Stability, Elastic and Electronic Properties of Ta₂N by First-Principles Calculations

Abstract

Owing to exploring the influence of the N atoms ordering in Ta₂N compounds on their properties, the stability, elastic, and electronic properties of Ta₂N compounds (Ta₂N-I: P$\overline{3}$ml and Ta₂N-II: P$\overline{3}$1m) were investigated using first-principles calculations based on density functional theory. Ta₂N-II is energetically favorable according to the enthalpy of formation. Elastic constants were employed to reveal the stronger resistance to deformation, but weaker anisotropy, in Ta₂N-II. A ductile-brittle transition was found between Ta₂N-I (ductile) and Ta₂N-II (brittle). The partial density of states showed a stronger orbital hybridization of Ta-d and N-p in Ta₂N-II, resulting in stronger covalent bonding. The charge density difference illustrated the interaction of the Ta-N bond and electron distribution of Ta₂N.

1. Introduction

The transition metal nitrides (TMNs) have widespread applications and motivate intense research because of their outstanding properties, such as good mechanical, thermal stability, electronic, and optical properties [1,2,3,4,5,6]. Tantalum nitrides (TaN_x) possess a series of equilibrium and metastable structures with various excellent properties, showing a remarkable richness of applications, including hard coatings for cutting tools, thin-film resistors, and diffusion barriers in integrated circuits [7,8,9,10,11,12]. The change of growth conditions generates different phase and chemical compositions of polycrystalline TaN_x, whose structures and properties vary greatly. Experimentally [7,13,14,15,16,17], ε-TaN (No.191, $P6/mmm$), π-TaN (No.189, $P\overline{6}2m$), δ-TaN (No.225, $Fm\overline{3}m$), ϑ-TaN (No.187, $P\overline{6}m2$), Ta₂N (No.162, $P\overline{3}1m$), Ta₃N₅ (No.63, $Cmcm$), Ta₄N₅ (No.87, $I4/m$), Ta₅N₆ (No. 193, $P{6}_3/mcm$), and η-Ta₂N₃ (No.62, $Pbnm$) etc., have been synthesized by controlling growth conditions, and have attracted further study on their properties. Limited by the imperfection of X-ray diffraction (XRD), the structural difference (slight shift of N) between ε-TaN and π-TaN had not been distinguished until the application of neutron diffraction [18]. After detailed investigation, a similar phenomenon was found in Ta₂N. In reality, there are two structures in Ta₂N compounds (which are called Ta₂N-I and Ta₂N-II for convenience in this work). Terao et al. [14] detected hexagonal close-packed γ-Ta₂N (Ta₂N-I), also called β-Ta₂N, with lattice parameters a = 3.05 Å, c = 4.92 Å (Space group, No.164) through XRD. Moreover, they also discovered the other structure of Ta₂N (Ta₂N-II) with lattice parameters a = 5.28 Å, c = 4.92 Å (Space group, No.162), due to a different ordering of N atoms, characterized by electron diffraction, which can display many weak peaks invisible in XRD. As the characterization techniques developed, neutron diffraction was employed by Conroy and Christensen to further confirm this structure (Ta₂N-II) [19]. It is because of the ordering of vacancies that Ta₂N-II come into being, which was presented by Friedrich et al. [20]. The same structure of Ta₂N-II was also found in Cr₂N [21], V₂N [22], and Nb₂N [23] compounds. By comparing the two structures of Ta₂N, it is found that partial N atoms migrate to the gap between two Ta atom layers and leave corresponding vacancies in the N atom layer. Thus, the atomic stacking model changes from N-Ta-Ta-N-Ta-Ta-··· of Ta₂N-I to N-Ta-N-Ta-··· of Ta₂N-II. To sum up, the shift of N atoms generates the vacancies of the initial N atom layers in Ta₂N-I, making a contribution to the formation of Ta₂N-II.

Compared to Ta₂N-II, Ta₂N-I was very exciting for researchers. Cu diffusion studies [24] applied using density functional theory (DFT) showed that Ta₂N-I can effectively prevent undesired Cu diffusion as an effective diffusion barrier material. The electronic and elastic properties of Ta₂N-I were explored using first-principles calculation by Yu et al. [25]. Hence, it is significant to explore the properties of Ta₂N-II, and clarify differences between Ta₂N-I and Ta₂N-II. In this work, the stability, elastic, and electronic properties of Ta₂N-I and Ta₂N-II were illustrated thoroughly using first-principles calculations based on DFT. The enthalpies of formation were calculated for stability comparison. Elastic constants were computed using a high-efficiency stress-strain method for elastic studies. Partial density of states (PDOS) and charge density difference (CDD) were applied for electronic research. Relevant results can promote the scientific study and commercial application of Ta₂N.

