Crystal and Magnetic Structures of Double Hexagonal Close-Packed Iron Deuteride

Neutron powder diffraction profiles were collected for iron deuteride (FeDx) while the temperature decreased from 1023 to 300 K for a pressure range of 4–6 gigapascal (GPa). The ε′ deuteride with a double hexagonal close-packed (dhcp) structure, which coexisted with other stable or metastable deutrides at each temperature and pressure condition, formed solid solutions with a composition of FeD0.68(1) at 673 K and 6.1 GPa and FeD0.74(1) at 603 K and 4.8 GPa. Upon stepwise cooling to 300 K, the D-content x increased to a stoichiometric value of 1.0 to form monodeuteride FeD1.0. In the dhcp FeD1.0 at 300 K and 4.2 GPa, dissolved D atoms fully occupied the octahedral interstitial sites, slightly displaced from the octahedral centers in the dhcp metal lattice, and the dhcp sequence of close-packed Fe planes contained hcp-stacking faults at 12%. Magnetic moments with 2.11 ± 0.06 μB/Fe-atom aligned ferromagnetically in parallel on the Fe planes.

deuterides/hydrides containing the ε′ phase as a major component 6 . The crystal structure, including the H/D atomic positions, was precisely determined, but the magnetic structure was not determined because of the weak magnetic scattering intensities. Second, the H content x is unknown for the high-temperature solid solution. The dhcp hydride has been considered to maintain x = 1.0 across almost the entire stable T-P range 1 . The most recent X-ray diffraction measurements revealed a substantial reduction in volume at high temperatures near the dhcp-fcc phase boundary, and the partial release of dissolved H atoms or the formation of the solid solution was suggested in this regard 16 .
We carried out in situ NPD measurements on FeD x in the T-P ranges of 300-1023 K and 4.2-6.1 GPa. The crystal and magnetic structures were refined for the dhcp deuteride using the model structures proposed in the early NPD study 6 and predicted in the electronic band structure calculation 26 . The structure of dhcp FeD 1.0 contained the off-central displacement of D atoms on octahedral interstitial sites and stacking faults in the dhcp sequence of Fe planes, consistent with the early results 6 . The atomic displacement and the stacking faults were partially or fully removed in the solid-solution states at high temperatures. The magnitude and alignment of the magnetic moments were in agreement with those theoretically calculated for ferromagnetic dhcp FeH 1.0 26 .

Results
NPD profiles were collected for the Fe deuteride at four T-P points (Fig. 1). The fcc solid solution was first prepared by deuterization of fcc Fe at 1023 K and 6.1 GPa and then cooled to 673 K, where the fcc deuteride partially transformed to the dhcp deuteride along with the formation of a small amount of a metastable hcp modification. The measured T-P point was located immediately above the γ-ε′phase boundary and was considered to be still within the stable range of the γ phase. The latest NPD study of Fe hydride revealed that the γ-ε′phase boundary was located at temperatures 100-200 K higher than those shown in Fig. 1 19 , and the appearance of the dhcp deuteride at 673 K and 6.1 GPa was consistent with the latest result. The formation of the metastable hcp phase was sensitive to the cooling rate; a larger amount of the hcp deuteride formed at a faster cooling rate 18 . The cooling rate was gradually decreased from 10 K/min to 1 K/min. The hcp formation, however, was not completely prevented. The coexisting state of the dhcp, fcc, and hcp deuterides was retained at 603 K and 4.8 GPa. When the temperature was decreased to 300 K, the hcp deuteride decomposed to dhcp monodeuteride and bcc Fe, whereas the dhcp and fcc deuteride remained almost unchanged.
