Single-Crystal Elasticity of Antigorite at High Pressures and Seismic Detection of Serpentinized Slabs

The subduction of serpentinized slabs is the dominant process to transport “water” into Earth's mantle, and plays a pivotal role for subduction dynamics. Antigorite, the most abundant serpentine mineral in subduction settings, may imprint a seismic signature on serpentinized slabs, making them seismically distinguishable from the dry, non-serpentinized ones. However, the complete single-crystal elasticity of antigorite has not been experimentally constrained at high pressures, hindering the use of seismological approaches to detect serpentinization in subducting slabs. Here, we report the full elastic stiffness tensor of antigorite by single-crystal Brillouin spectroscopy and X-ray diffraction up to 7.71(5) GPa. We use our results to model seismic properties of antigorite-bearing rocks and show that their seismological detectability depends on the geometrical relation between seismic wave paths and foliation of serpentinized rocks. In

Antigorite is the serpentine mineral stable at high pressures and temperatures, hence it is the most abundant serpentine in altered (serpentinized) slabs (Schwartz et al., 2013).Previous studies suggest that antigorite in subducting slabs may break down at relatively low depths, resulting in a discharge of upward migrating fluids, which might contribute to the further serpentinization of the mantle wedge (DeShon & Schwartz, 2004), as well as triggering arc magmatism (Schmidt & Poli, 1998) and episodic tremor (Campione & Capitani, 2013;Ferrand et al., 2017;Kaproth & Marone, 2013).In relatively cold subduction settings, however, antigorite may be preserved in the slab interior up to about 180 km depth, playing a key role in recycling water and other volatiles by carrying them to the deep Earth's mantle (Frost, 1999;Krantz et al., 2019;Ulmer & Trommsdorff, 1995), a process supported by the analysis of diamond inclusions (Smith et al., 2021).Therefore, mapping the distribution of antigorite-bearing rocks within subducting slabs becomes pivotal to evaluate different scenarios, and quantify the deep recycling of water and other volatiles in subduction zones.
Antigorite crystalizes in the monoclinic system, and its main structural features are sinusoidal-like 1:1 layers of octahedrally and tetrahedrally coordinated cation sites stacked perpendicularly to the (001) basal plane (Figure S1a in Supporting Information S1; Capitani & Mellini, 2004, 2006).Specifically, octahedra share edges with each other, while tetrahedra are connected via their vertices to form a pseudo-hexagonal ring arrangement with a periodic polarity reversal (Figure S1b in Supporting Information S1; Capitani & Mellini, 2005).Previous computational (Mookherjee & Capitani, 2011) and experimental investigations (Bezacier et al., 2010(Bezacier et al., , 2013;;Marquardt et al., 2015) reported antigorite single crystals to be relatively stiff along directions within the basal plane, but very compressible perpendicular to it.Thus, antigorite single crystals show an important elastic anisotropy at room pressure, where the shear waves polarized parallel to the layering are twice as fast as those polarized perpendicular to it (Bezacier et al., 2010).Importantly, serpentine minerals in subduction zones are expected to accommodate most of the deformation due to their relatively weak mechanical strength (Escartín et al., 1997(Escartín et al., , 2001;;Hirth & Guillot, 2013).Thus, the development of a crystallographic preferred orientation (CPO) is expected in antigorite, with crystallites aligning their (001) basal plane parallel to the flow deformation plane, as found in naturally and experimentally deformed serpentine-bearing samples (Katayama et al., 2009;Kern et al., 1997;Morales et al., 2013;Padrón-Navarta et al., 2012).The combination of a marked CPO with a large elastic anisotropy makes antigorite a strong candidate to explain the seismic shear wave anisotropy observed in subduction zones.In subducting slabs, antigorite-bearing rocks are predicted to eventually align their foliation vertically and parallel to the trench, as the slab rotates around an axis parallel to the trench line during subduction (Faccenda et al., 2008).Therefore, seismic waves traveling vertically and parallel along slabs may be sampling antigorite-bearing rocks in a direction parallel to foliation, possibly causing shear wave delay times in the order of seconds (Faccenda et al., 2008) and potentially making serpentinized slabs the major contributor to the delay times in shear waves observed in many subduction zones (Long & Silver, 2008).However, the single-crystal elastic stiffness tensor of antigorite has not yet been fully constrained at high pressures, and previous models largely rely on either room pressure measurements (Bezacier et al., 2010) or theoretical predictions (Mookherjee & Capitani, 2011).
In this study, and for the first time, the complete elastic stiffness tensor of antigorite single crystals was derived experimentally at high pressures.Our results are based on X-ray diffraction (XRD) and Brillouin spectroscopy measurements performed on two oriented, double-side polished single-crystal platelets of natural antigorite, that were pressurized simultaneously in a diamond-anvil cell (DAC) up to 7.71(5) GPa.The elasticity data set obtained in the present work was combined with previously determined crystallographic textures and microstructural information to model seismic properties of deformed antigorite-bearing rocks.Seismic properties at relevant pressure conditions were characterized in terms of the degree of serpentinization, that is, antigorite fraction, and pressure.Our model indicates that low serpentinization degrees, and/or particular geometrical relations between seismic wave propagation and antigorite foliation, may result in antigorite-bearing rocks showing low shear wave splitting, making them indistinguishable from dry, non-serpentinized rocks.Our findings provide new bounds on the seismic detectability on serpentinization in slabs, further suggesting that considering seismic wave paths is crucial to accurately map antigorite-bearing rocks in slabs through the interpretation of seismic anisotropy.

