Single‐Crystal Elasticity of Phase E at High Pressure and Temperature: Implications for the Low‐Velocity Layer Atop the 410‐km Depth

Dense hydrous magnesium silicate (DHMS) phase E is a potential water carrier in subducting slabs that can transport water to the Earth's deep mantle between the bottom of the upper mantle and the uppermost transition zone. Therefore, knowledge on the high pressure‒temperature (P‒T) full elastic moduli of phase E at relevant mantle conditions is important in deciphering the existence of DHMS phases and their influences on seismic profiles in the region; however, the high P‒T elasticity data of phase E still remains lacking. In this work, we determined the combined effect of P‒T on the single‐crystal elasticity of phase E up to 24 GPa and 900 K by in situ X‐ray diffraction and Brillouin scattering measurements in externally‐heated diamond anvil cells. The aggregate elastic moduli and compressional‐wave (VP) and shear‐wave (VS) velocities of phase E are then derived by analyzing the single‐crystal elasticity and density data using the third‐order finite‐strain equations. We found that phase E exhibits much lower bulk and shear moduli and acoustic velocities than the most abundant constituent minerals in the upper mantle and transition zone, such as olivine, clinopyroxene, garnet, and wadsleyite. The modeled results using the obtained elasticity results show that the existence of phase E in a hydrated pyrolite model can result in relatively lower Vp and Vs profiles and negative velocity anomalies in seismic observations. The existence of phase E with relatively lower velocity profiles could be a possible origin of the low‐velocity layers atop the 410‐km discontinuity in some cold and highly‐hydrated regions.

seismic velocity anomaly of the 410-LVL, including partial melting (Han et al., 2020;Sun et al., 2020;Thomson et al., 2016), thermal anomaly (Obayashi et al., 2006;Tang et al., 2014;Vinnik & Farra, 2007), and compositional heterogeneity (Fan et al., 2020;Lee, 2003). Among these mechanisms, water-induced partial melting has often been taken as the plausible cause of the 410-LVL in tectonic settings where water is enriched, such as the mantle transition zone with stagnant slabs or the mantle wedge above a subducted slab (Han et al., 2020;Tauzin et al., 2017;Wei & Shearer, 2017). Observations of natural hydrous ringwoodite and ice-VII inclusions in ultradeep diamonds have provided further evidence that water can be enriched at least in some regions of the mantle transition zone (Pearson et al., 2014;Tschauner et al., 2018).
It is widely accepted that water is mainly carried by hydrous minerals in subducted slabs in subduction zones and can be transported to the Earth's deep mantle (Ohtani, 2020). Based on phase-equilibrium studies of various slab components and geological observations of ancient subduction zones, a number of hydrous minerals have been identified as stable at high P-T conditions in subduction zones (e.g., Duan et al., 2018;Ohtani, 2020;Schmidt & Poli, 1998). Serpentine is the most abundant hydrous mineral in the ultramafic layer of a subducted slab and undergoes a sequence of phase transitions into dense hydrous magnesium silicates (DHMS, including phases A, superhydrous B (shy-B), D, E and H) along subducting depths. While the process of the aforementioned phase transitions can also release some of the water, the DHMS phases are found to be stable in the subduction zone conditions (Iwamori, 2004;Kawamoto et al., 1995;Komabayashi et al., 2004;Litasov & Ohtani, 2003;Ohtani, 2020). Therefore, serpentine and DHMS phases can be considered as the major potential water carriers in subduction zones, forming a continuous chain of water transport from the Earth's surface to the middle of the lower mantle. The DHMS phases have a relatively high-water content and hydrogen bonds in their crystal structures in comparison with the nominally anhydrous minerals of the constituent mantle phases. The high-water content in the DHMS phases contributes to their unique physical properties including the sound velocities and rheology (Mookherjee & Tsuchiya, 2015;Tsuchiya & Tsuchiya, 2008;Wang et al., 2022). Thus, determining the elastic properties of the DHMS phases, particularly at the high P-T conditions of the mantle is important to decipher the related seismic anomalies, to evaluate the potential storage sites, distribution and circulation of water in subduction zones and to deepen our understanding of the subduction-related geochemical and geodynamic processes (Duan et al., 2018;Karato, 2011;Karato et al., 2020;Li et al., 2016;Rosa et al., 2012;Xu et al., 2020). Several high-pressure experimental studies on elasticity have been reported for some DHMS phases, and the results obtained for phases shy-B and D have been used to explain the seismic anomalies in the mantle transition zone and the uppermost part of the lower mantle (Li et al., 2016;Rosa et al., 2012;Xu et al., 2020).
