Hydrogen Effect on the Sound Velocities of Upper Mantle Omphacite

Clinopyroxene (Cpx) is commonly believed to be the best structural water (hydrogen) carrier among all major upper mantle nominally anhydrous minerals (NAMs). In this study, we have measured the single-crystal elastic properties of a Cpx, a natural omphacite with ~710 ppm water at ambient pressure (P) and temperature (T) conditions. Utilizing the single-crystal X-ray diffraction (XRD) and electron microprobe data, the unit cell parameters and density were determined as a = 9.603(9) Å, b = 8.774(3) Å, c = 5.250(2) Å, β = 106.76(5)o, V = 255.1(4) Å3, and % = 3.340(6) g/cm3. We performed Brillouin spectroscopy experiments on four single crystals along a total of 52 different crystallographic directions. The best-fit single-crystal elastic moduli (Cijs), bulk and shear moduli were determined as: C11 = 245(1) GPa, C22 = 210(2) GPa, C33 = 249.6(9) GPa, C44 = 75.7(9) GPa, C55 = 71.2(5) GPa, C66 = 76(1) GPa, C12 = 85(2) GPa, C13 = 70(1) GPa, C23 = 66(2) GPa, C15 = 8.0(6) GPa, C25 = 6(1) GPa, C35 = 34.7(6) GPa, and C46 = 8.7(7) GPa, KS0 = 125(3) GPa, and G0 = 75(2) GPa, respectively. Compared with the anticipated elastic properties of an anhydrous omphacite with the same chemical composition, our results indicate that the incorporation of ~710 ppm structural water has no resolvable effect on the aggregate elastic properties of omphacite, although small differences (up to ~9 GPa) were observed in C13, C25, C44, and C66.


Introduction
Quantifying the water content in the Earth's upper mantle through seismic observations requires the knowledge of how structural water content affects the elastic properties for various nominally anhydrous minerals (NAMs) [1,2]. Whether the upper mantle is universally or locally hydrated is still controversial [3,4], although the water carried down by the subducting slabs is considered a major source of the water in the Earth's interior [5][6][7][8]. Subduction is one of the main driving forces of the mantle convection and is responsible for many geological processes in the Earth's interior [9,10]. The basaltic slab crust transforms into eclogite at depths greater than~100 km and it remains denser than the ambient mantle down to~600 km depths [11]. As the solid solution between diopside (Di, CaMgSi 2 O 6 ) and jadeite (Jd, NaAlSi 2 O 6 ), omphacite is the major mineral phase that constitutes up to 80 vol% of eclogite. The subducting slabs carry the surface water into the Earth's interior primarily in the form of structural water; thus, it is important to know how much structural water can be stored in the major mineral phases in the subducting slabs. The maximum solubility of H 2 O-depending on temperature (T) and pressure (P)-in pure Di ranges from 121-568 ppm, but in aluminous Di, this value increases up to 2500 ppm [12]. Natural Clinopyroxene (Cpx) samples can host as high as 2000 ppm water in their crystal structures [12,13], much higher than all other major upper mantle minerals such as olivine, orthopyroxene, or garnet. As a type of Cpx, which can retain the highest amount of water in its structure among all upper mantle NAMs, omphacite is likely both an important water carrier as well as a potential water reservoir in the Earth's interior [5,6,[14][15][16][17].
Structural water (hydrogen) is incorporated into the Cpx crystal structure through cation vacancies primarily on the M2 site [13,18]. Previous experimental studies on olivine, another NAM commonly found in the ambient upper mantle, have suggested that the incorporation of hydrogen into the NAMs decreases both the P-wave and S-wave velocities (V p and V s ) [19][20][21][22][23]. This softening effect of structural water can potentially affect our understanding of the upper mantle seismic structures and mineralogical composition, as well as the total water budget of the Earth's interior [6,[21][22][23][24][25]. In addition, there is a growing interest in the mineral physics and petrology communities in using various minerals' thermoelastic parameters to establish new elastic geobarometers for interpreting various deep geological processes that happened in the past [26,27]. Unfortunately, most previous investigations are restricted to hydrous olivine and its high-P polymorphs [21][22][23][28][29][30], and no experimental sound velocity measurements have previously been made for hydrous Cpx. Therefore, in this study, we performed single-crystal Brillouin spectroscopy experiments on a hydrous omphacite sample with~710 ppm water in order to study the possible structural water effect on the single-crystal elastic properties of omphacite.

