Water Content of the Dehydration Melting Layer in the Topmost Lower Mantle

The water‐rich mantle transition zone and dry lower mantle suggest that a dehydration melting layer can form at the 660‐km depth boundary. However, the water content of the melting layer ( CH2Omelt ), which dominates its gravitational stability and melt fraction, remains poorly constrained. Here, the CH2Omelt of hydrous silicate melt by mass balance calculations is investigated and found that CH2Omelt significantly decreases with increasing temperature, but is relatively insensitive to chemical composition (FeO and SiO2 contents) and coexisting phases. Melt at 660‐km depth should contain ∼50 wt.% water at 1600 K (slab geotherm) or ∼20 wt.% water at 2000 K (topmost lower mantle geotherm). The density of the hydrous melt is <3.9 g/cm3, which makes it buoyant. With a melt fraction of ≳0.5 vol.%, the melting layer is expected to significantly reduce the viscosity and seismic velocity near slabs, which may cause slab stagnation and prohibit whole mantle convection.


Introduction
The mantle transition zone is considered to be a water reservoir because its dominant minerals, wadsleyite, and ringwoodite, contain up to ∼1.0 wt.% based on several lines of evidence, including electrical conductivity (Kelbert et al., 2009), mineral viscosity (Fei et al., 2017), and naturally formed water-rich ringwoodite inclusion (Pearson et al., 2014). In contrast, the lower mantle is considered to be dry (Hirschmann, 2006) because bridgmanite and ferropericlase can contain ≤0.1 wt.% water in their crystal structures (e.g., Bolfan-Casanova et al., 2000;Fu et al., 2019). Dehydration melting should therefore occur during the phase transformation of hydrous ringwoodite to bridgmanite and ferropericlase by mass convection when crossing the 660-km boundary (Schmandt et al., 2014). Such a dehydration melting layer has been interpreted to explain the seismic velocity reduction at the topmost lower mantle (Schmandt et al., 2014).
The question arises regarding whether this melting layer is stabilized at 660-km depth or gravitationally unstable. This problem should be determined by the melt viscosity, wetting of mineral grain-boundaries, and most importantly density because the density contrast among the transition zone, lower mantle, and hydrous melt is the driving force for upward or downward melt migration. Melt density is known to decrease with increasing melt H O 2 C (e.g., Matsukage et al., 2005;Sakamaki et al., 2006). Therefore, although dry melt [4.0-4.4 g/cm 3 after correction to 23 GPa and 1600-2000 K (Bajgain et al., 2015;Ohtani & Maeda, 2001;Sanloup et al., 2013)] is denser than the mantle transition zone [3.9-4.0 g/cm 3 (Dziewonski & Anderson, 1981) C at 660-km depth is therefore essential for evaluating its density and stability.
Abstract The water-rich mantle transition zone and dry lower mantle suggest that a dehydration melting layer can form at the 660-km depth boundary. However, the water content of the melting layer ( significantly decreases with increasing temperature, but is relatively insensitive to chemical composition (FeO and SiO 2 contents) and coexisting phases. Melt at 660-km depth should contain ∼50 wt.% water at 1600 K (slab geotherm) or ∼20 wt.% water at 2000 K (topmost lower mantle geotherm). The density of the hydrous melt is <3.9 g/cm 3 , which makes it buoyant. With a melt fraction of ≳0.5 vol.%, the melting layer is expected to significantly reduce the viscosity and seismic velocity near slabs, which may cause slab stagnation and prohibit whole mantle convection.
Plain Language Summary A dehydration melting layer is predicted near the 660-km depth boundary by the phase transition of hydrous ringwoodite in the mantle transition zone to dry bridgmanite and ferropericlase in the lower mantle. However, the water content in the melt, which controls the melt density and thus gravitational stability, remains poorly constrained. In this study, the water content in hydrous melt under 660-km depth conditions is estimated as a function of temperature. At 2000 K, corresponding to topmost lower mantle geotherm, hydrous silicate melt should contain ∼20 wt.% water, which will cause the melt to be gravitationally unstable. The melt fraction at 660-km depth is estimated to be >0.5 vol.%, which may significantly reduce rock viscosity and seismic velocity.

