High‐Pressure Elasticity of δ‐(Al,Fe)OOH Single Crystals and Seismic Detectability of Hydrous MORB in the Shallow Lower Mantle

Oxyhydroxides like δ‐(Al,Fe)OOH may stabilize “water” in Mid‐Ocean Ridge Basalt (MORB) subducted into the Earth's lower mantle. The single‐crystal elasticity of δ‐(Al,Fe)OOH has not been experimentally constrained, hampering an accurate evaluation of the seismic detectability of this high‐pressure solid solution, and the presence of “water,” in the deep Earth. Here, we report the first experimental single‐crystal elasticity results of δ‐(Al0.97Fe0.03)OOH measured by X‐ray diffraction and Brillouin spectroscopy. We use our results to compute seismic properties of hydrous and anhydrous MORB at pressures and temperatures expected in slabs at shallow lower mantle conditions. We show that hydrous MORB is less dense than anhydrous MORB, but has faster aggregate seismic velocities. This suggests that hydration in MORB has an effect on velocities opposite to that observed in other lithologies, and further indicates that hydration of MORB increases the seismic contrast to the background mantle.

At ambient conditions, the crystal structure of δ-AlOOH and ε-FeOOH ( Figure S1a in Supporting Information S1) has space group P2 1 nm and consists of edge-sharing (Al,Fe)O 6 octahedral chains parallel to the c-axis, connected with each other through vertices (Gleason et al., 2008;Komatsu et al., 2006). A structural phase transition in δ-AlOOH and δ-(Al,Fe)OOH occurs at about 8-10 GPa, inducing an increase in symmetry from P2 1 nm to Pnnm (Ohira et al., 2019;Sano-Furukawa et al., 2018). This transition causes clear changes in the axial compressibility (Kuribayashi et al., 2014;Sano-Furukawa et al., 2009, 2018. Similar changes in the axial compressibility have been observed in ε-FeOOH at about 18 GPa, suggesting that Fe substitution increases the transition pressure of the P2 1 nm to Pnnm phase transition (Thompson et al., 2020). The Pnnm structure of δ-AlOOH displays a disordered configuration of the hydrogen (H) bonds (Figure S1b and S1c in Supporting Information S1) at the onset of the P2 1 nm to Pnnm phase transition. The H bond symmetrization is completed between 16 and 18.1 GPa (Sano-Furukawa et al., 2018). Therefore, the δ-AlOOH-rich solid solutions have Pnnm space group and symmetric H bonds in the lower mantle.
Here, we performed simultaneous X-ray diffraction (XRD) and Brillouin spectroscopy experiments on δ-(Al 0.97 Fe 0.03 )OOH single crystals up to 17.09(5) GPa to constrain the full elastic tensor of the Pnnm phase, that is, the stable phase at lower mantle conditions. XRD experiments were carried out up to 19.98(3) GPa. Our results were used, together with those available in the literature, to calculate aggregate properties of hydrous and anhydrous MORB in a P-T window relevant for slabs stagnating in the shallow lower mantle. Our model shows that despite being less dense, hydrous MORB is characterized by faster aggregate velocities with respect to anhydrous MORB, increasing the seismic velocity contrast to the background mantle.

Material Synthesis and Characterization
Single crystals of δ-(Al,Fe)OOH were synthesized in a multi-anvil apparatus at the Bayerisches Geoinstitut (BGI), University of Bayreuth, following the procedure described by Kawazoe et al. (2017). Two crystals, hereafter named H4765x1 and H4765x2, were selected based on their quality. These crystals have P2 1 nm space group at room conditions as determined by the presence of the h + l = 2n + 1 for k0l and k + l = 2n + 1 for 0kl reflections.
H4765x1 and H4765x2 crystals were oriented parallel to the   142 E and   201 E planes, and double-sided polished to a final thickness of about 15 μm. The oriented platelets were cut into half-circles for high-pressure experiments using a Focused Ion Beam (FIB) ( Figure S2 in Supporting Information S1) (Marquardt & Marquardt, 2012;Schulze et al., 2017). After FIB cutting, the final orientations in Cartesian coordinates (e 2 ║b, e 3 ║c) are (0.103, 0.836, 0.539) and (0.784, 0.021, 0.620) for H4765x1 and H4765x2, respectively. Further details on the synthesis procedure, quality assessment, sample selection, and FIB cutting can be found in Text S1 in Supporting Information S1.
