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Interacting magmatic sills at about 40-kilometer depth under the island of Hawai‘i feed into multiple different volcanoes. 

Abstract. Shear properties of mantle minerals are vital for interpreting seismic shear wave speeds and therefore inferring the composition and dynamics of a planetary interior. Shear wave speed and elastic tensor components, from which the shear modulus can be computed, are usually measured in the laboratory mimicking the Earth's (or a planet's) internal pressure and temperature conditions. A functional form that relates the shear modulus to pressure (and temperature) is fitted to the measurements and used to interpolate within and extrapolate beyond the range covered by the data. Assuming a functional form provides prior information, and the constraints on the predicted shear modulus and its uncertainties might depend largely on the assumed prior rather than the data. In the present study, we propose a data-driven approach in which we train a neural network to learn the relationship between the pressure, temperature and shear modulus from the experimental data without prescribing a functional form a priori. We present an application to MgO, but the same approach works for any other mineral if there are sufficient data to train a neural network. At low pressures, the shear modulus of MgO is well-constrained by the data. However, our results show that different experimental results are inconsistent even at room temperature, seen as multiple peaks and diverging trends in probability density functions predicted by the network. Furthermore, although an explicit finite-strain equation mostly agrees with the likelihood predicted by the neural network, there are regions where it diverges from the range given by the networks. In those regions, it is the prior assumption of the form of the equation that provides constraints on the shear modulus regardless of how the Earth behaves (or data behave). In situations where realistic uncertainties are not reported, one can become overconfident when interpreting seismic models based on those defined equations of state. In contrast, the trained neural network provides a reasonable approximation to experimental data and quantifies the uncertainty from experimental errors, interpolation uncertainty, data sparsity and inconsistencies from different experiments. 

Abstract Hydrated sulfates have been identified and studied in a wide variety of environments on Earth, Mars, and the icy satellites of the solar system. The subsurface presence of hydrous sulfur-bearing phases to any extent necessitates a better understanding of their thermodynamic and elastic properties at pressure. End-member experimental and computational data are lacking and are needed to accurately model hydrous, sulfur-bearing planetary interiors. In this work, high-pressure X-ray diffraction (XRD) and synchrotron Fourier-transform infrared (FTIR) measurements were conducted on szomolnokite (FeSO4·H2O) up to ~83 and 24 GPa, respectively. This study finds a monoclinic-triclinic (C2/c to P1) structural phase transition occurring in szomolnokite between 5.0(1) and 6.6(1) GPa and a previously unknown triclinic-monoclinic (P1 to P21) structural transition occurring between 12.7(3) and 16.8(3) GPa. The high-pressure transition was identified by the appearance of distinct reflections in the XRD patterns that cannot be attributed to a second phase related to the dissociation of the P1 phase, and it is further characterized by increased H2O bonding within the structure. We fit third-order Birch-Murnaghan equations of state for each of the three phases identified in our data and refit published data to compare the elastic parameters of szomolnokite, kieserite (MgSO4·H2O), and blödite (Na2Mg(SO4)2·4H2O). At ambient pressure, szomolnokite is less compressible than blödite and more than kieserite, but by 7 GPa both szomolnokite and kieserite have approximately the same bulk modulus, while blödite’s remains lower than both phases up to 20 GPa. These results indicate the stability of szomolnokite’s high-pressure monoclinic phase and the retention of water within the structure up to pressures found in planetary deep interiors. 

Abstract Transport of heat from the interior of the Earth drives convection in the mantle, which involves the deformation of solid rocks over billions of years. The lower mantle of the Earth is mostly composed of iron-bearing bridgmanite MgSiO 3 and approximately 25% volume periclase MgO (also with some iron). It is commonly accepted that ferropericlase is weaker than bridgmanite 1 . Considerable progress has been made in recent years to study assemblages representative of the lower mantle under the relevant pressure and temperature conditions 2,3 . However, the natural strain rates are 8 to 10 orders of magnitude lower than in the laboratory, and are still inaccessible to us. Once the deformation mechanisms of rocks and their constituent minerals have been identified, it is possible to overcome this limitation thanks to multiscale numerical modelling, and to determine rheological properties for inaccessible strain rates. In this work we use 2.5-dimensional dislocation dynamics to model the low-stress creep of MgO periclase at lower mantle pressures and temperatures. We show that periclase deforms very slowly under these conditions, in particular, much more slowly than bridgmanite deforming by pure climb creep. This is due to slow diffusion of oxygen in periclase under pressure. In the assemblage, this secondary phase hardly participates in the deformation, so that the rheology of the lower mantle is very well described by that of bridgmanite. Our results show that drastic changes in deformation mechanisms can occur as a function of the strain rate. 