High-Pressure Experiments
Mixtures with bulk compositions of (Mg,Fe) 2 SiO 4 and (Mg,Fe)SiO 3 plus 5-22 wt.% H 2 O (Table 1) were prepared from MgO, SiO 2 , Mg(OH) 2 , and FeO powders. After drying in a vacuum furnace at 400 K, the mixtures were sealed in Pt-Rh or Pt capsules by arc-welding (Fei & Katsura, 2020). The inner and outer diameters (ID/OD) of the Pt-Rh capsules were 1.0/1.2 mm for the 23 GPa runs, whereas Pt capsules with ID/ OD = 0.8/1.0 mm were used for the 23.5 GPa runs. The high-pressure experiments were performed using a Kawai-type multi-anvil apparatus with standard 10/4 and 7/3 cell assemblies at the Bayerisches Geoinstitut (supporting information). The experimental temperatures ranged between 1600 and 2300 K, measured by a D-type (W/Re) thermocouple, with annealing durations of 5-1800 min (Table 1).
Cross sections parallel to the axial directions of the capsules were prepared by polishing with sandpaper and diamond powder. The run products appear as coexisting crystals (majorly bridgmanite and ringwoodite) and quenched crystallized melts (Table 1), as confirmed by scanning electron microscope (SEM) and microfocus X-ray diffraction analyses ( Figure 1). The compositions of the melts were analyzed by electron microprobe (EPMA) operated with an acceleration voltage of 15 kV, beam current of 15 nA, beam size of 30-50 μm, and counting time of 20 s. The (Mg + Fe)/Si and Fe/(Fe + Mg) atomic ratios in the melts, which reflect the SiO 2 and FeO concentrations, respectively, were calculated from the EPMA data (supporting information).

Estimation
The melt and solid fractions were obtained from the SEM images using image processing software (Im-ageJ). Images of all recovered capsules are provided in the supporting information. The melt H O 2 C values were calculated by mass balance using the initial bulk water content in the starting materials, water content in ringwoodite (Fei & Katsura, 2020), and fractions of melts and solids. The water content in bridgmanite (and akimotoite) is negligible in comparison with ringwoodite and melt (Bolfan-Casanova et al., 2000;Fu et al., 2019) and therefore has a negligible effect on , although the water solubility in bridgmanite remains under debate (e.g., Fu et al., 2019;Litasov et al., 2002).