Phase E is a key member of the DHMS family which has been found to be stable at 10-18 GPa and 700°C-1100°C, corresponding to the P-T conditions of subducted slabs at the depths of 300-520 km in several experimental phase relation studies of the MgO-SiO 2 -H 2 O system and H 2 O-saturated peridotites (Frost & Fei, 1998;Iwamori, 2004;Kanzaki, 1991;Komabayashi et al., 2004;Ohtani et al., 2004). In addition, (Fe, Al)-bearing phase E was synthesized under P-T conditions near the normal mantle geotherm in hydrous KLB-1 peridotite, implying that Fe and Al incorporation can expand the stability field of phase E to stabilize it under the mantle geotherm (Kawamoto et al., 1995;Zhang et al., 2019). Thus far, these phase stability studies have indicated that as much as 50% of phase E (an upper bound) could be accommodated in the fully hydrated mantle conditions between the bottom of the upper mantle and the topmost transition zone (Ohtani et al., 2004). To decipher the seismological observations and determine the role of phase E in the water circulation in subduction zones as well as in low-velocity seismic anomalies, such as the 410-LVL, high P-T elastic properties of phase E, particularly single-crystal elasticity, are essential. To date, only the equations of state at high pressure and single-crystal elasticity under ambient conditions have been reported for phase E.
Phase E has trigonal symmetry and crystallizes in the rhombohedral space group 3 ; its structure consist of brucite-like octahedral layers with tilted O-H dipoles that are cross-linked by statistically distributed Si-tetrahedra and Mg-octahedra (Kudoh et al., 1993;Tomioka et al., 2016). It has a nonstoichiometric formula depending on the hydrogen content and composition, and the Mg-endmember has a general chemical formula of Mg 3−0.5x Si x-H 6−3x O 6 , where x varies between 1 and 1.3, with a H 2 O storage capacity of 11-18 wt% (Purevjav et al., 2020;Tomioka et al., 2016). Two previous X-ray diffraction (XRD) studies reported an isothermal bulk modulus of K T0 = ∼93 GPa and its pressure derivative of ′ 0 = 5(1) for both iron-free and iron-bearing phase E (Crichton & Ross, 2000;Shieh et al., 2000). Recent Brillouin scattering measurements on iron-bearing single-crystal phase E (Mg 2.12Fe 2+ 0.16 Fe 3+ 0.05 Ni0.01Si1.12O6H2.67 ) under ambient conditions determined an adiabatic bulk modulus of K S0 = 95.9(4) GPa and an adiabatic shear modulus of G 0 = 59.6(2) GPa (Satta et al., 2019), which are markedly lower than those of the representative constituent minerals in the upper mantle and the mantle transition zone (e.g., Fan et al., 2020;Irifune et al., 2008;Katsura et al., 2009;Mao et al., 2015;Wang et al., 2014). The low values of the adiabatic bulk and shear moduli for phase E imply that phase E has relatively low compressional-wave and shear-wave velocities, which could contribute to a detectable low-velocity seismic signature in hydrated regions of the mantle where a significant amount of phase E is present.
In this work, we performed in situ XRD and Brillouin light scattering (BLS) measurements on single-crystal phase E up to 24 GPa and 900 K to determine its high P-T equation of state and full elastic tensor. Using the obtained single-crystal elasticity data, we have derived the anisotropy factors and aggregate compressional-wave and shear-wave velocities of phase E at high P-T conditions relevant to a subducting slab. These results are used to model the velocity profiles of a hydrated pyrolite mantle model with ∼13% phase E and to compare with a dry pyrolite model and seismic profiles of the regions (the lowest upper mantle and the upper transition zone). Our results reveal that the existence of phase E in the mantle can lead to relatively lower Vp and Vs profiles that are consistent with the seismic signatures of the 410-LVLs.

Experimental Methods
The starting material for the synthesis of single-crystal phase E was a ground mixture of Mg(OH) 2 and SiO 2 in a 2:1 M ratio. The mixture was sealed in a Pt capsule of 2 mm in diameter and 2.5 mm in length, which was then placed in a 14/8 sample assembly (a 14 mm edge length of the MgO octahedron [pressure medium] and 8 mm truncations of tungsten carbide anvils). The synthesis was performed at 14 GPa and 1000°C for a duration of 14 hr using the Sakura 2500-ton multi-anvil apparatus at the Guangzhou Institute of Geochemistry, Chinese Academy of Sciences. The recovered product was composed of well-crystallized transparent single crystals with a maximum size of ∼500 μm. Single-crystal XRD analysis confirmed that these single crystals were phase E with the 3 symmetry and ambient lattice parameters a = 2.968(1) Å and c = 13.855(2) Å, and V 0 = 105.95(3) Å 3 . The chemical composition of several crystals was analyzed using an electron microprobe at the Guangzhou Institute of Geochemistry, Chinese Academy of Sciences, showing that the crystals were chemically homogenous with an average composition of 40.5(1) wt% SiO 2 and 47.6(1) wt% MgO. With the H 2 O content being estimated from the weight deficiency in the analysis totals, the mineral formula of the synthesized phase E is determined to be Mg 2.22(1) Si 1.27(2) H 2.48(1) O 6 , and the calculated density is 2.949(1) g/cm 3 .
