Polar Nitride Perovskite LaWN3‐δ with Orthorhombic Structure

Abstract Nitride perovskite LaWN3 has been predicted to be a promising ferroelectric material with unique properties for diverse applications. However, due to the challenging sample preparation at ambient pressure, the crystal structure of this nitride remains unsolved, which results in many ambiguities in its properties. Here, the authors report a comprehensive study of LaWN3 based on high‐quality samples synthesized by a high‐pressure method, leading to a definitive resolution of its crystal structure involving nitrogen deficiency. Combined with theoretical calculations, these results show that LaWN3 adopts an orthorhombic Pna2 1 structure with a polar symmetry, possessing a unique atomic polarization along the c‐axis. The associated atomic polar distortions in LaWN3 are driven by covalent hybridization of W: 5d and N: 2p orbitals, opening a direct bandgap that explains its semiconducting behaviors. The structural stability and electronic properties of this nitride are also revealed to be closely associated with its nitrogen deficiency. The success in unraveling the structural and electronic ambiguities of LaWN3 would provide important insights into the structures and properties of the family of nitride perovskites.

The difficulty in definitive structural resolution of nitride perovskites is primarily due to the challenging sample preparation using traditional approaches at ambient pressure. [1,4,5] In fact, most of those nitrides are thermodynamically unstable at atmospheric pressure and readily decompose by degassing N 2 . [1,4] Besides, oxygen is usually involved and difficult to avoid as an impurity species in preparing oxygen-free nitrides. As a result, most previously reported products are poorly-crystallized oxynitrides (e.g., LaWO 0.6 N 2.4 ) with unwanted impurities, [22][23][24][25][26] hindering solving their structures. An oxygen-free thin-film LaWN 3 sample www.advancedsciencenews.com www.advancedscience.com has recently been prepared; the piezoelectric measurement suggests it has a polar structure. [13,27] However, the crystallinity of the thin-film sample is still insufficient to produce excellent X-ray and electron diffraction signals for achieving definitive structural resolution, and there exists a number of structures that cannot be discernible including polar symmetries of R3c, P4mm, Pmc2 1 , and Pna2 1 . Because the polar structure is closely associated with the N atoms that are insensitive to both the x-ray and electrons, it is difficult to determine ferroelectric distortions by conventional methods.
The methodological advancement towards synthesizing highquality LaWN 3 samples is crucial for addressing the associated issues. High pressure (P) and temperature (T) synthesis is in this regard a powerful approach for preparation of nitrogen-rich metal nitrides. [28,29] A surge of recent studies along this direction has led to the discovery of many exotic metal nitrides with promising properties. [28][29][30][31][32][33] However, most of those syntheses involve a direct nitridation of metal and the required pressure is high (i.e., above 10 GPa), which is beyond the current technological capability for massive production. Using soft solid-state reaction routes, numerous nitrogen-rich nitrides have been obtained at moderate pressures. [9,[34][35][36][37] In stark contrast, reports on high-P synthesis of nitride perovskites are sparse except for a recentlyreported triclinic LaReN 3 metal. [38,39] Here, we extend the high P-T synthesis to the family of nitride perovskites with a focus on LaWN 3 by means of soft reaction routes and successfully synthesize high-quality LaWN 3 samples. The definitive structure of this nitride is determined to have a polar Pna2 1 symmetry, rather than previously proposed R3c based on thin-film samples. [27] The stabilities and properties of these samples are then explored, which provide powerful insights into the electronic origin of structural stability and the structureproperty relationship.

