Shun‐ichiro Karato

Most our knowledge about rocky exoplanets is based on their measure of mass and radius. These two parameters are routinely measured and are used to categorise different populations of observed exoplanets. They are also tightly linked to the planet's properties, in particular those of the interior. As such they offer the unique opportunity to interpret the observations and potentially infer the planet's chemistry and structure. Required for the interpretation are models of planetary interiors, calculated a priori, constrained using other available data, and based on the physiochemical properties of mineralogical phases. This article offers an overview of the current knowledge about exoplanet interiors, the fundamental aspects and tools for interior modelling and how to improve the contraints on the models, along with a discussion on the sources of uncertainty. The origin and fate of volatiles, and their role in planetary evolution is discussed. The chemistry and structure of planetary interiors have a pivotal role in the thermal evolution of planets and the development of large scale properties that might become observables with future space missions and ground-based surveys. As such, having reliable and well constrained interior models is of the utmost importance for the advancement of the field.

Most our knowledge about rocky exoplanets is based on their measure of mass and radius. These two parameters are routinely measured and are used to categorise different populations of observed exoplanets. They are also tightly linked to the planet's properties, in particular those of the interior. As such they offer the unique opportunity to interpret the observations and potentially infer the planet's chemistry and structure. Required for the interpretation are models of planetary interiors, calculated a priori, constrained using other available data, and based on the physiochemical properties of mineralogical phases. This article offers an overview of the current knowledge about exoplanet interiors, the fundamental aspects and tools for interior modelling and how to improve the contraints on the models, along with a discussion on the sources of uncertainty. The origin and fate of volatiles, and their role in planetary evolution is discussed. The chemistry and structure of planetary interiors have a pivotal role in the thermal evolution of planets and the development of large scale properties that might become observables with future space missions and ground-based surveys. As such, having reliable and well constrained interior models is of the utmost importance for the advancement of the field.

Abstract Seismic wave velocities in the hot mantle are affected by non‐elastic, time‐dependent deformation and hence depend on frequency (). We show that the principle of causality leads to a seismological Kramers‐Kronig relation where is attenuation caused by non‐elastic deformation. This relation indicates that the frequency dependence of seismic wave velocity comes from (attenuation) integrated over all frequencies above the frequency at which the wave velocity is measured. A frequently used relation can be derived from this relation if (with 0.3 for ) but for . The validity of this relation is tested using seismologically estimated seismic wave velocities and attenuation in the asthenosphere. We find that , that is, the above relation is not consistent with the seismological observations on the asthenosphere. This implies that there is a mechanism of attenuation at high frequencies ) that causes substantial (∼5%) velocity reduction (such as elastically accommodated grain‐boundary sliding (EAGBS)). Consequently, even when one uses low‐frequency seismic wave velocities to understand the Earth structure, the influence of high‐frequency anelasticity on seismic wave velocity needs to be included to infer properties related to anelasticity (e.g., temperature). Experimental results on EAGBS in olivine are reviewed and we conclude that EAGBS results in substantial velocity reduction when olivine contains a large amount of water (>100 ppm wt water) but not under water‐poor conditions. The reported large velocity reduction at the lithosphere‐asthenosphere boundary therefore suggests that the asthenosphere contains a substantial amount of water.

