Journal of Materials Science & Technology  2019 , 35 (10): 2297-2304 https://doi.org/10.1016/j.jmst.2019.05.035

Orginal Article

Prediction of stable high-pressure structures of tantalum nitride TaN2

Wandong Xingac, Zijie Weib, Rong Yuc, Fanyan Menga*

a Department of Physics, University of Science and Technology Beijing, Beijing Engineering Research Center of Detection and Application for Weak Magnetic Field, Beijing, 100083, China
b School of Automation, University of Science and Technology Beijing, Beijing, 100083, China
c National Center for Electron Microscopy in Beijing, School of Materials Science and Engineering, Key Laboratory of Advanced Materials of Ministry of Education of China, State Key Laboratory of New Ceramics and Fine Processing, Tsinghua University, Beijing, 100084, China

Corresponding authors:   * Corresponding author.E-mail address: meng7707@sas.ustb.edu.cn (F. Meng).

Received: 2018-12-3

Revised:  2019-02-21

Accepted:  2019-03-20

Online:  2019-10-05

Copyright:  2019 Editorial board of Journal of Materials Science & Technology Copyright reserved, Editorial board of Journal of Materials Science & Technology

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Abstract

Structure searches based on a combination of first-principles calculations and a particle swarm optimization technique unravel two new stable high-pressure structures (C2/m and Cmce) for TaN2. The structural features, mechanical properties, formation enthalpies, electronic structure, and phase diagram of TaN2 are fully investigated. Being mechanically and dynamically stable, the two phases could be made metastable experimentally at ambient conditions.

Keywords: Particle swarm optimization ; First-principles ; Tantalum nitride ; Crystal structure ; High pressure

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Wandong Xing, Zijie Wei, Rong Yu, Fanyan Meng. Prediction of stable high-pressure structures of tantalum nitride TaN2[J]. Journal of Materials Science & Technology, 2019, 35(10): 2297-2304 https://doi.org/10.1016/j.jmst.2019.05.035

1. Introduction

Transition metal (TM) nitrides are of great interests for their importance in both fundamental science and technological applications [[1], [2], [3], [4], [5]]. Experimentally, the progress of high pressure and high temperature (HPHT) experimental technique has greatly widened the territory of these materials. Recently, several TM dinitrides have been successfully synthesized under HPHT, including PtN2 [6], OsN2 [7], IrN2 [8], ReN2 [9], RuN2 [10], RhN2 [11], PdN2 [12], TiN2 [13], CoN2 [14], and FeN2 [15]. Theoretically, the first-principles pseudopotential plane-wave method has been proved to be a useful tool for predicting new materials. At present, there are two effective methods. Firstly, the USPEX or CALYPSO codes employ high-throughput calculations to search the stable structures and have a high success rate, such as in developing the low-temperature phase diagrams of Ti-N [16], Zr-N [17], Nb-N [18], Ru-N [19], Hf-N [20], Ta-N [21], W-N [22], and Re-N [23] systems. However, this takes enormous computing resources. Secondly, it is very likely to find stable structures employing in the prototypes of related compounds, since chemically related compounds might have similar structures. Recently, it has been shown that the structure types of transition metal phosphides can be stabilized in the corresponding nitrides at high pressures [24]. This intuitive and heuristic method requires much fewer computing resources and has been successfully used for the prediction of new materials, with many synthesized later. For example, PtN2, IrN2, and OsN2 were shown to have the pyrite-, CoSb2-, and marcasite-type crystal structures, respectively. They correspond to those of PtP2 [5], IrP2 [25,26], and OsP2 [25], respectively.

