High-P conditions were generated in a symmetric-type DAC with 300 μm flat culet diamond anvils. Body centered cubic (bcc) to hcp phase transformation of iron occurring around 13 GPa and 300 K is considered to be a prototypical martensitic transition. A number of studies reported that the texture of hcp iron is basically inherited from bcc iron across the transition (Merkel et al., 2004; Miyagi et al., 2008; Ishimatsu et al., 2014; Dewaele et al., 2015; Nishihara et al., 2018). Therefore, we anticipated synthesizing hcp iron samples with different textures in a DAC by using various types of textured bcc iron starting material. Here we used three types of bcc iron sample: foil, sintered powder, and wire. A high-purity iron foil (99.99%) with 10 μm initial thickness was cut into a disk shape and compressed to its thickness direction in a DAC (Figures 1A, 2A). The iron foil has a relatively heterogeneous grain-size distribution, with the largest grains being a few micro-meters in size (Figure 1A). This foil sample was also used in the previous studies (Gomi et al., 2013; Ohta et al., 2016). Iron powder (99.9% purity) with a few micro-meters grain size was sintered in a deformation-DIA apparatus (D-DIA), MADONNA-I, at the Geodynamics Research Center, Ehime University. It was sintered at 2 GPa and 600°C for 1 h, then deformed by advancing each differential-ram by 0.4 mm (Figure 1B). We cut a disk (90 μm in diameter and 10 μm initial thickness) out of the sintered and deformed iron batch and loaded it into a DAC (Figure 2B). Compression direction by a DAC is parallel to the deformation direction by a D-DIA. In the sintered iron powder, an array of iron oxide (black dots in Figure 1B) that originally formed on the surface of grains in the powder was observed. The volume fraction of the iron oxide was estimated to be < 2% based on the image analysis. The grain size of iron in this starting material is judged to be significantly smaller than that of the original powder (a few hundred nanometers). The bcc iron wire (99.99% purity) with 100 μm in diameter was sliced to about 10 μm thick, and then loaded into the sample chamber of a DAC. The iron wire has a homogeneous microstructure, which consists of very small, wavy grains with about 0.1 μm width (Figure 1C). The compression direction in a DAC is parallel to the length direction of the bcc iron wire (Figure 2C). We employed the two-stage amorphous boron plus Kapton gasket that enabled us to perform radial XRD measurement for sample texture analysis (Merkel and Yagi, 2005) (Figures 3, 4). SiO₂ glass was used as a pressure transmitting medium.

For phase identification and texture analyses, angle-dispersive two-dimensional XRD measurements were conducted on the iron samples in a DAC at BL10XU, SPring-8. The wavelengths of the monochromatic incident X-ray beam were 0.247~0.413 Å (30~50 keV) and the incident X-ray was collimated to about 10 μm in diameter. The XRD images were recorded on an imaging plate (IP) detector (RIGAKU R-AXIS V⁺⁺) with a typical exposure time of 30 s. The XRD data for the iron sample in a DAC were collected in both axial and radial diffraction geometries where the sample is irradiated with X-rays both parallel and perpendicular to the DAC compression axis, respectively, in order to increase pole figure coverage (Figure 3A). In runs 1 and 4, only the axial XRD spectrum was collected. Pressures were determined by using an equation of state (EOS) of hcp iron (Yamazaki et al., 2012).

Axial and radial XRD images were quantitatively analyzed for determination of CPO using the Rietveld method as implemented in the software package MAUD (Lutterotti et al., 2014). First, the XRD images were integrated from 0° to 360° azimuth angles over 5° sectors to produce 72 patterns (Figure 4). Sample to the IP distance, wavelength of incident X-ray, and the IP geometry were calibrated with CeO₂ standard. The sample CPO is calculated by the E-WIMV algorithm to produce an orientation distribution function (ODF) with a resolution of 15°. No symmetry constraint was applied in the analysis.

Thermal conductivity (κ) is a function of thermal diffusivity (D), density (ρ), and isobaric heat capacity (C_P): κ = DρC_P. The D of hcp iron at high P was measured by means of the pulsed light heating thermoreflectance technique in a DAC at Tokyo Institute of Technology (Figure 3B). Details of the measurement system and the analytical methods of this technique have been described in the literature (Yagi et al., 2011; Ohta et al., 2017). The density (ρ) of hcp iron was determined from the present XRD data. The isobaric specific heat capacity (C_P) was calculated from the thermodynamic relations and the reported thermoelastic parameters of hcp iron (Yamazaki et al., 2012).