High P-T BLS and XRD experiments were conducted on selected phase E crystal platelets at the 13-BMD beamline of GSECARS, Advanced Photon Source (APS), Argonne National Laboratory (Sinogeikin et al., 2006). High P-T conditions were generated using BX90-type externally-heated diamond-anvil cells (EHDAC) with an alumina heater coiled with platinum wires (Kantor et al., 2012;Lu et al., 2013;Yang et al., 2014). The culets of the diamond anvils were 300 and 500 μm in diameter. The sample, Au pressure calibrant and neon pressure medium were loaded into the sample chamber, which was drilled as a hole with a diameter of approximately 2/3 of the culet size in a pre-indented Re gasket. The temperature of the sample was determined by an R-type thermocouple that was attached to the surface of one diamond anvil ∼500 μm away from its culet and covered by thermally conductive ceramics. We performed one complementary series of BLS experiments at high pressure and room temperature using a short-symmetry DAC at the Mineral Physics Laboratory, University of Texas at Austin (UT Austin), following experimental procedures described in the literature (Fan et al., 2019;Fu et al., 2019;Yang et al., 2016;Zhang et al., 2021). To determine the density of phase E for the room-temperature BLS experiments, an additional run of XRD measurements at high pressures and room temperature was also performed at the 13-IDD beamline of GSECARS. For the room-temperature BLS experiments, the pressures were determined using a ruby pressure calibrant which is internally consistent with the Au pressure calibrant used in high P-T BLS experiments (Fei et al., 2007).
During XRD measurements in 13-BMD or 13-IDD beamline of GSECARS, each XRD pattern was obtained for phase E crystal platelets and Au pressure calibrants by integrating images collected in the single-crystal wide-scan mode or step-scan (1° per step) from −15° to +15°. In both beamlines, the X-ray beam energy was 37 keV (0.3344 Å in wavelength) and a stationary Perkin-Elmer image plate was used as the detector. The diffraction geometry parameters were calibrated using the LaB 6 standard. The obtained diffraction patterns were converted into one-dimensional profiles using DIOPTAS (Prescher & Prakapenka, 2015), which were then indexed by UNITCELL software to retrieve the lattice parameters at each given P-T point (Holland & Redfern, 1997). A representative integrated XRD pattern of phase E at 22.6 GPa and 300 K is shown in Figure 1a.

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Phase E with the trigonal 3 symmetry has six independent single-crystal elastic stiffness coefficients (C ij s) or elastic moduli (Nye, 1985). To obtain reliable data for all six single-crystal elastic moduli, high P-T experiments and data analysis must be carefully designed. To start with, we double-polished a number of phase E crystals to platelets with a thickness of ∼15 μm. The crystallographic orientations of the platelets were measured by single-crystal XRD at the 13-IDD beamline of GSECARS. We then selected three platelets (P1, P2, and P3) with the determined crystallographic planes of P1 (0.1 2.9 -4.7), P2 (−0.1 −0.1 6.9) and P3 (−0.8 2.9 −1.9) in the Cartesian coordinate system for the Brillouin scattering measurements. The sensitivity tests of these three platelets indicated that platelets P1 and P3 were highly sensitive to all six single-crystal elastic moduli and can be used to retrieve the full single-crystal elastic tensor of phase E, whereas platelet P2 was used to provide additional constraints on the derivation of the single-crystal elastic moduli (see Figure 1e and Text S1 in Supporting Information S1; Lin et al., 2018). The compressional and shear wave velocities of all three platelets as a function of azimuthal angle (i.e., the angle of rotation around an axis normal to the platelet face) were collected in BLS measurements under ambient conditions to tightly constrain the ambient single-crystal elastic moduli of phase E. For high-pressure BLS experiments at ambient temperature (300 K), we loaded P1 and P2 together in the short-symmetry DAC and collected the spectra at UT Austin (Fu et al., 2017. Only P3 was loaded in a BX90-type EHDAC for high P-T BLS and XRD experiments at the 13-BMD beamline of GSECARS. The BLS and XRD experimental system at the 13-BMD beamline allowed us to collect both BLS spectra and XRD patterns in situ at high P-T to simultaneously determine the acoustic velocities and the density of sample for the derivation of the elastic moduli (Sinogeikin et al., 2006). BLS spectra were measured in a symmetric forward scattering geometry, in which acoustic velocities (ν) were calculated from the measured Brillouin shifts (Δυ B ) using the following equation: (1) Figure 1. X-ray diffraction (XRD) and sound velocity measurements of phase E at high pressures. (a) An integrated XRD pattern of phase E with indexed diffraction peaks at 22.6 GPa and 300 K. (b-d) Representative Brillouin scattering spectra for platelets P1 (0.1 2.9 −4.7) and P2 (−0.1 −0.1 6.9) at 21.3 GPa and 300 K, and P3 (−0.8 2.9 −1.9) at 13.1 GPa and 650 K. P, S1, S2, and Ne denote the V P , V S1 , and V S2 signals of phase E and the compressional-wave signal of neon, respectively. Black open circles are raw data and red lines are fitting results. (e) Sensitivity analyses of C ij to the compressional-wave velocity V P and shear-wave velocities V S1 and V S2 of phase E for the three platelets. The highest sensitivity of C 44 in each platelet is set to 100% to normalize the sensitivity values of the other elastic moduli. Platelet P1 and platelet P3 are sensitive to all six elastic moduli with relatively high sensitivity values, while platelet P2 is not as sensitive to C 33 and C 13 .
where the scattering angle (θ) is 48.3° for the BLS system at UT and 50° for the BLS system at 13-BMD. The laser wavelength (λ 0 ) is 532 nm for both systems. Typical BLS spectra under high P-T conditions are shown in Figures 1b-1d.

