Here we report a new data on the equation of state of iron hydride up to 80 GPa measured by an in situ X-ray diffraction method. We observed anomalous compression behavior at 30 to 50 GPa, and found that iron hydride might be less compressible above 50 GPa than at lower pressures. The bulk modulus above 50 GPa is larger than that of pure hcp-iron. Our data support the ab initio calculation suggesting a magnetic transition of iron hydride at around 60 GPa. The density deficit of the Earth's inner core could be explained by dissolution of smaller amount of hydrogen than previously suggested.
 In situ X-ray diffraction patterns of FeHx were collected in the diamond anvil cell (DAC) up to 80 GPa and room temperature. Hydrogen was introduced into the sample chamber by putting the assembled cell into a hydrogen gas container initially pressurized to 0.18 GPa [Takemura et al., 2001]. The iron sample (99.99% purity) was compacted from a powder into a foil with 20∼70 μm in diameter and 5∼10 μm in thickness. Four sets of experiments were carried out using different culet sizes of diamond anvils, 450, 350, 250 and 150 μm in diameter. A rhenium or tungsten foil with a thickness of 250 μm was preindented to 25∼65 μm and used for a gasket. A hole with a diameter of 80∼200 μm was drilled in the gasket and used for a sample chamber. A clear transparent area around iron or iron hydride was optically visible at all pressures, indicating the presence of free hydrogen in the sample chamber.
 Powder X-ray diffraction experiments at high pressures were carried out by the angle dispersive method using an imaging plate detector (IP). X-ray diffraction patterns of iron hydride were collected using monochromatic synchrotron X-ray radiation at BL13A and BL18C beamlines in Photon Factory (PF), High Energy Accelerator Research Organization (KEK), Japan. The incident X-ray beam was monochromatized to wavelength of 0.4251 Å, 0.4258 Å and 0.4261 Å at BL13A and 0.6174 Å at BL18C beamline, respectively. The X-ray beam was collimated to a 15∼30 μm in diameter. The exposure time was varied from 15 to 90 min, depending on the experimental conditions. The data sets of the experiments were obtained during loading.
 Pressures were measured before and after each exposure using the ruby fluorescence technique [Mao et al., 1986] and the average of these values was used as the pressure value. The pressure distribution in the sample chamber was checked by measuring a few ruby grains distributed throughout the sample hole. The variation in pressure was about 0.5 GPa below 30 GPa increasing to 1 GPa at highest pressure of 80 GPa. Hydrogen acts not only as a hydrogen reservoir for the iron-hydrogen reaction but also as a pressure transmitting medium. Hydrogen is fluid below 5.5 GPa and solidifies above 5.5 GPa at room temperature [Mao and Bell, 1979]. Since fluid and/or solid hydrogen filled the sample chamber, all measurements were hydrostatic and/or quasi-hydrostatic and the R1–R2 ruby line splitting was well resolved up to 80 GPa, maximum pressure in this study. Ruby (Al2O3) was stable in hydrogen and was not reduced by hydrogen to form aluminum metal and aluminium hydroxide (diaspore; AlOOH) at 300 K as reported previously based on ruby fluorescence measurements [Mao et al., 1992].
3. Results and Discussion
 The bcc phase transformed at 3.8 GPa to a dhcp phase, indicating formation of FeHx [Badding et al., 1991] (Figure 1). The dhcp phase was stable up to at least 80 GPa and room temperature. The (102) line is broadened relative to the others, which is likely to be due to random stacking faults [Badding et al., 1992]. No significant change in relative intensity of diffraction peaks was observed, which indicates that the pressure dependence of host atomic coordinates is small. The absence of line broadening in the diffraction patterns shows little effect on non-hydrostatic stresses in the sample.
 The volume and lattice parameters of dhcp-FeHx are plotted in Figures 2 and 3 as a function of pressure. Each volume data was obtained at the pressure intervals of 1–2 GPa below 30 GPa and 4–5 GPa above 30 GPa. In contrast to the earlier work with sparse data points [Badding et al., 1991], our data has an enough resolution to find out anomalies in the compression curve. Our pressure-volume relation is in good agreement with the previous work below 62 GPa [Badding et al., 1991], and is reproducible within the error of measurements (Figure 2).
