Acta Metallurgica Sinica (English Letters) ›› 2019, Vol. 32 ›› Issue (9): 1099-1110.DOI: 10.1007/s40195-019-00873-8
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Yong Zhang1, Zi-Ran Liu2, Ding-Wang Yuan1, Qin Shao1, Jiang-Hua Chen1(), Cui-Lan Wu, Zao-Li Zhang3
Received:
2018-09-07
Revised:
2018-10-31
Online:
2019-09-10
Published:
2019-08-06
Yong Zhang, Zi-Ran Liu, Ding-Wang Yuan, Qin Shao, Jiang-Hua Chen, Cui-Lan Wu, Zao-Li Zhang. Elastic Properties and Stacking Fault Energies of Borides, Carbides and Nitrides from First-Principles Calculations[J]. Acta Metallurgica Sinica (English Letters), 2019, 32(9): 1099-1110.
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Fig. 1 Illustration of SF structure for SG F$\bar{4}$3m a, b, c and Fm$\bar{3}$m d, e, f. Horizontal direction [11$\bar{2}$], vertical direction [111], all viewed from [1$\bar{1}$0]. a, d Perfect supercells, b, e SF1, c, f SF2. Red dash line denotes the SF. Gray and blue spheres represent metal atom and N (or C) atoms, respectively
SG | LCs | C 11 | C 22 | C 33 | C 44 | C 55 | C 66 | C 12 | C 13 | C 23 | B | G | E | v | A | |||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
B | R $\bar{3}$ m | 5.050 | 565 | 505 | 195 | 224 | 117 | 32 | 222 | 220 | 495 | 0.128 | 0.893 | |||||
AlB2 | P6/mmm | 3.009, 3.285 | 557 | 387 | 47 | 229 | 98 | 5 | 191,197a, 191b | 158,132a, 95b | 371 | 0.176 | 0.696 | |||||
AuB2 | P6/mmm | 3.011, 4.245 | 207 | 127 | -23 | -30 | 267 | 87 | ||||||||||
Co2B | I4/mcm | 4.955, 4.259 | 427 | 335 | 103 | 116 | 199 | 173 | 253 | 107 | 282 | 0.314 | 1.019 | |||||
CoB | Pbnm | 3.925, 5.161, 3.065 | 514 | 421 | 484.4 | 159.9 | 201.4 | 147.1 | 217.7 | 216.6 | 223.7 | 304 | 152 | 392 | 0.285 | 1.193 | ||
Cr2B | I4/mcm | 5.127, 4.269 | 518 | 485 | 205 | 198 | 172 | 197 | 295 | 185 | 459 | 0.241 | 1.145 | |||||
CrB | Cmcm | 2.925, 7.841, 2.915 | 505 | 613 | 592 | 222 | 267 | 215 | 186 | 175 | 149 | 303 | 221 | 533 | 0.207 | 1.166 | ||
CrB2 | P6/mmm | 2.960, 3.031 | 550 | 423 | 158 | 209 | 133 | 97 | 242,300a, 239b | 185,171a, 140b | 442 | 0.195 | 0.769 | |||||
Fe2B | I4/mcm | 5.053, 4.232 | 410 | 376 | 144 | 153 | 149 | 126 | 222 | 142 | 350 | 0.237 | 1.169 | |||||
FeB | Pnma | 5.410, 2.948, 3.995 | 388 | 450 | 503 | 208 | 117 | 193 | 240 | 191 | 205 | 290 | 151 | 385 | 0.279 | 2.179 | ||
HfB | Fm$\bar{3}$m | 4.835 | 409 | 55 | 67 | 181 | 101 | 256 | 0.264 | 0.432 | ||||||||
HfB2 | P6/mmm | 3.143, 3.489 | 605 | 465 | 263 | 269 | 67 | 138 | 262,270a, 261b | 248,240a, 233b | 566 | 0.141 | 0.769 | |||||
MgB2 | P6/mmm | 3.073, 3.515 | 433 | 272 | 72 | 189 | 55 | 32 | 153, 157a, 152b | 134, 132a, 116b | 312 | 0.160 | 0.628 | |||||
