Abstract
Abstract. 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 57Fe atoms in δ-(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–Mössbauer factor, the mean kinetic energy per vibrational mode, and the mean force constant of 57Fe atoms. We further show how the anisotropy of the Lamb–Mössbauer factor can be translated into anisotropic displacement parameters for 57Fe atoms and relate our findings on vibrational anisotropy to the crystal structure of δ-(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 δ-(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.
Highlights
High-pressure experiments have shown that the oxyhydroxide phase δ-AlOOH and the dense hydrous magnesium silicate (DHMS) MgSiO2(OH)2, referred to as δ-phase and phase H, respectively, are stable at pressures and temperatures relevant to Earth’s lower mantle (Sano et al, 2008; Nishi et al, 2014; Duan et al, 2018)
This paper focuses on vibrational anisotropy, we note that an isotropic version of a projected vibrational property p(E) can be calculated from the trace of the tensor of the polarized property pij (E) as p(E) = pij (E)δij /3
We recorded nuclear resonant inelastic X-ray scattering (NRIXS) spectra with high statistical quality on single crystals of the high-pressure oxyhydroxide phase δ(Al,Fe)OOH at ambient conditions to investigate the effect of vibrational anisotropy of 57Fe atoms on the projected phonon density of states (PDOS) and related properties
Summary
High-pressure experiments have shown that the oxyhydroxide phase δ-AlOOH and the dense hydrous magnesium silicate (DHMS) MgSiO2(OH), referred to as δ-phase and phase H, respectively, are stable at pressures and temperatures relevant to Earth’s lower mantle (Sano et al, 2008; Nishi et al, 2014; Duan et al, 2018). Experiments that subjected natural chlorite and antigorite samples to pressures and temperatures of the lower mantle produced complex solid solutions with an FeOOH component in addition to AlOOH and MgSiO2(OH), again in coexistence with bridgmanite (Nishi et al, 2015). Solid solutions between δ-AlOOH and -FeOOH have been synthesized (Nishi et al, 2017; Kawazoe et al, 2017). These experimental observations suggests that high-pressure oxyhydroxide phases may form in Earth’s lower mantle when hydrous fluids react with bridgmanite-bearing mineral assemblages. The vibrational properties of crystalline solids and in particular the energy distribution of lattice vibrations as expressed by the phonon density of states (PDOS) determine central thermodynamic properties, such as heat capacity and vibrational entropy, that are needed to assess phase stabil-
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