Introduction

Seismological observations have repeatedly suggested that the Earth’s inner core, an iron-rich sphere with a radius of approximately 1300 km at the center of the Earth, is anisotropic (e.g., Deuss 2014; Romanowicz and Wenk 2017; Tkalčić 2015). The origin of the anisotropic properties is crucial for understanding the growth history of the inner core and its relationship with the outer core. The lattice preferred orientation (LPO) of iron-dominated crystals can explain the observed inner core anisotropy and strongly influence their thermal evolution. The elastic properties of solid iron at high pressure provide a direct link between geophysical models of the inner core and seismic observations to constrain the chemical composition and anisotropic structure of the inner core (e.g., Antonangeli and Ohtani 2015). It has been speculated that the iron’s crystal orientation-dependent transport properties, i.e., electrical conductivity, thermal conductivity, and viscosity, if present, affect the cooling process of the inner core and thus its internal structure and outer core dynamics (Secco and Balog 2001). Iron exhibits a pressure-induced structural phase transformation from a body-centered cubic (bcc) structure to a hexagonal close-packed (hcp) structure at approximately 13 GPa and 300 K. Hcp iron has a wide stability field under pressure and temperature conditions beyond the Earth's inner core (Smith et al. 2018; Tateno et al. 2010) and serves as a reasonable starting point for modeling the physical properties of the Earth’s inner core. Therefore, synthesizing hcp iron with several characteristic LPOs is crucial for studying its anisotropic physical properties. However, despite its importance, there have been few investigations regarding the anisotropy of various physical properties of hcp iron due to the difficulty of synthesizing single-crystalline or polycrystalline hcp iron with strong LPO textures (Antonangeli et al. 2004; Dewaele et al. 2023; Lin et al. 2010; Ohta et al. 2018).

Since hcp iron cannot be recovered under ambient conditions, hcp iron must be synthesized with a strong LPO texture, and then physical property measurements can be performed in situ at high pressures. The characteristic texture relationship between the bcc and hcp phases of iron has been studied on many experimental platforms and time scales via, e.g., dynamic compression (Hawreliak and Turneaure 2021; Kalantar et al. 2005; Merkel et al. 2021) and static compression (Dewaele et al. 2023, 2015; Fréville et al. 2023; Ishimatsu et al. 2020; Merkel et al. 2012, 2013, 2020; Miyagi et al. 2008; Ohta et al. 2018). In all cases, the transition is reported as martensitic, with large portions of the sample following the Burgers orientation relationship (Burgers 1934).

Ohta et al. (2018) used three different polycrystalline bcc iron starting materials (foil, sintered powder, and wire) to synthesize hcp iron with different LPOs. These researchers observed the LPO of hcp iron up to 44.5 GPa by performing X-ray diffraction (XRD) measurements through a Kapton and cBN composite gasket along a radial direction, perpendicular to the compression axis of a diamond anvil cell (DAC). To achieve a stronger LPO and to evaluate it at higher pressures with greater accuracy, in this study, multiangle XRD measurements are conducted using single-crystal bcc iron with different crystallographic orientations as the starting material.

Here, we report the unique combination of synchrotron multiangle XRD measurements of hcp iron transformed from single-crystal bcc iron with three different crystallographic orientations ([100], [110], and [111]) loaded in a DAC up to 80 GPa and 300 K (Table 1). The hcp iron samples prepared from the single-crystal bcc iron starting materials exhibited stronger and more pronounced LPOs than those in our previous study (Ohta et al. 2018) and are more suitable for estimating the anisotropic physical properties of hcp iron.

Table 1 Summary of the experimental conditions
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Materials and methods

Starting materials and diamond anvil cell assembly

The samples were bcc iron single-crystal wafers. Each wafer had a diameter of ~ 80 μm and was cut from a larger single-crystal cube (99.99% purity, Crystal Base Co., Ltd.) by UV pulse laser processing. The wafers were then embedded in solid wax (Adfix A, Maruto Instrument Co., Ltd.) and polished with 3M lapping film (3.0 micron film) to achieve a thickness of approximately 10 μm. The mosaicity of the iron samples were not characterized.