Thermal Equation of State of Phase E
XRD patterns of single-crystal phase E and polycrystal Au were collected at high pressures up to 22.6 GPa and temperatures of 300, 500, 650, 700, and 900 K. The collected XRD patterns were converted into one-dimensional XRD profiles, which were then indexed and analyzed to derive the unit-cell parameters ( Table S1 in Supporting Information S1). Pressures were calculated using the Au pressure scale of Fei et al. (2007). The obtained unit-cell volumes at the various P-T conditions are plotted in Figure 2.
The pressure-volume (P-V) data at the ambient temperature (300 K) were fitted with the third-order Birch-Murnaghan (BM) equation of state (Birch, 1947) that is expressed as follows: where V 0 , K T0, and ′ 0 are the zero-pressure unit-cell volume, ambient isothermal bulk modulus and its pressure derivative, respectively. With a fixed V 0 = 105.95(3) Å 3 , the best fitting yielded the values of K T0 = 94.7(1.3) GPa and ′ 0 = 4.73(21). These results are in good agreement with the results obtained in a previous study on phase E by Shieh et al. (2000).
To obtain the thermal elastic parameters of phase E, the high-temperature P-V data were analyzed with the high-temperature Birch-Murnaghan (HTBM) equation of state (Birch, 1947;Zhang & Kostak, 2002). The HTBM equation of state is in the same form as Equation 2, except that V 0 , K T0, and ′ 0 are replaced with V T0 , K T , and ′ , which are the zero-pressure unit-cell volume, isothermal bulk modulus and its pressure derivative at a constant temperature T, respectively. K T and V T0 can be related to the ambient temperature K T0 and V 0 by the following expressions: where (∂K T /∂T) P and α T are the temperature derivative of the isothermal bulk modulus and thermal expansion of the volume, respectively. Within the limited temperature range of our high P-T experiments, we assumed two approximations, namely α T = α 0 (thermal expansion at ambient temperature) and ′ = ′ 0 in the analysis (Nishihara et al., 2003). Coupled with the obtained V 0 , K T0 , and ′ 0 values at ambient temperature, fitting the P-V-T data at 500, 650, 700, and 900 K together yielded (∂K T /∂T) P = −0.014(3) GPa/K and α 0 = 4.7(4) × 10 −5 K −1 . The obtained thermal equation of state parameters of phase E match our P-V-T experimental data well (Figure 2), supporting the assumptions used in the modeling.

Single-Crystal Elastic Moduli (C ij s) of Phase E at High P-T Conditions
BLS measurements on phase E were performed at high pressures up to 24 GPa and temperatures of 300, 500, and 650 K (Figures 1b-1c). All three platelets were used for BLS measurements under ambient conditions, while platelets P1 and P2 were used for high-pressure and ambient-temperature BLS measurements and platelet P3 was used for high P-T BLS measurements. At given P-T conditions, the acoustic wave velocities were collected with an interval of 10° azimuthal angles over a range of 180° for each platelet (Figure 3). The density at high P-T was determined via analysis of the single-crystal XRD patterns before and after the Brillouin measurements, whereas Unit-cell volumes of phase E at high P-T conditions. Solid circles are the experimental data obtained by X-ray diffraction measurements, and solid lines are fitting results using the third-order thermal Birch-Murnaghan equation of state (Birch, 1947;Zhang & Kostak, 2002). Black, blue, red, purple and olivine denote 300, 500, 650, 700, and 900 K, respectively. the density at high pressure and 300 K was calculated by the thermal equation of state as mentioned above. The experimental velocity data along various crystallographic directions were fitted by Christoffel's equation at each P-T point to obtain six single-crystal elastic moduli (Every, 1980): where C ijkl are the elastic stiffness coefficients (or elastic moduli) with full suffix notation, ν is the measured acoustic velocity, ρ is the density derived from single-crystal XRD measurements, n i and n j are the wave-vector (phonon propagation) direction cosines and δ kl is the Kronecker delta. Representative fitting results of the single-crystal elastic moduli for P 1 and P 2 at 21.3 GPa and 300 K and P 3 at 13.1 GPa and 650 K are displayed in Figure 3, showing that the velocities determined by the BLS spectra agree well with the velocities calculated using the fitted single-crystal elastic moduli. All of the fitted single-crystal elastic moduli of phase E at various P-T conditions are given in Table S2 in Supporting Information S1 and plotted in Figure 4. Because the sign of C 14 would be reversed when the X-Y axes are rotated by (2n + 1) × 60°, the sign of C 14 reported by Satta et al. (2019) was flipped for comparison in Table S2 in Supporting Information S1. Notably, such a treatment does not affect the physical interpretation and the values of other single-crystal elastic moduli. Our values under ambient conditions are roughly consistent with those of Satta et al. (2019), with the small differences interpreted as a result of the iron-substitution effects in phase E.