The binary Ta-N system displays rich crystal chemistry. Experimentally, hexagonal (P63/mmc, No.194) and trigonal (P$\bar{3}$1m, No.162) Ta2N were synthesized [27,28]. The TaN includes three structures: CoSn- (P6/mmm, No.191), NaCl- (Fm$\bar{3}$m, No.225), and WC-type (P$\bar{3}$m2, No.187) [[29], [30], [31], [32]]. The Ta5N6 and Ta4N5 crystallize with hexagonal (P63/mcm, No.193) [33] and tetragonal (I4/m, No.87) [28], respectively. Single crystals of Ta3N5 are obtained by the reaction of TaCl5 with NH3Cl crystallizing in the orthorhombic space group Cmcm (No.63) [34]. Very recently, U3Te5- and U3Se5-type polymorphs of Ta3N5 were synthesized by combining metastable precursors with high pressure-temperature treatment [35]. The two structure types have the same space group (Pnma, No.62), but different atomic configurations. Recently, orthorhombic (Pbnm, No.62) Ta2N3 [36] was synthesized under HPHT conditions, exhibiting U2S3-type structure. Theoretically, Zhao et al. [37] considered eight structures of TaN and proved that TaN in hexagonal structure (P$\bar{6}$2m, No.189) is the most stable at ambient conditions. Jiang et al. [38] unveiled a tetragonal (P$\bar{4}$m2, No.115) Ta2N3 structure that is energetically more favorable than the experimentally observed orthorhombic U2S3-type Ta2N3 at zero pressure. In addition, Kroll et al. [2] investigated the possible preparation of novel nitrides of tantalum, and predicted the crystal structures of Ta3N5 (U3Te5- and U3Se5-type). It was shown that the U3Te5-type structure is thermodynamically more stable than the U3Se5-type [35,39]. Recently, however, tantalum nitrides with N-rich stoichiometries (TaNx, x ≥ 2) have also been widely investigated. TaN2, within four different structures fluorite-type (Fm$\bar{3}$m, No.225), pyrite-type (Pa$\bar{3}$, No.205) and two hexagonal structures (P63/mmc, No.194; P$\bar{6}$m2, No.187), have been systematically studied [40,41]. Besides, Yan et al. [42] indicated that TaN2, with the P4/mbm (No.127) structure, is mechanical and dynamically stable at ambient pressure. In addition, Li et al. [21] uncovered a synthesizable new composition monoclinic (P21/m, No.11) TaN3 with strong covalent N-N bonds chains along the crystallographic b axis.

In this study, crystal structures and their stabilities of TaN2 have been explored. Two stable high-pressure structures have been revealed, i.e. the monoclinic structure (C2/m, No.12, hereinafter referred to as TaN2-12-I) and the orthorhombic structure (Cmce, No.64, hereinafter referred to as TaN2-64). The energetics of all the tantalum nitrides aforementioned have been systematically calculated using first-principles method. The phase stability, elastic and electronic properties of TaN2 were investigated. The results show that TaN2-12-I and TaN2-64 are stable mechanically, dynamically, and thermodynamically, and can be synthesized at high pressures.

2. Computational methods

In this study, the structures of TaN2 with up to six formula units (f. u.) were searched at the pressures of 0, 30, 50, 70 and 100 GPa using the particle swarm optimization method as implemented in the CALYPSO code [43,44]. The density functional theory (DFT) calculations were performed using the projector-augmented wave (PAW) method [[45], [46], [47]], as implemented in the Vienna Ab-initio Simulation Package (VASP) code [48]. The generalized gradient approximation [49] (GGA) with the Perdew-Burke-Ernzerhof (PBE) scheme was used to describe the exchange-correlation function. For Ta and N, the electronic configurations of 5d36s2 and 2s22p3 were chosen, respectively. Geometry optimization was carried out using the conjugate gradient algorithm. The plane-wave cutoff energy was 520 eV. The k-points were generated using the Monkhorst-Pack mesh [50]. The k-point sampling in the Brillouin zone and the plane-wave cutoff energy were tested to ensure that the total energies converged to 1 meV per atom. The structural relaxations were performed until the residual forces and stresses were less than 0.001 eV/Å and 0.01 GPa, respectively. Lattice parameters and atomic positions were optimized simultaneously.

The elastic constants were calculated using the universal-linear-independent coupling-strains (ULICS) method [51], which is computationally efficient and has been widely used in calculations of single-crystal elastic constants [52,53]. Based on the single-crystal elastic constants, the bulk modulus B and the shear modulus G were calculated according to the Voigt-Reuss-Hill orientation-averaging scheme [54]. The hardness (Hv) values were estimated using an empirical formula [55,56], Hv = 2 (G3/B2)0.585 - 3.

Phonon dispersions were calculated using the direct supercell method, as implemented in the PHONOPY code [57,58]. The Crystal Orbital Hamilton Population (COHP) analysis [59] has been performed to determine the bonding properties of the electronic states close to the Fermi level, as implemented in the LOBSTER code [60,61].