Experimental Uncertainty Evaluation
A critical assumption in the above mass balance calculation is no water loss during the experiments. To examine if this assumption is reasonable or not, information regarding how the bulk water content in the capsule changes with time is required. A time series was therefore performed under the same pressure and temperature conditions (23 GPa, 2000 K) with the same starting material (Fo 90 + 15%H 2 O), but different durations (5-1800 min). The melt fraction in the run products, which is controlled by the bulk water content, 3 of 10 is found to be independent of duration (Figure 2a), which indicates that water loss was insignificant. This is understandable because hydrogen may diffuse through Pt capsule walls in the form of H 2 , but not as hydroxyl or H 2 O (e.g., Eugster, 1957;Shaw, 1963), which is the case in this study. Although H 2 O could be partially reduced to H 2 by Fe 2+ in the Fe-bearing runs, even if all the Fe 2+ were oxidized to Fe 3+ , the amount of H 2 O reduced to H 2 would be very small (e.g., the bulk water content would decrease from 13.0% to 12.1% in the Fo 90 + 15%H 2 O system).
Some may consider that a time series over a duration of 5-1,800 min does not indicate the extent water loss during the initial 5 min. However, if water loss had occurred, the loss rate should be controlled by the water fugacity contrast in and out of the capsule. As far as the melt phase presents, the water fugacity is constant and the loss rate should thus be constant. Therefore, if water loss were significant within the first 5 min, the melt phase should not be present over long-duration runs, which is clearly not the case in this study.
Another error source is the uncertainty of the melt fraction estimation. To minimize this uncertainty, (i) all capsules were polished to nearly the center; therefore, the melt fraction in the cross section most likely represents the entire capsule; (ii) only runs with high melt fractions (≳20%) were used; and (iii) the melt fractions based on SEM images were independently examined by mass balance calculations of MgO and SiO 2 concentrations in the solids and melts (Tables S1 and S2). As shown in Figures 2a and 2b, the melt fractions estimated by different methods follow the same trend and agree well with each other. The uncertainty of the melt fraction estimation is therefore limited.
Additional potential error sources include the following: (i) Uncertainty of the water content in solid phases. This should be negligible because the majority of water (>90%) within the capsule is stored by melt. (ii) Water gain during sample preparation. The sample powder may absorb moisture from the air, but this amount (<<0.5 wt.%) is small in comparison with the bulk H O 2 C in the starting materials. (iii) Pressure and temperature uncertainties. The appearance of both Fe-free and Fe-bearing ringwoodite at 2000 K and the coexistence of ringwoodite and bridgmanite in H4891 indicate a pressure uncertainty of less than 1.5 GPa (Presnall, 1995). The temperature gradient in a typical multi-anvil experiment is ∼100 K/mm (Hernlund et al., 2006). Considering the capsule lengths of 1.2-1.3 mm located at the center, the temperature uncertainty in this study should be less than 70 K. Because the magnitude of each error source is unknown, it is impossible to quantitatively evaluate the error bar for each data point.   (Figures 2b-2d). This is reasonable because the water partition coefficient between melt and solid should be constant at a given temperature. As shown in Table 1, the partition coefficient is nearly constant (18-25) at 2000 K even with various starting compositions (except runs H4711 and H4775, in which ringwoodite has a lower water content than the other runs because of different SiO 2 -activity conditions [Fei & Katsura, 2020] clearly decreases with increasing temperature, but shows no meaningful dependence of (Mg + Fe)/ Si and Fe/(Mg + Fe) ratios (Figures 2c, 2e, and 2f). Additionally, although the melt coexists with various solid phases in the run products (Table 1) has strong temperature dependence, but is relatively insensitive to chemical composition, coexisting phases, and bulk water content in the system. Therefore, even though experiments in this study were performed with a simple system (MgO-SiO 2 -FeO-H 2 O) and high bulk water content, they should still be able to represent

Temperature Dependence of C H O melt 2
As shown in Figure 3,  (Figure 3). However, their experimental temperature range was relatively small (1570-1870 K), which may mask the temperature dependence.
The melt H O 2 C determined in this study apparently follows an exponential function of reciprocal temperature (1/T). The data points are thus fitted to the equation, where melt H O 2 C is the water content in wt.%, T is the temperature, R is the ideal gas constant, C 0 is a constant, and ΔG is the chemical potential difference of H 2 O between melt and solid. By least square fitting, the C 0 and ΔG are found to be 10 −0.32±0.17 and −61.5 ± 5.3 kJ/mol, respectively.
In the view of thermodynamics, the chemical potential of H 2 O in solid (

