Vibrational anisotropy of <i>δ</i>-(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 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.

On EXAFS Debye-Waller factor and recent advances

The effects of structural and vibrational disorder on the EXAFS signals are parameterized in terms of the Debye Waller (DW) factor. Here the vibrational contribution is addressed, which for most systems can be singled out by studying the temperature dependence of the EXAFS DW factor, which corresponds to a good accuracy to the parallel mean square relative displacement (MSRD) around the inter-atomic equilibrium distance. By comparing the first-shell EXAFS thermal expansion with the crystallographic thermal expansion one can evaluate the perpendicular MSRD. The results of recent measurements on copper and on several tetrahedral semiconductors are here critically compared and some properties of the MSRDs are discussed, such as the dependence of correlation, force constants and vibrational anisotropy on crystal structure and bond ionicity as well as the relative merits of the correlated Debye and Einstein models. The anharmonic contribution to the parallel MSRD of CdTe has been evaluated and a quasi-harmonic analysis has been attempted, leading to an estimation of the bond Grüneisen parameter.