The chemical compositions of the H4765x1 and H4765x2 were measured on half-circles, one from each of the two platelets, using an Electron Microprobe. Mössbauer spectroscopy was used to determine their Fe 3+/ Fe tot ratio (Text S2 in Supporting Information S1). According to our results, the chemical formula normalized to two oxygens per formula unit is Al 0.972(7) Fe 3+ 0.028(1) OOH for H4765x1, and Al 0.977(9) Fe 3+ 0.023(1) OOH for H4765x2.

High-Pressure Experiments
High-pressure measurements were carried out in a BX90 diamond-anvil cell (DAC) (Kantor et al., 2012), equipped with diamonds having a culet size of 400 μm. A laser-drilled 250 μm diameter hole was used as pressure chamber in a pre-indented Re gasket. Two FIB-cut platelets were loaded in the pressure chamber together with a ruby sphere used for pressure determination (Dewaele et al., 2004). High-pressure data were collected during three distinct runs, in which either He or Ne was used as pressure transmitting medium (Text S3 in Supporting Information S1).
Simultaneous XRD and Brillouin spectroscopy experiments on the Pnnm phase of δ-(Al 0.97 Fe 0.03 )OOH were performed between 8.67(1) and 17.09(5) GPa at the BGI. Further XRD experiments were performed up to 19.98(3) GPa. Technical details of the instrument installed at BGI are reported in Text S4 in Supporting Information S1 and elsewhere (Trots et al., 2011(Trots et al., , 2013. In our XRD investigations, no reflections relative to the P2 1 nm space group have been detected (Text S5 in Supporting Information S1), confirming that the P2 1 nm to Pnnm phase transformation had occurred before 8.67(1) GPa.
Brillouin spectroscopy experiments were performed at six distinct pressure points, for each platelet at different rotation angle (χ) with 20° interval over a 360° angular range. Details on the data analysis are provided in Text S4 in Supporting Information S1. The Pnnm phase of δ-(Al,Fe)OOH has orthorhombic symmetry, hence its elastic stiffness tensor consists of nine independent, non-zero coefficients (c ij ) that in Voigt notation are (Nye, 1985): c 11 , c 22 , c 33 , c 44 , c 55 , c 66 , c 12 , c 13 , c 23 . All nine c ij were constrained at each pressure point (Table S3 in Supporting Information S1) by fitting the χ-dependent variation of the acoustic compressional velocity, v P , and the two shear wave velocities, v S1 and v S2 , for both H4765x1 and H4765x2 platelets in a least-square fitting procedure of the Christoffel equation (Haussühl, 2007): where c ijkl are the elastic stiffness coefficients in tensorial notation, n j, n l the phonon direction cosines, ρ the density calculated from the unit-cell volumes obtained by XRD (Text S4 in Supporting Information S1), and δ ik the Kronecker delta. Voigt and Reuss bounds of the adiabatic bulk (K S ) and shear moduli (G) were calculated using the c ij and elastic compliance coefficients, s ij , respectively.

High-Pressure Elasticity of δ-(Al,Fe)OOH
Unit-cell volumes of H4765x1 and H4765x2 of the Pnnm phase (Table S1 in Supporting Information S1) have been normalized with respect to their values measured at 8.67(1) GPa and fitted using a third-order Birch-Murnaghan equation of state (BM3) (Birch, 1947) implemented in the EoSFit7 software (Angel et al., 2014;Gonzalez-Platas et al., 2016) using 8.67 GPa as reference pressure. The room pressure volume (V 0 ), isothermal bulk modulus (K T0 ) and its corresponding first pressure derivative (K' T0 ) were then calculated by extrapolation to ambient pressure. Results are reported in Table S2 in Supporting Information S1, while volumes normalized with respect to the Equation of State (EoS) parameter V 0 are plotted in Figure 1a together with literature data. The difference between this and previous studies ( Figure 1a, Table S2 in Supporting Information S1) results from a trade-off in the V 0 , K T0 , and K' T0 fitting parameters which complicate a quantitative assessment of the effect of Fe substitution on the compressibility of δ-AlOOH. The Pnnm ε-FeOOOH end-member is more compressible than δ-AlOOH (Thompson et al., 2020). However, the K T0 values obtained using a second-order Birch-Murnaghan equation of state (BM2), with K' T0 fixed to the value of 4 (Sano-Furukawa et al., 2009;Su et al., 2020; Table S2 in Supporting Information S1) show that samples with 5% of FeOOH substitution have the same K T0 as δ-AlOOH. The very low K T0 values reported by Ohira et al. (2019) are due to the relatively large K' T0 which are, however, poorly constrained. Due to the high quality of our data, we were able to tightly constrain the value of K' T0 which is clearly larger than 4. As a consequence, the value of K T0 appears slightly smaller than those reported for δ-AlOOH and δ-(Al 0.956 Fe 0.044 )OOH (Table S2 in Supporting Information S1). A K T -K' T0 confidence ellipse is provided in Figure S4 in Supporting Information S1.