We pressurized single-crystal bcc iron disks with the surface normal parallel to [100], [110], and [111] using a symmetric-type DAC to undergo the hcp phase transition. We used NaCl or a combination of silicone oil (A12728, Alfa Aesar) and fused silica as the pressure transmitting medium. The pressure quality (i.e., nonhydrostaticity) of NaCl is not so different from that of silicone oil at 300 K (Tateiwa and Haga 2009). The culet size of the diamond anvils was 300 μm. To fabricate a gasket for the DAC experiments, rhenium foil with a thickness of 250 μm was preindented to a thickness of 30–40 μm, and sample chambers with a diameter of 80–100 μm were fabricated in the center of the preindented part of the rhenium gasket. The diamond anvils were mounted on tungsten carbide seats with a 90° opening to maximize the number of diffraction peaks collected while rotating the DAC stage (Fig. 1).

Fig. 1
figure 1

Schematic illustration of the geometry of a sample in the DAC with respect to the X-ray beam and detector (IP) used in the XRD experiments. We rotated the DAC and thus the sample to collect diffraction patterns from lattice planes at different angles

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Synchrotron XRD measurements and texture analysis

Crystallographic information on the produced hcp iron was obtained from synchrotron XRD experiments at beamline BL10XU at SPring-8 (Hirao et al. 2020). Monochromatic X-rays with an energy of 62 keV were used (Hirao and Ohishi 2022). The XRD patterns of the samples were collected with a two-dimensional imaging plate (IP) detector (Rigaku R-Axis V++). For reliable LPO analysis, diffraction patterns from lattice planes oriented at different angles were collected by rotating the DAC around the vertical axis (up to 25°) and rotating the compression axis of the DAC (up to 270°) during the experiments (Fig. 1). There are missing angles in our diffraction experiments because the X-rays were blocked by various obstacles, such as the tungsten carbide seats, the mechanical posts of the DAC, and the rhenium gasket. However, since hcp iron has high crystal symmetry, the pole figure coverage in this study is sufficient for texture analysis (Merkel et al. 2020). The pressure was determined from the lattice volume of hcp iron and its equation of state (Dewaele et al. 2006). Thermal annealing was not performed in this study.

After obtaining two-dimensional XRD patterns of the hcp iron samples in situ at high pressures, Rietveld analysis—using MAUD software on the collected diffraction patterns—was performed for texture characterization (Lutterotti et al. 2014). Rietveld analysis is a structure refinement technique for powder diffraction data. It uses the structural information of the sample to calculate the diffraction intensity and refines the model parameters to minimize the residual function between the observed and calculated data (Fig. 2). We used the E-WIMV algorithm for texture analysis of hcp iron, which is a modified version of the Williams-Imhof-Matthies-Vinel (WIMV) algorithm (Lutterotti et al. 2004). For the experiments at ~ 80 GPa, we chose an ODF resolution of 10° for texture analysis. For the experiments at ~ 20 and ~ 40 GPa, an ODF resolution of 5° was used to closely reproduce the single-crystal-like patchy diffraction patterns. There are several analysis packages other than MAUD for crystallographic orientation analysis of single crystal samples, such as GrainSpotter and Recipro (Schmidt 2013; Seto and Ohtsuka 2022). In this study, the same analysis method should be used to analyze the crystallographic orientation of polycrystalline iron that has been fine-grained by phase transition and pressurization from a single crystal iron sample. Also, in our previous study (Ohta et al. 2018), which we would like to directly compare, MAUD was used for LPO analysis. For these reasons, MAUD was consistently adopted as the analysis method in this study.

Fig. 2
figure 2

Comparisons between experimental observations and fitted results in two-dimensional diffraction patterns of hcp iron made from single-crystal bcc iron with the surface normal parallel to [100]

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Results and discussion

We pressurized three single crystals of bcc iron, each with a different orientation relative to the compression axis of the DAC, to approximately 20, 40, and 80 GPa and observed the preferred orientation of the synthesized hcp iron (Table 1). Although the crystallographic orientation dependence of the pressure of the bcc-hcp transition was discussed in the literature (Kadau et al. 2002; Liu et al. 2018; Wang et al. 2014), the onset pressure of hcp iron among bcc iron with each orientation ([100], [110], and [111]) was not precisely determined in this study. The diffraction patterns of bcc iron are consistent with its crystallographic orientation and show slight polycrystallization, possibly due to mechanical polishing and the UV laser processing during sample preparation (Fig. 3a). Figure 3b shows a representative XRD pattern of hcp iron at 19 GPa. The (0002) peak of the hcp iron corresponds to the (110) peak of the former bcc iron. This relationship can be explained by the transformation mechanism proposed by Burgers (Burgers 1934). The Burgers model explains the bcc-hcp transition as a result of shear deformation along the < 111 > direction and mixing motion in the {110} plane in bcc iron. Since there are two equivalent < 111 > directions on each {110} plane in a bcc structure, hcp iron with two different crystallographic orientations can arise from a single {110} plane of bcc iron. This is manifested by the splitting of the (10–10) and (10–11) peaks in the diffraction pattern of hcp iron (Ishimatsu et al. 2020) (see inset in Fig. 3b).