The observed diffraction profiles were simulated using model structures proposed for dhcp 6 , fcc 14 , and hcp hydrides/deuterides 18 in early NPD studies. Dissolved D atoms were located on the centers of the octahedral and tetrahedral interstitial sites (hereafter, referred to as the O site and T site, respectively) of the fcc and hcp metal lattices, whereas they were located on the off-centered positions of the octahedra in the dhcp lattice. The crystal structure of dhcp FeD 1.0 used as the model structure is schematically shown in Fig. 2 6 . This structure belongs to the P6 3 /mmc space group and has the stacking sequence of the Fe planes, ABACA • • • , which comprises "hexagonal" stacking of ABA or ACA and "cubic" stacking of BAC. Figure 2b shows the spatial configuration of the Fe octahedra available for accommodating D atoms, and the octahedra are connected in a face-shared configuration in the hexagonal stacking sequence and an edge-shared configuration in the cubic stacking sequence. Two structural irregularities were considered in the refinement of the dhcp structure according to 6 , i.e., the displacement of D atoms along the c-axis (δz) and the stacking fault of the Fe planes, which was described using f reg and f def , denoting occupancies on the regular sites equivalent to the (1/3, 2/3, 7/8) position and defect sites equivalent to the (1/3, 2/3, 1/8) position, respectively.
For ferromagnetic dhcp FeD 1.0 , two possible structures, in-plane and out-of-plane models, were examined when refining the magnetic structure 6,26 . The magnetic moments on the Fe atoms lay parallel within the metal planes in the in-plane model, whereas they stand vertically on the metal planes in the out-of-plane model. The calculations of neutron scattering intensities for the two model structures showed that their contributions to peak intensities were limited approximately to the 100, 101, 004, and 102 peaks, and relative intensities were www.nature.com/scientificreports www.nature.com/scientificreports/ substantially different between the two models 6 . These calculated peak intensities served as a guideline for the refinement of the magnetic structure in this study. Figure 3 shows the observed diffraction profiles and their simulated profiles fitted by Rietveld refinement using a Z-Rietveld software (Version 1.1.2) 35 . As shown in Fig. 3a, the single-phase profile at 1023 K and 6.1 GPa was fitted with the fcc structure with a composition of FeD 0.62(3) (hereafter, the numbers in parentheses denote experimental error). The profile at 673 K and 6.1 GPa had good a fit with the mixture of dhcp FeD 0.68(1) , hcp FeD 0.56 (2) , and fcc FeD 0.59 (1) , with mass ratios of x mass = 0.667(3), 0.171(2), and 0.162(2), respectively (Fig. 3b). The mass ratios slightly changed upon cooling to 603 K: x mass = 0.564(4) (dhcp), 0.277(4) (hcp), and 0.16 (fcc) (Fig. 3c). The diffraction profile at 300 K and 4.2 GPa was fitted with the mixture of dhcp FeD 1.0 , fcc FeD 1.0 , and bcc Fe at mass ratios of x mass = 0.708(4), 0.014(1), and 0.278(3), respectively (Fig. 3d).
Several fitting parameters were properly constrained to avoid convergence of the parameters into unphysical values. The atomic displacement parameters or temperature factors of D and Fe atoms were assumed equal among the coexisting deuterides. The occupancy ratio of f def /f reg was constrained to be equal between the Fe and D atoms in the refinement for the dhcp structure. The D composition was fixed at x = 1.0 for the dhcp and fcc deuterides in the refinement of the 300 K-4.2 GPa profile according to the early studies 6,16,18 . In addition, the magnetic moment of bcc Fe was fixed to an ambient pressure value of the 2.1 μ B /Fe-atom (μ B denotes the Bohr magneton). H atoms, which were included as an impurity by 4 atom% in the D source of AlD 3 , were assumed to randomly occupy the D-atom sites. For the sake of simplicity, the site occupancies of H atoms and the H composition are included in the notations g D and x, respectively.