Prior to the high-P experiments, we investigated the CPO of bcc iron starting materials loaded into a DAC at ambient conditions. Figure 4 presents the variations in the diffraction intensity for (110), (200), (211), and (220) diffractions of the three-types of bcc iron starting material. We used these four XRD peaks for texture analyses with the MAUD program, and acquired pole figures of the bcc samples (Figure 5). Pole densities are expressed in multiples of random distribution (m.r.d.). The bcc iron foil showed a single crystal-like CPO with an alignment of <111> along its compression axis and an alignment of <110> on the radial plane (Figure 5A). Since the foil included large grains, as shown in Figure 1A, the number of grains in a diffraction volume might be limited. This would be the reason for the single crystal-like CPO of this sample. Although the CPO of bcc iron foil was only determined in Run 3, the CPO could be entirely different in each run due to the limited number of grains in a sample volume of a DAC experiment. The sintered and deformed bcc iron powder showed an almost axi-symmetric CPO pattern with concentrations of <100> and <111> along its compression axis (Figure 5B). This is consistent with reports by Merkel et al. (2004) and Nishihara et al. (2018), where similar CPO was formed by uniaxial compression of randomly textured bcc iron. The bcc iron wire had an almost random texture as shown in Figure 5C.

The polycrystalline bcc iron starting materials loaded into a DAC were squeezed to transform them into hcp iron. In all eight runs, we collected XRD data for hcp iron and obtained their CPO patterns. Figure 6 shows the representative XRD data for hcp iron obtained at 41.6 GPa in both axial and radial geometries. Five XRD peaks from the (101̄0), (0002), (101̄1), (101̄2), and (112̄0) diffractions were used for texture analyses. The obtained pole figures of hcp iron clearly show that the CPO of hcp iron differs depending on the texture of the starting materials (Figure 7). The CPO of hcp phase derived from powder bcc iron is characterized by an alignment of <112̄0> parallel to the compression axis and <0001> on the radial plane (Figure 6B). This is largely consistent with the Burgers orientation relationship, {110}_bcc//{0001}_hcp and <111>_bcc// <112̄0>_hcp, for a martensitic transformation between bcc and hcp phases. The orientation of <0001> is not axi-symmetric, but lies along a particular direction (Figure 7B); although the orientation of <110> in the bcc starting material is nearly axi-symmetric (Figure 5B). This is presumably due to strong variant selection in the bcc to hcp phase transformation under high deviatoric stress in a DAC. The CPO pattern of hcp iron from bcc wire is characterized by a strong concentration of <0001> parallel to its compression axis (Figure 7C), and this pattern is accompanied by a weaker concentration of <0001> along the radial direction at lower P (Run 1). This observation is reasonably interpreted as follows. The <111> (and <100>) is aligned parallel to the compression axis from initial random texture by compression of bcc phase at low pressure. The bcc to hcp phase transformation yields an alignment of <0001> along the radial direction following the Burgers relationship, and subsequent uniaxial compression to higher pressure gradually aligns <0001> along the compression axis through the basal slip dominant viscous creep (e.g., Merkel et al., 2004; Nishihara et al., 2018). In hcp iron that was transformed from bcc foil, completely different CPO patterns were observed depending on the run: <101̄0> was aligned along the compression axis in Runs 2 and 7 (Figure 7A), whereas <0001> was aligned along the compression axis in Runs 3 and 4. This is probably because the CPO of bcc iron foil was different in each run due to its large grain size (Figure 1A). However, the CPO of the bcc phase is not perfectly inherited by the hcp phase along with the Burgers orientation relationship. In reality, the situation is complicated by the existence of internal stresses between grains that develop during the phase transformation. They also influence the orientation relations and variant selection and their effects cannot be deduced from simple crystallographic considerations.

Figure 8 indicates the emergence distributions of crystals with angle θ between the DAC compression axis and <0001> of hcp iron, which means the frequency of hcp iron grains with angles between the c axis and compressional axis. This was calculated from <0001> pole figure (hence from ODF), and a distribution is normalized such that its integration in the hole interval to be unity.