Materials and Methods
Samples investigated in this study belong to the MG 159 antigorite specimen extracted from the Malenco serpentinite body.A comprehensive description of the geological framework, and sampling details of the MG 159 antigorite specimen are available in Mellini et al. (1987).According to Capitani & Mellini (2006), the chemical formula for the MG159 samples is: Two samples, namely X1 and X2, were selected from a batch of MG 159 single crystals based on the sharpness of their optical extinction.Selected single crystals were subsequently oriented along chosen crystallographic planes (Text S1 in Supporting Information S1), and double-side polished to a final thickness of 25 (X1) and 15 μm (X2), respectively.In a Cartesian reference system (e 1 , e 2 , e 3 ) with e 2 ║b and e 3 ║c, the orientations in fractional coordinates of X1 and X2 platelets are (−0.131,0.022, 0.991) and (0.467, 0.808, −0.359), respectively.

High-Pressure Experiments
High-pressure experiments were conducted employing a BX90 DAC (Kantor et al., 2012) equipped with 500 μm culet size Boehler-Almax Ia-type diamonds (Boehler & De Hantsetters, 2004).A circular sample chamber with a diameter of 370 μm was laser-cut in a rhenium foil pre-indented to a thickness of 60 μm.Sample loading was performed following a multi-loading strategy (Figure S2 in Supporting Information S1; Schulze et al., 2017).
A ruby sphere was used for in-situ pressure determination (P ruby ) using the ruby fluorescence scale (Dewaele et al., 2004).Ruby fluorescence spectra were collected on the pressurized ruby before and after each experiment.Helium was employed as pressure-transmitting medium as it remains hydrostatic in the investigated pressure range (Klotz et al., 2009).Gas loading was performed using the facility at the Bayerisches Geoinstitut (BGI), University of Bayreuth (Kurnosov et al., 2008).
High-pressure XRD and Brillouin spectroscopy experiments were conducted at the BGI using the Xcalibur diffractometer and the Brillouin spectroscopy system, respectively.Technical details on these two systems are provided in Text S2 in Supporting Information S1, and in Trots et al. (2013).
The elastic stiffness tensor of antigorite is defined by thirteen independent, non-zero elastic stiffness coefficients (c ij ) that in Voigt notation (Nye, 1985) are: c 11 , c 22 , c 33 , c 44 , c 55 , c 66 , c 12 , c 13 , c 23, c 15 , c 25 , c 35 , c 46 .At each of the investigated pressure points, compressional (v P ), fast shear (v S1 ) and slow shear (v S2 ) wave velocities determined for both platelets were inverted together with the platelet orientations and density in a weighted nonlinear least-square fitting of the Christoffel equation (Haussühl, 2007): where c ijkl are the elastic stiffness coefficients in tensorial notation,  jl the phonon direction cosines, ρ the density and  ik the Kronecker delta.Density is calculated using the unit-cell volumes (V) resulting from XRD experiments, and using the molar mass constrained by previous studies (Capitani & Mellini, 2004, 2006).The best-fitting c ij (Table S1 in Supporting Information S1) were used to calculate Voigt and Reuss bounds (labeled with V and R superscripts, respectively, Table S2 in Supporting Information S1) for the isotropic aggregate K S and shear G moduli.This was done using an OriginPro (OriginLab corporation, USA) script employing the equations coded in POLYXSTAL (Watt, 1987).The Hill averaged values (superscripted H, Table S2 in Supporting Information S1) were then determined as the arithmetic mean of Voigt and Reuss bounds (Hill, 1952).

