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We examined pressure-induced phase transitions in Fe2S based on high-pressure and high-temperature X-ray diffraction measurements in a laser-heated diamond-anvil cell. Fe2S is not stable at ambient pressure but is known to form above 21 GPa with the Fe2P-type (C22) structure. Our experiments demonstrate a novel phase transition in Fe2S from the C22 to C23 phase with the Co2P-type cotunnite structure above ~30 GPa. The experiments also reveal a transformation from the C23 to C37 (Co2Si-type) phase above ~130 GPa. While the C23 and C37 structures exhibit the same crystal-lographic symmetry (orthorhombic Pnma), the coordination number of sulfur increases from nine in C23 to ten in C37. Such a sequence of pressure-induced phase transitions in Fe2S, C22 → C23 → C37, are similar to those of Fe2P, while they are not known in oxides and halogens that often adopt the C23 cotunnite-type structure. The newly found cotunnite-type Fe2S phase could be present in solid iron cores of planets, including Mars.

Seismic observations suggest that the Earth’s inner core has a complex structure (e.g., the isotropic layer at the top, innermost inner core, and hemispherical dichotomy). These characteristics are believed to reflect the history of dynamics and temperature profile of the inner core. One critical physical property is the inner core’s thermal conductivity. The thermal conductivity of metals can be estimated from their electrical resistivity using the Wiedemann-Franz law. Recent high-pressure and temperature experiments revealed that the temperature dependence of electrical resistivity is small for Fe-Si alloys. The small temperature coefficient means that it is essential to determine the impurity resistivity of Fe alloys to constrain the inner core’s thermal conductivity. Therefore, this study systematically calculated the impurity resistivities of 4- and 6-component alloys at inner core pressure by combining the Korringa-Kohn-Rostoker method with the coherent potential approximation. As a result, we obtained the thermal conductivity of the inner core to be 150-263 W/m/K. The inner core cannot maintain thermal convection with such a high thermal conductivity, resulting in a flat temperature profile. In materials science, it is widely known that polycrystals soften suddenly at high temperatures a few percent below their melting temperature. If such a pre-melting occurs in the inner core, the flat temperature profile due to high thermal conductivity causes variations in the attenuation within the inner core. This may explain the observation that the upper inner core is more strongly attenuated than the innermost inner core.

Background: Nail-patella syndrome (NPS) is a rare autosomal dominant systemic disorder that is characterized by dysplasia of the nails, hypoplasia or aplasia of the patella, dislocation of the elbow and the presence of iliac horns. Rheumatoid arthritis (RA) is an autoimmune disorder of the joints characterized by inflammatory arthritis and subsequent joint destruction. Of note, NPS and RA share some musculoskeletal symptoms such as swan-neck deformities of the fingers and joint dislocation, and renal and neural involvement is also observed in these diseases. The prevalences of NPS and RA are 1/50000 and 1/100-1/200, respectively, while no case of NPS co-existing with RA has been reported. Case presentation: Here, we present the first reported case of nail-patella syndrome co-existing with rheumatoid arthritis. A 74-year-old man who had a past history of glaucoma and elbow dislocation was admitted to our hospital due to an 8-month history of arthralgia in bilateral wrists, elbows and fingers. An X-ray showed deformity of bilateral radial heads and joint space narrowing in the right elbow, and magnetic resonance imaging of his hands showed synovitis and erosion in the multiple swollen joints of the wrists and fingers. In addition to these typical features of rheumatoid arthritis, he had bilateral thumb nail dysplasia with mild hypoplasia of bilateral patella and iliac horns as shown by the X-ray. He was diagnosed as having autosomal dominant disorder nail-patella syndrome co-existing with rheumatoid arthritis and he was treated with methotrexate in combination with an oral Janus kinase (JAK) inhibitor, leading to induction of remission. Conclusions: On the basis of their prevalences, the coexistence of nail-patella syndrome and rheumatoid arthritis with overlapped features, including arthralgia, joint deformity and dislocation, glomerulonephritis and neurological abnormality, could be observed in real-world clinical practice. Since the therapeutic strategy for and the prognosis of these diseases are different, appropriate diagnosis based on clinical and radiographic findings is required to improve future prognosis. (314 words)

Composition, chemical disorder, and magnetism significantly affect the volume and bulk modulus of iron–silicon (Fe–Si) alloys at ambient pressure. Here, we computed the equations of state for bcc-like (ordered B2 and disordered bcc) Fe–Si alloys available up to the inner-core pressure using the first-principles Korringa–Kohn–Rostoker method. Ferromagnetic (FM) and nonmagnetic (NM) states over a wide composition range, from Fe to FeSi, were investigated. The results revealed that magnetism and chemical disorder increased the volume and decreased the bulk modulus even at high pressures. Comparing the results with the preliminary reference Earth model, we found that an unrealistically large temperature gradient is required if the inner core is composed of a bcc-like Fe–Si alloy.

