Phase Stability and Compressibility of 3R-MoN2 at High Pressure

We report phase stability and compressibility of rhombohedral 3R-MoN2, a newly discovered layer-structured dinitride, using in-situ synchrotron high-pressure x-ray diffraction measurements. The obtained bulk modulus for 3R-MoN2 is 77 (6) GPa, comparable with that of typical transition-metal disulfides (such as MoS2). The axial compressibility along a axis is more than five times stiffer than that along c axis. Such strong elastic anisotropy is mainly attributed to its layered structure with loosely bonded N-Mo-N sandwich interlayers held by weak Van der Waals force. Upon compression up to ~15 GPa, a new hexagonal phase of 2H-MoN2 occurs, which is irreversible at ambient conditions. The structural transition mechanism between 3R and 2H phases is tentatively proposed to be associated with the rotation and translation of sandwich interlayers, giving rise to different layer stacking sequences in both phases. At high temperature, the decomposition of 3R-MoN2 leads to the formation of hexagonal δ-MoN and the onset degassing temperature increases as the pressure increases. In addition, the low-temperature electrical resistivity measurement indicates that 3R-MoN2 behaves as a semiconductor with an estimated band gap of Eg ≈ 0.5 eV. 3R-MoN2 also shows weak antiferromagnetic properties, which probably originates from the occurrence of magnetic zigzag edges in the structure.

atoms. The sandwich layers are vertically stacked and loosely bonded by weak van der Waals forces as suggested by theoretical simulations 9,18 , similar to that in the TM dichalcogenides 19 . Besides, our preliminary experiments indicate that 3R-MoN 2 demonstrates highly catalytic activities for hydrogenation processes, and it may hold great promise as the next-generation catalysts and energy storage materials for a wide range of applications 7,8 . Regarding physical properties of 3R-MoN 2 , to date, it has sparsely been explored, but store exciting physics, especially for the material has the form of an atomic-level thin MoN 2 sheet. Remarkably, recent theoretical calculations indicate that the monolayer MoN 2 may have intriguing structural, electronic, and magnetic properties 6,9,18 .
For the layer-structured material systems, it often exists a series of different polymorphs such as hexagonal 2H and rhombohedral 3R polytypes as demonstrated in MoS 2 20 . The only structural difference between 2H and 3R phases is their stacking sequences of close-packed sandwich layers. Because of the weak interlayer interaction, both polymorphs can readily be converted between them through the interlayer rotation coupled with translation at certain high pressure and temperature 20 . Apparently, it provides an effective protocol to prepare new polytype 2H-MoN 2 by treating the synthesized 3R-MoN 2 under high pressure conditions. To the best of our knowledge, in addition to its electronic and magnetic properties, the phase stability of the newly synthesized 3R-MoN 2 has not yet been investigated which further limits its industrial applications, calling for more experimental data on this material.
With these aims in this work, we present a comprehensive study on 3R-MoN 2 with focus on the phase stability and compressibility using high-P synchrotron XRD measurements, leading to the discovery of a new 2H-MoN 2 . The elastic, electronic, and magnetic properties of 3R-MoN 2 have also been explored in detail.

Experimental Section
High-purity Na 2 MoO 4 (>99.5%, ~50 μm) and hBN (>99.9%, ~50 μm) powders in the molar ratio Na 2 MoO 4 : BN = 1: 2 were homogeneously mixed for the synthesis of the nitride. High P-T synthesis experiments were performed using a DS 6 × 14 MN cubic press and the detailed experimental procedures have previously been described in refs 5,21 . The run products were washed with distilled water to remove the byproduct NaBO 2 and unreacted Na 2 MoO 4 , followed by drying in an oven at 348 K. To obtain phase-pure nitride, a two-step reaction route was adopted, referring to ref. 5 for more experimental descriptions.
High-P angle-dispersive synchrotron x-ray diffraction (XRD) experiments using a diamond-anvil cell (DAC) were performed up to 30 GPa at the HPCAT 16BM-D beamline of the Advanced Photon Source (APS). In each of the high-P experiment, the nitride powders with submicron grain size were loaded into the sample hole in a stainless-steel gasket pre-indented to ~30 microns in thickness with neon as the pressure-transmitting medium. A few ruby balls were also loaded into the sample hole to serve as the internal pressure standard. High P-T energy-dispersive synchrotron diffraction experiments were performed up to 10 GPa and 1273 K in a large-volume high-P apparatus installed at the X17B2 beamline of the National Synchrotron Light Source (NSLS). The experimental details for angle-and energy-dispersive synchrotron measurements have been described previously 16,22 . The crystal structure was determined from analysis of the x-ray data using the GSAS software 23 .
Low-T magnetic susceptibility and four-probe resistivity measurements were conducted on a bulk sample sintered at 3.5 GPa and 753 K for 8 hours to measure the electric and magnetic properties. The final bulk sample was 4 mm in diameter and 1 mm in thickness. The density of the sintered sample was measured using the Archimedes method, and the obtained value is within more than 90% of the x-ray determined density. Figure 1a shows a typical XRD pattern of the purified product synthesized at 3.5 GPa and 753 K for 20 hours through a step reaction. The refined lattice parameters a = 2.854 Å and c = 15.938 Å agree well with previously reported values 5 . The crystal structure of the rhombohedral 3R-MoN 2 is shown in Fig. 1b, exhibiting a layered structure similar to that of MoS 2 . Figure 2a shows selected high-P synchrotron XRD patterns of 3R-MoN 2 . During room-temperature compression, a new peak around 2Θ = 13° was observed at ~14.8 GPa, and with further increasing pressure its diffraction intensity increases progressively, indicating the formation of a new MoN 2 phase (also see Fig. S1). The two www.nature.com/scientificreports www.nature.com/scientificreports/ MoN 2 phases coexist up to the highest experimental pressure of 30 GPa. After the release of the pressure, this phase was recovered at ambient conditions. As will be discussed below, this phase is referred to 2H-MoN 2 . Shown in Fig. 2b is the pressure-volume data of 3R-MoN 2 fitted to the 3 rd order Birch-Murnaghan equation of state. In the inset, the normalized pressure (F) is plotted vs. the Eulerian strain (f). The obtained bulk modulus, B 0 , is 77 (6) GPa with B' = 8 (2), indicating that MoN 2 is slightly stiffer than MoS 2 (B 0 ≈ 53 GPa and B' ≈ 9) 24 . This difference is likely due to the enhanced cation-anion bonding in the nitride, because compared with sulfur, the nitrogen is more favorable for the formation of strong covalent bonding states with transition metals. In addition, as shown in Fig. 2c, the c-axis is substantially more compressible than the a-axis, a behavior that is usually expected in the layer-structured materials. Also noted is that the elastic compressibility of the newly formed 2H phase would be similar due to the structural similarity of both phases as will be discussed below.