Results and Discussion
A favorable route is exploited to synthesize LaWN 3 from a reaction between La 2 W 2 O 9 and NaNH 2 at 2-5 GPa and temperatures of 600-2100°C, leading to high-quality nitride samples. The material is compositionally constituted by La, W, and N with a molar ratio of ≈1:1:3 as determined by energy-dispersive Xray (EDX) experiments (Figures S1-S4, Supporting Information). Note that the nitride can also be synthesized from a distinct reaction between LaN, W, and NaNH 2 without involvement of oxygen ( Figure S3, Supporting Information), suggesting it is oxygen-free LaWN 3 . Complicating matter further is that our AES measurements indicate a small amount of oxygen may be involved, giving rise to a possible composition of LaWO x N 3-x (x ≈ 0.25) (Figure S4, Supporting Information). However, for most transitionmetal (TM) nitrides, the oxygen concentration cannot be accurately determined solely by any one of the commonly accessible methods. Instead, it requires complementary experimental measurements including AES, EDX, XPS, TG-MS, and structural refinements using XRD and NPD data, combined with careful analysis. Bearing this in mind, we have determined the oxygen concentration in our sample, showing a nearly negligible level with x ≈ 0 in LaWO x N 3-x , and more details will be shown below. Because the sample can be prepared at a moderate pressure of 2-5 GPa, the lowest among high-P syntheses of ternary metal nitrides, it is practically feasible for massive and industrial-scale production.
All the observed X-ray diffraction (XRD) peaks of the sample can initially be indexed by a Pm3m-perovskite structure with a ≈ 3.992 Å (Figure 1a), especially for the samples synthesized below 1200°C, showing increasing peak broadening as the temperature decreases ( Figure S1, Supporting Information). This, combined with the disordered lattice ( Figure S2, Supporting Information), indicates a low sample crystallinity. However, for the samples synthesized above 1600°C, the single-crystal samples can be obtained with crystallite size up to 200 μm ( Figure S1, Supporting Information), and each the otherwise broadened peak of the low-T sample splits into a set of reflection lines (Figure 1a), indicative of a low-symmetry derivative of cubic perovskite. Thus, the previously proposed rhombohedral and tetragonal structures are quickly excluded such as R3c and I-44 [19,25,27] (Figures S5-S6, Supporting Information). Instead, the XRD pattern can only be appropriately indexed with an orthorhombic cell. Due to the insensitivity of N to X-rays, the structure of LaWN 3 cannot be determined by the X-ray-only experiment. Indeed, several symmetries can reach the same refinement including Pnma, Pna2 1 , and Pmc2 1 ( Figure S7, Supporting Information), making them indistinguishable.
We thus perform the neutron powder diffraction (NPD) measurements to accurately determine nitrogen, because N has a greater scattering length than those of La and W. [40] The resultant NPD pattern in Figure 1b has a different subset of strong peaks that are almost invisible in the XRD pattern. Although the different N positions can be well refined for each orthorhombic model using our NPD data, a similar excellence of refinement is achieved and hence the structural ambiguity still retains. Using the refined Pnma, Pna2 1 , and Pmc2 1 , we simulate their electron powder diffraction (EPD) patterns, showing apparent peak differences in the low-2Θ range mainly associated with the N atoms ( Figures (Figure 1e), whereas other models cannot correctly reproduce the observed diffraction pattern (Figures 1f-g). We thus conclude that the polar Pna2 1 symmetry is most suitable for LaWN 3-. Note that the polar symmetry is also strongly evidenced by our SHG experiments ( Figure S10, Supporting Information). The refined lattice parameters are summarized in Table 1 and the crystal structure is plotted in Figure 1h and Figure S11, Supporting Information. The presence of vacancies at N1 and N2 sites leads to a composition of LaWN 2.6 . Note that previous calculations by Fang et al. indicate that stoichiometric Pna2 1 -LaWN 3 is a metastable phase, although it is dynamically favorable. [11] The presence of atomic defects may make Pna2 1 thermodynamically more stable, rather than the predicted ground state of R3c. However, for the previous thin-film samples prepared at a relatively low temperature of 900°C by Talley et al., [27] the sample crystallinity is seemingly not enough for obtaining high-quality XRD data with sharp diffraction peaks, especially for the high-angle peaks, similar to that of our high-P samples synthesized at 5 GPa and below 1200°C (see Figure  (1) are almost identical to their ideal coordinates of ¼ and ½, respectively, by which a same excellence of refinement reaches. S1, Supporting Information). Clearly, using XRD patterns with broadened peak profiles, it is difficult to determine its definitive crystal structure, leading to a misassigned R3c for LaWN 3-. From this viewpoint, the crystal structure of such-reported thin-film samples should also be Pna2 1 , rather than R3c.