The formation enthalpies of tungsten nitrides TaxNy for various stoichiometries were calculated using the equation, ΔH=HTaxNy-xHTa-yHN2/2, where the bcc phase of Ta and the experimental high-pressure phases of nitrogen were adopted in the calculations (the ζ-N2 was replaced by cg-N due to its structural uncertainty) [23,[62], [63], [64]].

3. Results and discussion

For structures that are stable in metal phosphides but not in nitrides at the ambient pressure, it is highly possible to stabilize them in nitrides at high pressures [24]. Hence, we have considered the tantalum phosphides, i.e. TaP2-type (C2/m, No.12, hereinafter referred to as TaN2-12-II). In addition, the structures we have considered are based on the chemically related compounds, i.e. NbN2-type (TaN2-64), which is predicted using the ab initio evolutionary algorithm [22]. The relaxed lattice parameters and formation enthalpy of TaN2 are listed in Table 1 at zero pressure together with calculated data. Besides, the crystal structures, relaxed lattice parameters, and formation enthalpy of the other Ta nitrides experimentally and theoretically, are listed in Tables S1 and S2 (see Supplementary materials). The calculated values in this study are in good agreement with the previous results. The total energies of TaN2 as a function of volume for different structure types are plotted in Fig. 1. It is clearly shown that none of them has the lowest energy at all the volume. The new phase TaN2-12-I was shown to be the most stable structure at low pressure, which is searched using the particle swarm optimization method as implemented in the CALYPSO code. At high pressures, the new phase TaN2-64 is thermodynamically stable.

Table 1   Calculated lattice parameters a, b, c, and formation enthalpy ΔH at 0 GPa.

Phasea(Å)b(Å)c(Å)ΔH(eV/atom)
TaN2-12-I6.8193.2898.259-0.765
TaN2-12-II7.2932.9246.171-0.551
TaN2-6412.3344.2044.205-0.497
TaN2-127 (P4/mbm)4.4092.846-0.293
4.403a2.839a-0.317a
TaN2-187 (P$\bar{6}$m2)3.1113.802-0.448
3.101b3.816b
TaN2-194 (P63/mmc)3.0667.780-0.456
3.054b7.788b
TaN2-205 (pyrite-type)5.120-0.138
5.127b

a Ref. [42].b Ref. [40].

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Fig. 1.   Energy-volume relationships for TaN2.

The crystal structures of TaN2 are schematically shown in Fig. 2. All of these phases have a common structural feature, namely the N2 units. Typical single N-N bond length in TaN2-12-I, TaN2-12-II, and TaN2-64 are 1.42 Å, 1.38 Å, and 1.37 Å, respectively. Similarly, the N-N distances in the noble-metal pernitrides are 1.41 Å for PtN2, 1.43 Å for OsN2, and 1.42 Å for IrN2. The crystal structures of TaN2-12-I and TaN2-12-II are very similar. The two structures have the same space group and Wyckoff positions. However, the atomic coordination in them is slightly different. The Ta atoms have seven coordinated N atoms in TaN2-12-I, but eight in TaN2-12-II. Both structures have two types of atomic coordination for N. A half of N atoms form one N-N and three Ta-N bonds like in the noble-metal pernitrides. The other half of N atoms form Ta-N bonds only, but the number is different for the two structures (four for TaN2-12-I but five for TaN2-12-II). The differences suggest that it is heuristic but not sufficient to consider the corresponding TM phosphides only for the prediction of TM nitrides.

Fig. 2.   Crystal structures for (a) TaN2-12-I: β = 138.4°, the Ta atoms occupy 4i (0.5560, 0, 0.7313) positions, and the N atoms occupy 4i (0.2154, 0, 0.3510) and 4i (0.2846, 0.5, 0.6490) positions; (b) TaN2-12-II: β = 118.8°, the Ta atoms occupy Wyckoff positions 4i (0.1791, 0, 0.2151), and the N atoms occupy 4i (0.1037, 0, 0.5294) and 4i (0.3963, 0.5, 0.4706) positions; (c) TaN2-64: the Ta atoms occupy the 8d (0.8687, 0, 0) positions, and the N atoms occupy 8d (0.8086, 0.5, 0) and 8f (0.5, 0.6151, 0.6151) positions. The large and small spheres represent W, Ta, and N atoms, respectively.

