate HPO(4)(2-) surface complexes were compared to H(2)PO(4)(-) outer-sphere complexes. Both the average potential energies from DFT molecular dynamics (DFT-MD) simulations and energy minimizations were used to estimate adsorption energies for each configuration. Molecular clusters were extracted from the energy-minimized structures of the periodic systems and subjected to energy reminimization and frequency analysis with MO-DFT. The modeled P-O and P---Fe distances were consistent with EXAFS data for the arsenate oxyanion that is an analog of phosphate, and the interatomic distances predicted by the clusters were similar to those of the periodic models. Calculated vibrational frequencies from these clusters were then correlated with observed infrared bands. Configurations that resulted in favorable adsorption energies were also found to produce theoretical vibrational frequencies that correlated well with experiment. The relative stability of monodentate versus bidentate configurations was a function of the goethite surface under consideration. Overall, our results show that phosphate adsorption onto goethite occurs as a variety of surface complexes depending on the habit of the mineral (i.e., surfaces present) and solution pH. Previous IR spectroscopic studies may have been difficult to interpret because the observed spectra averaged the structural properties of three or more configurations on any given sample with multiple surfaces.