Pressure-induced disordering of site occupation in iron–nickel nitrides

Iron and nickel are the most important components of the inner core of the Earth, with recent reports indicating that at 364 GPa and 5000–6000 K, the maximum nitrogen content in the inner core can vary from 2.0 to 3.2 wt. %.^1–5 The study of iron–nickel alloys and iron–nickel nitrides has been an important focus of experimental and computational research over the past few decades.^6–10 Iron–nickel alloys also have considerable potential for materials applications, owing to their high magnetoconductivities and low coefficients of thermal expansion.^11,12 Iron-based nitrides have been considered important candidates for use as corrosion-proof layers on steel and for magnetic data storage systems, thanks to their significant thermal stability and suitable magnetic properties.^13–15 The ordering of substitutional and interstitial site occupation at high pressures can lead to fundamental changes in structural phase relationships and in the properties of iron–nickel nitrides. The structural properties of iron–nickel nitrides are of considerable interest for a wide range of researchers, especially those in materials science, chemistry, physics, and earth science.

In iron-based nitrides, nitrogen atoms enter the lattice to form interstitial solid solutions, such as γ-Fe₄N and ε-Fe₃N. The crystal structures of γ-Fe₄N and ε-Fe₃N derive from the face-centered cubic (fcc) γ-Fe structure and the hexagonal close-packed (hcp) ε-Fe structure, respectively.^16,17 In the ideal binary nitride γ-Fe₄N (Pm-3m), Fe atoms occupy both the Wyckoff 3c and 1a sites [Fig. 1(a)], but in the case of the ternary nitride γ-Fe₃NiN (Pm-3m), Fe and Ni atoms occupy the Wyckoff 3c and 1a sites, respectively,^18,19 with the N atom occupying the 1b site [Fig. 1(b)]. In analogy with the aforementioned case, in the iron–nickel alloy γ-FeNi₃ (Pm-3m), the Fe and Ni atoms tend to occupy the Wyckoff 1a and 3c sites, respectively, with the interstitial 1b site remaining vacant [Fig. 1(c)]. In the standard structure of ε-Fe₃N (P6₃22), each iron atom at the 6g site coordinates with two nearest-neighbor nitrogen atoms at the 2c positions [the only available position for N atoms: see Fig. 1(d)]. Interestingly, Leineweber et al.¹⁷ suggested possible occupancy of the 2b site by the N atoms together with absence of occupancy for the 2d site. This was explained on the basis of N–N repulsive forces as being due to the minimized configurational entropy probed by time-of-flight (TOF) neutron diffraction.¹⁷ Our recent neutron powder diffraction (NPD) study of nitrogen-rich ε-Fe₃N and ε-Fe_2.322Co_0.678N_0.888 nitrides has shown that nitrogen atoms may enter the higher-entropy interstitial 2b and 2d sites, and the Co and Fe atoms could disorderly occupy the cation 6g site at high temperature and high pressure (HTHP).²⁰ The conditions for the formation of substitutional solid solutions in metals can be described by the Hume-Rothery rules.

The structure and properties of iron-based nitrides can be significantly affected by disordered interstitial N atoms and substitutional Co atoms. To the best of our knowledge, up to now, there have been only a few reports of detailed structural property studies of ternary iron-based nitrides. Despite important progress, the cation occupancy in ternary iron–nickel nitrides at high pressure remains poorly understood. A detailed investigation of the structural properties of iron–nickel nitrides is therefore needed, in order to shed light on the dynamics of cation occupancy at high pressure.

The preparation of metal nitrides is particularly challenging under ambient conditions, owing to difficulties in incorporating nitrogen into the metal lattice, given the thermodynamically disadvantageous conditions under ambient pressure. Instead, a high-pressure enclosing environment is thermodynamically beneficial for both the reactivity of nitrogen and the stability of the nitrides. Bulk single-crystalline ε-Fe₃N phases have been synthesized by Niewa et al.²¹ using microcrystalline ε-Fe₃N_1+x as starting material at 15 GPa and 1327 °C. Guo et al.²² have further shown that Co or Ni atoms can occupy Fe sites in ε-Fe₂CoN or ε-Fe₂NiN phases, synthesized from mixtures of ζ-Fe₂N and Co (or Ni) at 5 GPa and 1200 °C. High-pressure solid-state metathesis (HPSSM) reactions provide a useful synthetic method for fabrication of metal-based nitrides.^20,23 Metal oxides, such as Fe₂O₃, Co₂O₃, NiO, LiNiO₂, LiGaO₂, KGaO₂, NaReO₄, Na₂MoO₄, and K₂OsO₄, are used as precursors in HPSSM reaction routes for the production of spherical bulk iron-based nitride samples, such as ε-Fe₃N_1+x and γ-Fe₄N_x.^24–29 

The principal motivation for this study is the synthesis of bulk ternary iron–nickel nitrides under HTHP conditions and further investigation and explanation of the disordering of substitutional and interstitial site occupancy, with the aim of obtaining better understanding of the structural properties of iron–nickel nitrides at high pressure.

