Theoretical Study of Properties of Goethite (α-FeOOH) at Ambient and High-Pressure Conditions

Abstract

Magnetic, electronic, structural, vibrational, and mechanical properties of mineral goethite (α-FeOOH) at ambient conditions and their dependence on isostatic volume compression (corresponding pressure range 0–80 GPa) have been studied by means of spin-polarized density functional theory (spDFT), modified spDFT+U method, which includes a Hubbard-type on-site repulsion term U, and hybrid DFT functional MSE06. The antiferromagnetic high spin ground state has been confirmed as the most stable at low-pressure conditions. Calculated Fe magnetic moments differ from experiment by about 0.3–0.4 μB. The antiferromagnetic high spin state is stable over the whole compression range in the spDFT+U and MSE06 calculations. For the spDFT, a collapse from a high spin to low spin state has been induced by compression. In comparison to experiment, the spDFT method strongly underestimates electronic band gap, and the spDFT+U results are in a reasonable agreement (with a difference of 0.1–0.5 eV), while the hybrid MSE06 functional gives an overestimated value. The spDFT+U calculated band gap narrows upon increasing volume compression. Structural parameters calculated by all three methods are in very good agreement with experimental data with an error below 1–1.5%. The analysis of structural parameters has shown that the compression proceeds mainly through the compression of structural channels containing hydrogen bonds. Very narrow splitting in a range of ∼20 cm–1 has been found for the calculated OH stretching modes. The predicted bulk modulus of 114.3 GPa (spDFT+U) is in accord with an experimental value of 111 GPa. The calculated elastic constants document an anisotropic character of the single crystal structure of goethite. In general, the spDFT+U provides reliable results for all studied properties, while the MSE06 overestimates some of them (e.g., band gap).