For the dhcp FeD 1.0 at 300 K and 4.2 GPa, crystal structure including magnetic ordering was refined using the out-of-plane and in-plane models. In both models, one equivalent magnitude of magnetic moment was assumed. Figure 4 shows the fitting results obtained with (a) the nonmagnetic, (b) out-of-plane, and (c) in-plane models. The simulated profile of the nonmagnetic model showed substantial deficits in the intensities of the 100, 101, 004, and 102 peaks. A simulated profile for the out-of-plane model reproduced, with a reliability value of χ 2 = 11.3, the observed intensities of the 101 and 102 peaks but failed to reproduce that of the 004 peak. The in-plane model yielded a slightly less value of χ 2 = 10.3 and satisfactorily reproduced the intensities of all peaks with an optimized magnetic moment of 2.11(6) μ B /Fe-atom. The rather high value of χ 2 arose from misfits in peak shape likely attributed to enhanced distortion of the dhcp Fe lattice by interstitial D atoms fully occupying the O sites.
The structure refinements included preferred-orientation correction for the c axis of the dchp lattice. Pref. orient.
[001] is a parameter of the March-Dollase function implemented in the z-Rietveld program 35 , and is optimized to reproduce peak intensities modified by the preferred orientation of the c axis. The structure refinement of dhcp FeD at 300 K and 4.2 GPa yielded pref. orient.
[001] = 1.01. Calculations of peak intensities using a value of 1.01 and the March-Dollase function showed that the 100, 101, 004, and 102 peak intensities were modified by factors of 1.015 (+1.5%), 1.012 (+1.2%), 0.971(−2.9%), and 1.005 (+0.5%), respectively. These modification values are substantially less than the magnetic scattering components of the peak intensities as shown in Table 2 Table 1). Gray and blue spheres indicate the regular positions of Fe and D atoms, respectively. Arrows indicate the directions of displacement of D atoms from the centers of octahedral interstices. Here, A, B, and C represent the standard notation for close-packed planes. (b) Face-shared octahedra accommodating D atoms.
www.nature.com/scientificreports www.nature.com/scientificreports/ in the following paragraph: for example, the 004 peak, with a maximum modification value of −2.9%, has a magnetic scattering component 57.1%. The parameter for preferred-orientation correction dose not significantly correlate with the Bragg intensities and hence its bias to the assignment of magnetic structure can be ruled out.
The fitting parameters optimized for the dhcp deuteride and the coexisting fcc and hcp deuterides, and bcc Fe are listed in Table 1. The contributions of nuclear scattering (I nuc ) and magnetic scattering (I mag ) to the intensities of the 100, 101, 004, and 102 peaks of dhcp FeD 1.0 are derived from the simulated profile shown in Fig. 4c and listed in Table 2.

Discussion
Crystal structure of dhcp deuteride. The structural parameters optimized for the dhcp FeD 1.0 at 300 K The off-center displacement is attributed to the repulsive interactions between the interstitial D atoms 6 . As known as the empirical 2.1-Å rule -dissolved H atoms in metals cannot approach each other within 2.1-Å in metal hydrides 36 , because there are strong long-range repulsive interactions between interstitial H atoms. The nearest neighboring D-D distance is calculated as 2.18 Å (close to the critical value) for the D atoms, when assumed to occupy exactly the center positions of the face-shared octahedra. The displacement of D atoms from  (7) 1. www.nature.com/scientificreports www.nature.com/scientificreports/ the centers by δz = 0.0053c (0.045 Å) increases the D-D distance to 2.27 Å, significantly greater than the critical value. As a result, some reduction in repulsive energy is expected.  The regular dhcp stacking sequence of the Fe planes gradually recovers with elevating temperature. The occupancy of the Fe atoms at the defect sites f def , which represents the stacking fault degree, decreases from 0.123 at 300 K to 0.018 at 673 K via 0.043 at 603 K. This continuous variation with temperature contrasts the abrupt centering of the D atoms at 673 K. The atomic displacement parameter of the Fe atoms gradually increased from 0.33 to 0.74 Å 2 as the temperature increased from 300 to 673 K. Recovery of the regular stacking sequence appears unrelated to the centering of the D atoms and would be driven by the thermal activation of Fe atomic motions.