Fig. 3
figure 3

Representative XRD patterns (stage rotation 0°) of a single-crystal bcc iron foil with a surface normal parallel to ([111]bcc) under ambient conditions and b hcp iron produced by pressurizing a single-crystal bcc iron foil with a surface normal parallel to [111] at 19 GPa (run #3). The inset is an enlarged view of (b) showing the splitting of the (10–10) and (10–11) diffraction peaks (yellow arrows)

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From a Rietveld analysis of the two-dimensional diffraction patterns, we obtained pole figures that allowed us to graphically assess the texture evolution in hcp iron (Fig. 4). Up to pressures of ~ 40 GPa, the pole figures of hcp iron show orientation relationships between (1) the basal plane of hcp iron and (110) bcc and (2) the a-axis of hcp iron and [111]bcc or [100]bcc. Since bcc iron has six equivalent (110) bcc planes, the bcc-to-hcp phase transformation produces six different orientations of the basal planes in hcp iron in the absence of variant selection. Dewaele et al. (2015) showed that there is no variant selection during bcc-to-hcp phase transformation, while other experimental studies have shown evidence of strong variant selection (Ishimatsu et al. 2020; Merkel et al. 2020; Yadav et al. 2013). Since Dewaele et al. (2015) used single-crystal bcc iron with [100]bcc parallel to the compression axis, their result can be attributed to the unique angular relationship between the compression axis of the DAC and < 111 > bcc shear deformation (Ishimatsu et al. 2020). Interestingly, the pole figures at ~ 20 GPa in this study show evidence of variant selection during transformation from bcc iron, with the compression axis parallel to [110]bcc and [111]bcc. For example, the pole figure of hcp iron transformed from bcc iron with [111]bcc parallel to the compression axis shows only four major c-axis density concentrations (Fig. 4). On the other hand, the starting material with [100]bcc parallel to the compression axis produced all six possible basal planes of hcp iron, suggesting no variant selection, as in previous static compression studies (Dewaele et al. 2015). Here we used NaCl and silicone oil as pressure media. While there is no significant difference in the pressure quality (i.e., non-hydrostaticity) of these materials, they are less hydrostatic than helium and neon (Tateiwa and Haga 2009), which was used in many previous studies (Dewaele et al. 2015; Freville et al. 2023; Ishimatsu et al. 2020; Merkel et al. 2020). In this respect, this study is a less hydrostatic experiment than most of the previous studies using DAC. The degree of non-hydrostaticity can affect the mechanism of the phase transition of iron from bcc to hcp. For the extreme case, a uniaxial shock compression induced different orientation relationship between bcc and hcp iron from static compression (Hawreliak and Turneaure 2021).

Fig. 4
figure 4figure 4figure 4

Pole figures of the c-axis and a-axis of hcp iron made from single-crystal bcc iron with different orientations. For the ~ 20 and ~ 80 GPa experiments, the stage was rotated up to 25°, and the DAC was rotated up to 270° around its compression axis. For the ~ 40 GPa experiments, only a single XRD image taken without rotation was used. The compression axis of the DAC is in the center of the pole figure. Each pole figure represents a different experimental run. a Pole figures of hcp iron produced by pressurizing a single-crystal bcc iron foil with the surface normal parallel to [100], b [110], and c [111]. The direction of DAC compression is in the center of the pole figure

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In contrast to the samples at ~ 20 and ~ 40 GPa, which show LPO consistent with the Burgers orientation relationship, the c-axis of hcp iron is essentially parallel to the compression axis of the DAC for all the samples at ~ 80 GPa (Fig. 4). This preferred orientation of the c-axis has been reported and attributed to the deformation of hcp iron by activation of the (0001) < -12–10 > basal slip system under differential stress (Merkel et al. 2013; Miyagi et al. 2008; Nishihara et al. 2018; Wenk et al. 2000). The deformation-induced textures of the samples at ~ 80 GPa can be attributed to the silicone oil pressure medium used in the experiments. Since the quality of silicone oil as a hydrostatic pressure medium deteriorates rapidly after solidification (Klotz et al. 2009; Torikachvili et al. 2015), deformation of the samples occurs. We are hopeful that a more hydrostatic medium, such as helium, could produce hcp iron with a significant difference in LPO at higher pressures.