Results and Discussion
High-pressure XRD and Brillouin spectroscopy experiments were performed at 8 different pressures, and up to 7.71(5) GPa.A typical Brillouin spectrum is provided in Figure S3 in Supporting Information S1.Observed and calculated acoustic wave velocities collected for both platelets at 7.71(5) GPa versus the rotation angle χ are shown in Figure S4 in Supporting Information S1.

Single-Crystal Elasticity of Antigorite
At room pressure, we find the c 11,0 and c 22,0 (where the subscript 0 refers to room pressure) to have a similar magnitude, both exhibiting values about twice that of c 33,0 (Figure 1a).Also, c 44,0 and c 55,0 are three and four times smaller than c 66,0 , respectively (Figure 1b).Moreover, we find c 12,0 to be about three times larger than c 13,0 and c 23,0 (Figure 1c).On the other hand, c 15,0 , c 25,0 , c 35,0 and c 46,0 are relatively small in terms of magnitude, that is, <2 GPa (Figure 1d).In general, our results at room pressure are in good agreement with previous theoretical predictions of static (0 K) elastic properties based on the Generalized Gradient Approximation (GGA) (Mookherjee & Capitani, 2011;Mookherjee & Steinle-Neumann, 2009a, 2009b) and Brillouin spectroscopy investigations (Bezacier et al., 2010).Specifically, all c ij determined in this study are essentially identical in terms of absolute values to those predicted by GGA, except for c 55,0 and c 44,0 , which are about twice than those determined in this study.The main difference with respect to the study of Bezacier et al. (2010) is that c 11,0 > c 22,0 .However we note that this discrepancy is likely due to the misassignment by Bezacier et al. (2010) of the mentioned c ij,0 to the a-and b-axes (Marquardt et al., 2015).We employed 3rd-order Eulerian strain equations (Text S3 in Supporting Information S1, Stixrude & Lithgow-Bertelloni, 2005) to describe the variation with pressure of individual c ij .Only experimental data collected at P ruby ≤ 5.17(2) GPa were employed in the fitting procedure as antigorite has been found to display elastic anomalies at pressures of about 6.5 GPa (Bezacier et al., 2013;Marquardt et al., 2015;Nestola et al., 2010).The parameters resulting from the fit are listed in Table 1, and fits to the observed c ij are plotted against the absolute pressure (Text S4 in Supporting Information S1) in Figure 1.Within the considered pressure range (P ruby < 5.17(2) GPa), our results are in agreement with previous Brillouin spectroscopy investigations (Bezacier et al., 2013), except for the c 11 -c 22 mismatch, as already observed in the room pressure data.Note that only c 11 , c 22 , c 33 , c 66 and c 12 were actually constrained by Bezacier et al. (2013) at high pressures.In contrast, we see only partial agreement with previous GGA estimates, as these did not predict any softening of c 11 , c 22 and c 12 in the pressure range considered in this study, although they predicted it to occur at larger pressures (Mookherjee & Capitani, 2011).At relatively low pressures (P < 6 GPa), the compression mechanism of antigorite is expected to be governed by a reduction of the interlayer distance, together with the flattening of octahedral and tetrahedral layers, improving the geometrical match between these two structural units (Capitani & Stixrude, 2012).Therefore, it is likely that the softening exhibited by c 11 , c 22 and c 12 is coupled to the reduction of the geometrical mismatch between layers upon compression, while the shortening of interlayer distance likely causes the abrupt stiffening of c 33 , c 13 and c 23 .
Extrapolation of the 3rd-order Eulerian strain equation fits to larger pressures shows that at least a subset of the c ij , for example, c 11 and c 33 , deviates from the low-pressure behavior (Figure 1), suggesting the presence of anomalies in the elastic behavior of antigorite as previously experimentally detected in acoustic wave velocities (Bezacier et al., 2013;Marquardt et al., 2015), and unit-cell volume compression at pressures of about 6.5 GPa (Nestola et al., 2010).We speculate that the observed deviation may reflect a change in the compression mechanism of antigorite, as predicted by Capitani & Stixrude (2012) occurring at about 6 GPa.Specifically, the compression mechanism of antigorite is expected to evolve from being primarily dominated by a shortening of the interlayered distance and a flattening of the sinusoidal-like layers (P < 6 GPa), to being essentially controlled by ditrigonalization, that is, in-plane rotation of the tetrahedra at pressures between 6 and 20 GPa (Capitani & Stixrude, 2012).