Abstract We review our current understanding of the rheological properties of the lower mantle based both on materials science and geophysics points of view. We assume a simple model of the lower mantle that is made of only two minerals: bridgmanite (Br) (Mg,Fe)SiO 3 and ferropericlase (Fp) (Mg,Fe)O, and address a question of (i) which mineral is weaker (lower viscosity), (ii) how does lower mantle viscosity change with depth and location, and (iii) discuss implications for shear localization. We first review plausible mechanisms of deformation based on the deformation mechanism map on the normalized stress and temperature space. We conclude that likely mechanism of deformation in the lower mantle is either diffusion creep or power-law dislocation creep. Based on this review, we discuss recently proposed models by Cordier and his group (Cordier in Nature 481:177–181, 2012; Cordier in Nature 613:303–306 , 2023) where either asthermal creep (i.e., low-temperature plasticity) or pure climb creep (not power-law dislocation creep) would play an important role. We conclude that these models are not acceptable because (1) many aspects of their models are incompatible with experimental observations and theoretical models of deformation of most materials including oxides and metals and (2) these models are not consistent with the distribution of seismic anisotropy. Hence, we focus on power-law dislocation creep and diffusion creep. We review previously published results on deformation (by dislocation creep) and diffusion, we conclude that Fp is weaker than Br. The radial (depth) depth and lateral variation of viscosity is discussed based on the estimated activation volume and estimated variation of grain-size. Geophysical studies suggest only modest depth variation of viscosity that demands relatively small activation volume (V* (&lt; 3 $$\times$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>×</mml:mo> </mml:math> 10 –6 m 3 /mol)). Plausible models to explain small activation volume are discussed including the role of extrinsic diffusion. Grain-size also controls viscosity if deformation is by diffusion creep. Okamoto and Hiraga (J Geophys Res, 2024. 10.1029/2023JB027803), Solomatov et al. (Phys Earth Planet Inter 129:265–282, 2002) estimated the grain-size evolution in the lower mantle based on the kinetics of grain-growth and the role of a phase transformation. In contrast, there are other papers (e.g., Paul et al. in Prog Earth Planet Sci 11:64, 2024; Rozel in Geochem Geophys Geosyst, 2012. 10.1029/2012GC004282) where grain-size distribution is estimated assuming that grain-size is controlled by dynamic recrystallization. The validity of assumption is questionable because dynamic recrystallization occurs due to deformation by dislocation creep but not by diffusion creep and the absence of seismic anisotropy indicates that diffusion creep dominates in most of the lower mantle. Finally, we review the published models of shear localization that would explain the long-term preservation of geochemical reservoirs in the lower mantle. Accepting that two minerals (Fp and Br) in the lower mantle have largely different viscosity, Ballmer et al. (Nat Geosci 10:236–240, 2017) proposed that the presence of regions of compositional difference (difference in Fp/Br ratio) leads to localized deformation (deformation mainly in the weaker regions). However, in addition to the ad hoc nature of this model, there is no strong evidence for the presence of large variation in Fp/Br in the lower mantle that makes the validity of this model questionable. There are some papers where processes of shear localization are explored without invoking the presence of regions of large rheological contrast. Thielmann et al. (Geochem Geophys Geosyst, 2020. 10.1029/2019GC008688) presented the results of theoretical study of deformation of initially homogeneous two-phase mixture (Fp and Br) and showed that deformation causes the elongation of a weak Fp that promotes shear localization. In this model, the rheological contrast between Fp and Br was assumed to be independent of strain. However, Cho and Karato (J Geophys Res 2022. 10.1029/2021JB022673 ; Phys Earth Planet Inter, 2024. 10.1016/j.pepi.2024 ) showed that when deformation is by diffusion creep, the rheological contrast increases with strain due to the evolution of stress concentration caused by grain elongation. They showed that this will promote strain weakening particularly in simple shear that would lead to shear localization. Consequently, the tendency for shear localization is stronger in their model than a model where rheological contrast is assumed to be independent of strain.

Abstract Understanding hydrogen dissolution mechanisms in bridgmanite (Bgm), the most abundant mineral in the lower mantle, is essential for understanding water storage and rheological and transport properties in the region. However, interpretations of O‐H bands in Fourier transform infrared spectroscopy (FTIR) spectra of Bgm crystals remain uncertain. We conducted density functional theory (DFT) calculations on vibrational characteristics of O‐H dipoles and performed polarized FTIR measurements to address this issue. DFT calculations for four substitution models—Mg vacancies, Si vacancies, Al 3+ + H + substitution for Si 4+ , and Al substitution with Mg vacancies—reveal distinct O‐H bands with different polarizations. Deconvolution of polarized FTIR spectra on Mg 0.88 Fe 2+ 0.035 Fe 3+ 0.065 Al 0.14 Si 0.90 O 3 and Mg 0.95 Fe 2+ 0.033 Fe 3+ 0.027 Al 0.04 Si 0.96 O 3 crystals shows five major O‐H bands with distinct polarizations along principal crystallographic axes. These experimental and calculated results attribute O‐H bands centered at 3,463–3,480, 2,913–2,924, and 2,452–2,470 cm −1 to Mg vacancies, Si vacancies, and Al 3+ + H + substitution for Si 4+ , respectively. The total absorbance coefficient of bridgmanite was calculated to be 82,702(6,217) L/mol/cm 2 . Mg and Si vacancies account for 43%–74% of the total water content, making them dominant hydrogen dissolution mechanisms in Bgm. The band frequencies for the Mg and Si vacancies in Bgm are drastically different from those in olivine and ringwoodite, corresponding to the significant changes in O‐H bond strengths and in the Si and Mg coordination environments from upper‐mantle to lower‐mantle minerals. These results highlight the need to incorporate hydrogen dissolution mechanisms in Bgm for understanding electrical conductivity and rheology of the lower mantle.