Results and Discussion
For the newly emerged phase at high pressure, as mentioned above it is well known that the layer-structured MoS 2 often exists in two different polymorphs: rhombohedral 3R and hexagonal 2H phases; the major difference between them is in the layer stacking sequence 20 . Accordingly, the 2H-MoS 2 -type structure with the space group P6 3 /mmc was used for analyzing the XRD data of this new MoN 2 phase. As shown in Fig. 3a, the structure refinement shows that the calculated XRD profile is in excellent agreement with the observed data taken at 20.4 GPa with the coexistence of both rhombohedral and hexagonal polytypes. It is noted that the large background of high-P XRD patterns should originate from the sample crystallinity, because the synthesis of high-quality MoN 2 sample is still challenging as descripted in our previous report, referring to ref. 5 . This hexagonal phase is therefore referred to as 2H-MoN 2 , and the refined structural parameters are listed in Table 1. The phase transition between 2H-and 3R-MoN 2 is presumably associated with the rotation and translation of N-Mo-N sandwich layers as previously reported in MoS 2 20 . Because of their slight structural difference, it is challenging to distinguish between the 2H and 3R phases using the TEM techniques (Fig. S3). It is found that the pressure-induced phase transition from the rhombohedral 3R-MoN 2 phase to a hexagonal 2H-MoN 2 structure is irreversible, as referred from the experimental and theoretical x-ray diffraction patterns of MoN 2 at ambient conditions in Fig. 3b. Also noted is that the density of high-P 2H phase is anomalously lower than that of 3R-MoN 2 at 20.4 GPa as listed in Table 1. This is not unexpected because the transition from 3R to 2H is often kinetically difficult for achieving a complete conversion; as a result, the final 2H phase would involve a large fraction of the layer stacking disorder and strain in the lattice, which will lead to a significant lattice expansion, hence the reduced the density. For 2H-MoN 2 , compared with simulated XRD pattern (see Fig. 3b), a slight peak shift of the 102 and 105 suggests a severe strain or stress that may build up between the interlayer at relatively low pressure. This is because the 2H phase is metastable phase and trends to transform into 3R phase upon decompression, involving a certain degree of the N-Mo-N interlayer rotation and translation. Compared with the 105 reflection, the 102 peak has a large shift relative to the calculated, probably because of the different stress as induced by interlayer stacking disorder involving different number of layers. The similar phenomenon has been observed in refs 5,20 . As depicted in Fig. 3c, the only crystal structural difference between of 3R-and 2H-MoN 2 is the interlayer stacking mode. In fact, for most known layer structured materials, they often adopt a common structure of hexagonal 2H polytype (AB|AB|…) with space    Table 1. Summary of structural parameters for MoN 2 phases determined by analyses of x-ray and neutron diffraction data. a,b D Interlayer is the distances between the two nearest neighboring Mo planes, and D Layer distance corresponds to the distance between the N planes. c,d Proposed atomic positions for 2H-MoN 2 , which cannot be refined accurately using the current high-P XRD data. e R P and wR P represent the profile residual and the weighted profile R-factor of refined XRD patterns.
www.nature.com/scientificreports www.nature.com/scientificreports/ To study the phase stability at high temperature, we performed in-situ energy-dispersive high P-T synchrotron XRD measurement using a large volume pressure. As shown in Fig. 4a, the XRD patterns were collected on heating at a constant load of 80 ton. Because of the thermal effect of the sample cell, the corresponding pressure decreases from 9.5 GPa at 300 K to 8.2 GPa at 1273 K. The strongest Bragg reflection (003) of 3R-MoN 2 is located at the low-energy region, and it is thus undetectable by the energy-dispersive XRD measurement. Clearly, δ-MoN is formed at ~1200 (20) K and 8.3 GPa through nitrogen degassing of 3R-MoN 2 . The decomposition process is expressed by, The phase stability of 3R-MoN 2 , however, is substantially enhanced with increasing pressure, leading to highly increased N 2 decomposing temperature (see Fig. 4b). At 8.3 GPa, for example, the reaction (1) happens at a higher temperature of ~1200 K based on in-situ high P-T synchrotron XRD measurement. The phase diagram of MoN 2 is eventually determined and summarized in Fig. 4b. Apparently, at high temperature, the δ-MoN can be formed through nitrogen degassing of 3R-MoN 2 , on the basis of our previous study of this material in ref. 5 . However, it is experimentally difficult to determine the phase boundary between 2H and 3R at high temperatures above 15 GPa. Nevertheless, the 3R phase seems thermodynamically more stable than 2H phase at high temperature as shown in Fig. 4b. Further experimental work is warranted to determine the detailed phase boundary between 3R and 2H using the state-of-the-art high-P techniques. Figure 5 shows the magnetic and electrical resistivity measurements. At first glance, the low-T magnetic susceptibility (χ) data plotted in Fig. 5a suggests a weak paramagnetic-like behavior, as also reported in LiXN 2 (X = Mo and W) 27,28 . However, after further analyses, the data can be fitted to the Curie-Weiss law in two temperature ranges, 130-300 K and 2-30 K. The obtained Weiss constants are T Θ = −283 (10) K and −6 (2) K, respectively, indicating that there exist two weakly antiferromagnetic (AFM-I and -II) phases for 3R-MoN 2 . The corresponding magnetic moments of Mo atom are μ eff = 0.12 (1) and 0.05 (1) μ B /f.u. Such weak antiferromagnetism in 3R-MoN 2 presumably originates from the magnetic zigzag edges at the grain boundaries as reported for MoS 2 29 . The detailed magnetic measurements are listed in Table 2. Moreover, it is worthwhile to mention that the atomically-thin MoN 2 layers possess intrinsic high-T ferromagnetic properties on the basis of recent ab-initial calculations 18 , which may be closely associated with the observed magnetism in this work.
As shown in Fig. 5b, the electrical resistivity of 3R-MoN 2 increases dramatically as temperature decreases, which is characteristic of a semiconductor. Based on the typical law for a semiconductor, ρ ρ = T e ( ) , a linear fit of the lnρ -1/T data yields a narrow band gap of E g = 0.50 (1) eV, which is comparable to the value of 0.47 eV for PbS 30 . However, it is substantially smaller than that of MoS 2 , an indirect semiconductor with E g ≈ 1.2 eV 29 . In contrast, LiMoN 2 and LiWN 2 both behave as an intrinsic metal; the two ternary nitrides also adopt the 3R symmetry of its parent MoN 2 with intercalated Li layers 27,28 . The measured semiconductor-like behavior in 3R-MoN 2 may be partially associated with the degrees of crystallinity and defects, such as layer stacking faults. Hence, further resistivity measurements on well-crystallized samples are warranted to clarify this issue. www.nature.com/scientificreports www.nature.com/scientificreports/