To explore the electronic structure of LaWN 3-, the binding energies of La3d, W4f, and N1s are determined by x-ray photoelectron spectroscopy (XPS) measurements. Due to the spin-orbit coupling, both the La3d 5/2 and 3d 3/2 states split into a doublet with a similar energy split of ∆E ≈ 3.4 eV (Figure 2a), close to that of nearly purely ionic La 3+ [41,42] (Figure S13, Supporting Information), indicating that La has an excellent electropositivity in analogy to alkali and alkaline-earth metals for donating electrons during reaction. Thus, the role of La played in the formation LaWN 3-is to donate electrons to its adjacent N, leading to nitrogen reduction; this in turn oxidizes more electronegative W and eventually drives covalent hybridization of W and N under the inductive effect. [4] In fact, the determined high hardness of the sample (i.e., ≈9 GPa) also suggests its strong covalency ( Figure S12, Supporting Information). In Figure 2b, the doublet of W4f 7/2 and 4f 5/2 for LaWN 2.6 has intermediate binding energies between those of W and WO 2 , [43] using the established relationship between the binding energy and valence state of W, based on a number of known W-bearing materials (see Figure  S13, Supporting Information). The thus-evaluated valence W 2+ is much distinct from the nominal valence W 4.8+ , further signaling the strong W-N covalency. Due to the surface oxidation effect, an additional W4f doublet is also observed and likely associated with a WO 2+x compound, [44] which can profoundly be reduced if the sample surface is etched and cleaned by Ar + irradiation before experiments (Figure 2b and Figure S4j), Supporting Information. By contrast, the La3d line are nearly intact after etching [ Figure  S4(k)], implying that LaWN 3-has a similar valence state to that of the surface La-O oxide; this is not unexpected because La is so electropositive for donating the same number of electrons during the formation of LaWN 3-or surface La-O oxide. For the N1s, a small binding energy is determined with a value close to that of ScN semiconductor (i.e., ≈396.1 eV) (Figure 2c), [45] implying a similar metal-N bonding state for opening a bandgap. Our ultraviolet-visible (UV-Vis) absorption experiment of the sample shows a clear absorption edge with a small bandgap of ≈0.66 eV, in conjunction with resistivity measurements (Figures 2d-e), suggesting it is likely a semiconductor. Besides, its resistivity is ≈2 mΩ cm, comparable with that of ScN with a bandgap of ≈0.9 eV [46] or graphite with characteristics of a bad metal. Such an unexpectedly small bandgap in LaWN 2.6 is probably due to the suppression of polar distortion that results from nitrogen deficiency as discussed later ( Figure S18, Supporting Information). Besides, due to the electron-filling effect induced by nitrogen deficiency, our calculations show that LaWN 2.6 should have metallic band structures ( Figure S18, Supporting Information), inconsistent with semiconducting behaviors as observed in optical absorption experiments. Such contraindicated properties may be attributed to the size effect and other types of crystalline imperfections such as lattice disorder/stress, atomic deficiencies at cation positions, and low crystallinity, which would greatly alter electronic properties of nitride materials, as previously reported in other metal nitrides (e.g., CrN and TiN). [47][48][49][50] Those intriguing properties of metal nitrides are probably attributed to the unique electronegativity of N. [4,5] Our thermogravimetric analysis indicates LaWN 2.6 starts to oxidize at ≈600°C in air and transforms into La 2 W 2 O 9 (Figure 2f), by which the nitrogen concentration x in LaWN x is estimated to be ≈2.5 (5), consistent with the refined x = 2.6. In argon, it decomposes by degassing N 2 at ≈990°C. The situation is greatly changed at high pressure, and the sample's thermal stability is profoundly prompted up to 2100°C at 5 GPa without obvious decomposition ( Figure S3, Supporting Information), showing the effectiveness of pressure for synthesizing nitrides. Nevertheless, the nitrogen deficiency of the high-P samples is still difficult to alleviate, mainly because of a relatively smaller electronegativity of nitrogen, compared with oxygen.
