Elasticity of <i>ε</i>‐FeOOH: Seismic implications for Earth's lower mantle

<jats:title>Abstract</jats:title><jats:p>We have calculated the structure and elasticity of low‐spin ferromagnetic ε‐FeOOH to 140 GPa using density functional theory calculations with a Coulombic self‐interaction term (<jats:italic>U</jats:italic>). Using these data, the elastic moduli and sound velocities of ε‐FeOOH were calculated across the pressure stability of the hydrogen bond symmetrized structure (30 to 140 GPa). The obtained values were compared with previously published values for phase H (MgSiH<jats:sub>2</jats:sub>O<jats:sub>4</jats:sub>) and δ‐AlOOH, which likely form a solid solution with ε‐FeOOH. In contrast to these Mg and Al end‐members, ε‐FeOOH has smaller diagonal and larger off‐diagonal elastic constants, leading to an eventual negative pressure dependence of its shear wave velocity. Because of this behavior, iron‐enriched solid solutions from this system have smaller shear wave velocities than surrounding mantle and therefore are a plausible contributor to large low‐shear velocity provinces (LLSVPs) which exhibit similar seismic properties. Additionally, ε‐FeOOH has substantial shear wave polarization anisotropy. Consequently, if iron‐rich solid solutions from the FeOOH–AlOOH–MgSiH<jats:sub>2</jats:sub>O<jats:sub>4</jats:sub> system at the core‐mantle boundary exhibit significant lattice‐preferred orientation due to the strong shear stresses which occur there, it may help explain the seismically observed <jats:italic>S</jats:italic><jats:sub><jats:italic>H</jats:italic></jats:sub> > <jats:italic>S</jats:italic><jats:sub><jats:italic>V</jats:italic></jats:sub> anisotropy in this region.</jats:p>