2. Model and Calculation Method

2.1. First-Principles Calculations

The crystal structure information of Ta₂N-I and Ta₂N-II with space groups $P\overline{3}m1$ and $P\overline{3}1m$, respectively, are shown in

Table 1. Crystal structure information of Ta₂N-I and Ta₂N-II with space groups $P\overline{3}m1$ and $P\overline{3}1m$, respectively.

Structure	Space Group	Atom	Wyckoff Notation	x	y	z
Ta2N-I	$P\overline{3}m1$	Ta	2d	1/3	2/3	z
		Ta	2d	2/3	1/3	z
		N	1a	0	0	0
Ta2N-II	$P\overline{3}1m$	Ta	6k	1/3	0	z
		Ta	6k	2/3	0	z
		Ta	6k	0	1/3	z
		Ta	6k	0	2/3	z
		Ta	6k	1/3	1/3	z
		Ta	6k	2/3	2/3	z
		N	2d	1/3	2/3	1/2
		N	2d	2/3	1/3	1/2
		N	1a	0	0	0

.

Figure 1 illustrates clearly the difference of crystal structure from different viewpoints. First-principles calculations were used for the Ta₂N-I and Ta₂N-II using the Vienna Ab initio Simulation Package (VASP) 5.4.1 version [26,27]. The generalized gradient approximation (GGA) parameterized by Perdew-Burke-Ernzerhof (PBE) [28] and the projector augmented wave (PAW) [29] method, with an energy cut-off of 600 eV, were employed for the exchange-correlation effects and ion-electron interactions, respectively.

The k-point meshes were Γ-centered 17 × 17 × 9, 9 × 9 × 11, 15 × 15 × 15 for the bulk Ta₂N-I, Ta₂N-II, bcc Ta; and 1 × 1 × 1 for the molecule (N₂), respectively. Herein, total energy calculations were performed in a large supercell of 14 Å × 15 Å × 16 Å for the N₂ molecule. The tetrahedron method with Blöchl corrections [30] was adopted for accurate total energy and electronic structure in integration of reciprocal space. The selected valence electrons were 5p⁶5d⁶6s² for Ta, and 2s²2p³ for N. All systems were calculated with the convergence criteria 0.02 eV/Å for forces on ions, and 0.01 meV/atom for electrons, respectively.

In order to obtain the equilibrium structure, the four-parameter Birch-Murnaghan equation of state (EOS) was applied to fit the energy vs. volume (E-V) data points [31,32]:

$$E(V)=a+b{V}^{-\frac{2}{3}}+c{V}^{-\frac{3}{4}}+d{V}^{-\frac{3}{6}}$$

(1)

where a, b, c, and d are fitting parameters. This EOS can estimate the equilibrium total energy E₀, volume V₀, bulk modulus B₀, and its pressure derivative B₀′.

To compare Ta₂N-I and Ta₂N-II in terms of their thermodynamic stability, enthalpy of formation at 0 K, $E_{\mathrm{f}}$ (kJ/mol), was calculated as:

$$E_{\mathrm{f}}=\frac{(E_{{\mathrm{Ta}}_2\mathrm{N}}-n{E}_{\mathrm{Ta}}-\frac{n}{2}{E}_{\mathrm{N}})F}{N}$$

(2)

where $E_{{\mathrm{Ta}}_2\mathrm{N}}$ is the total energy of Ta₂N, and $E_{\mathrm{Ta}}$, $E_{\mathrm{N}}$ are the energy per atom of bcc Ta and one N₂ molecule, respectively. n and N are the atom numbers of Ta and all atoms in bulk Ta₂N. F is Faraday’s constant.

The charge density difference (also called deformation charge density) can be calculated as [33]:

$$\Delta \rho =\rho ({\mathrm{Ta}}_2{\mathrm{N}}_{\mathrm{self}\text{-}\mathrm{consistent}})-\rho ({\mathrm{Ta}}_2{\mathrm{N}}_{\mathrm{atomic}})$$

(3)

where ρ(Ta₂N_{self-consistent}) is the total charge densities obtained by self-consistent calculation. The superposition of the atomic charge densities, ρ(Ta₂N_atomic), can be acquired by non-self-consistent calculation.