After the XRD experiments and the subsequent CPO analyses, we measured high-P thermal conductivity of the polycrystalline hcp iron by means of the pulsed light heating thermoreflectance technique (Table 1). The transient temperature change in a hcp iron sample by pulse laser heating was recorded at high P as shown in Figure 9A. The obtained temperature history curve was analyzed considering the one-dimensional heat diffusion in iron and pressure medium (SiO₂ glass):

where T(t) is temperature, T̄ is a constant, t is time, and γ expresses heat effusion to pressure medium (Yagi et al., 2011). τ is the heat diffusion time across the iron sample. We obtained T̄, γ, and τ by fitting the measured curves to Equation (2). The sample thickness (d) was measured in a sample recovered from the DAC. Its cross section was prepared by using the focused ion beam (FIB) apparatus, and the thickness of the iron sample was measured under a scanning microscope (SEM) (Figure 9B). The effect of lattice volume expansion due to decompression and transformation from hcp to bcc phase was corrected to determine d by using the EOSs of hcp iron (Yamazaki et al., 2012). The τ and d gives high-P thermal diffusivity;

Multiplication of the D, ρ, and C_P yields the high-P thermal conductivity of hcp iron.

The obtained thermal conductivity of hcp iron at high P and 300 K is shown in Figure 10. The hcp iron samples from the wire starting material show higher conductivity than those from the foil and powder samples at similar pressures. The aforementioned CPO analyses showed that hcp iron from bcc wire shows a strong orientation of <0001> parallel to the compression axis, while hcp iron from powder and foil tends to show an alignment of <0001> on the radial plane. This CPO information and polycrystalline hcp iron conductivity imply that the thermal conductivity of hcp iron along the c axis (κ_c) is higher than that along the a axis (κ_a). For comparison, we calculated high-P/room-T κ_el of polycrystalline hcp iron from the reported electrical resistivity (Gomi et al., 2013) and the Wiedemann-Franz law with the L₀ (Equation 1) (Figure 10). The present values of thermal conductivity of hcp iron are about half of the calculated κ_el. Such a difference could be due to anisotropy in the thermal conductivity of hcp iron because (Gomi et al., 2013) measured the high-P resistivity during decompression after squeezing the iron foil up to 100 GPa at 300 K. The measurement direction of the high-P resistivity was perpendicular to that of the present thermal conductivity. Since all the compared data are at 300 K, the influence of electron-electron scattering on thermal conductivity should be negligible (Pourovskii et al., 2017).

Here we quantitatively evaluate the anisotropy in the crystallographic thermal conductivity of hcp iron single crystal based on the present results of CPO analyses and thermal conductivity measurements (Figures 7, 8, 10). The thermal conductivity of polycrystalline hcp iron we measured can be regarded as the effective thermal conductivity of a hcp iron single crystal aggregate along the obtained CPO (Figure 10). First, we define the effective thermal conductivity of a hcp crystal along a direction θ (κ(θ)) as follows:

where θ is an angle between the heat flow direction and the c axis (Figure 8 inset) (see Appendix). In this study, the heat flow direction is parallel to the DAC compression direction (Figure 3B). Then, we calculated the anisotropy in thermal conductivity of a hcp iron crystal assuming two-types of κ(θ) mixing model as described below.

