Pressure-induced structural and electronic transitions in FeOOH from first principles

Using density-functional theory, we investigate the stability, structural, magnetic, and electronic properties of the iron oxyhydroxide polymorphs [$\alpha$-, $\beta$-, $\gamma$-, and $hp\left(ϵ\right)\text{-FeOOH}$] under hydrostatic pressure. At ambient conditions goethite $\left(\alpha \right)$ is the lowest energy phase, consistent with recent calorimetric measurements. Around 6–7 GPa we predict a transformation to the high-pressure $hp\left(ϵ\right)$ phase. This structural transformation is followed by a high-spin to low-spin transition at 7.7 GPa, at much lower pressure than for other currently discussed iron-bearing minerals. While in the ground state the ${\text{Fe}}^{3+}$ ions are coupled antiferromagnetically, at high pressures a strong competition to a ferromagnetic alignment is found in $hp\left(ϵ\right)\text{-FeOOH}$. Concerning the electronic properties, including an on-site Coulomb repulsion parameter $U$ ($\text{LDA}/\text{GGA}+U$ method) improves the size of the zero-pressure band gaps substantially but shifts the spin transition to higher pressure (56.5 GPa). The predicted spin crossover is associated with a blueshift of 0.4 eV.

Figure 1

(Color online) The structures of the FeOOH polymorphs represented in terms of ${\text{FeO}}_3{\left(\text{OH}\right)}_3$ octahedra where the hydrogen atoms (in light blue/gray) reside in the $2\times 1$, $2\times 2$, and $1\times 1$ channels of (a) $\alpha \text{-FeOOH}$ (goethite), (b) $\beta \text{-FeOOH}$ (akaganeite), and (c) $hp\left(ϵ\right)\text{-FeOOH}$, respectively, or between the zigzag sheets of (d) $\gamma \text{-FeOOH}$ (lepidocrocite)

Figure 2

(Color online) Energy as a function of volume and enthalpy-pressure relation $\Delta H\left(p\right)$ for the different polymorphs within GGA (left panels) and $\text{GGA}+U$ (right panels). The total energy at the equilibrium volume, $V_0$, of the most stable $\alpha$ phase is set to zero. $\Delta H\left(p\right)<0$ indicates phases that are more stable than the $\alpha$-phase [or $hp{\left(ϵ\right)}_{\text{AFM,HS}}$ in the inset in (d)] for a given pressure.

Figure 3

(Color online) Volume as a function of pressure within GGA (filled circles) and $\text{GGA}+U$ (open circles). For comparison, the experimental data of Nagai et al. (Ref. 26) (black squares) is added and shows very good agreement with the GGA results.

Figure 4

(Color online) (a) Bond lengths in $\alpha \text{-FeOOH}$ as a function of pressure within GGA. (b) Pressure dependence of the Fe-O bonds in $\alpha \text{-FeOOH}$ within GGA: the filled symbols denote the different Fe-O1 bonds, the open symbols the different Fe-O2 bonds. Additionally, the bond lengths up to 9 GPa obtained by Nagai et al. (Ref. 26) from XRD measurements (black stars).

Figure 5

(Color online) Variation in the hydroxyl bonds (O-H) and the hydroxyl bridges $\left(\text{O}\cdots \text{H}\right)$ for the different phases. The length of the hydrogen-bridge bond exhibits the strongest variation with pressure. In the case of $hp\left(ϵ\right)\text{-FeOOH}$, a symmetrization of the OH bonds is observed above 40 GPa.

Figure 6

(Color online) DOS of $\alpha \text{-FeOOH}$ at $V_{\text{exp}}$. The left panel shows the GGA results for the FM (dashed line) and AFM coupling (solid line, gray area), the right one the $\text{GGA}+U$ results for AFM. $V_{\text{exp}}$ corresponds to pressures of 2 GPa within GGA and 4 GPa within $\text{GGA}+U$, respectively.

Figure 7

DOS of $hp\left(ϵ\right)\text{-FeOOH}$ illustrating the spin transition associated with a change in magnetic order obtained within $\text{GGA}+U$: (a) $hp\left(ϵ\right)\text{-FeOOH}$ (AFM, HS) at the phase transition pressure of 5.9 GPa; at 56.5 GPa the spin crossover takes place in $hp\left(ϵ\right)\text{-FeOOH}$ from (b) an AFM, HS state to (c) an FM, LS state.

Figure 8

(Color online) Spin-density distribution of $hp\left(ϵ\right)\text{-FeOOH}$ at 56.5 GPa for ${\text{Fe}}^{3+}$ in (a) HS, AFM and (b) LS, FM state. Fe is octahedrally coordinated by oxygen (light blue/gray); the hydrogen positions are not shown.