We investigate seismic discontinuities across the middle of Earth’s mantle beneath a large seismic array that spans the North American continent. We provide robust constraints on the depth distribution, sharpness, and spatial variation of seismic discontinuities by processing high-resolution Ps-converted seismic waves (~0.5 Hz) through a novel denoising filter called CRISP-RF (Clean Receiver function Imaging with Sparse Radon Filters). In the upper mantle, above the mantle transition zone (MTZ), we observe a sharp velocity decrease at depths that vary from ~290 km to ~390 km. In the lower mantle, below the MTZ, we observe another sharp velocity decrease at depths that vary from ~800 km to 1,200 km. The lower-mantle discontinuities cluster at a depth of ~885 km, while deeper converters (&gt; 1,000 km) are less likely. The spatial distribution of these seismic features appears stochastic, but we detect collocated upper-mantle and lower-mantle discontinuities only at 8% of observed locations. We interpret our results with a dehydration melting model, in which MTZ water is transported into either the upper or the lower mantle, but rarely simultaneously, during Earth’s long history of subduction and mantle upwelling.

Abstract This study investigates the effect of pressure on diffusion creep of dry San Carlos and synthetic (prepared by sol-gel method) olivine. We prepared dry (water content &amp;lt;9 ppm wt) fine-grained (&amp;lt;1 μm grain size) olivine and deformed the samples (both San Carlos and sol-gel olivine) in the same sample assembly under high pressure (P = 2.9–8.8 GPa) and moderate temperatures (T = 980–1250 K) at a fixed strain rate. The evolution of the sample’s strength was studied using radial X-ray diffraction from various diffraction planes. We found that San Carlos and sol-gel olivine show similar rheological behavior (when normalized to the same grain size). Stress estimated by the radial X-ray diffraction increases with time and initially shows similar values for all diffraction planes. In many cases, stress values start to depend on the diffraction planes in the later stage, and time dependence becomes minor. The microstructural observations show that grain size increases during an experiment. The results are interpreted using a theory of radial X-ray diffraction and the theoretical models of diffusion and dislocation creep. We conclude that the initial stage of deformation is by diffusion creep, but deformation in the later stage is by dislocation creep. For dislocation creep, our results are in reasonable agreement with previous low-temperature dislocation creep results after correcting the temperature effect. For diffusion creep, we obtain an activation volume of 7.0 ± 2.4 cm3/mol that is substantially smaller than the values reported on dislocation creep but agrees well with the results on grain growth. By comparing the present results on dry olivine with the previous results on wet (water-saturated) olivine, we found that water enhances diffusion creep but only modestly compared to dislocation creep. The difference in the pressure and water content dependence between diffusion and dislocation creep has an important influence on the dominant deformation mechanisms of olivine in the upper mantle.

Abstract The interplay between crystal–melt and grain boundary interfaces in partially melted polycrystalline aggregates controls many physical properties of mantle rocks. To understand this process at the fundamental level requires improved knowledge about the interfacial structures and energetics. Here, we report the results of first-principles molecular dynamics simulations of two grain boundaries of (0 l 1)/[100] type for tilt angles of 30.4° and 49.6° and the corresponding solid–liquid interfaces in Mg 2 SiO 4 forsterite at the conditions of the upper mantle. Our analysis of the simulated position time series shows that structural distortions at the solid–liquid interfacial region are stronger than intergranular interfacial distortions. The calculated formation enthalpy of the solid–solid interfaces increases nearly linearly from 1.0 to 1.4 J/m 2 for the 30.4° tilt and from 0.8 to 1.0 J/m 2 for the 49.6° tilt with pressure from 0 to 16 GPa at 1500 K, being consistent with the experimental data. The solid–liquid interfacial enthalpy takes comparable values in the range 0.9 to 1.5 J/m 2 over similar pressure interval. The dihedral angle of the forsterite–melt system estimated using these interfacial enthalpies takes values in the range of 67° to 146°, showing a decreasing trend with pressure. The predicted dihedral angle is found to be generally larger than the measured data for silicate systems, probably caused by compositional differences between the simulation and the measurements.