Isotropic Aggregate Properties of Antigorite
The isotropic aggregate properties of antigorite calculated for each of the investigated pressure points are listed in Table S2 in Supporting Information S1, and plotted against absolute pressure in Figure 2. At room pressure, the Hill averaged value of adiabatic bulk (   H S0 ) and shear (   H S0 ) moduli are identical within uncertainties to those determined by previous Brillouin spectroscopy experiments (Bezacier et al., 2010), and broadly consistent with GGA predictions (Mookherjee & Capitani, 2011).At high pressures, K S exhibits a monotonic increase in the investigated pressure range, while G S is essentially not sensitive to pressure.The high-pressure behavior of both aggregate moduli can be described using 3rd-order Eulerian finite strain equations (Stixrude & Lithgow-Bertelloni, 2005).The room pressure isotropic aggregate elastic moduli and their first pressure derivative resulting from the fitting are tabulated in Table 1, and presented in Figure 2a.Our results of   R S0 = 62.1(10)GPa and   ′R S0 = 5.7(4) are different from the values (  0 = 52 GPa,   ′ 0 = 8.5) resulting from the 3rd-order equation of state fit to the unit-cell volumes predicted by GGA-based calculations (Mookherjee & Capitani, 2011).This difference may be due to GGA overestimating unit-cell volumes, as discussed by Mookherjee and Capitani (2011).On the other hand, our results in better agreement with computational predictions at 300 K (  0 = 64.55GPa,   ′ 0 = 6.94,Capitani & Stixrude, 2012), and in perfect agreement with previous XRD investigations on powdered samples (  T0 = 62(2) GPa and   ′ T0 = 6.4(10),Hilairet et al., 2006), and single-crystal (  T0 = 62.9(4)GPa and   ′ T0 = 6.1(2),Nestola et al., 2010)  Note.Parameters listed here are obtained by fitting 3rd-order Eulerian strain equations to high-pressure data and up to 5.17( 2) GPa (Text S3 in Supporting Information S1, Stixrude & Lithgow-Bertelloni, 2005).pressures, eventually exceeding the Voigt bound determined in the present study at P > 3 GPa.This difference is likely due to the stiffening of the c 11 , c 22 and c 12 calculated in the GGA study for compression up to about 6 GPa, whereas the same c ij determined in this study show softening (Figure 1).On the other hand, the weak dependence on pressure observed in G agrees well with computational predictions (Mookherjee & Capitani, 2011) (Table 1).