2.2. Elastic Calculations

The elastic constants were calculated by the strain-stress method, as demonstrated by Shang et al. [6,34,35,36]. For this methodology, the strains ($\epsilon =({\epsilon }_1,{\epsilon }_2,{\epsilon }_3,{\epsilon }_4,{\epsilon }_5,{\epsilon }_6)$, where ${\epsilon }_1$, ${\epsilon }_2$, ${\epsilon }_3$ are normal strains and ${\epsilon }_4$, ${\epsilon }_5$, ${\epsilon }_6$ are shear strains) of a crystal are imposed through specifying the lattice vectors in Cartesian coordinates, as shown in Equation (4). The lattice vectors, R, after deformation can be described as:

$$R=\left[\begin{array}{ccc}{a}_1& a_2& a_3\\ b_1& b_2& b_3\\ c_1& c_2& c_3\end{array}\right]\left[\begin{array}{ccc}1+{\epsilon }_1& {\epsilon }_6/2& {\epsilon }_5/2\\ {\epsilon }_6/2& 1+{\epsilon }_2& {\epsilon }_4/2\\ {\epsilon }_5/2& {\epsilon }_4/2& 1+{\epsilon }_3\end{array}\right]$$

(4)

where $\overrightarrow{a}=(a_1,a_2,a_3)$ is the lattice vector before deformation. $\overrightarrow{a}$, $\overrightarrow{b}$, and $\overrightarrow{c}$ are the same.

In this work, linearly independent and isotropic strains were used, and the strain was set to ±0.01. By first-principles calculations, the corresponding set of stresses $\sigma =({\sigma }_1,{\sigma }_2,{\sigma }_3,{\sigma }_4,{\sigma }_5,{\sigma }_6)$ of the deformed crystal with set of strains $\epsilon =({\epsilon }_1,{\epsilon }_2,{\epsilon }_3,{\epsilon }_4,{\epsilon }_5,{\epsilon }_6)$ could be obtained. The elastic constants ($C_{ij}$) are then acquired through the general Hook’s law $C_{ij}={\epsilon }^{-1}\sigma$:

$$\left[\begin{array}{cccccc}{C}_{11}& C_{12}& C_{13}& C_{14}& C_{15}& C_{16}\\ C_{21}& C_{22}& C_{23}& C_{24}& C_{25}& C_{26}\\ C_{31}& C_{32}& C_{33}& C_{34}& C_{35}& C_{36}\\ C_{41}& C_{42}& C_{43}& C_{44}& C_{45}& C_{46}\\ C_{51}& C_{52}& C_{53}& C_{54}& C_{55}& C_{56}\\ C_{61}& C_{62}& C_{63}& C_{64}& C_{65}& C_{66}\end{array}\right]={\epsilon }^{-1}\sigma$$

(5)

This equation can be solved via the singular value decomposition method to get the least square solutions of the elastic constants.

For a trigonal crystal with space groups $P\overline{3}m1$ and $P\overline{3}1m$, there are six independent single crystal elastic constants (C₁₁, C₁₂, C₁₃, C₁₄, C₃₃, and C₄₄). The mechanical stability can be determined by the Born-Huang [37] criterion as:

$$C_{11}-\left|C_{12}\right|>0,(C_{11}+C_{12})C_{33}>2C_{13}^2,(C_{11}-C_{12})C_{44}>2C_{14}^2$$

(6)

Then, the Voigt and Reuss bounds of bulk modulus and shear modulus are [38]:

$$B_{\mathrm{V}}=\frac{1}{9}(2C_{11}+2C_{12}+4C_{13}+C_{33})$$

(7)

$$B_{\mathrm{R}}=\frac{(C_{11}+C_{12})C_{33}-2C_{13}^2}{(C_{11}+C_{12}-4C_{13}+2C_{33})}$$

(8)

$$G_{\mathrm{V}}=\frac{1}{30}(7C_{11}-5C_{12}-4C_{13}+3C_{33}+12C_{44})$$

(9)

$$G_{\mathrm{R}}=\frac{15}{2}{\left[\frac{2C_{11}+2C_{12}+4C_{13}+C_{33}}{(C_{11}+C_{12})C_{33}-2C_{13}^2}+\frac{3C_{11}-3C_{12}+6C_{44}}{(C_{11}-C_{12})C_{44}-2C_{14}^2}\right]}^{-1}$$