An open question raised above is whether the discrepancy in experimentally determined thermal conductivity of iron at the core conditions can be explained by anisotropy in the conductivity of single crystal hcp iron (Konôpková et al., 2016; Ohta et al., 2016). As a matter of fact, both studies did not determine the room-T conductivity of iron from their own experiments. Ohta et al. (2016) measured T dependence of electrical resistance of iron samples at high P and referred to the high-P/room-T resistivity of hcp iron from Gomi et al. (2013) to calculate high-P/high-T resistivity. The κ_el of hcp iron at 135 GPa and 300 K was obtained as 165(+56/−22) W/m/K. The method employed in Konôpková et al. (2016) cannot determine high-P/room-T conductivity in principle, as they acquired time-dependent thermal radiation spectra from a laser-heated iron sample. To construct a model of high-P/high-T thermal conductivity of hcp iron, they referred to a value of electrical resistivity of hcp iron at 135 GPa and 300 K inferred from the experimental results of Seagle et al. (2013) and converted it to κ_el of 120(+20/−30) W/m/K via the Wiedemann-Franz law with an unusual Lorenz number of 1.9 × 10⁻⁸ WΩ/K². In this study, we found highly anisotropic thermal conductivity of hcp iron at least up to 44.5 GPa and 300 K based on the present XRD and thermal conductivity measurements. Based on the pressure derivatives (dκdP) of the obtained κ_a and κ_c of hcp iron that are 0.43 and 0.98 W/m/K/GPa, respectively, we estimated κ_a and κ_c of hcp iron at higher P, indicating the anisotropy in the conductivity is maintained to the core pressures (Figure 12). At 135 GPa, the pressure of the Earth's core-mantle boundary, κ_a and κ_c of hcp iron are 61.4 ± 8.9 and 157.3 ± 72.6 W/m/K, respectively, and κ_c/κ_a is 2.6. Therefore, thermal conductivity anisotropy in single crystal hcp iron can explain the discrepancy in the reference conductivities at 135 GPa and 300 K (Figure 12). However, the reported values of the thermal conductivity of hcp iron at 135 GPa and high T conditions shows about a seven-fold difference (Konôpková et al., 2016; Ohta et al., 2016). It remains unclear whether the conductivity anisotropy of single crystal hcp iron is kept to a few thousand K. In some hcp analog metals, their κ_c/κ_a was getting smaller with increasing T (Nellis and Legvold, 1969; Alderson and Hurd, 1975; Secco and Balog, 2001). Only for magnesium, its κ_c/κ_a increases with increasing T, but the T response of κ_c/κ_a was examined only from 3 to 300 K. Unless hcp iron shows strongly positive T dependence of κ_c/κ_a, the conductivity anisotropy is unlikely to be the main cause of the controversial reports (Konôpková et al., 2016; Ohta et al., 2016). In this context, T enhanced electron-electron scattering in compressed iron would be a key factor as shown in Pourovskii et al. (2017). Within their calculations, the thermal conductivity is depressed by 39% by electron-electron scattering. For more detailed discussion, further studies for direct determination of both electrical and thermal conductivities are required at extremely high P-T conditions.

If the thermal conductivity anisotropy in hcp iron single crystal is preserved to the Earth's inner core conditions, it may have important implications for evolution and dynamics there. The seismological exploration of the Earth's inner core has revealed its structural complexities (e.g., Tkalčić, 2015; Romanowicz and Wenk, 2017). One of the main features in the inner core is that a seismic wave along the polar direction propagates by about 3% faster than one along the equatorial direction (Poupinet et al., 1983; Morelli et al., 1986). The preferred alignment of hcp iron alloy crystals with the c axis parallel to the fast-seismic axis has been repeatedly suggested to explain the cause of the seismic anisotropy in the inner core (Yoshida et al., 1996; Bergman, 1997; Karato, 1999; Buffett and Wenk, 2001), although a consensus has not reached among theoretical studies to calculate sound velocity difference between a and c axes of hcp iron. Early theoretical calculations at 0 K showed that c axis was the faster direction than a axis in hcp iron (e.g., Stixrude and Cohen, 1995), but later studies at high temperatures showed that the sense of anisotropy changes, and the a axis becomes the fast direction (Steinle-Neumann et al., 2001), or nearly isotropic (Sha and Cohen, 2010). If the c axis of hcp iron alloy preferentially aligns along the Earth's rotational axis in the inner core, strong anisotropy of the thermal conductivity in hcp iron as observed in this study implies an anisotropic thermal conductivity of the inner core with higher conductivity in the polar direction and lower conductivity in equatorial radial directions. In addition, recent first-principles calculations showed that incorporation of silicon and nickel into iron enhances anisotropy in the conductivity (Gomi et al., 2016). The Taylor column type outer core convection extracts more heat away from the ICB in equatorial regions than in polar regions, even in the absence of anisotropic thermal conductivity. As a result, greater heat loss and lower thermal conductivity of the inner core along the equatorial direction than the polar direction would produce large temperature heterogeneity at the ICB, which would enhance the directionality of inner core growth and keep the crystallographic origin of the inner core anisotropy through the geological timescale via the plastic core flow mechanism (Yoshida et al., 1996). In the recent years, detailed modeling of the inner core evolution and dynamics have been reported, but no study considered the thermal conductivity anisotropy in the inner core (e.g., Alboussière and Deguen, 2012; Deguen, 2012). The magnitude of thermal conductivity anisotropy in hcp iron (iron alloy) at the ICB conditions needs to be confirmed for more detailed discussion about the inner core evolution and dynamics.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.