The global stability of TM nitrides can be quantified by constructing the thermodynamic convex hull within considered pressures, which is defined as the average atom formation enthalpy of the most stable phases at each composition. Fig. 3 shows the calculated convex hulls and pressure-composition phase diagrams of the Ta-N system at pressures of 0-100 GPa.

Fig. 3.   Convex hull diagrams for W-N system at pressures of (a) 0, (b) 20, and (c) 70 GPa, respectively. Stable phases are denoted black solid squares. (d) Pressure-composition phase diagrams of Ta-N system.

As shown in Fig. 3, the ground states of the Ta-N system include Ta2N-162, TaN-189, Ta5N6-193, and Ta3N5-63 at zero pressure, and the result is different from that of Li et al. [21]. Ta2N-162 is thermodynamically stable at 0-100 GPa, which is the only stable stoichiometric Ta-N compound with the N concentration less than 50% at 0-100 GPa. TaN-189 can be thermodynamically stable up to 7 GPa, and then a phase transition to TaN-187 appears at this pressure. The result is in accordance with previous study [37]. For the ground state Ta5N6-193 and Ta3N5-63, they are thermodynamically stable up to 9 GPa and 6 GPa, respectively. Besides, our calculations indicate that Ta4N5-87 is a metastable phase, which is accord with the results of Stampfl et al. [65]. However, the stoichiometric 3:5 phases are unstable at pressures between 6-18 GPa toward decomposition into N and Ta2N3 compound, and Ta3N5-62 (U3Te5-type) can be stable at pressures above 18 GPa. The stable pressure of Ta2N3-115 should be more than 2 GPa with respect to decomposition into Ta3N5-63 and Ta5N6-193, and a phase transition from Ta2N3-115 to Ta2N3-62 can be detected at 8 GPa. The N-rich tantalum nitrides are all high-pressures phases. And for Ta dinitrides, we proposed that TaN2-12-I and TaN2-64 can be synthesized at elevated pressures of above 9 GPa and 65 GPa, respectively. However, our proposed TaN2-12-I can be thermodynamically stable at wide pressures of 9-21 GPa, while TaN3-11 can be thermodynamically stable at pressures of 12-71 GPa.

The dynamical and mechanical stabilities of TaN2-12-I and TaN2-64 are examined by calculating phonon dispersions and elastic constants. As shown in Fig. 4, it is clear that no imaginary phonon frequency can be found in the whole Brillouin zone at zero pressure and high pressures. This indicates that both TaN2-12-I and TaN2-64 are dynamically stable at different pressures, and it is important for the technological applications of the new phase. The calculated elastic constants Cij, bulk modulus B, shear modulus G, Young’s modulus E, and hardness HV of the Ta-N system compounds are summarized in Tables 2 and S3 (see Supplementary materials). The calculated values in this work are in good agreement with the previous calculation values. Clearly, the TaN2-12-I and TaN2-64 satisfying the elastic stability criteria [26] indicates that it is mechanically stable. In addition, the TaN2-64 having high bulk modulus indicates that it is difficult to be compressed. The hardness of the TaN2-12-I and TaN2-64 being 7.9 GPa and 13.8 GPa suggests that they are hard materials.

Fig. 4.   Phonon dispersion curves of TaN2-12-I at (a) 0 GPa and (b) 20 GPa, and TaN2-64 at (c) 0 GPa and (d) 70 GPa.

Table 2   Calculated elastic constants Cij (GPa), bulk modulus B (GPa), shear modulus G (GPa), Young’s modulus E (GPa) and hardness HV (GPa) at 0 GPa.

C11C22C33C44C55C66C12C13C23BGEHV
TaN2-12-I57640842716990981702162252861143027.9
TaN2-64647647639344697111211526932315840813.8

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In order to explain the origin of the stability of the TaN2-12-I and TaN2-64, the electronic structures of the two new phases have been analyzed. The density of states and band structure at zero pressure and high pressures are plotted in Fig. 5, Fig. 6. It is revealed that the two phases are metallic with non-zero DOS values at the Fermi level. And, Ta-d orbital hybridizes strongly with N-p orbital and forms covalent bonding below the Fermi level.

Fig. 5.   The total density of states (TDOS) and partial density of states (PDOS) for TaN2-12-I at (a) 0 GPa and (b) 20 GPa, and TaN2-64 at (c) 0 GPa and (d) 70 GPa. The black vertical dashed lines denote the Fermi level at zero.