To obtain the P-T derivatives of the single-crystal elastic moduli, the experimental single-crystal elastic data were fitted using third-order finite-strain equations (Birch, 1978;Duffy & Anderson, 1989) (Figure 4 and Table S3 in Supporting Information S1): (0, ) = (0, 300 ) + ( − 300) ( ∕ ) where C ij (0,300 K) is the elastic modulus under ambient conditions; C ij (0,T) is the elastic modulus at high temperature and ambient pressure; C ij (P,T) is the elastic modulus at given P-T conditions; (∂C ij /∂T) P and (∂C ij /∂P) T are the isobaric temperature derivative and the isothermal pressure derivative of the elastic modulus, respectively; K T (0,T) is the isothermal bulk modulus at high temperature and ambient pressure; f is the finite strain; V is the unit-cell volume determined by single-crystal XRD; and V 0 is the unit-cell volume under ambient conditions. The parameter a 2 is 3 for C 11 and C 33 , 1 for C 44 , C 12 and C 13 , and 0 for C 14 .

Aggregate Elastic Property of Phase E (Ks, G, Vp and Vs)
At each given P-T point, the aggregate adiabatic elastic moduli K S and G were calculated using the derived single-crystal elastic moduli in the Voigt-Reuss-Hill average (Hill, 1952). Then, with the K S at ambient conditions fixed to 98.3(7) GPa, we derived the P-T derivatives of the adiabatic bulk modulus ( Figure 5 and Table S3 in Supporting Information S1) by fitting the Ks values at various P-T conditions using the following equations (Angel et al., 2014;Birch, 1978;Stixrude and Lithgow-Bertelloni, 2005): where K S (0,T) is the adiabatic bulk modulus at high temperature and ambient pressure, K S (P, T) is the adiabatic bulk modulus at given P-T conditions, (∂K S /∂T) P is the temperature derivative of the adiabatic bulk modulus, and (∂K S /∂P) T is the pressure derivative of the adiabatic bulk modulus. The derived P-T derivatives were 5.00(4) and −0.018(1) GPa/K for the adiabatic bulk modulus, respectively. Note that Equation 11 requires the assumptions K S (0,T) = K T (0,T) and (∂K S /∂P) T = (∂K T /∂P) T .
Similarly, the P-T derivatives of the shear modulus were derived by fitting the G values at various P-T conditions using the following equations (Birch, 1978;Stixrude & Lithgow-Bertelloni, 2005) ( Figure 5 and Table S3 in Supporting Information S1): where G(0,T) is the shear modulus at high temperature and ambient pressure, G(P,T) is the shear modulus at given P-T conditions, (∂G/∂T) P is the temperature derivative of the shear modulus, and (∂G/∂P) T is the pressure Figure 4. Single-crystal elastic moduli of phase E at high P-T conditions. Black, blue and red circles represent the experimental data at 300, 500, and 650 K, respectively. Solid lines are the fitting results obtained using thermal third-order finite strain equations (Birch, 1978). The aggregate V P and V S velocities of phase E were determined by the bulk and shear moduli (K S , G) using the following equations: The calculated results at various P-T conditions are given in Table S2 in Supporting Information S1 together with the results at ambient conditions reported by Satta et al. (2019). Our V P and V S values under ambient conditions are 7.80(2) and 4.55(1) km/s, which are close to but slightly higher by ∼2.

Anisotropic Factors of Phase E at High P-T
The V P and V S azimuthal anisotropies of phase E were analyzed by using its single-crystal elasticity data at high P-T conditions. We calculated the compressional-wave anisotropy factor (AV P ) and the shear-wave splitting anisotropy factor (AV S ) at each P-T point (Table S2 in Supporting Information S1), which are defined as follows (Karki et al., 2001;Mainprice et al., 2000): where V Pmax and V Pmin represent the maximum and minimum V P velocities of the mineral, respectively, and V S1 and V S2 are two orthogonally polarized V S velocities propagating along the same direction. Under ambient conditions, the AV P and AVs values of phase E are 8.9% and 19.5%, respectively, which are close to those of iron-bearing phase E (Satta et al., 2019), implying that 9 mol% iron in phase E does not significantly affect the anisotropy under ambient conditions.