To examine the dependence of phase stability on nitrogen deficiency, the energies of two competing structures of R3c and Pna2 1 are calculated by introducing nitrogen vacancies ( ) in LaWN 3-. [51][52][53][54][55][56][57] In Figure 3a, R3c is more stable if is below 0.3, while increasing above 0.375 can lead to a R3c-to-Pna2 1 crossover, which well explains the reason why Pna2 1 -LaWN 2.6 is more favorable for our samples. In principle, the nitrogen vacancies serve as electron donors and make the material conductive.
To check this, we performed calculations by adding excess electrons into its conduction band, resulting in a similar trend of stabilities for R3c and Pna2 1 . The most stable Pna2 1 -LaWN 3-can be achieved when an additional 0.124 -0.20 electrons/formula cell (f.u.) are added, indicating that nitrogen deficiency is key to stabilizing Pna2 1 -LaWN 2.6 . On the other hand, the thus-enhanced metallicity of LaWN 2.6 with free carries would screen the longrange Coulomb field [58] and hence destabilize ferroelectricity (see Figures S17-S18, Supporting Information).
Exploring the lattice instabilities of cubic-LaWN 3 allows for gaining deep insights for rationalizing the stability of Pna2 1 -LaWN 2.6 . Phonon dispersions of cubic-LaWN 3 along the highsymmetry lines of ГX, ГM, and ГR correspond to the [100], [110], and [111] directions of the cell, [57] respectively (Figure 3c-d). It can be seen that the imaginary frequencies mainly arise from a branch of transverse optic (TO) unstable modes that are primarily associated with the W and N atoms.
The unstable R and M modes are related to antiphase and in-phase antiferrodistortive instabilities, characterized by the rotation of neighboring WN 6 octahedra (Figure 3e-f), as commonly seen in oxide perovskites like SrTiO 3 . [59] The unstable modes near Г are dominated by a relative W-N displacement, which breaks the centrosymmetric symmetry, similar to that in BaTiO 3 . [60] The phonon instabilities along the Г-X line can be alleviated and even quenched if enough free electrons are added in Figure 3b), as indicated above. Meanwhile, the instability at R is substantially reduced, which is in contrast to that at M with increased instability, indicating the orthorhombic symmetry becomes more favorable. Therefore, such unique crystal and electronic properties of our LaWN 3-samples can be expected in the presence of excess electrons originated from the nitrogen deficiency.
We further explore electronic properties of Pna2 1 -LaWN 3 . The band structure and density of states (DOS) are shown in Figure 4a-b. It is interesting to see that Pna2 1 -LaWN 3 has a direct bandgap of 1.36 eV without consideration of spin-orbit coupling (SOC) (Figures S14-S15, Supporting Information), different from the metallic cubicPm3m-and Pnma-LaWN 3 . The band edges around the Fermi level are mainly associated with the hybridized W: t 2g -N: p states (i.e., pd bonding/antibonding) (Figure 4b-c), an analogy to that in most oxide perovskites. [61] We find that the bandgap opening in polar-LaWN 3 is primarily due to the cooperative displacement of N relative to W that can lead to more efficient W-N bonding/antibonding (Figure 4c and Figures S15-S16, Supporting Information). Such behaviors correspond to the second-order Jahn-Teller (SOJT) effect, [62] which is responsible for bandgap opening, as seen in many perovskite materials (e.g., BaTiO 3 ). In contrast, the nonpolar phases involve a large portion of W-N antibonding state at the Fermi level ( Figure S15c). The effectively hybridized W-N bonds through the SOJT effect are believed to be essential to compete against the short-range repulsion that favors the nonpolar symmetry, resulting in a polar phase with a large bandgap.