(10)

Through the Viogt-Reuss-Hill approximation [39], the bulk modulus B, shear modulus G, Young’s modulus E, and Poisson’s ratio ν can be further obtained by:

$$B=\frac{1}{2}(B_{\mathrm{V}}+B_{\mathrm{R}})$$

(11)

$$G=\frac{1}{2}(G_{\mathrm{V}}+G_{\mathrm{R}})$$

(12)

$$E=\frac{9BG}{3B+G}$$

(13)

$$v=\frac{3B-2G}{2(3B+G)}$$

(14)

The anisotropy of elastic properties can induce microcracks and reduce the mechanical durability. Thus, to characterize the elastic anisotropies, the universal elastic anisotropic index (A^U) [40] is described as follow:

$$A^{\mathrm{U}}=\frac{5G_{\mathrm{V}}}{G_{\mathrm{R}}}+\frac{B_{\mathrm{V}}}{B\mathrm{R}}-6$$

(15)

Besides, for trigonal crystals, the three-dimensional (3D) anisotropy of Young’s modulus E can be obtained by the reciprocals of E [41]:

$$E^{-1}=S_{11}(1-l_3^2)+S_{33}{l}_3^4+(2S_{13}+S_{44})l_3^2(1-l_3^2)+2S_{14}{l}_2{l}_3(3l_1^2-l_2^2)$$

(16)

where S_ij are the elastic compliance constants and l_i (i = 1, 2, 3) are the direction cosines:

$$l_1=\sin \theta \cos \varphi$$

(17)

$$l_2=\sin \theta \sin \varphi$$

(18)

$$l_3=\cos \theta$$

(19)

here, $\theta$ is the angle between a certain direction and crystal orientation [001]. $\varphi$ is crystal orientation [100]. The greater the deviation of the 3D anisotropy diagram from a sphere (isotropy) is, the higher the degree of anisotropy is.

3. Results and Discussions

3.1. Structure Stabilities

The differences of structure between Ta₂N-I and Ta₂N-II are illustrated in Figure 1 and Table 1. It was revealed that the shift of N atoms between layers changes the symmetry and atomic stacking model of Ta₂N-I, promoting the formation of Ta₂N-II. To compare the structure and stability of Ta₂N-I and Ta₂N-II, the lattice parameters and enthalpies of formation were calculated, as shown in

Table 2. The calculated lattice parameters (Å) and enthalpies of formation E_f (kJ/mol) of Ta₂N-I and Ta₂N-II.

Method	Structure	Space Group	a = b (Å)	c (Å)	Enthalpy of Formation (kJ/mol)
this work	Ta2N-I	$P\overline{3}m1$	3.110	4.896	−78.61
Exp. [14]			3.05	4.92	-
Exp. [42]			3.047	4.918	−84.81
Exp. [43]			3.054	4.996	-
USPP-GGA [25]			3.1756	4.9433	-
PBE-GGA [24]			3.11	4.88	-
this work	Ta2N-II	$P\overline{3}1m$	5.325	4.962	−89.43
Exp. [14]			5.28	4.92	-
Exp. [19]			5.285	4.919	-
GGA [23]			5.38	4.98	−95.62

. With regard to lattice parameters, a good agreement is shown between our calculated values and the reference data [14,19,24,25,42,43]. Especially, the calculated lattice parameters (a = 3.110 Å, c = 4.896 Å) of Ta₂N-I were very close to the results (a = 3.11 Å, c = 4.88 Å) [24] calculated through the same pseudo-potential (GGA-PBE), which confirms the reliability of this work.

In Figure 2, the total energies of Ta₂N-I and Ta₂N-II are plotted as a function of volume through Birch-Murnaghan equation of state fitting. It is shown that Ta₂N-II has lower energies in the whole variation range of volume. As for the enthalpies of formation, the negative values, −78.61 kJ/mol for Ta₂N-I and −89.43 kJ/mol for Ta₂N-II, declare that both structures are stable, agreeing well with experimental [42] and theoretical [23] results.

It is worth noting that a more negative enthalpy of formation of Ta₂N-II means it is more energetically favorable than Ta₂N-I. Therefore, the ordering change of N atoms in Ta₂N-II brings a more stable atomic stacking model (N-Ta-N-Ta-···) for Ta₂N compound, comparing to the close-stacking (N-Ta-Ta-N-Ta-Ta-···) in Ta₂N-I. That is because the N atoms between the two Ta atom layers can generate covalent bond (Ta-N) layer by layer in Ta₂N-II but not in Ta₂N-I. In addition, Figure 3 demonstrates the variation of bond length between the two structures.