A model of core formation is reviewed a nd its consequences on mantle chemistry and core-mantle interaction are discussed. A growing planet forms a cold proto-core made of a mixture of various materials including primitive materials rich in highly siderophile elements (HSE) as well as volatiles. These primitive materials are squeezed out to the bottom of the magma ocean when Fe accumulated above the proto-core sinks to the center. After heated, the proto-core materials are mixed with the magma ocean. Consequently, mantle is made of a mixture of materials equilibrated with Fe at modest pressure and temperature and a small amount of primitive materials from the proto-core. This model explains the observed abundance pattern of all siderophile elements and predicts that most of HSE (+ volatiles) came from the proto-core formed early in the process of Earth formation rather than added in the later stage. The model implies that most of the core materials are in equilibrium with the mantle at the lower pressure and temperature than those of the current core-mantle boundary (CMB). Therefore, the core is undersaturated with volatile and siderophile elements at the CMB and, consequently, the core is likely a sink (not a source) of these elements even if the concentrations of these elements in the bulk of the core exceed those in the mantle. The transport of light elements from the mantle to the core provides a mechanism for a low-velocity layer on top of the core. The core-mantle disequilibrium promotes the migration of molten Fe into the mantle by the morphological instability in regions of the CMB where (Mg,Fe)O is interconnected. In these regions (presumably the ultralow-velocity regions), volatile (and siderophile) elements are carried by the molten Fe ∼tens km into the mantle providing a window for the core chemistry.

High conductivity anomalies in the shallow mantle are frequently attributed to minor partial melt (basalt or carbonatite) in the olivine-dominated peridotites. Conductivity of a melt-mineral mixture depends on the configuration of melt that could be affected by grain size of the constitutive mineral(s), but this has rarely been explored. Here, we provide experimental evidence using a conductive carbonatite analog and olivine that the bulk conductivity decreases systematically with increasing olivine grain size. The required amount of melt for producing the geophysically resolved high conductivities in the asthenosphere is much greater than previously assumed. We suggest that the effect of partial melt on many conductive regions in the asthenosphere is small. Instead, the electrical anomalies (especially those away from mid-ocean ridges) originate more likely from subsolidus solid assemblages in the upper mantle. This reconciles well the geochemical and petrological constraints of the shallow mantle with its geophysically determined electrical properties.

Abstract Hydrogen solubility was determined in olivine and orthopyroxene under water‐saturated conditions at P = 3–5 GPa and T = 1373–1573 K. For olivine, polycrystalline samples were prepared from San Carlos olivine, and for orthopyroxene synthetic samples were prepared from oxide mixture containing 1.5–5 wt% of Al 2 O 3 . Olivine and orthopyroxene were placed next to each other and annealed under various pressure and temperature conditions for 3–5 hr. Hydrogen content was measured across each sample by FTIR spectroscopy. Under the water‐saturated conditions, the hydrogen solubility in olivine increases with pressure and temperature similar to previous results. Hydrogen solubility in Al 2 O 3 ‐bearing orthopyroxene also increases with temperature and pressure for a fixed Al 2 O 3 content. Based on these observations we calculated the partition coefficients of hydrogen between orthopyroxene and olivine assuming the fugacity dependence of hydrogen solubility in olivine and Al 2 O 3 ‐bearing orthopyroxene reported by previous studies. We find that the partition coefficient depends weakly on temperature but strongly on pressure and water fugacity. Our results are extended to an open system where Al 2 O 3 content in orthopyroxene changes with pressure and temperature. At relatively low pressures and low water fugacity (in the lithosphere (shallower than ∼50 km)), the partition coefficient is high and a majority of hydrogen is present in orthopyroxene. Consequently, the influence of water on the bulk physical properties is small. In contrast, at higher pressures and higher water fugacity (in the asthenosphere), the partition coefficient is smaller and a substantial amount of hydrogen is present in olivine. Consequently, hydrogen has a strong effect on the bulk properties of the asthenosphere reducing viscosity and increasing electrical conductivity.