Vibrational anisotropy of δ-(Al,Fe)OOH single crystals as probed by nuclear resonant inelastic X-ray scattering

The formation of high-pressure oxyhydroxide phases spanned by the components AlOOH-FeOOH-MgSiO2(OH) 2 in experiments suggests their capability to retain hydrogen in Earth's lower mantle. Understanding the vibrational properties of high-pressure phases provides the basis for assessing their thermal properties, which are required to compute phase diagrams and physical properties. Vibrational properties can be highly anisotropic, in particular for materials with crystal structures of low symmetry that contain directed structural groups or components. We used nuclear resonant inelastic X-ray scattering (NRIXS) to probe lattice vibrations that involve motions of Fe-57 atoms in delta-(Al0.87Fe0.13)OOH single crystals. From the recorded single-crystal NRIXS spectra, we calculated projections of the partial phonon density of states along different crystallographic directions. To describe the anisotropy of central vibrational properties, we define and derive tensors for the partial phonon density of states, the Lamb-Mossbauer factor, the mean kinetic energy per vibrational mode, and the mean force constant of Fe-57 atoms. We further show how the anisotropy of the Lamb-Mossbauer factor can be translated into anisotropic displacement parameters for Fe-57 atoms and relate our findings on vibrational anisotropy to the crystal structure of delta-(Al,Fe)OOH. As a potential application of single-crystal NRIXS at high pressures, we discuss the evaluation of anisotropic thermal stresses in the context of elastic geobarometry for mineral inclusions. Our results on single crystals of delta-(Al,Fe)OOH demonstrate the sensitivity of NRIXS to vibrational anisotropy and provide an in-depth description of the vibrational behavior of Fe3+ cations in a crystal structure that may motivate future applications of NRIXS to study anisotropic vibrational properties of minerals.