The linear moduli, k, their first pressure derivatives, k´, and the unit-cell parameters at ambient conditions (a 0 , b 0, and c 0 ) have been obtained by fitting of a linearized BM3 implemented in EosFit7 (Angel et al., 2014), following the same procedure described for the unit-cell volumes. Results are tabulated in Table S2 in Supporting Information S1, and unit-cell parameters normalized to their EoS room pressure values are plotted versus pressure in Figure S5 in Supporting Information S1. No anomalies in the axial compressibility or the unit-cell axial ratios a/b, b/c, and a/c ( Figure S6 in Supporting Information S1) have been observed up to the highest pressure point, that is, 19.98(3) GPa.
Measured and calculated acoustic wave velocities obtained for both platelets at a pressure of 17.09(5) GPa are shown in Figure 1b, while a representative Brillouin spectrum is reported in Figure S7 in Supporting Information S1. The c ij and density values for each individual pressure are summarized in Table S3 and Figure S8 in Supporting Information S1. All c ij smoothly increase across the investigated pressure range, and their high-pressure behavior can be described by third-order finite strain expressions reported for individual c ij (Stixrude & Lithgow-Bertelloni, 2005; Text S6 in Supporting Information S1).
Ab initio Density Functional Theory (DFT) calculations have reported discrepant results on the c ij behavior of δ-AlOOH at high pressures (Cortona, 2017;Pillai et al., 2018;Tsuchiya & Tsuchiya, 2009). Our results are plotted together with Cortona (2017) and Tsuchiya and Tsuchiya (2009) in Figure S8 in Supporting Information S1. There is a very good agreement between our measured c 22 , c 44 , c 55 , c 66 , and c 13 values and those reported in the literature, whereas the other experimental c ij exhibit a different evolution with pressure ( Figure S8 in Supporting Information S1). However, discrepancies are negligible for the aggregate elastic moduli ( Figure 2a, the next section).

Aggregate Properties of δ-(Al,Fe)OOH
Voigt and Reuss bounds of the adiabatic bulk modulus K S and shear modulus G were calculated at each pressure using the c ij constrained in this study (Nye, 1985). Reuss-Voigt-Hill averages of K S and G were calculated as the arithmetic mean between Reuss and Voigt values (Hill, 1952; Table S4 in Supporting Information S1). Both K S and G show a monotonic increase with absolute pressure (Text S7 in Supporting Information S1) that can be described with third-order Eulerian finite strain equations (Stixrude & Lithgow-Bertelloni, 2005), as shown in Figure 2a. Fit results are reported in Table S5 in Supporting Information S1. To facilitate comparison, we used the same approach to fit theoretical data (Cortona, 2017) between 10 and 30 GPa (Figure 2a). Moreover, our K S and G values show negligible differences with the theoretical prediction from Cortona (2017).
The aggregate compressional, v P , and shear, v S wave velocities (Text S4 in Supporting Information S1) of the sample investigated in this study are slightly faster than those reported by previous Brillouin spectroscopy results on powdered samples of δ-AlOOH (Mashino et al., 2016) and δ-(Al 0.956 Fe 0.044 )OOH (Su et al., 2020;Figure 2b). The discrepancies between our results and those available in the literature cannot be simply explained by compositional differences since the small amount of Fe 3+ present in our samples and in that of Su et al. (2020) should have a limited effect on the wave velocity of Pnnm phase of δ-AlOOH as it has no detectable effect on  (Table S1 in Supporting Information S1), and pressures calculated using the BM3 EoS parameters (P calc , Table S2 in Supporting Information S1) as function of P ruby . Differences are well within uncertainties, with an average deviation of 0.08 GPa and maximum deviation of 0.2 GPa (about 1%). (b) Observed (filled symbols) and calculated (solid curves) acoustic wave velocities of both single-crystals platelets of δ-(Al 0.97 Fe 0.03 )OOH as a function of the rotation angle χ at 17.09(5) GPa.