Conclusions
In summary, the structural stability and compressibility of a newly discovered layer-structured rhombohedral 3R-MoN 2 have been studied using high-P compression measurements. A recoverable 2H-MoN 2 , isotypic with hexagonal MoS 2 , is also discovered via high-pressure processing of 3R-MoN 2 , probably involving the interlayer rotation and translation as reported in MoS 2 . Because of their structural similarity, the obtained bulk modulus and axial compressibility for 3R-MoN 2 are comparable to those of MoS 2 . The obtained the bulk modulus for 3R-MoN 2 is B = 77(6) GPa and the axial compressibility along c axis is much softer than that along a axis, confirming that the sandwich interlayers are loosely bonded by Van der Waals force. At a high temperature exceeding ~873 K, 3R-MoN 2 transforms into hexagonal δ-MoN through the degassing of N 2 and this disassociation temperature increases as pressure increases. Besides, 3R-MoN 2 is weakly antiferromagnetic, may resulting from the occurrence of magnetic zigzag edges in the structure. Moreover, the nitride behaves as a semiconductor with E g = 0.50(1) eV.  Table 2. Magnetic parameters of 3R-MoN 2 derived from the magnetic susceptibility measurements. The magnetic susceptibility data were fitted to the Curie-Weiss law χ = C/(T − T Θ ) in two different temperature ranges of 130-300 K and 2-30 K.