Elasticity of Phase E and Its Comparison With Relevant Mantle Minerals
Using the data obtained from Brillouin scattering spectroscopy and single-crystal XRD measurements, we have determined the single-crystal elasticity of the Mg-endmember phase E at high P-T conditions. Analysis of the elasticity data by the third-order finite-strain equations yields high P-T derivatives of all C ij s, Ks and G, allowing us to extrapolate the elasticity data of phase E to the P-T conditions relevant to the upper mantle and the mantle transition zone. The C ij s, aggregate K S , and G under ambient conditions obtained in the present study, with the exception of C 11 , C 12, and C 14 , are 2%-9% higher than the experimental results of Satta et al. (2019). These differences are most likely due to the effect of iron substitution for magnesium because phase E used in the BLS experiments of Satta et al. (2019) contained 9.0 mol% iron (Fe/ (Mg + Fe) ratio). The longitudinal moduli, C 11 and C 12 , are not sensitive to iron substitution, while C 14 appears to be highly sensitive. The effect of iron substitution on the elasticity (C ijS , K S , and G) has been studied for many minerals, such as olivine, diopside, wadsleyite, and bridgmanite (Fan et al., 2019(Fan et al., , 2020Fu et al., 2019;Wang et al., 2014). In many cases, the content of iron that substitutes magnesium shows a negative effect on the single-crystal elastic moduli, and especially on aggregate K S , G, V P , and V S ; that is, iron-bearing minerals have relatively lower single-crystal and aggregate elastic moduli than their iron-free counterparts.
A pyrolite model is usually employed to describe the chemical composition and mineralogy of the Earth's mantle. The phase relations of dry pyrolite in the Earth's mantle have been well constrained by high P-T experiments (Irifune & Isshiki, 1998;Ishii et al., 2011). According to the experimental studies on the phase relations of the hydrated pyrolite model and similar compositions (Kawamoto et al., 1995;Komabayashi et al., 2004;Litasov & Ohtani, 2003;Zhang et al., 2019), phase E could coexist with olivine, clinopyroxene and majorite in the lowest part of the upper mantle and with wadsleyite and majorite in the upper part of the mantle transition zone. A comparison of the elastic properties of phase E with its relevant (coexisting) mantle mineral phases could thus help us understand the potential effect of hydration with the existence of phase E on the seismic velocities and anisotropies in the Earth's upper mantle and the mantle transition zone. Using the thermoelastic parameters for phase E obtained in this study and the parameters for olivine, diopside, majorite and wadsleylite reported in the literature (See Table  S4 in Supporting Information S1; Fan et al., 2020;Irifune et al., 2008;Isaak et al., 2006Isaak et al., , 2010Katsura et al., 2009;Mao et al., 2015;Pandolfo et al., 2015;Wang et al., 2014;Zou et al., 2012), we have modeled V P and V S velocity profiles of these minerals along a slab geotherm that is 400 K colder than the adiabatic temperature profile (Katsura et al., 2010). As shown in Figure 6, we found that both the V P and V S velocities of phase E are significantly lower than those of the other mineral phases. Phase E is ∼7% lower in V P and ∼8% lower in V S than olivine at the depth of the upper mantle and ∼13% lower in V P and ∼14% lower in V S than wadsleylite at the depth of the mantle transition zone. The low V P and V S velocities of phase E imply that it might be a potential cause for the low-velocity anomalies observed at the depths of the lowest part of the upper mantle and the upper part of the mantle transition zone in the water-rich tectonic settings related to slab subduction (Han et al., 2020;).
Using the obtained high P-T single-crystal elastic parameters of phase E, we have also calculated the compressional-wave anisotropy factor AV P and shear-wave splitting anisotropy factor AV S along a slab geotherm Figure 6. Modeled V P and V S profiles of phase E and other relevant mantle phases along a slab geotherm that is 400 K colder than the adiabatic temperature profile (Katsura et al., 2010). Blue solid lines: olivine (Ol, Mao et al., 2015); purple solid lines: clinopyroxene (Cpx, Fan et al., 2020); black solid lines: majorite (Maj-Gt, Irifune et al., 2008); green solid line: wadsleyite (Wad, Wang et al., 2014); red solid lines: phase E (PhE, this study). Black and red dashed lines show the seismic profiles of AK135 (Kennett et al., 1995) and PREM (Dziewonski & Anderson, 1981), respectively. 400 K lower than the adiabatic temperature profile (Katsura et al., 2010) and as a function of pressure at 300 K, respectively (Figure 7). Both AV P and AV S show a decrease with pressure and an enhancement with temperature. Due to a lack of constraints on the effect of temperature on the single-crystal elasticity of clinopyroxene and wadsleylite, we only calculated the AV P and AV S of olivine, clinopyroxene and wadsleylite as a function of pressure at the ambient temperature using the literature single-crystal elasticity data (Hao et al., 2020;Mao et al., 2015;Wang et al., 2014;Zhang et al., 2018) for a comparison with phase E. Majorite was not included in the comparison because it is nearly elastically isotropic at high pressures and 300 K (Murakami et al., 2008;Sanchez-Valle et al., 2019). As seen in Figure 7, the AV P of phase E is significantly lower than that of olivine, clinopyroxene and anhydrous wadsleylite but is comparable to that of hydrous wadsleyite. The AV S of phase E is only lower than that of clinopyroxene but is higher than those of olivine, anhydrous wadsleyite and hydrous wadsleyite. The intrinsic elastic anisotropy of phase-E would produce a seismic signature in the case of texturing by lattice preferred orientation. Phase E with a relatively high AV S may contribute to the shear-wave splitting anisotropy observed at the depth of the mantle transition zone in some subduction zones (Chang & Ferreira, 2019;Zhang et al., 2018).