The structural properties of the as-synthesized iron–nickel nitride samples were investigated by microfocus x-ray diffraction (XRD) (Rigaku, RAPIDII-V/DW, Cu Kα). The quantitative accuracy was estimated to not exceed 0.5%. The elemental distribution of the samples was analyzed by high-angle annular dark field scanning transmission electron microscopy (HAADF-STEM) (JEOL-TEM, Japan). The crystal structure was determined by selected area electron diffraction (SAED). The homogeneity of the iron–nickel nitrides was measured by scanning electron microscopy (JSM-7000F field emission SEM, JEOL), and the elemental composition was determined using energy dispersive x-ray spectroscopy (EDX) (INCA E250, Oxford Instruments). A 5 nm thick osmium coating on the surface of each sample was produced using an osmium coater (Neoc-STB, Meiwafosis Co., Ltd.) before EDX measurement. FeS₂, Ni, and BN were used as the EDX standards for the quantification of Fe, Ni, and N, respectively.³⁰ 

An in situ high-pressure synchrotron angle-dispersive x-ray diffraction (ADXRD) study was performed at ambient temperature on a symmetric type of diamond anvil cell (DAC) with 500 µm culet anvils at the 4W2 high-pressure beamline of the Beijing Synchrotron Radiation Facility (BSRF). Each iron–nickel nitride sample together with a small ruby ball of approximately 10 µm was placed in the 120 µm chamber of a rhenium gasket for indentation to a thickness of about 40 µm.

The ruby fluorescence technique was used to calibrate the pressure, while methanol/ethanol 4:1 (by volume) was used as the pressure-transmitting medium.³¹ For the ADXRD measurements, a Si (111) monochromator was used to produce synchrotron radiation x rays of wavelength 0.6199 Å. The ADXRD patterns of the samples thus obtained were integrated using FIT2D software.^32,33

Neutron powder diffraction (NPD) is an effective and exact technique to accurately determine atomic occupancy. In this work, we performed NPD experiments on the iron–nickel nitride samples at room temperature using the Fenghuang neutron diffractometer at the China Mianyang Research Reactor (CMRR) of the Institute of Nuclear Physics and Chemistry, China.³² The elemental neutron scattering length parameters in the iron–nickel nitride samples are b(Fe) = 0.954 × 10⁻¹² cm, b(Ni) = 1.031 × 10⁻¹² cm, and b(N) = 0.936 × 10⁻¹² cm. A thin-walled copper chamber of diameter 6 mm was used to enclose the iron–nickel nitride samples (each weighing approximately 3 g). The NPD data were collected in the range of 2θ = 20°–140° in steps of 0.1° s⁻¹ and at a wavelength λ = 1.57 Å. The sampling time was 10 h, and the neutron flux at the sample position was 2.84 × 10⁶ n s⁻¹ cm⁻². The data were refined using FullProf Suite Toolbar version 2.05 Rietveld refinement software.³⁴ For the refined NPD patterns of the iron–nickel nitrides, the reliability factors were R_wp = 30.2% and χ² = 2.09.

Owing to the effects of the lower surface energy, the as-synthesized nitride samples from the HPSSM reaction were spherical in shape [Fig. 2(a)]. In the HPSSM reaction, nitrogen degassing leads to formation of abundant cavities inside the iron–nickel nitride samples, as shown in Fig. 2(b). Typical bone-shaped interdendrite phases were also detected, together with elemental segregation [Fig. 2(c)]. This effect is associated with dendritic segregation in nickel-based superalloys, as a side-effect of solidification.^35,36 The different grayscale regions in the SEM image in Fig. 2(d) (marked as A, B, and C) indicate different phases in the sample. In fact, although we have conducted many high-pressure experiments in which the pressure–temperature–composition–time parameters (P–T–x–t) were varied, almost all the successful experiments resulted in multiple-phase products.

The typical result of an HAADF-STEM acquisition is shown in Fig. 3(a), while Fig. 3(b) shows SAED patterns of the iron–nickel nitrides, containing phases A, B, and C corresponding to the three sets of diffraction spots. Figure 3(c) is a schematic diagram of the SAED pattern, with the diffraction spots corresponding to phases A, B, and C in red, blue, and green, respectively. The elemental distributions within different nitride phases was investigated further. Typical elemental maps obtained from STEM-EDX measurements are shown in Figs. 3(d)–3(f). Phase A has the highest Ni and lowest N content, while phase C has the highest Fe and lowest Ni content. An identical conclusion is obtained from a consideration of the dynamics of dendrite segregation.