In the field of materials science and engineering, statistical analysis and machine learning techniques have recently been used to predict multiple material properties from an experimental design. These material properties correspond to response variables in the multivariate regression model. This study conducts a penalized maximum likelihood procedure to estimate model parameters, including the regression coefficients and covariance matrix of response variables. In particular, we employ $l_1$-regularization to achieve a sparse estimation of regression coefficients and the inverse covariance matrix of response variables. In some cases, there may be a relatively large number of missing values in response variables, owing to the difficulty in collecting data on material properties. A method to improve prediction accuracy under the situation with missing values incorporates a correlation structure among the response variables into the statistical model. The expectation and maximization algorithm is constructed, which enables application to a data set with missing values in the responses. We apply our proposed procedure to real data consisting of 22 material properties., 18 pages

Constraining the core’s composition is essential for understanding Earth accretion, core formation and the sustainment of Earth’s magnetic field. Earth’s outer and inner core exhibit a density deficit relative to pure iron, attributed to the presence of substantial amounts of low atomic number ‘light’ elements, such as sulfur, silicon, oxygen, carbon and hydrogen. However, owing to its inaccessibility, estimates of core composition can only be indirectly obtained by matching results from high-pressure experiments and theoretical calculations with seismic observations. In this Review, we discuss the properties and phase relations of iron alloys under high-pressure and high-temperature conditions relevant to the Earth’s core. We synthesize mineral physics data with cosmochemical and geochemical estimates to give the likely range of compositions for the outer (Fe + 5% Ni + 1.7% S + 0–4.0% Si + 0.8–5.3% O + 0.2% C + 0–0.26% H by weight) and inner (Fe + 5% Ni + 0–1.1% S + 0–2.3% Si + 0–0.1% O + 0–1.3% C + 0–0.23% H by weight) core. While the exact composition of the core remains unknown, tighter constraints on core temperature and better connections between the solid inner core and the liquid outer core compositions will help narrow the range of potential light element compositions. Although the presence of ‘light’ elements (such as S, Si, O, C and H) can explain the core’s density deficit, the exact composition of the Earth’s core remains unknown. This Review explores the likely range of outer and inner core compositions and their implications.

The density of liquid iron-nickel-sulfur (Fe46.5Ni28.5S25) alloy was determined at pressures up to 74 GPa and an average temperature of 3400 K via pair distribution function (PDF) analysis of synchrotron X-ray diffraction (XRD) data obtained using laser-heated diamond-anvil cells. The determined density of liquid Fe46.5Ni28.5S25 at 74 GPa and 3400 K is 8.03(35) g/cm3, 15% lower than that of pure liquid Fe. The obtained density data were fitted to a third-order Vinet equation of state (EoS), and the determined isothermal bulk modulus and its pressure derivative at 24.6 GPa are KTPr = 110.5(250) GPa and KTPr′ = 7.2(25), respectively, with a fixed density of rPr = 6.43 g/cm3 at 24.6 GPa. The change in the atomic volume of Fe46.5Ni28.5S25 upon melting was found to be ~10% at the melting temperature, a significantly larger value than that of pure Fe (~3%). Combined with the above EoS parameters and the thermal dependence reported in the literature, our data were extrapolated to the outer core conditions of the Earth. Assuming that S is the only light element and considering the range of suggested Ni content, we estimated a 5.3–6.6 wt% S content in the Earth’s outer core.

The least absolute shrinkage and selection operator (lasso) and principal component regression (PCR) are popular methods of estimating traits from high-dimensional omics data, such as transcriptomes. The prediction accuracy of these estimation methods is highly dependent on the covariance structure, which is characterized by gene regulation networks. However, the manner in which the structure of a gene regulation network together with the sample size affects prediction accuracy has not yet been sufficiently investigated. In this study, Monte Carlo simulations are conducted to investigate the prediction accuracy for several network structures under various sample sizes. When the gene regulation network is a random graph, a sufficiently large number of observations are required to ensure good prediction accuracy with the lasso. The PCR provided poor prediction accuracy regardless of the sample size. However, a real gene regulation network is likely to exhibit a scale-free structure. In such cases, the simulation indicates that a relatively small number of observations, such as $$N=300$$ N = 300 , is sufficient to allow the accurate prediction of traits from a transcriptome with the lasso.

In maximum likelihood exploratory factor analysis, the estimates of unique variances can often turn out to be zero or negative, which makes no sense from a statistical point of view. In order to overcome this diculty, we employ a Bayesian approach by specifying a prior distribution for the variances of unique factors. The factor analysis model is estimated by EM algorithm, for which we provide the expectation and maximization steps within a general framework of EM algorithms. Crucial issues in Bayesian factor analysis model are the choice of adjusted parameters including the number of factors and also the hyper-parameters for the prior distribution. The choice of these parameters can be viewed as a model selection and evaluation problem. We derive a model selection criterion for evaluating a Bayesian factor analysis model. Monte Carlo simulations are conducted to investigate the eectiveness of the proposed procedure. A real data example is also given to illustrate our procedure. We observe that our modeling procedure prevents the occurrence of improper solutions and also chooses the appropriate number of factors objectively.