Abstract The Fe3+/FeT ratios (Fe3+/[Fe2++Fe3+]) in minerals can be used to understand their crystallization and post-crystallization conditions. However, as natural minerals are often zoned and contain inclusions, bulk techniques, e.g., wet chemistry, may not provide accurate Fe3+/FeT values for a single phase of interest. We determined Fe3+/FeT ratios of amphiboles in different crystallographic orientations by single-crystal synchrotron Mössbauer spectroscopy (SMS) in energy and time domain modes from four volcanic localities (Long Valley Caldera, Mount St. Helens, Lassen Volcanic Center, U.S.A., and Mt. Pinatubo, Philippines). The high spatial resolution (as low as 12 × 12 μm spot size) and standard-free nature of SMS allow the detection of intra-grain compositional heterogeneities in Fe3+/FeT with relatively low uncertainties. We combine SMS with major element compositions, water contents, and hydrogen isotope compositions to document the Fe3+/FeT ratios as a function of mineral composition and post-crystallization dehydrogenation. Spectra were fitted with up to five distinct sites: ferrous iron on M(1), M(2), M(3), and ferric iron on M(2) and M(3), consistent with X-ray diffraction studies on single crystals of amphibole. The Fe3+/FeT ratios range from 0.14 ± 0.03 (Long Valley Caldera), 0.51 to 0.63 ± 0.02 (representing intra-grain heterogeneities, Mount St. Helens) to 0.86 ± 0.03 (Lassen Volcanic Center). The latter grain experienced post-crystallization dehydrogenation, shown by its low water content (0.6 ± 0.05 wt%) and its elevated hydrogen isotope composition (δD = +25 ± 3‰ relative to SMOW). The Fe3+/FeT ratios of 0.62 ± 0.01 and 0.20 ± 0.01 of two Mt. Pinatubo grains correlate with high-Al2O3 cores and low-Al2O3 rims and smaller phenocrysts in the sample, respectively. This study shows that SMS is capable of distinguishing two different domains with dissimilar Fe3+/FeT values formed under different crystallization conditions, demonstrating that SMS in combination with major element, water, and hydrogen isotope compositions allows the interpretation of amphibole Fe3+/FeT ratios in the context of crystallization and post-crystallization processes. 

Abstract Isotopic fractionation has been linked to the lattice vibrations of materials through their phonon spectra. The Lamb-Mössbauer factor (fLM) has the potential to provide information about the lattice vibrations in materials. We constrain the temperature evolution of the fLM of γ- and ε-Fe at in situ high-P-T conditions between 1650 K and the melting point. We find that the vibrations of γ- and ε-Fe can be described using a quasiharmonic model with a pressure- and temperature-dependent Debye temperature computed from the measured fLM. From the Debye temperature, we derive the equilibrium isotopic fractionation β-factor of iron. Our results show that the quasiharmonic behavior of metallic iron would lower the value of lnβFe57/54 by 0.1‰ at 1600–2800 K and 50 GPa when compared to the extrapolation of room temperature nuclear resonant inelastic X-ray scattering data. Our study suggests that anharmonicity may be more prevalent in Fe metal than in lower mantle minerals at 2800 K and 50 GPa, a relevant condition for the core formation, and the silicate mantle may be isotopically heavy in iron. 

Abstract The high-pressure phases of oxyhydroxides (δ-AlOOH, ε-FeOOH, and their solid solution), candidate components of subducted slabs, have wide stability fields, thus potentially influencing volatile circulation and dynamics in the Earth’s lower mantle. Here, we report the elastic wave velocities of δ-(Al,Fe)OOH (Fe/(Al + Fe) = 0.13, δ-Fe13) to 79 GPa, determined by nuclear resonant inelastic X-ray scattering. At pressures below 20 GPa, a softening of the phonon spectra is observed. With increasing pressure up to the Fe 3+ spin crossover (~ 45 GPa), the Debye sound velocity ( v D ) increases. At higher pressures, the low spin δ-Fe13 is characterized by a pressure-invariant v D . Using the equation of state for the same sample, the shear-, compressional-, and bulk-velocities ( v S , v P , and v Φ ) are calculated and extrapolated to deep mantle conditions. The obtained velocity data show that δ-(Al,Fe)OOH may cause low- v Φ and low- v P anomalies in the shallow lower mantle. At deeper depths, we find that this hydrous phase reproduces the anti-correlation between v S and v Φ reported for the large low seismic velocity provinces, thus serving as a potential seismic signature of hydrous circulation in the lower mantle.