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To search new hard or superhard materials in transition-metal light-element compounds is a current research focus. Most of the past researches focused on binary phases such as transition metal borides, carbides and nitrides, while the researches on ternary phases were relatively rare. The single crystals Nb 3B 3C and Nb 4B 3C 2were synthesized recently by using Al-Cu alloys as auxiliary metals and their structures were determined by Hillebrechtand Gebhardt. In the present paper, 29 TM 3B 3C and 29 TM 4B 3C 2configurations are constructed by TMatoms ( TM= Sc to Zn, Y to Cd, Hf to Hg) replacing Nb atoms in the known Nb 3B 3C and Nb 4B 3C 2configuration. By calculating the formation energy from first-principles density functional theories, only 13 TM 3B 3C and 11 TM 4B 3C 2phases are stable compared with the three elemental substances of TM, boron and carbon. However compared with the most competing phases, only Ta 3B 3C, Nb 3B 3C and Nb 4B 3C 2phases are stable thermodynamically. The metastable Ta 4B 3C 2phase at 0 K becomes stable when temperature is higher than 250 K. Thus two new phases of Ta 3B 3C and Ta 4B 3C 2are uncovered to be stable thermodynamically. Global structure searches conducted by the popular USPEX and CALYPSO softwares prove the Ta 3B 3C and Ta 4B 3C 2phases to be the most favorable energetically. By calculating the phonon dispersion curves of the Ta 3B 3C and Ta 4B 3C 2phase, no imaginary phonon frequencies are observed in the whole Brillouin zone, which demonstrates the dynamical stability of the Ta 3B 3C and Ta 4B 3C 2phase. The calculated elastic constant of the Ta 3B 3C and Ta 4B 3C 2phases satisfy the criteria of mechanical stability, showing that the Ta 3B 3C and Ta 4B 3C 2phase are stable mechanically. The calculations of band structure and density of state show that the Ta 3B 3C and Ta 4B 3C 2phases are both conducting, which mainly arises from the d electrons of Ta atoms. The calculated bulk modulus and shear modulus of the Ta 3B 3C and Ta 4B 3C 2phases show their brittle nature. The hardness of Ta 3B 3C and Ta 4B 3C 2phase are nearly the same and calculated to be about 26 GPa by Chen’s and Tian’s models, which illuminates that the two phases are hard but not superhard.
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Keywords:
- hard materials/
- first-principles calculations/
- stability/
- hardness
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模型 晶系和空间群 晶格参数(Å, degree) 原子坐标 Nb3B3C OrthorhombicCmcm a= 3.284, 3.265a,b= 28.877, 28.710a,c= 3.144, 3.129a,α=β=γ= 90 Nb1 (4c) (0, 0.2128, 0.25), Nb2 (4c) (0, 0.3620, 0.25), Nb3 (4c) (0, 0.4532, 0.25), B1 (4c) (0, 0.1120, 0.25), B2 (4c) (0, 0.0155, 0.25), B3 (4c) (0, 0.0790, 0.25), C (4c) (0, 0.2878, 0.25) Nb4B3C2 OrthorhombicCmcm a= 3.257, 3.229a,b= 37.874, 37.544a,c= 3.153, 3.133a,α=β=γ= 90 Nb1 (4c) (0, 0.1621, 0.75), Nb2 (4c) (0, 0.2805, 0.75), Nb3 (4c) (0, 0.3946, 0.75), Nb4 (4c) (0, 0.4642, 0.25), B1 (4c) (0, 0.0854, 0.75), B2 (4c) (0, 0.0118, 0.25), B3 (4c) (0, 0.0602, 0.25), C1 (4c) (0, 0.2202, 0.75), C2 (4c) (0, 0.3383, 0.75) Ta3B3C OrthorhombicCmcm a= 3.267,b= 28.688,c= 3.133,α=β=γ= 90 Ta1 (4c) (0, 0.2121, 0.25), Ta2 (4c) (0, 0.3619, 0.25), Ta3 (4c) (0, 0.4531, 0.25), B1 (4c) (0, 0.1130, 0.25), B2 (4c) (0, 0.0155, 0.25), B3 (4c) (0, 0.0791, 0.25), C (4c) (0, 0.2874, 0.25) Ta4B3C2 OrthorhombicCmcm a= 3.243,b= 37.609,c= 3.141,α=β=γ= 90 Ta1 (4c) (0, 0.1615, 0.75), Nb2 (4c) (0, 0.2806, 0.75), Nb3 (4c) (0, 0.3945, 0.75), Nb4 (4c) (0, 0.4641, 0.25), B1 (4c) (0, 0.0861, 0.75), B2 (4c) (0, 0.0118, 0.25), B3 (4c) (0, 0.0602, 0.25), C1 (4c) (0, 0.2202, 0.75), C2 (4c) (0, 0.3380, 0.75) 注:a文献[17]中的实验值. 
