Nominally anhydrous minerals (NAMs) are the primary carriers of water in rocky planet mantles. Therefore, studying water solubilities in the major mantle NAMs can help us estimate the water storage capacities of rocky planet mantles and indirectly constrain the actual water contents of their interiors. Using data science methods such as statistics and statistical learning algorithms, this paper presents and summarizes current modeling studies on the mantle water storage capacities of Earth, Mars, and exoplanets. The paper first reviews the thermodynamic model for mantle water storage capacity. Then, two case studies on Earth and Mars explore how to translate atomic-scale experimental data of water solubility and their measurement errors into planetary-scale models of mantle water storage capacity, based on robust regression, Monte Carlo methods, and bootstrap aggregation algorithms. Then, it is presented how a large sample from the exoplanet observational campaigns can help us understand the statistical nature of their mantle water storage capacities. Finally, the paper discusses the limitations of data science methods and how to combine statistics and statistical algorithms with mineral physics data.

Water has been stored in the Martian mantle since its formation, primarily in nominally anhydrous minerals. The short-lived early hydrosphere and intermittently flowing water on the Martian surface may have been supplied and replenished by magmatic degassing of water from the mantle. Estimating the water storage capacity of the solid Martian mantle places important constraints on its water inventory and helps elucidate the sources, sinks, and temporal variations of water on Mars. In this study, we applied a bootstrap aggregation method to investigate the effects of iron on water storage capacities in olivine, wadsleyite, and ringwoodite, based on high-pressure experimental data compiled from the literature, and we provide a quantitative estimate of the upper bound of the bulk water storage capacity in the FeO-rich solid Martian mantle. Along a series of areotherms at different mantle potential temperatures (T_p), we estimated a water storage capacity equal to 9.0_−2.2^+2.8 km Global Equivalent Layer (GEL) for the present-day Martian mantle at T_p = 1600 K and 4.9_−1.5^+1.7 km GEL for the initial Martian mantle at T_p = 1900 K. The water storage capacity of the Martian mantle increases with secular cooling through time, but due to the lack of an efficient water recycling mechanism on Mars, its actual mantle water content may be significantly lower than its water storage capacity today.

The water content in Earth's mantle today remains poorly constrained, but the bulk water storage capacity in the solid mantle can be quantified based on experimental data and may amount to a few times the modern surface ocean mass (OM). An appreciation of the mantle water storage capacity is indispensable to our understanding of how water may have cycled between the surface and mantle reservoirs and changed the volume of the oceans through time. In this study, we parameterized high pressure-temperature experimental data on water storage capacities in major rock-forming minerals to track the bulk water storage capacity in Earth's solid mantle as a function of temperature. We find that the mantle water storage capacity decreases as mantle potential temperature (T_p) increases, and its estimated value depends on the water storage capacity of bridgmanite in the lower mantle: 1.86–4.41 OM with a median of 2.29 OM for today (T_p = 1600 K), and 0.52–1.69 OM with a median of 0.72 OM for the early Earth's solid mantle (for a T_p that was 300 K higher). An increase in T_p by 200–300 K results in a decrease in the mantle water storage capacity by 1.19^+0.9_−0.16 –1.56^+1.1_−0.22 OM. We explored how the volume of early oceans may have controlled sea level during the early Archean (4–3.2 Ga) with some additional assumptions about early continents. We found that more voluminous surface oceans might have existed if the actual mantle water content today is > 0.3–0.8 OM and the early Archean T_p was ≥1900 K.

Calcium-rich carbonate may be preserved in fast-descending slabs to reach the mantle transition zone (MTZ), which is known to be at least locally hydrous. At MTZ pressures, the melting curve of CaCO₃ crosses the geotherm and is further depressed by water; hence, Ca-rich carbonate may be mobilized by hydrous melting and escape the MTZ. Here we show that aragonite reacts with wadsleyite to produce magnesite under the pressure and temperature conditions of cold slabs in the MTZ. Water considerably enhances conversion of Ca-rich carbonate into more refractory magnesite, helping to retain carbonate in the deep mantle.