its compressibility (Table S2 in Supporting Information S1). However, Brillouin spectroscopy experiments on powdered samples can be affected by crystallographic preferred orientation, grain-grain interactions, and/or opto-elastic coupling effects that can influence wave velocities (Marquardt & Thomson, 2020) and may explain the observed discrepancies. The acoustic wave velocities measured for ε-FeOOH up to 24 GPa (Ikeda et al., 2019) are much slower than those reported here. However, they cannot be used to assess quantitively the effect of Fe substitution as ε-FeOOH has the P2 1 nm space group below about 17 GPa (Thompson et al., 2020).

Implications for the Detection of Water in Stagnant Slabs in the Shallow Lower Mantle
The interpretation of seismological observations is crucial to track the transport of hydrous material in subduction zones (Wang et al., 2020), including that associated with the subduction of hydrous MORB (e.g., Garth & Rietbrock, 2014, 2017. Seismic tomography indicates that subducting slabs enter the lower mantle in several locations, and sometimes stagnate at the top of the lower mantle (e.g., Fukao & Obayashi, 2013). Analysis of diamond inclusions further suggests that oceanic crust is recycled into the lower mantle (Nestola et al., 2018), where it might explain low-velocity seismic wave observations detected at the top of the lower mantle (Gréaux et al., 2019).
Recent phase relation experiments have shown that hydrous MORB is capable of retaining water down to the lower mantle through a continuous chain of stable hydrous phases, ending with the solid solution formed by phase H (MgSiO 4 H 2 ), δ-AlOOH, and ε-FeOOH (H-δ-ε) at pressures exceeding 25 GPa . Here, we combine our single-crystal elasticity data set on δ-(Al 0.97 Fe 0.03 )OOH with previous results (Table S6 in Supporting Information S1) to compute the aggregate properties of hydrous and anhydrous MORB in a P-T window relevant for slabs in the shallow lower mantle. Our model is based on the thermodynamic formalism of Stixrude and Lithgow-Bertelloni (2005), and relies on mineral volume fractions and compositions constrained by previous experimental studies at relevant P-T conditions (Ishii et al., 2019;Liu et al., 2019;Tables S7 and S8 in Supporting Information S1). The aggregate elastic moduli and density of the Pnnm phase of δ-(Al 0.97 Fe 0.03 )OOH have been extrapolated to 30 GPa. This is justified by the fact that previous XRD results (e.g., Sano-Furukawa et al., 2009) show a smooth and continuous behavior of the unit-cell volume compression for Pnnm δ-AlOOH up to pressures above 30 GPa, suggesting that the H bond symmetrization does not cause any detectable discontinuity in the elastic behavior of these H-δ-ε oxyhydroxides. In our model, H-δ-ε oxyhydroxide in hydrous MORB is treated as a two-component mixture with molar ratio of MgSiO 4 H 2 :(Al 0.97 Fe 0.03 )OOH = 25:75. The small Fe content is consistent with the recent phase relations reported for hydrous MORB (Liu et al., 2019). The bulk modulus  Cortona's (2017) data. All fits are based on 3rd-order Eulerian finite strain equations (Stixrude & Lithgow-Bertelloni, 2005). Most uncertainties are within the symbol size.
used for the modeling of phase H is determined from the P-V-T data reported by Nishi et al. (2018) data, while our single-crystal elasticity data set is used to model δ-(Al 0.97 Fe 0.03 )OOH. Since no experimental constraints on the shear modulus at ambient pressure or its pressure derivative is currently available for phase H, they are assumed identical to those of δ-(Al 0.97 Fe 0.03 )OOH. Moreover, the thermal parameters of δ-(Al 0.97 Fe 0.03 )OOH are assumed identical to those of δ-AlOOH (Duan et al., 2018), while those of phase H are determined by refitting the P-V-T data of Nishi et al. (2018) using a Debye model (Stixrude & Lithgow-Bertelloni, 2005). Our model does not solely consider the formation of H-δ-ε oxyhydroxides as a distinctive feature of MORB hydration, but it also takes into account various factors including the reduction of SiO 2 stishovite content and a depletion of its Al concentration, as well as the complete dissolution of minerals such as calcium ferrite and (Mg,Fe)O-all based on the latest phase relation results used as references for our modeling (Ishii et al., 2019;Liu et al., 2019). Isotropic aggregate properties were calculated between 25 and 30 GPa, corresponding to depths of 700-800 km, and at temperatures of 800°C-1200°C, covering the P-T range expected in subducting slabs entering the lower mantle (Kirby et al., 1996). Further details of the modeling are included in Text S8 in Supporting Information S1.