Materials and Methods
The omphacite crystals were hand-selected from the natural omphacite sample SBB-46 from the South African Bobbejaan mine. Four different crystals were double-side polished to less than 30 µm thickness. Under optical examination, all crystals were inclusion-and scratch-free. The chemical composition (Na 0.396 K .005 )(Mg 0.537 Ca 0.550 Fe 0.072 Cr 0.022 Ti 0.007 Mn 0.001 )Al 0.433 Si 1.971 O 6 (simplified to Di 59.1 Jd 40.9 ) and the~710 ppm hydrogen content of SBB-46 was determined in [13].
In order to determine the unit cell parameters and crystal orientation, we carried out the single-crystal XRD experiments for the 2 crystals a and b at ambient P-T condition at experimental station 13-BM-C, GeoSoilEnviroCARS (GSECARS), Advanced Photon Source, Argonne National Laboratory. The remaining 2 crystals c and d were measured at ambient P-T condition in the X-Ray Atlas Diffraction Lab at the University of Hawai'i at Manoa.
At GSECARS, the X-ray beam was monochromated to 28.6 keV with the beam size of~12 µm × 18 µm determined at the full width at half maximum. The omphacite crystal was placed in an empty DAC, which had an opening angle of ±38 • . Two separate detector positions were used by rotating a MAR165 Charge Coupled Device detector on a rotational arm [31]. The first detector angle was perpendicular to the incident X-Ray beam, while the second detector position was offset from the first position by 20 • around the horizontal axis. Sample-to-detector distance and detector tilting were calibrated in the Dioptas program [32] using NIST standard LaB 6 powder. The diffraction images were collected in both wide-angle images that covered the whole ±38 • opening angle range and 1 • step-segments with 1 s/ • exposure time. At the X-Ray Atlas Diffraction Lab in University of Hawai'i, a Bruker D8 Venture XRD diffractometer with Incoatec IµS 3.0 AgKα microfocus source, Helios focusing optics, Photon II detector was used for collecting the single-crystal diffraction images at a wide range of scattering angles. Diffraction data from both experiments was processed using Bruker APEX III software. For the needs of this study, full structure refinement was not performed, and only unit cell parameters were refined.
We performed the Brillouin spectroscopy experiments on all 4 double-polished SBB-46 omphacite single crystals at the High-P Laser Spectroscopy Laboratory at University of New Mexico. The light source was a 532-nm 300-mW single-mode diode-pumped solid-state laser. The experiment utilized a 50 • symmetric forward scattering geometry, with the scattering angle precisely calibrated to be 50.42(5) o using the Corning 7980 standard silica glass [33,34]. V p and V s were determined for all 4 pre-oriented samples at ambient P-T condition for a total of 52 crystallographic directions. Each sample was measured at 13 different χ angles (0 to be 50.42(5) o using the Corning 7980 standard silica glass [33,34]. Vp and Vs were determined for all 4 pre-oriented samples at ambient P-T condition for a total of 52 crystallographic directions. Each sample was measured at 13 different χ angles (0°, 30°, 60°, 120°, 150°, 180°, 195°, 225°, 255°, 285°, 315°, 345° and 360°) along the 360° azimuth to account for any possible geometric errors with an average collection time of 10 min per spectrum. The resulting Brillouin spectra all have very high signal-tonoise ratios ( Figure 1).

Results and Discussion
The single-crystal XRD measurements for all four crystals yielded the averaged unit cell parameters of the SBB-46 omphacite of a = 9.603 (9) (Figure 2). The density at ambient condition was then calculated as ρ0 = 3.340(6) g/cm 3 . Omphacite crystals are known to assume one of two different symmetries, depending on the crystallization conditions: the disordered high-temperature phase crystallizes with space group C2/c, whereas the cation-ordered phase crystallizes with space group P2/n [35]. At ambient pressure, the order-disorder transition takes place at 725 °C [36]. The omphacite SBB-46 had a C2/c symmetry based on its high T thermal history. The difference in cation ordering was not found to have a resolvable effect on the elastic properties beyond experimental uncertainties [37].