Only one kind of Ta-N bond with the bond length 2.184 Å exists in Ta₂N-I. However, two types of Ta-N bond, with the shorter bond length (2.155 Å and 2.174 Å), are found in Ta₂N-II, owing to the different ordering of N atoms. The covalent bond (Ta-N) with a shorter bond length means a stronger bond strength. This also makes a contribution to the higher stability of Ta₂N-II.

3.2. Elastic Properties

To further investigate the difference in properties between Ta₂N-I and Ta₂N-II, elastic constants were calculated to reveal their elastic properties. There are six independent elastic constants in a trigonal system: C₁₁, C₁₂, C₁₃, C₁₄, C₃₃, and C₄₄, as shown in

Table 3. The calculated independent elastic constants $C_{ij}$ (GPa) of Ta₂N-I and Ta₂N-II.

Method	Structure	C11	C12	C13	C14	C33	C44
this work	Ta2N-I -	440	136	214	−51	432	125
USPP-GGA [25]		403	125	215	−52	385	123
this work	Ta2N-II	476	168	195	0	473	167

. According to the Born-Huang [37] criterion, both structures are mechanically stable. The difference between our calculated data of Ta₂N-I and the other theoretical values [25] was acceptable because of the different pseudo-potential (ultrasoft pseudo-potential, USPP) used for calculations. Comparing the C_ij of Ta₂N-I and Ta₂N-II, all the absolute values of C_ij increased except for C₁₃ and C_14. The reduction of the C₁₄ absolute value reveals that the Ta₂N-II became less anisotropic than Ta₂N-I.

The calculated bulk modulus B, shear modulus G, Youngs’ modulus E, Poisson’s ratio ν, B/G ratio, the universal elastic anisotropic index A^U, and mechanical stability are summarized in

Table 4. The calculated bulk modulus B (GPa), shear modules G (GPa), Youngs’ modulus E (GPa), Poisson’s ratio ν, B/G ratio, universal elastic anisotropic index A^U, and mechanical stability of Ta₂N-I and Ta₂N-II.

Structure	BV	BR	B	GV	GR	G	E	v	B/G	AU	Mechanical Stability
Ta2N-I	271	269	270	145	113	129	334	0.29	2.09	1.42	stable
Ta2N-II	282	282	282	171	154	163	410	0.26	1.73	0.55	stable

. A crystal with a higher bulk modulus B signifies a lesser compressibility. Shear modulus G describes the resistance of a material to shear stress. Young’s modulus is considered as a measure of the stiffness of a solid.

It was shown that Ta₂N-II possesses a higher bulk modulus B, shear modulus G, and Youngs’ modulus E. This means Ta₂N-II is harder to deform than Ta₂N-I. In addition, the intrinsic ductility and brittleness of Ta₂N can be estimated by Poisson’s ratio ν [44] and B/G ratio [45]. ν> (<)0.26, B/G ratio> (<)1.75 can be regarded as a performance index to distinguish brittle (ductile) materials. Notably, as shown in Table 4, the ν (0.29) and B/G ratio (2.09) decreased to 0.26 and 1.73 in the structural change from Ta₂N-I to Ta₂N-II, respectively. Namely, Ta₂N-I is ductile and Ta₂N-II is brittle. Hence, a different ordering of N atoms in Ta₂N-II leads to a ductile-brittle transition in Ta₂N compounds, which can markedly impact the mechanical properties. Furthermore, the universal elastic anisotropic index (A^U) and the 3D Young’s modulus anisotropy were calculated to characterize the elastic anisotropy of Ta₂N compounds. Ta₂N-II with A^U = 0.55 behaved with a weaker elastic anisotropy than Ta₂N-I (1.42). Isotropic materials show the shape of a sphere in the 3D diagram of Young’s modulus anisotropy. Figure 4 clearly demonstrates the difference of anisotropy between Ta₂N-I and Ta₂N-II. Obviously, the shape is more like a sphere in Figure 4b, corresponding to the weaker anisotropy of Ta₂N-II. A crystal with weaker anisotropy means the possibility of stress concentration is lower and the microcracks are harder to extend. Therefore, the higher resistance to deformation of Ta₂N-II was further confirmed.