Magnetic structure of dhcp deuteride. The in-plane magnetic ordering determined for the dhcp FeD 1.0 is consistent with that proposed for dhcp FeH 1.0 in the early theoretical study 26 . The in-plane ordering of magnetic moments, proposed as a stable magnetic structure by the DFT calculations, is experimentally confirmed by the present NPD study. The calculations also predicted the magnetic moments of 1.90 and 2.08 μ B /Fe-atom at sites 2a and 2c, respectively 26 . In fact, two distinct values of hyperfine fields were correspondingly observed by MB spectroscopy [30][31][32][33][34] . In the present structure refinement, the magnetic moment of 2.11(6) μ B /Fe-atom is obtained under an assumption of one equivalent magnetic moment for the two sites. This value is slightly larger than the calculated moments and slightly less than the experimental moment of 2.22 μ B /Fe-atom for dhcp FeH x , that was measured for 0.65 ≤ x ≤ 0.81 at temperatures of 4.2-80 K at ambient pressure 7,29 . The magnetic moment tends to increase with both decreasing T and x 27 . The value of 2.11(6) μ B /Fe-atom of the dhcp FeD 1.0 at 300 K can be interpreted in terms of these T and x dependencies.
The large magnetic moment of the dhcp FeD 1.0 suggests a high critical temperature, Curie temperature T c , for its ferromagnetic-paramagnetic transition upon temperature elevation. High T c is expected from the temperature-dependence of the magnetization measured for the quenched dhcp FeH x 29 . However, the measured temperature range of 4.2-80 K is too limited to estimate a T c most likely far above room temperature. Pure iron, bcc Fe, has a magnetic moment of 2.218 μ B /Fe-atom at 0 K and 0.1 GPa and undergoes a magnetic transition at 1043 K. The dhcp deuteride with a comparable magnetic moment is hence expected to exhibit a corresponding T c of around 1000 K. Unfortunately, the magnetic moment was not determined for the dhcp solid solutions at high temperatures because observation of the magnetic scattering peaks was hindered by the rather intense peaks from the coexisting fcc FeD x . The variation of T c with x is essential for understanding the ferromagnetism in relation to the volume expansion and electron doping caused by dissolved D atoms. NPD investigation of dhcp deuteride, including solid solution states at high temperatures and high pressures, is a future research subject.

Methods
Reagent-grade pure iron flakes (purity: 99.9%) with a lateral particle size <100 μm and a thickness <20 μm were used as a starting material. A compacted Fe disc 3 mm in diameter and 2.5 mm in height was prepared by pressing the flakes in a piston-cylinder-type mold. The Fe disc was placed at the center of a NaCl capsule 5.5 mm in outer diameter and 8.2 mm in height, along with the internal deuterium source of AlD 3 (isotopic purity: 96 atom% D) pellets, placed above and below the disc. An excess amount of AlD 3 (Fe/D molar ratio of ~1.5) was charged into the cell to form Fe deuteride with equilibrium-D compositions during NPD measurements. The NaCl capsule containing the Fe disc and AlD 3 pellets was inserted into a cylindrical graphite heater and embedded in a pressure-transmitting medium (15-mm edge cube) made of MgO with a 5% Cr 2 O 3 weight.
The high-pressure cell containing the Fe disc and AlD 3 pellets was first pressurized to ~6 GPa at 300 K and then heated to 1023 K. During heating, the AlD 3 pellets decomposed to provide a D 2 fluid, which dissolved into the Fe specimen to form fcc FeD x . After confirming the deuteride formation at 1,023 K and 6.1 GPa by NPD diffraction, we lowered the temperature stepwise to 300 K for NPD measurements. Diffraction profiles were collected at four T-P points (Fig. 1), with an exposure time from 2 to 6 h, using a neutron source operating at a proton beam power of 300 kW. h k l I nuc I mag I mag /(I nuc + I mag )  Table 2. Nuclear (I nuc ) and magnetic scattering (I mag ) components of the 100, 101, 004, and 102 reflections of dhcp FeD 1.0 with the in-plane model. Each value isnormalized by I nuc = 100 for the 102 peak.