The elemental composition was determined by EDS, and the outcome of the refined NPD and XRD patterns is shown in Table I. For all three phases, neither NPD nor EDX detected boron and oxygen elements, which is consistent with the results of our previous studies of HPSSM reactions.^{20,23–25,37,38} Determination of elemental compositions by different methods can yield different outcomes owing to the working principles of the particular method. For example, EDX determines elements according to their different characteristic x-ray emissions, XRD is based on interactions between x rays and electrons, and NPD is based on neutron and nuclear interactions. The analytical scales also differ between these methods: micro-focused XRD measurements cover a few tens of micrometers, and EDX analysis is effective within the order of a micrometer, while NPD requires a significantly larger sample volume. Therefore, the differences in chemical composition determined by the various methods may be caused by the different sizes of the area analyzed. Taking into account that the NPD method is more reliable for samples that contain neighboring elements (such as Fe and Ni) and light elements (such as N), in this work the ratios of atomic composition were determined from the NPD results alone.^39–41 

According to the Hume-Rothery rules, when the difference in atomic size between two elements is greater than 15%, it is difficult for them to form a substitutional solid solution.⁴⁰ Owing to the atomic-size difference δ_{{Fe, Ni}} = 18.25% > 15%, therefore, it is difficult to form pure phases of iron–nickel nitrides by employing Ni as a substitute for Fe. On the other hand, because the mixing enthalpy reflects the atomic binding energy, the mixing enthalpy and atomic-size difference were selected in order to study the law of phase formation of iron–nickel nitrides. The segregation phenomenon can be explained by the enthalpy of mixing between the principal elements. The mixing enthalpies values are as follows: $Δ H { F e , N } m i x =−87kJ/mol$⁠, $Δ H { N i , N } mix =−69kJ/mol$⁠, and $Δ H { F e , N i } m i x =−2kJ/mol$⁠.⁴² Since Fe shows a higher negative enthalpy when mixed with Ni, it is partially attracted to the dendrite region by the Ni component. By contrast, N exhibits lower negative enthalpy with Fe and Ni, and thus it is repelled from the dendrite region.

The micro-focused XRD patterns of iron–nickel nitrides collected under ambient conditions (Fig. 4) were analyzed using the Rietveld refinement method. This yielded three nitride phases with reliability factors R_wp = 22.5% and χ² = 0.74. The refined lattice constants are listed in Table II, and it can be seen that no obvious lattice distortion was found in the present experiments. According to the structural and compositional analysis, the bone-shaped interdendrite phase is mainly of γ-FeNi₃ type, which is recorded as phase A, while the dendrite matrix is composed of Fe, Ni, and N, and this is recorded as phase B (γ-Fe₄N type) and phase C (ε-Fe₃N type). These phases correspond to the areas marked A, B, and C in Fig. 2(d). The existence of three N-bearing compounds was further confirmed by XRD, and this is consistent with our observations from SEM.

The Rietveld refinements of NPD patterns acquired from the iron–nickel nitrides are shown in Fig. 6(a). In the NPD refinements, phases A, B, and C and copper were considered. From the refined NPD patterns, copper makes little contribution to the diffraction. With cation disorder taken into account, the reliability factors of the refinements were found to be the lowest (R_wp = 30.2% and χ2 = 2.09). The R_wp factor may be related to the nonstoichiometry, since the nonstoichiometric ratios of transition metal nitrides have an impact on their structural stability.⁵³  Figure 6(b) shows the crystal structure of phase A. Ni atoms partially substitute for Fe atoms at 1a sites, and Fe atoms partially substitute for Ni atoms at 3c sites. On the basis of the NPD refinement results, the measured site occupancies of Fe/Ni atoms for 3c and 1a sites are 0.198/0.801 and 0.750/0.248, respectively (Table IV, phase A). A possible explanation for this is that the 1a sites are occupied by Fe and the 3c sites by Ni in the ordered L1₂ structure, with significant difference with respect to the ordered L1₂ structure (L1₂ is defined as fcc-based, with different types of atoms at the eight vertices and six face centers). In this work, the measured site occupancies of Fe atoms for 3c and 1a sites were 0.198 and 0.750, respectively, and the site occupancies of Ni atoms for 3c and 1a sites were 0.801 and 0.248, respectively. Therefore, phase A should correspond to the completely cation-disordered compound. Meanwhile, the measured 1b site occupancy for N atoms is 0.061 (occ._1b = 0.061). As a consequence, interstitial N atoms can still enter the γ-FeNi₃-type lattice and form interstitial solid solutions under high pressure.