The externally heated diamond anvil cell (EHDAC) conducts high pressure and temperature experiments with spatial uniformity and temporal stability. These are conventionally combined with various spectroscopies and x-ray diffraction measurements. EHDAC techniques perform Joule heating on a heater placed close to or directly in contact with diamond anvils. However, the electrical wiring and heater required for Joule heating complicate EHDAC setups, hindering easy access for the measurement of physical properties. This study proposes an EHDAC technique using laser- instead of Joule-heating. We successfully achieved temperatures reaching 900 K by applying heat to diamond anvils through laser-heating of the gaskets with thermally insulating anvil seats. To test this setup, we measured the melting temperature of H2O ice VII, which was consistent with previous studies. We also measured the high-pressure and temperature impedance of H2O VII and verified the capability of electrical resistivity measurements in this setup. This technique allows various physical property measurements owing to its simple setup required for externally laser-heated diamond anvil cell experiments. The unique characteristics of this heating technique are that (1) no heaters or wiring are required, (2) it exhibits the most efficient heating among EHDAC studies, (3) it maintains the DAC body at room temperature, and (4) diamond anvils do not detach from anvil seats after the EHDAC experiment. This method significantly simplifies the experimental setup, which allows much easier access to various physical property measurements using an EHDAC.

We found a new phase transition in Fe2P from Co2P-type (C23) to Co2Si-type (C37) structure above 42 ± 2 GPa based on in situ X-ray diffraction experiments. While these two structures have identical crystallographic symmetry, the orthorhombic unit cell is shortened in a-axis but elongated in c-axis, the coordination number of phosphorous increases from nine to 10, and the volume reduces by 2% across the phase transition. The new C37-type Fe2P phase has been found to be stable, at least to 83 GPa at high temperature. The Birch-Murnaghan equation of state for C37 Fe2P was also obtained from pressure-volume data, suggesting that phosphorous contributes to 17% of the observed density deficit of the Earth's outer core when it includes the maximum 1.8 wt% P as observed in iron meteorites. In addition, since both Fe2S and Ni2Si are also known to have the C37 structure under high pressure, (Fe,Ni)2(S,Si,P) could have wide solid solution and constitute planetary iron cores, although it is not dense enough to be a main constituent of the Earth's inner core.

Sulfur has been considered to be a predominant light element in the Martian core, and thus the sound velocity of Fe-S alloys at relevant high pressure and temperature is of great importance to interpret its seismological data. Here we measured the compressional sound velocity (VP) of liquid Fe, Fe80S20 and Fe57S43 using ultrasonic pulse-echo overlap method combined with a Kawai-type multi-anvil apparatus up to 20 GPa, likely corresponding to the condition at the uppermost core of Mars. The results demonstrate that the VP of liquid iron is least sensitive to its sulfur concentration in the Mars’ whole core pressure range. The comparison of seismic wave speeds of Fe-S liquids with future observations will therefore tell whether the Martian core is molten and contains impurity elements other than sulfur., Applying high-pressure and -temperature experiments, the authors here measure sound velocities in various liquid Fe-S alloys under conditions expected for the upper Martian core. The results together with future InSight mission data will help to understand whether the Martian core is molten Fe-S.

Hydrogen could be an important light element in planetary cores, but its effect on phase diagrams of iron alloys is not well known because the solubility of H in Fe is minimal at ambient pressure and high-pressure experiments on H-bearing systems have been challenging. Considering that silicon can be another major light element in planetary cores, here we performed melting experiments on the Fe-Si-H system at ~50 GPa and obtained the ternary liquidus phase relations and the solid/liquid partition coefficient, D of Si and H based on in-situ high-pressure X-ray diffraction measurements and ex-situ chemical and textural characterizations on recovered samples. Liquid crystallized hexagonal close-packed (hcp) (Fe0.93Si0.07)H0.25, which explains the observed density and velocities of the Earth’s solid inner core. The relatively high DSi = 0.94(4) and DH = 0.70(12) suggest that in addition to Si and H, the liquid outer core includes other light elements such as O, which is least partitioned into solid Fe and can thus explain the density difference between the outer and inner core. H and O, as well as Si, are likely to be major core light elements, supporting the sequestration of a large amount of water in the Earth’s core.

Supplementary Information Table S1 and S2. Table S1 contains experimental data of melting in the Fe-O-H ternary system. Table S2 shows data of subsolidus experiments in the Fe-FeH binary system.

We conducted in situ high-pressure and -temperature X-ray diffraction measurements of a pyrolitic mantle material up to 4480 K at 122–166 GPa in a laser-heated diamond anvil cell. Results demonstrate that the phase transition between bridgmanite and post-perovskite occurs in pyrolite within the lowermost mantle pressure range even at >4000 K. It suggests the ubiquitous occurrence of post-perovskite above the core-mantle boundary, which may be consistent with recent high-quality seismology data that non-observations of D” reflections are exceptions. Combining with earlier experiments performed at and below the normal lower-mantle geotherm, our data show that the bridgmanite + post-perovskite two-phase region is ∼5 GPa thick and the dP/dT slope of the boundary is +6.5 ± 2.2 MPa/K, slightly smaller than previous theoretical calculations in MgSiO3. The global presence of rheologically weak post-perovskite at the bottom of the mantle has profound implications in seismology, geodynamics, and heat transfer from the core.