Mn2B | I4/mcm | 5.059, 4.100 | 534 | 495 | 218 | 163 | 223 | 221 | 321 | 180 | 454 | 0.264 | 1.052 | |||||
MnB | Pnma | 5.446, 2.983, 4.119 | 402 | 518 | 495 | 213 | 164 | 214 | 175 | 151 | 140 | 261 | 181 | 442 | 0.218 | 1.530 | ||
MnB2 | P6/mmm | 2.936, 2.986 | 613 | 388 | 129 | 227 | 159 | 125 | 271, 220b | 177, 122b | 437 | 0.231 | 0.632 | |||||
Mo2B | I4/mcm | 5.545, 4.756 | 500 | 463 | 155 | 162 | 189 | 215 | 300 | 150 | 386 | 0.285 | 1.040 | |||||
MoB | I41/amd | 3.126, 16.990 | 560 | 533 | 213 | 241 | 196 | 204 | 318 | 203 | 503 | 0.236 | 1.325 | |||||
MoB2 | P6/mmm | 3.030, 3.331 | 610 | 431 | 145 | 236 | 137 | 223 | 313, 311a, 303b | 177, 192a, 186b | 446 | 0.263 | 0.708 | |||||
NbB | Cmcm | 3.315, 8.784, 3.180 | 479 | 532 | 519 | 189 | 234 | 207 | 135 | 165 | 118 | 263 | 200 | 478 | 0.197 | 1.119 | ||
NbB2 | P6/mmm | 3.120, 3.338 | 581 | 417 | 207 | 234 | 114 | 196 | 288, 299a, 286b | 201, 220a, 210b | 489 | 0.217 | 0.716 | |||||
Ni2B | I4/mcm | 4.981, 4.269 | 404 | 353 | 85 | 131 | 199 | 169 | 248 | 102 | 268 | 0.320 | 1.279 | |||||
NiB | Cmcm | 2.953, 7.370, 2.986 | 325 | 484 | 405 | 104 | 108 | 120 | 193 | 193 | 160 | 256 | 111 | 291 | 0.311 | 1.198 | ||
OsB2 | Pmmn | 4.705, 2.889, 4.094 | 566 | 552 | 743 | 73 | 184 | 190 | 178 | 172 | 121 | 311 | 182 | 457 | 0.255 | 0.999 | ||
Pd2B | Pnnm | 4.764, 5.150, 3.156 | 218 | 229 | 244 | 55 | 39 | 91 | 175 | 128 | 138 | 175 | 54 | 146 | 0.361 | 3.718 | ||
PtB | P63/mmc | 3.766, 3.647 | 330 | 301 | 47 | 58 | 214 | 247 | 264 | 47 | 134 | 0.416 | 0.912 | |||||
ReB2 | P63/mmc | 2.914, 7.505 | 643 | 1024 | 260 | 244 | 154 | 127 | 348, 355c | 280, 289c | 661 | 0.183 | 1.592 | |||||
RuB2 | Pmmn | 4.667, 2.882, 4.061 | 518 | 460 | 678 | 101 | 210 | 171 | 189 | 142 | 122 | 285 | 176 | 439 | 0.243 | 1.145 | ||
Ta2B | I4/mcm | 5.794, 4.879 | 506 | 429 | 185 | 184 | 104 | 165 | 256 | 178 | 433 | 0.218 | 0.915 | |||||
TaB | Cmcm | 3.294, 8.703, 3.163 | 525 | 594 | 553 | 204 | 261 | 232 | 156 | 198 | 140 | 296 | 218 | 525 | 0.204 | 1.155 | ||
TaB 2 | P6/mmm | 3.099, 3.326 | 598 | 450 | 214 | 227 | 144 | 221 | 313, 341a, 296b | 202, 244a, 192b | 498 | 0.235 | 0.752 | |||||
TiB | Pnma | 6.114, 3.050, 4.561 | 425 | 532 | 417 | 194 | 174 | 218 | 96 | 120 | 62 | 214, 207d | 190, 186d | 441 | 0.157 | 1.155 | ||
TiB2 | P6/mmm | 3.034, 3.225 | 653 | 463 | 256 | 292 | 70 | 116 | 264, 261a, 250b | 258, 271a, 261b | 584 | 0.130 | 0.708 | |||||
VB | Cmcm | 3.041, 8.023, 2.965 | 510 | 665 | 616 | 211 | 275 | 208 | 129 | 157 | 70 | 278 | 235 | 549 | 0.171 | 0.925 | ||