Given the definitively refined structure, the electric polarization of Pna2 1 -LaWN 2.6 can then be well explored, which involves complex octahedral distortions (Figure 4d). A prominent feature is the relative W-N displacement along the N2-W-N2 line with a relative W shift of ≈0.035 Å from the N2-N2 center ( Figure S16, Supporting Information). A smaller displacement occurs along one of the N1-W-N3 lines with a shift of ≈0.016 Å towards N3, while the shift along the other N1-W-N3 line is negligible. Apparently, the electric dipoles of LaWN 2.6 have a unique long-range order along the c-axis with a sinusoidal-like chain of dipole orientation (Figure 4d). The thermal expansion coefficients of the material along the c-axis are greater than those along other axes, suggesting the temperature sensitivity of its structure along the polarization direction, and no phase transition is involved in the 4 -1100 K range, based on our variable-T XRD experiments (Figures S19-S21 and Table S1, Supporting Information). Attempts to identify electric polarization of LaWN 2.6 are unsuccessful by various measurements, due to the current leakage originated from the electron-filling effect of nitrogen deficiency. Future work along this line is warranted to obtain stoichiometric sample and explore exciting ferroelectric properties for driving interesting functionality. Re-treatment of LaWN 3-in N 2 gas at higher pressures (e.g., above 10 GPa) using diamond-anvil cells and laser heating techniques may lead to stoichiometric LaWN 3 with as-predicted semiconducting properties. Alternatively, element substitution would provide another promising approach for obtaining semiconducting nitride perovskites; of particular interest is to replace W with Ta or Hf for reducing the number of 5d valence electrons, because 5d electrons are spatially so delocalized to be itinerant and unfavorable for opening a bandgap.

Conclusions
In summary, we have formulated an effective high-P route for preparing oxygen-free LaWN 3 bulk samples with excellent crystallinity, leading to definitive identification of the crystal structure and composition of Pna2 1 -LaWN 2.6 with a polar symmetry for producing ordered dipoles along the c-axis. Due to the electronfilling effect, the nitrogen deficiency of this nitride is explored to have a profound influence on its phase stability and electronic properties. The strong W: t 2g -N: p hybridization in LaWN 3 formed through the SOJT effect is revealed to be the driving force for polar distortion and bandgap opening. The well-explored structure and properties of LaWN 3 would offer important baseline data for understanding the complex relationships between the composition, chemistry, and crystal and electronic structures of ternary nitrides. Besides, the methodology established in this work can be extended to other nitride perovskites for discovering functional materials that may offer a fertile platform for exploring exotic phenomena at the frontier of condensed matter physics.

Experimental Section
High P-T Synthesis: High-purity La 2 W 2 O 9 and sodium amide (NaNH 2 ) powders in a molar ratio of La 2 W 2 O 9 : NaNH 2 = 1:10 was homogenously mixed for the synthesis of LaWN 3 . The excess NaNH 2 was used to establish a nitrogen-rich environment for a complete ammonization of La 2 W 2 O 9 . Note that La 2 W 2 O 9 was obtained from a stoichiometric reaction between WO 3 and La 2 O 3 (i.e., in a molar ratio of 2:1) at 1400°C for 10 h, using a muffle furnace. High P-T synthesis were carried out using a DS 6 × 10 MN cubic press installed in the high-P lab of SUSTech. [63] Before the experiment, the powder mixture was compacted into a cylindrical pellet of 12 mm in diameter and 10 mm in height, which was then loaded in an hBN or Mo capsule and assembled with the preprepared cell parts. More experimental details can be found elsewhere. [63] Due to the sensitivity of NaNH 2 precursor to air, all the procedures were done in an argon-filled glovebox to avoid possible contaminations. The synthesis was carried out in a wide temperature range of 600 to 2100°C at 5 GPa for 10 -30 min to prepare various samples with different crystallinities for comparative studies. The recovered nitride products were washed with distilled water to remove possible byproducts (e.g., NaOH) and unreacted NaNH 2 , followed by drying in an oven at 80°C. For comparison purposes, we also performed the synthesis from a different reaction between oxygen-free reactants of LaN, W, and NaNH 2 in a molar ratio of 1:1:5 at 5 GPa and 1800°C for 30 min.