Implications for the Low-Velocity Layers Atop the 410-km Depth
Seismic observations using mainly P and S receiver functions revealed the existence of a low-velocity layer atop the mantle transition zone in some subduction zones and continental platforms (Han et al., 2020;Li et al., 2022;Tauzin et al., 2017;Vinnik & Farra, 2007). A water-induced partial-melting model is often employed to interpret the origin of the 410-LVL (Kuritani et al., 2019;Tauzin et al., 2010Tauzin et al., , 2017. Water, which was predicted to be released through the upwelling of a hydrous mantle transition zone and dehydration reactions of a subducted slab or stagnant slab, has been proposed to result in partial melting that can significantly reduce the seismic velocities (V P and V S ) in the lowest part of the upper mantle above the 410 km discontinuity. However, while the existence of water can induce partial melting, it may also lead to the formation of phase E, which is stable at the pressures of 10-18 GPa under slab geotherms and even under normal mantle geotherms (Kawamoto et al., 1995;Zhang et al., 2019). The low V P and V S velocities of phase E imply that it may contribute to the origin of the 410-LVL.
To evaluate the effect of phase E on the 401-LVL, we have modeled the velocity profiles of dry and hydrated pyrolite models as well as the profiles of phase E at the depths of 300-520 km corresponding to 10-18 GPa pressure range along a slab geotherm that is 400 K colder than the surrounding mantle geotherm (Katsura et al., 2010). The thermal elastic parameters of the minerals used for the modeling are listed in Table S4 in Supporting Information S1. The mineral assemblages and the proportions of the dry pyrolite model are taken from the experimental results of Irifune and Isshiki (1998) with the olivine or wadsleyite content fixed at ∼60 vol% in the entire modeling pressure range. For hydrated pyrolite, the amount of phase E was added at the expense of olivine or wadsleyite, based on a previous study (Satta et al., 2019). According to the water content reported for a hydrous ringwoodite inclusion in an ultradeep diamond (Pearson et al., 2014), we assumed a H 2 O content of 1.5 wt% for the hydrated pyrolite model, corresponding to ∼13 vol% phase E. As depicted in Figure 8, the hydrated pyrolite model shows lower velocities than the dry pyrolite counterpart, while the  Mao et al., 2015), wadsleyite (blue lines, Wang et al., 2014), hydrous wadsleyite (green lines, Zhang et al., 2018) and clinopyroxene (pink lines, Hao et al., 2020) as a function of pressure at 300 K. The red dashed lines represent the anisotropy factors of phase E along a slab geotherm that is 400 K colder than the adiabatic temperature profile (Katsura et al., 2010). The vertical gray dashed line marks the boundary between the upper mantle and the mantle transition zone. Modeled velocity profiles of dry pyrolite (red lines) and hydrated pyrolite with ∼13 vol% phase E (blue lines) and phase E (brown lines) along a slab geotherm that is 400 K colder than the adiabatic temperature profile (Katsura et al., 2010). Seismic profiles, AK135 (Kennett et al., 1995) and PREM (Dziewonski & Anderson, 1981), are shown as black and blue dashed lines, respectively. (b) The velocity contrast between dry and hydrous pyrolites (ΔV P,S = 100 × [(V P,S ) hydrous −(V P,S ) dry ]/(V P,S ) dry ). The black and red lines are the compressional velocity contrast (ΔV P ) and shear velocity contrast (ΔV S ), respectively. The vertical gray dashed line marks the boundary between the upper mantle and the mantle transition zone. reductions in V P and V S , ΔV P,S = 100*[(V P,S ) dry −(V P,S ) hydrous ]/(V P,S ) dry , are similar to each other. Both the V P and V S velocity profiles of phase E are ∼8% lower than those of the dry pyrolite model (Figure 8a). Compared with the dry pyrolite model, phase E with ∼13 vol% in the hydrated pyrolite model can lead to a decrease in both V P and V S by ∼1.0% at the depth of the lowermost upper mantle and by ∼1.6% at the depth of the mantle transition zone, respectively (Figure 8b). The modeled V P and V S profiles of phase E are much lower than those of AK135 and PREM; hence, it is expected that the enrichment of phase E in the hydrous regions of the lowest part of the upper mantle and the mantle transition zone can lead to a negative seismic anomaly. We note that the modeled velocity profiles of the dry and hydrated pyrolite models are slightly higher than those of the AK135 and PREM models (Dziewonski & Anderson, 1981;Kennett et al., 1995), which is most likely due to the lower temperature of the selected slab geotherm. The use of the elasticity of the Mg-endmember phase E in the present modeling calculations may also overestimate the V P and V S profiles. In the pyrolite model, phase E should contain some amounts of iron and aluminum, which can significantly reduce the aggregate elastic moduli and acoustic velocities of phase E (Satta et al., 2019;Xu et al., 2020).