VB2 | P6/mmm | 2.997, 3.025 | 684 | 487 | 221 | 284 | 117 | 138 | 293, 284a, 280b | 243, 247a, 241b | 571 | 0.176 | 0.711 | |||||
W2B | I4/mcm | 5.572, 4.770 | 563 | 528 | 154 | 176 | 211 | 243 | 338 | 161 | 416 | 0.295 | 0.998 | |||||
WB | I41/amd | 3.143, 16.924 | 569 | 551 | 227 | 252 | 230 | 249 | 350 | 205 | 515 | 0.254 | 1.483 | |||||
WB2 | P6/mmm | 3.018, 3.364 | 623 | 421 | 132 | 234 | 154 | 254 | 332, 330a, 323b | 166, 172a, 164b | 428 | 0.285 | 0.675 | |||||
YB2 | P6/mmm | 3.299, 3.867 | 364 | 337 | 158 | 158 | 49 | 79 | 164, 157a, 171b | 152, 150a, 145b | 348 | 0.146 | 0.927 | |||||
YB6 | Pm $\bar{3}$ m | 4.102 | 451 | 30 | 30 | 170 | 102 | 256 | 0.250 | 0.201 | ||||||||
ZrB | Fm$\bar{3}$m | 4.918 | 369 | 55 | 66 | 167 | 94 | 237 | 0.264 | 0.478 | ||||||||
ZrB2 | P6/mmm | 3.175, 3.558 | 563 | 441 | 250 | 252 | 59 | 136 | 247, 229a, 239b | 233, 231a, 231b | 532 | 0.142 | 0.783 |
Table 1 LCs (in ?) and elastic properties (Cij, B, G and E in GPa) of borides at zero pressure
SG | LCs | C 11 | C 22 | C 33 | C 44 | C 55 | C 66 | C 12 | C 13 | C 23 | B | G | E | v | A | |||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
B | R $\bar{3}$ m | 5.050 | 565 | 505 | 195 | 224 | 117 | 32 | 222 | 220 | 495 | 0.128 | 0.893 | |||||
AlB2 | P6/mmm | 3.009, 3.285 | 557 | 387 | 47 | 229 | 98 | 5 | 191,197a, 191b | 158,132a, 95b | 371 | 0.176 | 0.696 | |||||
AuB2 | P6/mmm | 3.011, 4.245 | 207 | 127 | -23 | -30 | 267 | 87 | ||||||||||
Co2B | I4/mcm | 4.955, 4.259 | 427 | 335 | 103 | 116 | 199 | 173 | 253 | 107 | 282 | 0.314 | 1.019 | |||||
CoB | Pbnm | 3.925, 5.161, 3.065 | 514 | 421 | 484.4 | 159.9 | 201.4 | 147.1 | 217.7 | 216.6 | 223.7 | 304 | 152 | 392 | 0.285 | 1.193 | ||
Cr2B | I4/mcm | 5.127, 4.269 | 518 | 485 | 205 | 198 | 172 | 197 | 295 | 185 | 459 | 0.241 | 1.145 | |||||
CrB | Cmcm | 2.925, 7.841, 2.915 | 505 | 613 | 592 | 222 | 267 | 215 | 186 | 175 | 149 | 303 | 221 | 533 | 0.207 | 1.166 | ||
CrB2 | P6/mmm | 2.960, 3.031 | 550 | 423 | 158 | 209 | 133 | 97 | 242,300a, 239b | 185,171a, 140b | 442 | 0.195 | 0.769 | |||||
Fe2B | I4/mcm | 5.053, 4.232 | 410 | 376 | 144 | 153 | 149 | 126 | 222 | 142 | 350 | 0.237 | 1.169 | |||||
FeB | Pnma | 5.410, 2.948, 3.995 | 388 | 450 | 503 | 208 | 117 | 193 | 240 | 191 | 205 | 290 | 151 | 385 | 0.279 | 2.179 | ||
HfB | Fm$\bar{3}$m | 4.835 | 409 | 55 | 67 | 181 | 101 | 256 | 0.264 | 0.432 | ||||||||
HfB2 | P6/mmm | 3.143, 3.489 | 605 | 465 | 263 | 269 | 67 | 138 | 262,270a, 261b | 248,240a, 233b | 566 | 0.141 | 0.769 | |||||
MgB2 | P6/mmm | 3.073, 3.515 | 433 | 272 | 72 | 189 | 55 | 32 | 153, 157a, 152b | 134, 132a, 116b | 312 | 0.160 | 0.628 | |||||