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TM TM3B3C TM4B3C2 $\Delta {H_{{\rm{elements}}}}$ $\Delta {H_{{\rm{comp}}}}$ 最稳定竞争组合 $\Delta {H_{{\rm{elements}}}}$ $\Delta {H_{{\rm{comp}}}}$ 最稳定竞争组合 Sc –0.637 0.071 6ScB2+ Sc4C3+ Sc2C = 4Sc3B3C –0.520 0.144 10ScB2+ 4Sc4C3+ Sc2BC2= 7Sc4B3C2 Ti –0.896 0.019 9TiB2+ TiC + Ti8C5= 6Ti3B3C –0.863 0.018 9TiB2+ 7TiC + Ti8C5= 6Ti4B3C2 V –0.687 0.101 3VB + C = V3B3C –0.628 0.092 18VB + 7C + V6C5= 6V4B3C2 Cr –0.294 0.159 3CrB + C = Cr3B3C –0.194 0.178 9CrB + 4C + Cr3C2= 3Cr4B3C2 Mn –0.100 0.195 3MnB + C = Mn3B3C 0.024 Fe 0.002 0.139 Co 0.094 0.255 Ni 0.296 0.456 Cu 0.738 0.959 Zn 0.713 0.929 Y –0.385 0.089 9YB2+ 5Y2C + Y2B3C2= 7Y3B3C –0.283 0.160 6YB2+ 8Y2C + 3Y2B3C2= 7Y4B3C2 Zr –0.851 0.019 3ZrB2+ 2ZrC + Zr = 2Zr3B3C –0.838 0.020 3ZrB2+ 4ZrC + Zr = 2Zr4B3C2 Nb –0.698 –0.023 3NbB + C = Nb3B3C –0.661 –0.002 C + 6Nb3B3C + Nb6C5= 6Nb4B3C2 Mo –0.257 0.175 3MoB + C = Mo3B3C –0.155 0.202 3MoB + C + MoC = Mo4B3C2 Tc –0.005 0.326 12TcB2+ 11C + 3Tc7B3= 11Tc3B3C 0.138 Ru 0.211 –0.369 Rh 0.230 –0.406 Pd 0.552 0.744 Ag 1.027 1.295 Cd 0.846 1.112 Hf –0.920 0.016 3HfB2+ 2HfC + Hf = 2Hf3B3C –0.922 0.018 3HfB2+ 4HfC + Hf = 2Hf4B3C2 Ta –0.704 0.003 3Ta3B4+ C + 3TaC = 4Ta3B3C –0.691 –0.010 3Ta3B4+ C + 7TaC = 4Ta4B3C2 W –0.094 0.227 3WB + C = W3B3C –0.007 0.273 3WB + C + WC = W4B3C2 Re 0.281 0.425 Os 0.590 0.755 Ir 0.604 0.758 Pt 0.708 0.855 Au 1.096 1.310 Hg 1.186 1.333 DownLoad:
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结构 弹性常数 力学性能a 硬度 C11 C22 C33 C44 C55 C66 C12 C13 C23 B G B/G HChen HTian Ta3B3C 569.6 514.4 563.5 194.1 180.0 261.8 187.1 147.3 173.9 295.9 200.8 1.47 25.3 25.3 Ta4B3C2 581.1 535.3 602.1 197.3 185.1 275.8 200.3 146.0 170.2 305.7 209.0 1.46 26.2 26.2 Nb3B3C 544.3 479.8 522.8 181.5 171.9 245.3 170.9 132.9 162.2 275.3 189.7 1.45 24.8 24.7 Nb4B3C2 551.5 499.2 548.5 184.0 175.1 257.1 183.2 132.7 157.8 282.9 195.8 1.44 25.5 25.4 TaB2 302 200 1.51 24.4 24.5 NbB2 287 195 1.47 24.8 24.8 TaC 324 215 1.51 25.6 25.9 NbC 239 161 1.48 21.6 21.4 SiC 213 187 1.14 33.6 32.2 Al2O3 232 147 1.58 18.7 18.7 TiN 259 180 1.44 24.3 24.0 注:a二元相力学性能数据来自Materials Project网站. DownLoad:
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[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28]
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