Fig. 6.   Calculated band structures of TaN2-12-I at (a) 0 GPa and (b) 20 GPa, and TaN2-64 at (c) 0 GPa and (d) 70 GPa. The black horizontal lines denote the Fermi level at zero.

For TaN2-12-I, there is a valley (sometimes called pseudogap) close to the Fermi level. In general, the electronic states with lower energies than the valley are bonding orbitals, and those with higher energies are antibonding orbitals [66]. To clarify the nature of the chemical bonding near the Fermi level, we have performed the -COHP analysis at zero pressure and high pressures, which gives an idea about the participating orbital pair. The results are shown in Fig. 7 for the Ta-N and Ta-Ta bonds in the TaN2-12-I and TaN2-64. The calculation results are consistent at different pressures. The Ta-N interactions are much stronger than the Ta-Ta interactions and dominate the bonding states for both TaN2-12-I and TaN2-64. The positive value of the projected COHP (-pCOHP) represents the bonding states and negative value represents the antibonding states. As shown in Fig. 7a for TaN2-12-I, it is clear that the pseudogap separates the bonding and antibonding states. It is suggested that the high stability and strong bonding of the TaN2-12-I are derived from an optimized electronic situation that involves the nearly full-filling of bonding states. A deeper valley means that the bonding orbitals are more stabilized and the antibonding orbitals are more destabilized, forming strong chemical bonds. Therefore, the stability and the abnormal mechanical properties of TaN2-12-I can be attributed to the pseudogap effect [67,68]. While in TaN2-64, it can be seen that one finds partially filled antibonding states at the Fermi level. This is consistent with the results of DOS, since there is a peak at the Fermi level. The integrated projected COHP (-IpCOHP) for pairwise interactions are listed in Table 3. The calculated results are in good agreement with the above discussions. Though there are two non-equivalent N sites in TaN2-12-I, the two types of Ta-N bonds are identical. For TaN2-64, there are two different types of Ta-N bonds, and both Ta-N-I and Ta-N-II have the same tendency near the Fermi level.

Fig. 7.   Crystal orbital Hamilton population analyses (-pCOHP) for (a) TaN2-12-I and (b) TaN2-64 at zero pressure and high pressures.

Table 3   Bond distances (Å) and average values of -IpCOHP (eV) of TaN2-12-I and TaN2-64 at 0 GPa and high pressures.

TaN2-12-ITaN2-64
BondLength-IpCOHPBondLength-IpCOHP
0 GPa20 GPa0 GPa20 GPa0 GPa70 GPa0 GPa70 GPa
Ta—N—I2.087-2.1962.059-2.1554.0004.236Ta—N—I2.186, 2.2292.086, 2.1303.3683.880
Ta—N—II2.087-2.1962.059-2.1554.0004.236Ta—N—II2.3402.2052.4152.976
Ta—Ta3.289, 3.2993.206, 3.2290.4160.492Ta—Ta2.973, 3.2392.834, 3.0370.5550.725

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Note that TaN2 is thermodynamically less stable than the mixture of Ta3N5 and N2 at ambient condition according to the convex hull. Since it is mechanically and dynamically stable, however, it could be made metastable experimentally at ambient condition. A recent example is FeO2 (FeS2-type structure), which is stable above 70 GPa but metastable at lower pressures [69,70].

4. Conclusions

In summary, the ground state and high-pressure phases have been systematically explored in the Ta-N system at 0-100 GPa using a combination of first-principles calculations and swarm-intelligence-based CALYPSO method. The crystal structure, phase stability, electronic structure, and mechanical properties of tantalum pernitride TaN2 have been studied. It is demonstrated that the two new phases (C2/m and Cmce phases) of TaN2 are thermodynamically, mechanically, and dynamically stable, and can be synthesized under pressures above 9 GPa and 65 GPa, respectively.

Acknowledgements

This work was supported by National Natural Science Foundation of China (Nos. 51871021, 51788104, 51525102, 51390475), and the Fundamental Research Funds for the Central Universities (FRF-BD-18-005A). We used the resources of Shanghai Supercomputer Center and National Center for Electron Microscopy in Beijing.

Appendix A. Supplementary data

Supplementary material related to this article can be found, inthe online version, at doi:https://doi.org/10.1016/j.jmst.2019.05.035.


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