3.3. Electronic Properties

To further probe the influence of the ordering change of N atoms in Ta₂N compounds, the total and partial density of states were calculated, and are presented in Figure 5. Comparing Figure 5a,b, the similarities of the two structures are as follows.

The positive values of DOS at the Fermi level indicate the metallic characteristic of Ta₂N-I and Ta₂N-II. The conduction bands and the upper valence bands (−5~0 eV) mainly consist of Ta-d states. While, the middle valence bands (−10~−5 eV) are primarily dominated by Ta-d states and N-p states. N-s states occupy the lower valence bands around −17 eV. Both Ta₂N-I and Ta₂N-II revealed the hybridization between N-p and Ta-d orbitals, proving the formation of the covalent bond, which was confirmed to be favorable to the hardness and shear resistance of the materials [46]. However, the energy region of Ta-N hybridization broadens (from −6~−8eV to −5~−8eV) in Ta₂N-II. It is implied that the ordering change of N atoms enhances the hybridization of Ta-d and N-p states and the overlaps of valence bonds between N and Ta atoms. The shorter bond lengths in Figure 3 of Ta-N bond in Ta₂N-II also contribute to the hybridization enhancement. This can explain the elevation of shear modulus in Ta₂N-II. Furthermore, the max energy of density of states distribution decreases from 7 eV in Ta₂N-I, to 3 eV in Ta₂N-II, which is beneficial to the higher stability of Ta₂N-II.

For analyzing the bonding interaction and electron transfer of Ta and N atoms, charge density difference was calculated, as shown in Figure 6. Herein, Figure 6a,b illustrate the sectional view of charge density difference of the (110) lattice plane in Ta₂N-I and the (100) lattice plane in Ta₂N-II, respectively. The lattice plane (110) of Ta₂N-I and (100) of Ta₂N-II are equivalent. The red areas denote the gain in electrons, and the blue areas are the loss of electrons.

Moreover, Figure 6c–f exhibit the side and top view of charge density difference of Ta₂N-I and Ta₂N-II, in which the blue and yellow regions indicate the gain and the loss of electrons, respectively. Electrons transfer from Ta to N during the formation of the Ta-N bond. The electrons shared between the Ta and N atoms show the interaction of Ta and N, indicating the orbital hybridization of Ta-d and N-p. Moreover, in Figure 6a, the electron distribution is also found between two Ta atom layers in Ta₂N-I. That means there is an interaction between Ta and Ta atoms in Ta₂N-I. However, such a phenomenon becomes unapparent in Ta₂N-II, owing to the ordering change of N atoms, as shown in Figure 6b. It is clear that the electrons no longer accumulate around the Ta atoms like Ta₂N-I. It can be seen in Figure 6d,f that these electrons transfer and assemble around the new N atom layer formed in the Ta₂N-II. Thus, the ordering change of N atoms has an outstanding influence on the electron distribution of Ta₂N. As seen in Figure 6c–f, the electron distribution of Ta₂N-II is more homogeneous in the unit cell than that of Ta₂N-I, which may explain why the anisotropy of Ta₂N-I is stronger.

4. Conclusions

The stability, elastic, and electronic properties of Ta₂N-I and Ta₂N-II were investigated using DFT-based first-principles calculations. The calculated lattice parameters, enthalpies of formation, and elastic constants were a good match with the references, which confirms the reliability of our calculations. According to the enthalpy of formation, Ta₂N-II is energetically favorable compared to Ta₂N-I, due to the formation of a more stable atomic stacking model (N-Ta-N-Ta···) and the stronger covalent bond (Ta-N) in Ta₂N-II. As for the elastic properties, Ta₂N-II possesses a higher bulk modulus B, shear modulus G, and Youngs’ modulus E; but a weaker anisotropy. Especially, a ductile-brittle transition was found between Ta₂N-I (ductile) and Ta₂N-II (brittle). It can be assumed from the partial density of states that both Ta₂N-I and Ta₂N-II are metallic. In addition, Ta₂N- II revealed the stronger orbital hybridization of Ta-d and N-p, resulting in stronger covalent bonding, which can explain the elevation of shear modulus. The charge density difference clearly illustrates the interaction of the Ta-N bond and electron distribution difference between Ta₂N-I and Ta₂N-II. These analyses of property differences, because of the ordering change of N atoms in Ta₂N compounds can further promote their application and research.