Results and Discussion
The single-crystal XRD measurements for all four crystals yielded the averaged unit cell parameters of the SBB-46 omphacite of a = 9.603 (9) (Figure 2). The density at ambient condition was then calculated as 0 = 3.340(6) g/cm 3 . Omphacite crystals are known to assume one of two different symmetries, depending on the crystallization conditions: the disordered high-temperature phase crystallizes with space group C2/c, whereas the cation-ordered phase crystallizes with space group P2/n [35]. At ambient pressure, the order-disorder transition takes place at 725 • C [36]. The omphacite SBB-46 had a C2/c symmetry based on its high T thermal history. The difference in cation ordering was not found to have a resolvable effect on the elastic properties beyond experimental uncertainties [37].
The single-crystal C ij s for the SBB-46 hydrous omphacite under ambient conditions were calculated through the least-squares inversion using the Christoffel equation. The best-fit C ij model was:  The single-crystal elastic properties of anhydrous omphacite at ambient conditions had been measured [39][40][41][42][43][44] and systematically analyzed within a wide compositional range [44]. As shown in Figure 3, within the Di-Jd solid solution, most elastic moduli showed a close-to-ideal linear mixing trend except C13 and C23. The C33, C55, and C35 presented in Ref. [44] lay outside the trends determined from other measurements, which can be explained by the high Tschermak content of the sample (12 mol%). The bulk and shear elastic moduli (Ks and G), as well as most of the single-crystal Cijs of the hydrous omphacite SBB-46, were well within the 95% confidence interval determined by all of the previous measurements of anhydrous omphacite samples within the Di-Jd solid solution (Table 1). A few single-crystal elastic moduli such as C13, C25, C44, and C66 showed a small decrease within the Di-Jd solid solution (up to ~9 GPa), deviating outside of the 95% confidence interval, which might have been caused by the incorporation of water into its crystal structure (Table 1). However, the decrease of these single-crystal elastic moduli caused by hydration is unlikely to produce a strong seismic anomaly. For example, the ~7% decrease of C44 and C66 caused by ~710 ppm water transforms to about 3.5% reduction in [010] polarized Vs propagating along the [001] and [100] directions, respectively. Considering the 50-70 vol% of omphacite in the eclogite rock, as well as the elastically isotropic nature of the garnet, it is difficult for the decrease of Vs in the eclogite rock in a realistic scenario to exceed 1%, unless near-perfect alignment of the omphacite crystals takes place in the form of SL-type fabrics [45][46][47][48]. In addition, the aggregate Vp and Vs did not show any structural waterinduced softening either ( Figure 4). Therefore, it is unlikely that the hydration of omphacite crystals would affect the seismic properties of the subducted slab crust. Diamonds, circles, and triangles represent experimentally determined V p , V s1 , and V s2 , respectively. The dashed lines were calculated from the best fit single-crystal C ij model. Errors were smaller than the symbols.
The single-crystal elastic properties of anhydrous omphacite at ambient conditions had been measured [39][40][41][42][43][44] and systematically analyzed within a wide compositional range [44]. As shown in Figure 3, within the Di-Jd solid solution, most elastic moduli showed a close-to-ideal linear mixing trend except C 13 and C 23 . The C 33 , C 55 , and C 35 presented in Ref. [44] lay outside the trends determined from other measurements, which can be explained by the high Tschermak content of the sample (12 mol%). The bulk and shear elastic moduli (K s and G), as well as most of the single-crystal C ij s of the hydrous omphacite SBB-46, were well within the 95% confidence interval determined by all of the previous measurements of anhydrous omphacite samples within the Di-Jd solid solution (Table 1). A few single-crystal elastic moduli such as C 13 , C 25 , C 44 , and C 66 showed a small decrease within the Di-Jd solid solution (up to~9 GPa), deviating outside of the 95% confidence interval, which might have been caused by the incorporation of water into its crystal structure (Table 1). However, the decrease of these single-crystal elastic moduli caused by hydration is unlikely to produce a strong seismic anomaly. For example, the~7% decrease of C 44 and C 66 caused by~710 ppm water transforms to about 3.5% reduction in [010] polarized Vs propagating along the [001] and [100] directions, respectively. Considering the 50-70 vol% of omphacite in the eclogite rock, as well as the elastically isotropic nature of the garnet, it is difficult for the decrease of V s in the eclogite rock in a realistic scenario to exceed 1%, unless near-perfect alignment of the omphacite crystals takes place in the form of SL-type fabrics [45][46][47][48]. In addition, the aggregate V p and V s did not show any structural water-induced softening either (Figure 4). Therefore, it is unlikely that the hydration of omphacite crystals would affect the seismic properties of the subducted slab crust.  [44]. The results are compared with the hydrous omphacite measured in (g) this study. Dashed lines show the compositional dependence of Cijs, Ks, and G. Shaded regions represent the 95% confidence intervals determined in [44]. Table 1. Elastic moduli of the hydrous omphacite sample measured in this study and the anhydrous omphacite with the same chemical composition predicted from Hao et al., 2019 [44]. The uncertainties for the anhydrous omphacite are defined by the 95% confidence intervals shown in   [44]. The results are compared with the hydrous omphacite measured in (g) this study. Dashed lines show the compositional dependence of C ij s, K s , and G. Shaded regions represent the 95% confidence intervals determined in [44]. Table 1. Elastic moduli of the hydrous omphacite sample measured in this study and the anhydrous omphacite with the same chemical composition predicted from Hao et al., 2019 [44]. The uncertainties for the anhydrous omphacite are defined by the 95% confidence intervals shown in Figure 3.

