Solving enigmas of the Earth's inner core is a grand challenge in mineral physics, and first-principles studies play a significant role for our understanding. Iron is expected to be a major component of the inner core, and first-principles calculations have shed new light on the stable crystal structure and elasticity of iron at the inner core conditions. In this article, reviewing recent first-principles studies, we discuss the stable crystal structure and the elasticity of pure iron at the inner conditions, the effect of light element on them, and an outlook for the future direction.

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  The Earth's core has been considered to contain light elements, and sulfur, in particular, is one of the most plausible light elements. Knowledge of the melting relationships of the iron-sulfide system is thus essential in understanding of the physical and chemical properties of the core. In situ X-ray diffraction experiments in the Fe-Fe₃S system were performed up to 220 GPa and 3300 K using a laser-heated diamond anvil cell. Hcp Fe and Fe₃S coexisted stably up to 220 GPa and 3300 K. Both phases are therefore candidates of the constitution of the inner core. The solid iron (hcp Fe) contained 7.5 at% of sulfur at 126 GPa and 2370 K. This suggests that the inner core might be able to contain significant amount of sulfur. Our results revealed that the eutectic composition becomes nonsensitive to pressure. This is likely that the eutectic composition becomes to be constant around 20 at% of sulfur at pressures above 40 GPa.

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  We confirmed availability of measurements of sound velocity and Hugoniot relations for laser-shocked iron using side-on radiography. The sound velocity and physical parameters of pure iron were measured on the pressure over 400 GPa. The sound velocities of liquid iron indicated the trend of monotonic increase with pressures up to nearly 1 TPa.

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  The inner core, most remote part of our planet, is composed of solid iron. Because the relevant ultrahigh pressure and temperature conditions were only accessible by dynamical shock-wave compression experiments, the crystal structure of iron at the inner core has long been under debate. Our first static experiments show that the hexagonal close-packed (hcp) structure is a stable form of iron up to 377 GPa and 5700 K, corresponding to inner core conditions. The observed weak temperature-dependence of the c/a axial ratio suggests that hcp-Fe is elastically anisotropic at core temperatures. Preferred orientation of the hcp phase may cause inner core seismic anisotropy.

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  Carbon and hydrogen are possible candidates of the light elements in the Earth's core. I report effects of carbon and hydrogen on the melting temperature and density of the Earth's core. To investigate phase relations and thermoelastic properties of iron-carbide and -hydride, high-pressure experiments were performed using Kawai-type apparatus and diamond anvil cell. From phase relation in the Fe-C system, it was found that Fe₇C₃ rather than Fe₃C could be the stable phase under the core pressures and one of the candidates of the inner core constituent. On the basis of equations of state for Fe₇C₃ and γ-FeH_x, carbon and hydrogen can reasonably reduce the density of pure Fe to explain the core density deficit. If carbon and hydrogen are the major light elements in the core, the temperature of the core should be lower than previous estimates.

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  The so-called “Missing Xe” problem is a long standing unsolved problem and is related to many fields in Earth science: formation process and evolution of the Earth, origin and evolution of the atmosphere, and geochemistry. Although the long-held expectation was the retention of xenon in the iron-rich core, present experimental result clarified that it is unlikely to occur. This implies that we have to reconsider the missing xenon problem and encourage many scientists to pursuit other possibilities.

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  In this paper, the history of the relationship of Bob Liebermann's laboratory at Stony Brook and high-pressure, multi-anvil laboratories in Japan over the past 40 years is recounted. As the field of high-pressure mineral physics in Japan has evolved during this period, the major players and their laboratory sites have changed, but this field is alive and well today and in the capable hands of the new young generation.

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  Due to the lack of appropriate instrumentation, the amount of accurate and precision data is limited on basic physical properties connected with quantum effects and low-energy excitations in the fields of combined high pressure and low temperature. A technical breakthrough has been achieved with a set-up at ISSP, University of Tokyo, equipped with a cubic-anvil device and a top-loading cryostat. Many interesting phenomena originated from electron-electron correlation effects, such as high-T_c superconductivities, spin fluctuations, charge and valence fluctuations, and others near a quantum critical point, have been revealed at pressures extended far beyond 10 GPa and at temperatures down to ca. 2 K, some topics of which are reviewed.

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  Experimental studies on rheology of mantle minerals at pressures higher than 3 GPa and at high temperature have been conducted based on recent experimental techniques in order to address the material transport in the Earth's interior. The high-pressure deformation experiments using deformation-DIA apparatus and rotational Drickamer apparatus have been carried out with in situ stress and strain measurements. The rheological data for olivine, wadsleyite, garnet and periclase at high pressure provide useful information necessary to discuss the rheological structure in the Earth's mantle. Further systematic studies are required to understand the effects of temperature, pressure, stress, chemical composition, water content and microstructure on rheology of deep Earth materials.

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