Iron oxides and oxyhydroxides are challenging to model computationally as competing phases may differ in formation energies by only several kJ mol${}^{-1}$, they undergo magnetization transitions with temperature, their structures may contain partially occupied sites or long-range ordering of vacancies, and some loose structures require proper description of weak interactions such as hydrogen bonding and dispersive forces. If structures and transformations are to be reliably predicted under different chemical conditions, each of these challenges must be overcome simultaneously while preserving a high level of numerical accuracy and physical sophistication. Here we present comparative studies of structure, magnetization, and elasticity properties of iron oxides and oxyhydroxides using density-functional-theory calculations with plane-wave (PW) and locally-confined-atomic-orbital basis sets, which are implemented in vasp and siesta packages, respectively. We have selected hematite ($\alpha$-Fe${}_2$O${}_3$), maghemite ($\gamma$-Fe${}_2$O${}_3$), goethite ($\alpha$-FeOOH), lepidocrocite ($\gamma$-FeOOH), and magnetite (Fe${}_3$O${}_4$) as model systems from a total of 13 known iron oxides and oxyhydroxides, and we used the same convergence criteria and almost equivalent settings to make consistent comparisons. Our results show that both basis sets can reproduce the energetic stability and magnetic ordering, and are in agreement with experimental observations. There are advantages to choosing one basis set over the other, depending on the intended focus. In our case, we find the method using PW basis set the most appropriate, and we combine our results to construct the first phase diagram of iron oxides and oxyhydroxides in the space of competing chemical potentials, generated entirely from first principles.

• Received 19 October 2010

DOI:https://doi.org/10.1103/PhysRevB.83.094112