 We found that the P-V data are less compressible at high pressures above 50 GPa (Figure 2). The a-axis decreases smoothly with increasing pressure up to 30 GPa and then exhibits a change in slope at 50∼60 GPa (Figure 3). The a-axis of dhcp-FeHx is less compressible than that of hcp-Fe above 50∼60 GPa. The slope of the c axis changes in the same manner. Although the error and the scattering above 50 GPa are large, the axis ratio (c/a) for dhcp-FeHx shows that there are two discontinuities at around 30 and 50 GPa (Figure 3). The c/a ratio decreases monotonically with pressure below 30 GPa, and the ratio increases to 3.275 at 30 GPa, followed by a slight decrease to 43 GPa. It is likely that a decrease of c/a with pressure produces the decrease of the Fe-H bond length and a change in the Fe-H-Fe bond angle. On the other hand, the 2c/a of hcp-Fe decreases continuously with increasing pressure [Jephcoat et al., 1986]. Based on these observations, we divided the pressure region into three; below 30 GPa (LP), 30∼50 GPa (IP), and above 50 GPa (HP). In the previous study, these anomalies could not be detected because of the limited number of data above 30 GPa and lack of data above 62 GPa [Badding et al., 1991].
Figure 2 shows the pressure-volume relation for dhcp-FeHx. The dhcp-FeHx in the LP region is more compressible than hcp-Fe (Table 1), which is consistent with the previous observation [Badding et al., 1991]. The tight-binding calculation suggests that the strong Fe-H interaction causes the Fe-Fe bond weakening [Pronsato et al., 2003] and results lowering the bulk modulus of dhcp-FeHx [Badding et al., 1991]. We calculated the equation of state (EOS) parameters for each pressure region, although no structural phase transitions were observed. When the all data up to 80 GPa are fitted by a single EOS, we obtain V0 = 55.3(2) Å3, K0 = 150(5) GPa and K′0 = 4 (fixed), which are consistent with those of Badding et al. . However, the measured volumes above 60 GPa show a large deviation from the fitting curve. The fact indicates that the EOS of dhcp-FeHx cannot be represented by a pair of K0 and K′0 throughout the experimental pressure range.
Table 1. EOS Parameters for dhcp-FeHx and hcp-Fe
The values in parentheses are standard deviations.
 Because the zero-pressure volume (V0) expected from the HP region cannot be well constrained by our limited data alone, we adopted the theoretically calculated V0 [Elsässer et al., 1998] (Table 1) for the reason discussed below. The estimated bulk modulus in the HP region is much higher than that below 30 GPa and that of the hcp-Fe (Table 1).
 There is a possibility that these compression behaviors of iron hydride are associated with a change of the magnetic properties [Elsässer et al., 1998]. The Mössbauer studies and neutron diffraction measurement show that a dhcp-FeHx is ferromagnetic at low pressures below 10 GPa [Choe et al., 1991; Antonov et al., 2002]. However, there is no experimental data available on magnetic properties of FeHx above 10 GPa. Elsässer et al.  have calculated the effect of pressure on the magnetic moment for iron hydride by ab initio calculation. The calculation for dhcp-FeHx showed that the magnetic spin moments decrease almost linearly between about 30 and 60 GPa and the magnetic ordering vanishes roughly at 60 GPa, which indicates ferromagnetic to nonmagnetic transition [Elsässer et al., 1998]. The pressure interval of the magnetic transition predicted by the calculation seem to be consistent with the anomalous behavior in the observed P-V data and the cell parameters. It is likely that the LP region corresponds to the ferromagnetic state (FM) and the HP region is the nonmagnetic state (NM).
 Magnetic collapse such as FM to NM transition and high-spin to low-spin transition would lead to the change in bonding character, affecting the elasticity [Pasternak and Taylor, 1996; Kobayashi et al., 1997]. It is generally known from the self-consistent spin-polarized energy band-structure calculations that vanishing of the magnetism can lead to a large increase in the bulk modulus in d-band metals [Moruzzi et al., 1978]. The ab initio calculation for iron hydride also shows that the NM state is less compressible than the FM state [Elsässer et al., 1998]. The bonding in transition metals is strongly related to the electronic structure in which d-electrons play an important role. The compression on transition metals and their alloys has profound effects on their electronic structure.