𝜌𝜌
, and shear,  S = √   wave velocities (Figure 2b) values determined at room pressure in this study match those determined by previous Brillouin spectroscopy experiments (Bezacier et al., 2010), while GGA predicts higher values for both velocities (Mookherjee & Capitani, 2011).Specifically, GGA-based Hill averaged values exceed the Voigt bound determined in this study.This is linked to the differences in isotropic aggregate moduli and their pressure derivative as mentioned above, and may be further enhanced by unit-cell volumes overestimation (i.e., smaller density than experiments at equivalent pressure) intrinsic to the

The Seismic Signature of Serpentinized Slabs
Seismically, serpentinized slabs may be distinguishable from dry slabs because of their characteristic S-wave anisotropy -a feature that has been directly attributed to the presence of antigorite-bearing rocks constituting the serpentinized fraction of slabs, as well as the hydrated mantle above most subduction zones (Faccenda et al., 2008).
Here, we use our experimental data to calculate the seismic properties of antigorite-bearing rocks at relevant pressures assuming different degrees of serpentinization.We use our results to estimate the potential shear wave anisotropy signature characterizing serpentinized slabs.In particular, we focus on the dependence of the shear wave splitting on the incidence angle β, a parameter defining the geometrical relation between the propagation direction of seismic waves and the orientation of the antigorite foliation plane in antigorite-bearing rocks.In our model, a seismic wave with zero degree incidence angle would be propagating parallel to the antigorite foliation plane, hence normal to the pre-existing lithospheric mantle olivine foliation plane (Morales et al., 2013).Our modeling relies on the high-pressure elasticity data set determined in this study with the CPO of antigorite determined by electron backscatter diffraction (EBSD) in a serpentinite from Val Malenco, Italy (Morales et al., 2018).Antigorite-bearing rocks were treated as mixtures between olivine and antigorite, and their seismic properties were determined through a self-consistent approach using the MATLAB software AnisEulerSC (Kim et al., 2020, see also: https://github.com/ekim1419/AnisEulerSC).Specifically, this code allows for the implementation of multi-phase elasticity, grain shape constraints, and elastic inclusions.For the olivine input, we have modeled a "A-type" CPO using the unimodal Orientation Distribution Function (ODF) option of MTEX (https:// mtex-toolbox.github.io/UnimodalODFs.html)and the aggregate elastic coefficients were calculated using results from single crystal measurements of Zha et al. (1998).Although olivine CPO may change considerably due to variations of stress conditions, temperature and water content (e.g., Jung et al., 2006), the A-type is by far the dominant olivine CPO observed in most tectonic environments (e.g., Tommasi & Vauchez, 2015).Different degrees of serpentinization were modeled by changing the ratio between olivine and antigorite, ranging from a dry dunite (100% olivine), to a fully serpentinized rock (100% antigorite), hence following a simplified approach that does not necessarily reflect realistic pre-hydration mantle composition.Calculations were performed at three different pressure points, covering the pressure range relevant for antigorite in subduction environments (Syracuse et al., 2010;Ulmer & Trommsdorff, 1995).No experimental constraints on the temperature effect on individual c ij are currently available.However, previous calculations within the quasi-harmonic approximation suggest temperature to have a relatively weak influence on the elasticity of antigorite (Bezacier et al., 2013).Hence, our modeling was limited to room temperature.Further details of the modeling are reported in Text S5 in Supporting Information S1, and input parameters are reported in Table S3 in Supporting Information S1.
According to our model, a fully serpentinized rock at room pressure exhibits maximum shear wave splitting (about 0.09 s/km) for seismic waves travelling parallel to the antigorite foliation plane (Figure 3).Therefore, an ∼11-km path through a fully serpentinized antigorite-bearing body is needed to produce a 1 s delay of the slow shear wave, granted this is traveling parallel to the antigorite foliation.At room pressure (Figure 3a), our findings are in good qualitative agreement with previous calculations (Bezacier et al., 2010).However, our model suggests an absolute value that is about 30% lower than that previously determined (Bezacier et al., 2010).Also, we predict the shear wave splitting to show a high sensitivity to the incidence angle.An increase in incidence angle results in shear wave splitting decreasing rapidly as it approaches a local minimum at about 35-55° from the foliation-parallel direction.In the case of a fully serpentinized rock at room pressure, the modeled shear wave splitting reaches a local minimum of about 0.005 s/km at an incidence angle of ∼53°.Therefore, our findings suggest that the shear wave anisotropy caused by a serpentinized slab largely changes through a mechanism independent of the serpentinization degree, providing an additional explanation for the spatial shear wave delay time variations detected by seismic waves sampling subducting slabs (e.g., Long & van der Hilst, 2005).Maximum and minimum shear wave splitting values exhibit a relatively weak sensitivity to pressure, hence suggesting that also temperature would have a negligible effect on shear-wave splitting in antigorite-bearing rocks.However, the minimum shifts toward lower incidence angle values as pressure is increased (∼43° at 5 GPa).This suggests that spatial variation in shear wave delay times may be further enhanced at depth, being of particular relevance for slabs that show abrupt steepening while subducting, as for example, observed in the Tonga-Kermadek (Bonnardot et al., 2007), and Japan (Zhao et al., 1997) subduction systems.Also, our results show that sampling antigorite-bearing rocks with relatively large incident angles would always lead to low shear wave delay times, independent of the serpentinization degree and/or pressure.This finding is important when interpreting shear wave delay times from vertical seismic waves traveling through steeply dipping slabs, such as the southern Mariana subduction zone (Miller et al., 2006).
Our model clearly shows that reducing the serpentinization degree, that is, the antigorite fraction in the modeled lithologies, suppresses maximum shear wave splitting, eventually leading the entire dispersion curve to collapse to values lower than 0.02 s/km at all investigated pressures.Interestingly, we note that for rocks having serpentinization degrees lower than 30%, the magnitude of shear wave splitting would be similar, or even lower, than those calculated for dry dunite (i.e., 100% olivine).This poses an important threshold for quantifying the serpentinization in slabs through the interpretation of shear wave delay times.
Ultimately, we note that the combined effect of incidence angle and serpentinization degrees possibly results in fully serpentinized rocks showing shear wave splitting values lower than dry dunites, hence considering seismic ray path is crucial when constraining serpentinization in slabs through the interpretation of shear wave delay times.