Mn2B | I4/mcm | 5.059, 4.100 | 534 | 495 | 218 | 163 | 223 | 221 | 321 | 180 | 454 | 0.264 | 1.052 | |||||
MnB | Pnma | 5.446, 2.983, 4.119 | 402 | 518 | 495 | 213 | 164 | 214 | 175 | 151 | 140 | 261 | 181 | 442 | 0.218 | 1.530 | ||
MnB2 | P6/mmm | 2.936, 2.986 | 613 | 388 | 129 | 227 | 159 | 125 | 271, 220b | 177, 122b | 437 | 0.231 | 0.632 | |||||
Mo2B | I4/mcm | 5.545, 4.756 | 500 | 463 | 155 | 162 | 189 | 215 | 300 | 150 | 386 | 0.285 | 1.040 | |||||
MoB | I41/amd | 3.126, 16.990 | 560 | 533 | 213 | 241 | 196 | 204 | 318 | 203 | 503 | 0.236 | 1.325 | |||||
MoB2 | P6/mmm | 3.030, 3.331 | 610 | 431 | 145 | 236 | 137 | 223 | 313, 311a, 303b | 177, 192a, 186b | 446 | 0.263 | 0.708 | |||||
NbB | Cmcm | 3.315, 8.784, 3.180 | 479 | 532 | 519 | 189 | 234 | 207 | 135 | 165 | 118 | 263 | 200 | 478 | 0.197 | 1.119 | ||
NbB2 | P6/mmm | 3.120, 3.338 | 581 | 417 | 207 | 234 | 114 | 196 | 288, 299a, 286b | 201, 220a, 210b | 489 | 0.217 | 0.716 | |||||
Ni2B | I4/mcm | 4.981, 4.269 | 404 | 353 | 85 | 131 | 199 | 169 | 248 | 102 | 268 | 0.320 | 1.279 | |||||
NiB | Cmcm | 2.953, 7.370, 2.986 | 325 | 484 | 405 | 104 | 108 | 120 | 193 | 193 | 160 | 256 | 111 | 291 | 0.311 | 1.198 | ||
OsB2 | Pmmn | 4.705, 2.889, 4.094 | 566 | 552 | 743 | 73 | 184 | 190 | 178 | 172 | 121 | 311 | 182 | 457 | 0.255 | 0.999 | ||
Pd2B | Pnnm | 4.764, 5.150, 3.156 | 218 | 229 | 244 | 55 | 39 | 91 | 175 | 128 | 138 | 175 | 54 | 146 | 0.361 | 3.718 | ||
PtB | P63/mmc | 3.766, 3.647 | 330 | 301 | 47 | 58 | 214 | 247 | 264 | 47 | 134 | 0.416 | 0.912 | |||||
ReB2 | P63/mmc | 2.914, 7.505 | 643 | 1024 | 260 | 244 | 154 | 127 | 348, 355c | 280, 289c | 661 | 0.183 | 1.592 | |||||
RuB2 | Pmmn | 4.667, 2.882, 4.061 | 518 | 460 | 678 | 101 | 210 | 171 | 189 | 142 | 122 | 285 | 176 | 439 | 0.243 | 1.145 | ||
Ta2B | I4/mcm | 5.794, 4.879 | 506 | 429 | 185 | 184 | 104 | 165 | 256 | 178 | 433 | 0.218 | 0.915 | |||||
TaB | Cmcm | 3.294, 8.703, 3.163 | 525 | 594 | 553 | 204 | 261 | 232 | 156 | 198 | 140 | 296 | 218 | 525 | 0.204 | 1.155 | ||
TaB 2 | P6/mmm | 3.099, 3.326 | 598 | 450 | 214 | 227 | 144 | 221 | 313, 341a, 296b | 202, 244a, 192b | 498 | 0.235 | 0.752 | |||||
TiB | Pnma | 6.114, 3.050, 4.561 | 425 | 532 | 417 | 194 | 174 | 218 | 96 | 120 | 62 | 214, 207d | 190, 186d | 441 | 0.157 | 1.155 | ||
TiB2 | P6/mmm | 3.034, 3.225 | 653 | 463 | 256 | 292 | 70 | 116 | 264, 261a, 250b | 258, 271a, 261b | 584 | 0.130 | 0.708 | |||||
VB | Cmcm | 3.041, 8.023, 2.965 | 510 | 665 | 616 | 211 | 275 | 208 | 129 | 157 | 70 | 278 | 235 | 549 | 0.171 | 0.925 | ||