 In many transition metal-oxide compounds, the pressure-induced disappearance of the magnetism causes a structural change [e.g., Kondo et al., 2000], indicating a spin-crossover from high-spin to low-spin state [Pasternak et al., 1990]. However, there are a couple of examples showing a magnetic transition without any structural changes. In NiI2 [Pasternak et al., 1990; Pasternak and Taylor, 1996] and Fe7S8 [Kobayashi et al., 1997], the Mössbauer studies showed the magnetic collapse, while X-ray diffraction measurements exhibit no structural phase transitions. It has been reported that the compression behavior of Fe7S8 changes around the pressure of the magnetic transition and the nonmagnetic phase is less compressible than the magnetic phase [Kobayashi et al., 1997]. Therefore, a sudden change of the compressibility for dhcp-FeHx may be related to the decrease of the magnetic moments under pressure, although the Mössbauer spectroscopy and/or X-ray emission spectroscopy under high pressures should be required in order to confirm the change of the magnetic state in iron hydride. The electrical conductivity measurements also would be necessary to investigate the effect of pressure on the electronic properties of iron hydride.
 Another explanation for the anomalous compression behavior is a change of the chemical composition in iron hydride. The solubility of hydrogen in the dhcp lattices should not increase any more because the composition of FeHx would be nearly the stoichiometric value of x = 1 [Badding et al., 1991], which indicates that all interstitial octahedral-sites are filled by hydrogen. However, another interstitial site, such as the tetrahedral-site, has a capacity to accommodate hydrogen atom at high pressures. Therefore, we cannot rule out a possibility of the change in solubility of hydrogen into iron around 30–50 GPa.
 In contrast to the earlier work [Badding et al., 1991], our data suggests that hydrogen makes iron less compressible at higher pressure. The result has great importance to the composition of the Earth's core. The Earth's inner core is 2–5% less dense than pure iron at the core pressures and temperatures. The density of hcp-Fe is estimated from static compression experiments to be 13.8 g/cm3 at 330 GPa [Mao et al., 1990]. Our EOS shows the density of iron hydride is 10.9(5) g/cm3 at 330 GPa. According to the calculation for the mass fraction of the light element [Poririer, 1994], the solubility of light element(s) in iron at 330 GPa is estimated to be significantly lower than that reported previously (20–50 atm.% [Fukai, 1984; Suzuki et al., 1984; Badding et al., 1991; Yagi and Hishinuma, 1995; Okuchi, 1997]). Only 6–21 atm.% (0.12–0.48 wt.%) of hydrogen can satisfy the observed density deficit of the Earth's inner core, assuming that iron hydride with the dhcp structure is stable in the inner core [Badding et al., 1991] and that the inner core is solely composed of a mixture of iron and iron hydride, although existence of the other high pressure and high temperature polymorphs of iron hydride can not be ruled out. This result could lead to the presence of hydrogen with 1–3 hydrospheres in the Earth's inner core. Assuming the outer core is the similar amount of hydrogen in the inner core, the amount of hydrogen in the whole Earth's core could be estimated to be 8–24 hydrosphere, in contrast to Williams and Hemley  who suggested the possibility that the Earth's core could contain hydrogen up to 100 hydrospheres.
 We thank Y. Fukai and T. Yagi for useful discussions. This work is supported by a Grant-in-aid for the Scientific Research of Priority Area (no. 12126201) and the Scientific Research (S) (no. 14102009) of Ministry of Education, Culture, Sport, Science and Technology of Japanese Government to E. Ohtani, and partly by the Sasagawa Scientific Research Grant from the Japan Science society to N. Hirao. X-ray diffraction experiments were performed under the approval of the Photon Factory Program Advisory Committee (Proposal numbers: 01G059 and 02G055). We thank anonymous reviewer for their comments on the manuscript.