Figure 1 .
Figure 1.Single-crystal elastic stiffness coefficients (c ij ) of antigorite.Solid symbols are c ij constrained in this study; open symbols are literature data.Note that only c 11 , c 22 , c 33 , c 66 and c 12 were constrained by Bezacier et al. (2013) at high pressures.Solid lines are fits to our data up to P ruby = 5.17 GPa using 3rd-order finite strain equations (Text S3 in Supporting Information S1).Dashed lines are extrapolations of the fitted curves to larger pressures.

Figure 2 .
Figure 2. Isotropic aggregate elastic moduli (a) and velocities (b) of antigorite as function of pressure.Solid symbols are values obtained this study; open symbols are literature data.Solid lines are fits to our data up to P ruby = 5.17 GPa using 3rd-order finite strain equations (Text S3 in Supporting Information S1).Shadings in (a) and (b) show the full range between Voigt and Reuss bounds on the results from this study.

Figure 3 .
Figure 3. Shear wave splitting of antigorite-bearing rocks as function of the incident angle.Calculated values performed at room pressure, 3 and 5 GPa are reported in (a), (b) and (c) respectively.Y-axis range is shared.The legend shows the color scale used to distinguish modeled lithologies with different serpentinization rate.The legend reported in (a) applies to (b) and (c) as well.Solid lines show the value determined from the result on this study, while the dashed line shows literature results obtained for an entirely serpentinized rock.
of antigorite, supporting the robustness of our single-crystal elasticity data set.Comparison with literature shows that the GGA-derived H fromMookherjee and Capitani (2011)diverges from ours at high

Table 1
Room Pressure Elastic Stiffness Coefficients (c ij,0 ) of Antigorite and Isotropic Aggregate Elastic Moduli (M S0 ), Together With Their First Pressure Derivatives (c′ ij,0 and M′ S0 , Respectively) Determined in This Study