Nitrogen, the most abundant element in Earth's atmosphere, is also a primary component of solid nitride minerals found in meteorites and on Earth's surface. If they remain stable to high pressures and temperatures, these nitrides may also be important reservoirs of nitrogen in planetary interiors. We used synchrotron X-ray diffraction to measure the thermal equation of state and phase stability of titanium nitride (TiN) in a laser-heated diamond anvil cell at pressures up to ∼70 GPa and temperatures up to ∼2,500 K. TiN maintains the cubic B1 (NaCl-type) crystal structure over the entire pressure and temperature range explored. It has K₀ = 274 (4) GPa, K₀′ = 3.9 (2), and γ₀ = 1.39 (4) for a fixed V₀ = 76.516 (30) ų (based on experimental measurements), q = 1, and θ₀ = 579 K. Additionally, we collected Raman spectra of TiN up to ∼60 GPa, where we find that the transverse acoustic (TA), longitudinal acoustic (LA), and transverse optical phonon modes exhibit mode Grüneisen parameters of 1.66(17), 0.54(15), and 0.93 (4), respectively. Based on our equation of state, TiN has a density of ∼5.6–6.4 g/cm³ at Earth's lower mantle conditions, significantly more dense than both the mantle of the Earth and the estimated densities of the mantles of other terrestrial planets, but less dense than planetary cores. We find that TiN remains stable against physical decomposition at the pressures and temperatures found within Earth's mantle, making it a plausible reservoir for deep planetary nitrogen if chemical conditions allow its formation.

We report experimental constraints on the melting curve of potassium chloride (KCl) between 3.2 and 9 GPa from in situ ionic conduction measurements using a multi-anvil apparatus. On the basis of concurrent measurements of KCl and sodium chloride (NaCl) at 1 bar using the differential thermal analysis (DTA) method and Pt sphere marker, we show that the peak rate of increase in ionic current with temperature upon heating coincides with latent heat ledge and fall of Pt sphere, thus establishing the criterion for melting detection from ionic conduction measurements. Applying this criterion to high pressures, we found that the melting point of KCl rose steeply with increasing pressure to exceed 2443 ± 100 K at 9 GPa. Fitting the results of this study together with existing data at pressures below 4 GPa and above 20 GPa, we obtained the Simon’s melting equation for KCl in the simple cubic B2 structure between 1.8 and 50 GPa: T_m=1323(P/1.872.2(1)+1)^1/2.7(1) , where T is in K and P is in GPa. Starting at 1 bar, the melting point of KCl increases at an average rate of ~150 K/GPa to cross that of Pt near 9 GPa. The highly refractory nature of KCl makes it a sensitive pressure calibrant for the large-volume pressure at moderate pressures and a potential sample container for experiments at moderate pressures and very high temperatures.

Metallic melt containing iron (Fe) and carbon (C) may be present at depths greater than 250 km inside the Earth. Depending on its wetting behavior, such dense melt may be trapped locally or drain into deep mantle and core. Here, we report experimental data on the wetting behavior of Fe-C melt in silicates at the conditions of Earth’s mid-mantle between 10 and 23 GPa and 1600 and 1800 ˚C. The measured dihedral angles of Fe-C melt in olivine, ringwoodite or bridgmanite and ferropericlase matrixes are 117±14°, 120±14° and 107±16° respectively, well above the critical value of 60° for complete wetting. The estimated percolation thresholds are at least 7% in volume, far exceeding the amount of metal in the mantle. Consequently, slab-derived Fe-C melt in the mid-mantle is expected to occur as isolated pockets and would not percolate through its silicate matrix.

The melting point of barium carbonate (BaCO₃) was determined at pressures up to 11 GPa using the ionic conductivity and platinum (Pt) sphere methods in a multi-anvil press. The melting point decreases with pressure from 2149 ± 50 K at 3 GPa to a fitted local minimum of 1849 K at 5.5 GPa, and then it rises with pressure to 2453 ± 50 K at 11 GPa. The fitted melting curve of BaCO₃ based on the ionic conductivity measurements is consistent with the Pt sphere measurements that were carried out independently at selected pressures. The negative slope of the BaCO₃ melting curve between 3 and 5.5 GPa indicates that the liquid is denser than the solid within this pressure range. Synchrotron X-ray diffraction (XRD) measurements in a laser-heated diamond-anvil cell (LH-DAC) showed that BaCO₃ transformed from the aragonite structure (Pmcn) to the post-aragonite structure (Pmmn) at 6.3 GPa and 1026 K as well as 8 GPa and 1100 K and the post-aragonite structure remained metastable upon quenching and only reverted back to the witherite structure upon pressure release. The local minimum near 5 GPa is attributed to the triple point where the melting curve of BaCO₃ meets a phase transition to the denser post-aragonite structure (Pmmn). Local minima in the melting curves of alkaline earth carbonates would lead to incipient melting of carbonated rocks in Earth's mantle.

Some studies suggested that the Earth’s mantle transition zone (MTZ) consists of hydrous silicates while others proposed that it contains iron metal. Here we show that the metallic iron dehydrates hydrous silicates at MTZ conditions, implying that global hydration of silicates and metal saturation are incompatible. Comparing iron production in and water injection to the MTZ, we found that the hydration of MTZ silicates is likely limited to <0.1 wt%, while large amount of the hydrogen can be stored as iron hydride and hydrogen fluid instead. Water-rich domains may still exist near the modern active subducted slabs. Our finding connects the water content to the oxidation state of the MTZ, thus providing a different perspective on volatile cycles in the mantle.