Refining hydrogen positions in {\alpha}-FeOOH through combined neutron diffraction and computational techniques

The hydrogen positions and magnetic structure of goethite $\alpha$-FeOOH, a key component of iron rust, were examined through neutron diffraction. All symmetry-allowed magnetic structures under the space group $Pnma$ with the magnetic wavevector $\vec{q}_{\rm m} = (0, 0, 0)$ r.l.u. were analysed using irreducible representation and magnetic space group approaches. The magnetic moments aligned along the $b$-axis form antiferromagnetic spin arrangements, as reproduced by first-principles calculations. Accurately determining the hydrogen positions is crucial for understanding the mechanism of catalytic reduction of CO$_2$ in $\alpha$-FeOOH. These positions were precisely identified through diffraction and calculations, highlighting the effectiveness of using both methods for undeuterated compounds.