J. Mater. Sci. Technol. ›› 2019, Vol. 35 ›› Issue (10): 2297-2304.DOI: 10.1016/j.jmst.2019.05.035
• Orginal Article • Previous Articles Next Articles
Wandong Xingac, Zijie Weib, Rong Yuc, Fanyan Menga*()
Received:
2018-12-03
Revised:
2019-02-21
Accepted:
2019-03-20
Online:
2019-10-05
Published:
2019-08-28
Contact:
Meng Fanyan
Wandong Xing, Zijie Wei, Rong Yu, Fanyan Meng. Prediction of stable high-pressure structures of tantalum nitride TaN2[J]. J. Mater. Sci. Technol., 2019, 35(10): 2297-2304.
Phase | a(?) | b(?) | c(?) | ΔH(eV/atom) |
---|---|---|---|---|
TaN2-12-I | 6.819 | 3.289 | 8.259 | -0.765 |
TaN2-12-II | 7.293 | 2.924 | 6.171 | -0.551 |
TaN2-64 | 12.334 | 4.204 | 4.205 | -0.497 |
TaN2-127 (P4/mbm) | 4.409 | 2.846 | -0.293 | |
4.403a | 2.839a | -0.317a | ||
TaN2-187 (P$\bar{6}$m2) | 3.111 | 3.802 | -0.448 | |
3.101b | 3.816b | |||
TaN2-194 (P63/mmc) | 3.066 | 7.780 | -0.456 | |
3.054b | 7.788b | |||
TaN2-205 (pyrite-type) | 5.120 | -0.138 | ||
5.127b |
Table 1 Calculated lattice parameters a, b, c, and formation enthalpy ΔH at 0 GPa.
Phase | a(?) | b(?) | c(?) | ΔH(eV/atom) |
---|---|---|---|---|
TaN2-12-I | 6.819 | 3.289 | 8.259 | -0.765 |
TaN2-12-II | 7.293 | 2.924 | 6.171 | -0.551 |
TaN2-64 | 12.334 | 4.204 | 4.205 | -0.497 |
TaN2-127 (P4/mbm) | 4.409 | 2.846 | -0.293 | |
4.403a | 2.839a | -0.317a | ||
TaN2-187 (P$\bar{6}$m2) | 3.111 | 3.802 | -0.448 | |
3.101b | 3.816b | |||
TaN2-194 (P63/mmc) | 3.066 | 7.780 | -0.456 | |
3.054b | 7.788b | |||
TaN2-205 (pyrite-type) | 5.120 | -0.138 | ||
5.127b |
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.
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.
C11 | C22 | C33 | C44 | C55 | C66 | C12 | C13 | C23 | B | G | E | HV | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
TaN2-12-I | 576 | 408 | 427 | 169 | 90 | 98 | 170 | 216 | 225 | 286 | 114 | 302 | 7.9 |
TaN2-64 | 647 | 647 | 639 | 344 | 69 | 71 | 112 | 115 | 269 | 323 | 158 | 408 | 13.8 |
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.
C11 | C22 | C33 | C44 | C55 | C66 | C12 | C13 | C23 | B | G | E | HV | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
TaN2-12-I | 576 | 408 | 427 | 169 | 90 | 98 | 170 | 216 | 225 | 286 | 114 | 302 | 7.9 |
TaN2-64 | 647 | 647 | 639 | 344 | 69 | 71 | 112 | 115 | 269 | 323 | 158 | 408 | 13.8 |
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.
TaN2-12-I | TaN2-64 | ||||||||
---|---|---|---|---|---|---|---|---|---|
Bond | Length | -IpCOHP | Bond | Length | -IpCOHP | ||||
0 GPa | 20 GPa | 0 GPa | 20 GPa | 0 GPa | 70 GPa | 0 GPa | 70 GPa | ||
Ta—N—I | 2.087-2.196 | 2.059-2.155 | 4.000 | 4.236 | Ta—N—I | 2.186, 2.229 | 2.086, 2.130 | 3.368 | 3.880 |
Ta—N—II | 2.087-2.196 | 2.059-2.155 | 4.000 | 4.236 | Ta—N—II | 2.340 | 2.205 | 2.415 | 2.976 |
Ta—Ta | 3.289, 3.299 | 3.206, 3.229 | 0.416 | 0.492 | Ta—Ta | 2.973, 3.239 | 2.834, 3.037 | 0.555 | 0.725 |
Table 3 Bond distances (?) and average values of -IpCOHP (eV) of TaN2-12-I and TaN2-64 at 0 GPa and high pressures.
TaN2-12-I | TaN2-64 | ||||||||
---|---|---|---|---|---|---|---|---|---|
Bond | Length | -IpCOHP | Bond | Length | -IpCOHP | ||||
0 GPa | 20 GPa | 0 GPa | 20 GPa | 0 GPa | 70 GPa | 0 GPa | 70 GPa | ||
Ta—N—I | 2.087-2.196 | 2.059-2.155 | 4.000 | 4.236 | Ta—N—I | 2.186, 2.229 | 2.086, 2.130 | 3.368 | 3.880 |
Ta—N—II | 2.087-2.196 | 2.059-2.155 | 4.000 | 4.236 | Ta—N—II | 2.340 | 2.205 | 2.415 | 2.976 |
Ta—Ta | 3.289, 3.299 | 3.206, 3.229 | 0.416 | 0.492 | Ta—Ta | 2.973, 3.239 | 2.834, 3.037 | 0.555 | 0.725 |
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