Previous studies have shown that Ni substitution is beneficial to 1a sites in γ-Fe₄N.⁴³ In this work, however, we have shown the possibility of stabilizing a random alloy of Ni atoms on the 1a and 3c sites, if configurational entropy is considered. In phase B [Fig. 6(c)], Ni atoms partially substitute for Fe atoms at 3c sites, Fe atoms partially substitute for Ni atoms at 1a sites, and the N atom occupies the 1b position. The measured site occupancies of Fe/Ni atoms for 3c and 1a sites are 0.543/0.455 and 0.378/0.621 (Table IV, phase B). It can be seen here that the disorder of the cations leads to an increase in entropy, with consequent significant improvements in structural stability. Extra stability is also provided by the addition of interstitial nitrogen into phases A and B as compared with the γ-Fe structure.

In addition, Fig. 6(d) shows that Ni atoms partially substitute for Fe atoms at 6g sites, and all the voids (2c, 2b, and 2d sites) formed by hcp-Fe may be occupied by N atoms in the N-rich phase C (ε-Fe₃N type). When these positions are completely occupied, the coordination number of each iron atom is equal to 6 (CN = 6). The measured site occupancies of N atoms for 2c, 2b, and 2d sites are 0.552, 0.313, and 0.133 according to the Rietveld-refined NPD pattern (Table IV, phase C). As can be seen, the main N site is the 2c site, while the 2b and 2d positions can also be occupied. We denote Fe atoms with CN = 1, 2, 3, 4, 5, and 6 by Fe(1), Fe(2), Fe(3), Fe(4), Fe(5), and Fe(6), respectively. It has been found that in ε-Fe₃N_1.098 (P6₃22 structure), the probabilities of occurrence P^Fe(0), P^Fe(1), P^Fe(2), P^Fe(3), P^Fe(4), P^Fe(5), and P^Fe(6) are 2.0%, 17.6%, 45.8%, 28.5%, 5.9%, 0.3%, and 0.004%, respectively.¹⁸ We employ a similar notation for phase C, with, for example, Fe/Ni(0) representing an Fe/Ni atom whose N-coordination number (Fe/Ni by N) is 0. Then, P^Fe/Ni(0) ≈ 7.5% in phase C, since P^Fe/Ni(0) = (1 − occ._2c)²(1 − occ._2b)²(1 − occ._2d)². The values of occ._2c, occ._2b, and occ._2d are shown in Table IV (phase C). Similarly, P^Fe/Ni(1), P^Fe/Ni(2), P^Fe/Ni(3), P^Fe/Ni(4), P^Fe/Ni(5), and P^Fe/Ni(6) are 27.1%, 36.1%, 22.1%, 6.4%, 0.8%, and 0.038%, respectively. Because P^Fe/Ni(0) > P^Fe(0) and P^Fe/Ni(1) > P^Fe(1), the local magnetic moments of iron–nickel nitrides are higher.

On the basis of the Hume-Rothery rules,⁵⁴ it is challenging to achieve substitution between Fe and Ni, owing to the difference in atomic size being greater than 15%. In this work, however, Fe and Ni atoms were substituted to form substitutional solid solutions despite the atomic-size difference being as high as 18.25%. However, it can be expected that changes in interatomic distances and interactions under extreme HTHP conditions will lead to broadening of energy bands and allow deep modification of bonding patterns and electronic orbitals. HTHP confinement conditions favor substitutional and interstitial site disordering in ternary iron–nickel nitrides.

In summary, novel spherical bulk iron–nickel nitrides were successfully synthesized through an HPSSM reaction under a pressure of 5 GPa and a temperature of 1673 K. The structural properties of the as-prepared samples were fully characterized by NPD, SEM, HAADF-STEM, SAED, micro-focus XRD, and synchrotron radiation ADXRD. The obtained spherical-like bulk samples were found to include three N-bearing compounds (γ-FeNi₃ type, γ-Fe₄N type, and ε-Fe₃N type) owing to dendrite segregation of the nickel-based alloy. The crystal structure and site occupation of each phase were analyzed and discussed in detail. The Fe and Ni atoms were found to occupy the lattice positions in a disorderly manner. These significant elastic properties can be attributed to the joint action of interstitial N atoms and disorderly substituted Ni atoms.

We thank Professor Filippo for helpful discussions. We acknowledge support by the National Natural Science Foundation of China (Grant Nos. U2030107 and 11774247) and the Joint Usage/Research Center PRIUS, Ehime University, Japan.