A number of evidences from high P-T experiments and geophysical and geological observations indicate that at least in some regions, the mantle transition zone should be highly hydrated (Karato, 2011;Karato et al., 2020;Ohtani et al., 2004;Pearson et al., 2014;Tschauner et al., 2018). The dominant minerals in the mantle transition zone, wadsleyite and ringwoodite, can accommodate up to ∼3 wt% H 2 O, which is much higher than the H 2 O storage capacity of olivine (∼0.1 wt%) (Fei & Katsura, 2020;Ferot & Bolfan-Casanova, 2012;Ohtani, 2020). Hence, water is expected to be released when materials from the hydrous mantle transition zone are transported above the 410 km discontinuity via mantle upwelling, triggering partial melting that can be used to explain the low-velocity layer atop 410 km (Han et al., 2020;Yang & Faccenda, 2020). In addition, subducted slabs or stagnant slabs with water stored mainly in hydrous minerals may undergo dehydration reactions and release water that migrates into the overlying mantle wedge or upper mantle Richard & Iwamori, 2010;Richard et al., 2006;Sheng et al., 2016;. While the released water can induce partial melting in the lowermost upper mantle, it can also be re-absorbed by forming phase E according to the previous experimental studies on the phase relations of peridotites (Kawamoto et al., 1995;Komabayashi et al., 2004;Zhang et al., 2019). Based on the results obtained in the present study, the formation of phase E would lead to low V P and V S velocities in the regions and thus helps explain the seismic observations of the 410-LVL. Experimental studies on hydrous KLB-1 peridotite have also shown that (Fe, Al)-bearing phase E is stable under the P-T conditions along a nearly normal mantle geotherm (Kawamoto et al., 1995;Zhang et al., 2019). The 410-LVLs are characterized by a negative anomaly for both V P and V S seismic velocities. A recent seismological study indicated that the seismic anomalies of the 410-LVL beneath the northwest Pacific subduction zone were ∼1.0%-1.5% for V P and ∼2.5% for V S (Han et al., 2020). According to our modeling results on the velocity profiles of phase E and the dry and hydrated pyrolite models, it is estimated that the hydrated pyrolite model containing 13-19 vol% phase E, which corresponds to an H 2 O content of 1.5-2.2 wt%, shows a velocity reduction of ∼1.0-1.5% for both V P and V S relative to the dry pyrolite model. The pyrolite model containing 13-19 vol% phase E can reproduce the observed V P anomaly of the 410-LVL beneath the northwest Pacific subduction zone; however, it is insufficient to reproduce the observed V S anomaly. Therefore, the oversimplified model of hydrated pyrolite containing phase E alone cannot explain the genesis of 410-LVL, and other mechanisms, including partial melting that can lead to significantly lower V S (Berryman, 2000;Hammond & Humphreys, 2000;Karato, 2014;Takei, 2017), should also be taken into consideration.

Conclusions
The high P-T single-crystal elasticity of phase E has been determined by performing XRD and Brillouin scattering measurements up to 24 GPa and 900 K. Analysis of the obtained single-crystal elasticity data using the third-ordered finite-strain equations allowed us to derive the aggregate elastic parameters of phase E. The adiabatic bulk and shear moduli of phase E under ambient conditions are determined to be K S0 = 98.3(7) GPa and G 0 = 61.0(1) GPa, respectively. Their pressure derivatives and temperature derivatives are determined to be (∂K S /∂P) T = 5.00(4) and (∂K S /∂T) P = −0.018(1) GPa/K for the adiabatic bulk modulus and (∂G/∂P) T = 1.64 (2) and (∂G/∂T) P = −0.013(2) GPa/K for the shear modulus, respectively. Phase E has lower compressional velocity and shear velocity than other relevant or potentially coexisting minerals in the upper mantle and the upper part of the mantle transition zone. Based on the modeled velocity profiles of phase E, dry pyrolite and hydrated (or phase E-bearing) pyrolite models along a slab geotherm 400 K colder than the surrounding mantle, we found that the existence of phase E would result in low-velocity seismic signatures, implying that phase E is a potential cause for the low-velocity layer atop 410-km depth in some cold and highly-hydrated regions and may also account for some low velocity anomalies in the mantle transition zone.

Data Availability Statement
P-V-T data are listed in Table S1 in Supporting Information S1. Single-crystal and aggregate elastic data are listed in Tables S2 and S3 in Supporting Information S1. Thermoelastic parameters used in the modeling of seismic profiles are given in Table S4 in Supporting Information S1. All these data can also be downloaded online in the Zenodo data repository (https://zenodo.org/record/7243256). and XRD measurements were performed at the 13-BMD and 13-IDD beamlines of GSECARS, APS, Argonne National Laboratory. GSECARS is supported by the National Science Foundation-Earth Sciences (EAR-1634415) and Department of Energy-GeoSciences (DE-FG02-94ER14466). This research used resources of the APS, a U.S. Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under Contract No. DE-AC02-06CH11357. This is contribution No. IS-3272 from GIGCAS.