VB2 | P6/mmm | 2.997, 3.025 | 684 | 487 | 221 | 284 | 117 | 138 | 293, 284a, 280b | 243, 247a, 241b | 571 | 0.176 | 0.711 | |||||
W2B | I4/mcm | 5.572, 4.770 | 563 | 528 | 154 | 176 | 211 | 243 | 338 | 161 | 416 | 0.295 | 0.998 | |||||
WB | I41/amd | 3.143, 16.924 | 569 | 551 | 227 | 252 | 230 | 249 | 350 | 205 | 515 | 0.254 | 1.483 | |||||
WB2 | P6/mmm | 3.018, 3.364 | 623 | 421 | 132 | 234 | 154 | 254 | 332, 330a, 323b | 166, 172a, 164b | 428 | 0.285 | 0.675 | |||||
YB2 | P6/mmm | 3.299, 3.867 | 364 | 337 | 158 | 158 | 49 | 79 | 164, 157a, 171b | 152, 150a, 145b | 348 | 0.146 | 0.927 | |||||
YB6 | Pm $\bar{3}$ m | 4.102 | 451 | 30 | 30 | 170 | 102 | 256 | 0.250 | 0.201 | ||||||||
ZrB | Fm$\bar{3}$m | 4.918 | 369 | 55 | 66 | 167 | 94 | 237 | 0.264 | 0.478 | ||||||||
ZrB2 | P6/mmm | 3.175, 3.558 | 563 | 441 | 250 | 252 | 59 | 136 | 247, 229a, 239b | 233, 231a, 231b | 532 | 0.142 | 0.783 |
SG | LCs | C 11 | C 22 | C 33 | C 44 | C 55 | C 66 | C 12 | C 13 | C 23 | B | G | E | v | A | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Diamond | F$\bar{4}$3m | 3.572 | 1029 | 540 | 106 | 414, 433a | 509, 534a | 1083 | 0.064 | 1.153 | ||||||
CrC | Fm$\bar{3}$m | 4.069, 4.068b | 624 | 127 | 194 | 337, 318b | 162, 156b | 419 | 0.293 | 0.717 | ||||||
4.107* | 461* | 80* | 121* | 234 | 116 | 298 | 0.287 | 0.608 | ||||||||
Cr3C2 | Pnma | 5.475,2.790, 11.467 | 504 | 566 | 484 | 239 | 111 | 238 | 228 | 236 | 233 | 327, 313b, 329c | 175, 162b, 162c | 445 | 0.273 | 1.560 |
Cr23C6 | Fm$\bar{3}$m | 7.443 | 479 | 139 | 196 | 290, 283b, 300c | 140, 145b, 137c | 362 | 0.292 | 0.988 | ||||||
Fe3C | Pnma | 4.919, 6.738 | 441 | 371 | 322 | 26 | 148 | 144 | 183 | 160 | 212 | 249 | 102 | 270 | 0.320 | 1.304 |
HfC | Fm$\bar{3}$m | 4.646 | 530 | 172 | 114 | 253, 236d, 263e | 186, 166d, 200e | 448 | 0.204 | 0.862 | ||||||
MoC | Fm$\bar{3}$m | 4.375 | 662 | 113 | 187 | 345 | 163 | 422 | 0.296 | 0.623 | ||||||
NbC | Fm$\bar{3}$m | 4.506 | 643 | 167 | 126 | 298, 285d, 331e | 204, 167d, 193e | 498 | 0.222 | 0.716 | ||||||
OsC | P$\bar{6}$m2 | 2.950, 2.727 | 429 | 869 | 82 | 17 | 396 | 252 | 392, 393f | 92, 82f | 255 | 0.392 | 2.024 | |||
ReC | Fm$\bar{3}$m | 4.358 | 632 | -79 | 256 | |||||||||||
RuC | P$\bar{6}$m2 | 2.937, 2.680 | 408 | 745 | 94 | 45 | 319 | 225 | 344 | 99 | 271 | 0.369 | 1.829 | |||
SiC | Fm$\bar{3}$m | 4.379 | 375 | 236 | 121 | 206 | 193 | 440 | 0.143 | 1.579 | ||||||
TaC | Fm$\bar{3}$m | 4.475 | 711 | 173 | 150 | 337, 317d, 357e | 216, 209d, 214e | 534 | 0.236 | 0.698 | ||||||
TiC | Fm$\bar{3}$m | 4.337 | 527 | 161 | 133 | 265, 257d | 176, 162d | 431 | 0.228 | 0.863 | ||||||