Elastic Moduli
Anhydrous Di59.1Jd40.9 SBB-46 Di59.1Jd40.9~710 ppm Water Universal Anisotropy Index (A U ) which described the overall elastic anisotropy for any materials with arbitrary symmetry, (2) V p azimuthal anisotropy Index (A Vp ) which was the maximum difference in V p along all crystallographic directions divided by the aggregate V p , and (3) the polarization anisotropy Index for V s (D Vs ) which measured the maximum velocity difference between two orthogonally polarized V s that propagated in the same direction. Among these indices, only the A U for SBB-46 was slightly lower than the expected value for its anhydrous counterpart. This again suggested that the effect of~710 ppm water on the aggregate elastic properties of omphacite was very small if not negligible. It was also worth noting that Ref. [44] again lay outside the trends determined from all of the other studies probably due to the high Tschermak content (12 mol%) of the sample. This observation is also important for the recent development of elastic geobarometry [26,27]. The elastic anisotropy seems to be a major factor that needs to be taken into account for calculating the Ps for various geological processes, in particular when the rock has experienced high-grade metamorphism and eclogite facies are found [49][50][51].
Minerals 2019, 9, x FOR PEER REVIEW 6 of 9 The Universal Anisotropy Index (A U ) which described the overall elastic anisotropy for any materials with arbitrary symmetry, (2) Vp azimuthal anisotropy Index (A Vp ) which was the maximum difference in Vp along all crystallographic directions divided by the aggregate Vp, and (3) the polarization anisotropy Index for Vs (D Vs ) which measured the maximum velocity difference between two orthogonally polarized Vs that propagated in the same direction. Among these indices, only the A U for SBB-46 was slightly lower than the expected value for its anhydrous counterpart. This again suggested that the effect of ~710 ppm water on the aggregate elastic properties of omphacite was very small if not negligible. It was also worth noting that Ref. [44] again lay outside the trends determined from all of the other studies probably due to the high Tschermak content (12 mol%) of the sample. This observation is also important for the recent development of elastic geobarometry [26,27]. The elastic anisotropy seems to be a major factor that needs to be taken into account for calculating the Ps for various geological processes, in particular when the rock has experienced high-grade metamorphism and eclogite facies are found [49][50][51].

Conclusions
For the first time, we have experimentally explored the effect of structural water on the single-crystal elastic properties of a hydrous omphacite sample SBB-46. Most of the single-crystal elastic moduli of the hydrous omphacite SBB-46 were well within the 95% confidence interval determined by all the previous measurements of anhydrous omphacite samples within the Di-Jd solid solution. The small decrease of the shear elastic moduli C 13 , C 25 , C 44 , and C 66 is unlikely to result in a strong seismic anomaly unless the eclogite has experienced extremely high strain and a near-perfect alignment of most omphacite crystals takes place. Based on this study, low to moderate amounts of structural water (~710 ppm) are unlikely to have significant impact on the seismic velocities of the subducted oceanic crust. Further studies of hydrous omphacite at a much higher water concentration (e.g., 1800 ppm [13]) and at high P-T conditions might provide additional insights.