Characterization: The final products were checked by X-ray diffraction (XRD) with a Cu K radiation. Variable-T XRD experiments were also carried out in the 4 -1100 K temperature range to study possible phase transitions and lattice thermal expansion at ambient pressure. The neutron powder diffraction (NPD) measurement was performed at the neutron beamline of the China Mianyang Research Reactor (CMRR) and the wavelength of incident neutron beam is = 1.5925 Å. The XRD and NPD data were analyzed using the GSAS and FullProf programs, respectively. The scanning electron microscopy (SEM) equipped with energy-dispersive Xray (EDX), Auger electron spectroscopy (AES), and transmission electron microscopy (TEM) experiments were conducted to study the morphologies, chemical composition, and crystal structure of as-synthesized samples. AES measurements were conducted with a PHI 710 scanning Auger nanoprobe equipped with an argon ion source, and the oxygen detection limit of the instrument is ≈5%. [64,65] To investigate the variation of chemical composition of the sample with depth, the AES data was taken at different depths of 50, 100, 150, and 200 nm, respectively, etched by Ar + ion beam with an etching rate of 23.8 nm min −1 . X-ray photoelectron spectroscopy (XPS) measurements were performed to study the binding energiey of the involved elements of sample.
The ultraviolet-visible (UV-Vis) absorption and electrical transport experiments were performed to determine bandgap and resistivity of the sample, based on single-crystal samples. The dc magnetization data was collected using a Quantum Design SQUID VSM magnetometer. The secondary harmonic generation (SHG) measurements were carried out to check the symmetry of the material with an incident laser wavelength of 880 nm. The thermogravimetric mass spectrometer (TG-MS) measurements were carried out in air and argon, respectively, to investigate the sample's thermal stabilities. The Vickers hardness test was performed on a well-sintered polycrystalline sample prepared at 5 GPa and 1200°C for 30 min. The hardness of the sample was measured at different loads of 50, 100, 200, 500, and 1000 g. At each load, the measurement was repeated for more than five times to obtain statistic averages.
Attempts to identify the ferroelectric properties of our samples were unsuccessful by measuring the hysteresis loop of electric polarization against an external electric field using a ferroelectric analyzer, due to the current leakage originated from the electron-filling effect of nitrogen deficiency that is unfavorable for obtaining robust ferroelectricity.
Computational Methods: First-principles calculations were performed within the density functional theory (DFT) by using the projector augmented wave (PAW) method with a plane-wave basis set with an energy cutoff of 500 eV, as implemented in the VASP code. [51][52][53][54] The generalized gradient approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE) was used to treat the exchange-correlation interactions for structural relaxations, while the HSE06 hybrid function was employed for the simulation of electronic structures. [55,56] The k-point sampling was performed with a Monkhoust-Pack scheme of a 11 × 9 × 11 grid with the Γ point included for orthorhombic cell. The convergence criteria for the Hellmann-Feynman force and total energy were set at 0.005 eV Å −1 and 10 −6 eV, respectively, for structural relaxations. The phonon calculations were done with the help of the phonopy package. [57] The crystal orbital Hamilton population (COHP) analyses were calculated with the LOBSTER package. [66] The energies of the two competing structures of R3c and Pna2 1 were calculated with PBE functional and based on a pristine 2 × 2 × 2 supercell (i.e., La 8 W 8 N 24 ) with involvement of different numbers of nitrogen vacancies (i.e., 0, 1, 2, and 3), by which the supercell can be re-scaled down to one formula unit of LaWN 3-, where corresponds to a normalized nitrogen vacancy number of 0, 1/8, 2/8, and 3/8. In addition, we also simulated the influence of nitrogen deficiency on the structural stability by adding free electrons into the dispersive conduction bands of LaWN 3 . In this case, a homogenous background charge was added for compensation of incorporated free electrons. During electron doping, the internal coordinates, shapes, and unit-cell volume of crystal structure were freely relaxed; besides, the calculated results were weakly affected by volume relaxation. Note that there is no direct numerical equivalence between the number of nitrogen vacancy and free electron doped to the conduction bands. Our calculations indicate that nitrogen vacancy acts as a donor for supplying free electrons into conduction bands. The dipole moments of the electron-doped systems were estimated from the calculations of Born effective charge using polar phases of R3c and Pna2 1 .

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.