Figure 5 shows the distribution of α, the angle between the c-axis of the hcp iron and the compression axis of the DAC, calculated by MAUD. The distributions at ~ 20 GPa are closely related to the orientations of the {110}bcc in the starting materials. The hcp iron transformed from bcc iron with a surface normal parallel to the [110] axis shows a strong single peak at approximately α = 60°, which is the angle between the compression axis and the normal vectors of the four equivalent {110}bcc. The absence of a peak at approximately α = 90°, where the other {110}bcc is oriented, suggests a variant selection during the phase transformation from bcc iron with [110]bcc parallel to the compression axis. Similarly, samples transformed from single-crystal bcc iron with the surface normal parallel to [100] and [111] show peaks at approximately α =  ~ 45 and ~ 35.2°, respectively. Both samples also have a strong peak at α =  ~ 90°, as shown in the pole figures. The angle between the compression axis and the c-axis decreases at ~ 40 GPa, probably due to deformation of the samples by differential stress. Although all the samples have c-axes concentrated approximately parallel to the compression axis of the DAC at ~ 80 GPa, the distribution patterns differ among the samples (Fig. 5c). The angle distributions of the samples transformed from single-crystal bcc iron are significantly different from the random angle distributions of hcp iron (Fig. 5d), as reported by Ohta et al. (2018).

Fig. 5
figure 5

Distribution of angles of the c-axis with respect to the compression axis of the DAC (α) under pressure conditions of a  ~ 20 GPa, b  ~ 40 GPa, and c  ~ 80 GPa in this study. d Results for hcp iron produced from polycrystalline bcc iron (Ohta et al. 2018). The black dotted curve represents the theoretical random distribution of hcp iron

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What further improvements are needed to make hcp iron with a stronger LPO at even higher pressures? Dewaele et al. (2023) first reported the synthesis of single-crystal hcp iron. These researchers succeeded in synthesizing good-quality single-crystal iron by using single-crystal bcc iron as the starting material and synthesizing hcp iron through a P–T pathway via face-centered cubic (fcc) iron. Dewaele et al. (2023) reported direct measurements of elastic constants of the synthesized single-crystal hcp iron up to 32 GPa. It is not known if this hcp iron single crystal could be maintained to higher pressures. With the recently developed rotational DAC (rDAC), the development of LPO according to the slip system of hcp iron can be achieved by the torsional deformation caused by the rotation of the diamond anvil (Azuma et al. 2017; Nomura et al. 2017; Park et al. 2022). For example, if the dominant slip system of hcp iron is (0001) < -12–10 > , as reported in previous studies (e.g., Merkel et al. 2013; Nishihara et al. 2018), then the rDAC can produce a microstructure where the (0001) normal is aligned in the compression direction and < -12–10 > is oriented in the deformation direction (i.e., rotation direction). In addition to its ability to control strain and strain rate, the rDAC causes torsional deformation of the sample (Azuma et al. 2017), enabling the realization of microstructures with various degrees of LPO along the radial direction from the sample’s rotational axis.

As shown in several previous studies (e.g., Ohta et al. 2018; Dewaele et al. 2023), various physical properties measured on iron with known crystallographic orientation contribute to the elucidation of the crystallographic anisotropy in iron properties. Compared to the results of Ohta et al. (2018), the present method synthesizes hcp iron at about 40 GPa, where the difference in LPO is more obvious (Fig. 5b,d). In other words, it is possible to determine the crystallographic orientation anisotropy of thermal conductivity with greater precision. Furthermore, measurement techniques of elastic wave velocity (or elastic constants) (e.g., Antonangeli et al. 2004; Dewaele et al. 2023; Lin et al. 2010; Wakamatsu et al. 2018, 2022) and elemental diffusivity (e.g., Park et al. 2023) for hcp iron with strong LPO will contribute to our understanding of the seismic anisotropy observed in the Earth’s inner core and its origin in the dynamics of the inner core.

In summary, in this study, we performed synchrotron multiangle XRD on statically compressed [100], [110], and [111] single-crystal bcc iron at pressures up to 80 GPa and 300 K in a DAC to characterize the LPO of hcp iron and its stability during further compression. Our data show the formation of textured polycrystalline hcp iron, in which the LPO of the hcp phase depends on the three crystallographic compression directions in the bcc phase. It was found that by applying pressure up to 80 GPa, the LPO of hcp iron was strongly affected by plastic deformation due to the uniaxial compression of the DAC. Further efforts to synthesize hcp iron with a stronger LPO at higher pressures are expected to improve our understanding of the velocity anisotropy of seismic waves and the heterogeneous structure of the Earth’s inner core.