LDA + U and GGA + U studies of Al-rich and bulk goethite (α-FeOOH)

The electronic and structural properties of bulk goethite and Al-rich goethite were studied on the basis of spin-polarized DFT at the LDA + U and GGA(PW91) + U levels. Firstly, the periodic model of bulk goethite was optimized varying the value of Ueff. Considering all the results obtained we can conclude that the bulk goethite described at the GGA + U level with Ueff = 6 eV gives us the better agreement with different physical properties. The results of magnetic moments of Fe ions, the DOS analysis and the Bader atomic charges identify goethite as an antiferromagnetic Fe(III) compound. For Al-rich goethite the GGA + U (Ueff = 6 eV) approach was used. The isomorphous substitution of one Fe ion with Al ion produces the reduction of the cell parameters with respect to the bulk goethite. Regarding the magnetic ordering, it was observed that Fe atoms surrounding the Al atom must have the same spin projection, i.e., spin-up or -down. The charge density was changed with the addition of Al ion, producing a depletion where the ion is located and some electron redistribution in the zone of the oxygen atoms surrounding the Al ion. This behavior produces some small magnetization in these O ions.