Stability of the Melting Layer at 660-km Depth
A dehydration melting layer caused by downwelling flow (e.g., subducted slabs) is seismically interpreted at the topmost lower mantle near the 660-km discontinuity (Schmandt et al., 2014). The gravitational stability of this melting layer should be dominated by the melt density and therefore controlled by   Table 1. The data by N19 (Nakajima et al., 2019) with peridotite + H 2 O as starting material are also shown for comparison. mantle temperatures. The geotherm of the topmost lower mantle is ∼2000 K (Katsura et al., 2010), whereas the slabs are 300-500 K lower, that is, ∼1600 K (Litasov et al., 2013;Tan et al., 2002). Sink/float experiments using multi-anvil techniques (Ohtani & Maeda, 2001;Sakamaki et al., 2006;Suzuki & Ohtani, 2003;Suzuki et al., 1995) suggest a melt density of 4.0 and 4.1 g/cm 3 at 2000 and 1600 K, respectively, for both dry MORB and peridotitic melts after adjusting to 660-km depth pressure (∼23.5 GPa). However, this value might be slightly underestimated because small amounts of water are always inevitable in multi-anvil experiments.
According to the results from this study, is ∼20 and 50 wt.% at 2000 and 1600 K, respectively. Using a H 2 O partial mole volume of 6.2-6.4 cm 3 /mol in silicate melt (Sakamaki et al., 2006), the density of a hydrous melt with 20 wt.% water (2000 K) is estimated to be 3.7-3.9 g/cm 3 , and 3.4-3.5 g/cm 3 for a melt with 50 wt.% water (1600 K). This is comparable with that reported by Nakajima et al. (2019) (3.6-3.9 g/cm 3 ) at 23.5 GPa and 1570-1870 K, as shown in Figure 4. However, as explained previously, the absolute values of Although density may increase with Fe content (Matsukage et al., 2005), the FeO wt.% in hydrous peridotitic melt that coexists with bridgmanite is even lower than anhydrous melt (Ito & Takahashi, 1987;Nakajima et al., 2019). The hydrous melt at the topmost lower mantle is therefore always less dense than the transition zone. It should be maintained by downward flow and moves upward by buoyancy. By upwelling, ringwoodite with ∼1 wt.% H 2 O is expected to crystallize from the melt. Because  . Density contrast of the transition zone, topmost lower mantle, and hydrous melt at 660-km depth. The blue and yellow regions are MORB melt density ranges at 1600 K (slab) and 2000 K (ambient mantle), respectively. The upper limit of each region is based on the dry MORB melt density given by Bajgain et al. (2015) and Sanloup et al. (2013). The lower limit is based on dry MORB and peridotitic melt given by Ohtani and Maeda (2001) and Suzuki et al. (1995), with a partial mole volume of 6.2-6.4 cm 3 /mol for H 2 O at 23.5 GPa and 1600-2000 K (Sakamaki et al., 2006). All data are recalculated to 23.5 GPa and 1600 K (blue) or 2000 K (yellow) using their reported Birch-Murnaghan equation of state parameters and corresponding temperature dependences. PREM: density of the preliminary reference Earth model (Dziewonski & Anderson, 1981).

Melt Fraction at the Topmost Lower Mantle
The melt fraction at the topmost lower mantle can be estimated from melt H O 2 C by a given water-content in the mantle transition zone. If we consider 55 vol.% ringwoodite in the mantle transition zone with ∼1.0 wt.% water (e.g., Fei & Katsura, 2020;Fei et al., 2017;Pearson et al., 2014), using melt H O 2 C = 50 wt.% at 1600 K determined in this study, the melt fraction in the topmost lower mantle is estimated to be 1.3 vol.% based on mass balance by assuming negligible water in ferropericlase and bridgmanite (Bolfan-Casanova, 2000;Fu et al., 2019). Even if using a relatively dry transition zone model (∼0.4 wt.% water based on seismic velocity [Houser, 2016]), the melt fraction will be ∼0.5 vol.% (calculation details are given in the supporting information). Note that the secondary minerals in the slabs and ambient mantle including CaSiO 3 -perovskite, garnet, and stishovite may also contain large amounts of water Katayama et al., 2003;Lin et al., 2020;Nisr et al., 2020). However, they have no phase transition when crossing 660-km depth. Their water contents should therefore remain nearly constant and not affect the melt fraction estimation in this study.
Although the dihedral angle of the bridgmanite + silicate melt system is unknown, it is expected to decrease with increasing pressure and estimated to be < 10° or nearly 0° at 660-km depth when extrapolated from the dihedral angle in the olivine-silicate melt system (Freitas & Manthilake, 2019). With such a low dihedral angle (<10°), 0.5-1.3 vol.% of melt is sufficient to completely wet the grain boundaries of bridgmanite, which will substantially affect the dynamics at the topmost lower mantle. For example, the melt may account for the seismic velocity reduction near 660-km depth (Schmandt et al., 2014). Another relevant example is viscosity. By complete wetting of grain boundaries, the viscosity of rocks could be significantly reduced by the pressure-solution creep mechanism, which may cause the topmost lower mantle to be rheologically much weaker (low viscosity) than the transition zone and deep lower mantle. Such a low-viscosity layer will largely prohibit whole mantle convection and may cause slab stagnation within the mantle transition zone (Fukao et al., 2009) because the resistance for horizontal flow is largely reduced (Mao & Zhong, 2018).

Data Availability Statement
The data sets for this research are given in Zenodo (10.5281/zenodo.4288962).