Our model indicates that densities of hydrous MORB are reduced by 2.5% with respect to anhydrous MORB. However, the hydration of MORB through the formation of H-δ-ε oxyhydroxides results in an increase of all the aggregate velocities, v S , v P , and v ϕ , of up to 1.6% for v S (Figure 3). Noticeably, MORB hydration through the formation of H-δ-ε oxyhydroxides is coupled with a depletion in the SiO 2 stishovite content; hence, the faster aggregate velocities characterizing hydrous MORB cannot be reconciled with an increase in the SiO 2 stishovite content.
Typically, slab hydration is associated with a decrease of the slab aggregate velocity as, for example, recently shown for harzburgite and peridotite above and below the 660 km discontinuity . Our model suggests that the opposite is true for MORB-like lithologies at lower mantle depths. Our model predicts no marked difference in terms of aggregate velocity ratios, v P /v S and v ϕ /v S , and relative differences of the aggregate velocities between hydrous and anhydrous MORB tend to decrease with pressure.
Based on our data, we evaluated the seismic signature and densities of hydrous MORB in the shallow lower mantle, in a scenario where it is in contact with mantle of pyrolitic composition. Aggregate properties of the pyrolitic mantle were modeled at two different P-T conditions, that is, 26 GPa, 1600°C and 28 GPa, 1800°C, corresponding to depths of about 720-760 km (Katsura et al., 2010). Aggregate properties of both hydrous and anhydrous MORB were also calculated at 26 and 28 GPa, but the MORB temperature (T MORB ) was varied between 800°C and 1200°C to cover the T range expected in slabs in the shallow lower mantle (Kirby et al., 1996). Our model was then used to express the relative differences dln in % between MORB and pyrolite in terms of density ρ and aggregate velocities v P and v S (Figure 4). Cold, anhydrous MORB shows the largest difference in terms of density with respect to the pyrolitic mantle-a difference that can reach up to 4.9% if T MORB is assumed to be 800°C. Hydration is expected to decrease MORB density, however, hydrous MORB appears still denser than the pyrolitic mantle at the investigated P-T conditions. For example, at 26 GPa and 1200°C T MORB , hydrous MORB is ∼1.6% denser than pyrolite at 1600°C (Figure 4). The reduced negative buoyancy of hydrous MORB would make it more likely to stagnate and accumulate in the shallow lower mantle when encountering a viscosity increase at the 660 km discontinuity or in the lower mantle (Deng & Lee, 2017;Marquardt & Miyagi, 2015;Rudolph et al., 2015). Sinking to the deeper mantle may be favored in anhydrous MORB for the opposite reason. At the same time, hydrous MORB produces a significantly stronger seismic contrast with the background mantle, for both shear and compressional velocities (Figure 4), making accumulated hydrous MORB more visible in seismic tomography models. The velocity contrast generally decreases as the MORB in the slab heats up and the P-wave contrast between anhydrous MORB and ambient mantle drops below 1% when their temperature difference is smaller than 600°C (i.e., T MORB > 1000°C) at 26 GPa, suggesting that it may be difficult to detect relatively hot anhydrous MORB in P-wave tomography models (e.g., Fukao & Obayashi, 2013). Hydrous MORB at the same temperature, instead, is still about 2.5% faster as compared to pyrolite and would likely produce a substantially stronger "slab signature" in P-wave tomography models, for example, in the Tonga subduction system (Fukao et al., 2001;van der Hilst, 1995). Since the increase in aggregate velocities is coupled with a density reduction, the seismic contrast between pyrolite and MORB in terms of acoustic impedance,   E Z v , is not very sensitive to hydration ( Figure S9 in Supporting Information S1).
This observation is opposite to previous inferences made on the seismic visibility of hydration in the transition zone, where changes in impedance contrast across the 410 km discontinuity were suggested as a characteristic feature of hydration .