VC | Fm$\bar{3}$m | 4.155 | 636 | 185 | 140 | 305, 307d | 210, 171d | 513 | 0.220 | 0.802 | ||||||
WC | P$\bar{6}$m2 | 2.919, 2.845 | 706 | 944 | 306 | 235 | 235 | 190 | 398 | 286 | 691 | 0.211 | 1.338 | |||
ZrC | Fm$\bar{3}$m | 4.724 | 477 | 148 | 113 | 234, 217d, 247e | 162, 124d, 177e | 394 | 0.220 | 0.856 |
Table 2 LCs (in ?) and elastic properties (Cij, B, G and E in GPa) of carbides at zero pressure
SG | LCs | C 11 | C 22 | C 33 | C 44 | C 55 | C 66 | C 12 | C 13 | C 23 | B | G | E | v | A | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Diamond | F$\bar{4}$3m | 3.572 | 1029 | 540 | 106 | 414, 433a | 509, 534a | 1083 | 0.064 | 1.153 | ||||||
CrC | Fm$\bar{3}$m | 4.069, 4.068b | 624 | 127 | 194 | 337, 318b | 162, 156b | 419 | 0.293 | 0.717 | ||||||
4.107* | 461* | 80* | 121* | 234 | 116 | 298 | 0.287 | 0.608 | ||||||||
Cr3C2 | Pnma | 5.475,2.790, 11.467 | 504 | 566 | 484 | 239 | 111 | 238 | 228 | 236 | 233 | 327, 313b, 329c | 175, 162b, 162c | 445 | 0.273 | 1.560 |
Cr23C6 | Fm$\bar{3}$m | 7.443 | 479 | 139 | 196 | 290, 283b, 300c | 140, 145b, 137c | 362 | 0.292 | 0.988 | ||||||
Fe3C | Pnma | 4.919, 6.738 | 441 | 371 | 322 | 26 | 148 | 144 | 183 | 160 | 212 | 249 | 102 | 270 | 0.320 | 1.304 |
HfC | Fm$\bar{3}$m | 4.646 | 530 | 172 | 114 | 253, 236d, 263e | 186, 166d, 200e | 448 | 0.204 | 0.862 | ||||||
MoC | Fm$\bar{3}$m | 4.375 | 662 | 113 | 187 | 345 | 163 | 422 | 0.296 | 0.623 | ||||||
NbC | Fm$\bar{3}$m | 4.506 | 643 | 167 | 126 | 298, 285d, 331e | 204, 167d, 193e | 498 | 0.222 | 0.716 | ||||||
OsC | P$\bar{6}$m2 | 2.950, 2.727 | 429 | 869 | 82 | 17 | 396 | 252 | 392, 393f | 92, 82f | 255 | 0.392 | 2.024 | |||
ReC | Fm$\bar{3}$m | 4.358 | 632 | -79 | 256 | |||||||||||
RuC | P$\bar{6}$m2 | 2.937, 2.680 | 408 | 745 | 94 | 45 | 319 | 225 | 344 | 99 | 271 | 0.369 | 1.829 | |||
SiC | Fm$\bar{3}$m | 4.379 | 375 | 236 | 121 | 206 | 193 | 440 | 0.143 | 1.579 | ||||||
TaC | Fm$\bar{3}$m | 4.475 | 711 | 173 | 150 | 337, 317d, 357e | 216, 209d, 214e | 534 | 0.236 | 0.698 | ||||||
TiC | Fm$\bar{3}$m | 4.337 | 527 | 161 | 133 | 265, 257d | 176, 162d | 431 | 0.228 | 0.863 | ||||||
VC | Fm$\bar{3}$m | 4.155 | 636 | 185 | 140 | 305, 307d | 210, 171d | 513 | 0.220 | 0.802 | ||||||
WC | P$\bar{6}$m2 | 2.919, 2.845 | 706 | 944 | 306 | 235 | 235 | 190 | 398 | 286 | 691 | 0.211 | 1.338 | |||
ZrC | Fm$\bar{3}$m | 4.724 | 477 | 148 | 113 | 234, 217d, 247e | 162, 124d, 177e | 394 | 0.220 | 0.856 |
SG | LCs | C 11 | C 22 | C 33 | C 44 | C 55 | C 66 | C 12 | C 13 | C 23 | B | G | E | v | A | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
AlN | Fm$\bar{3}$m | 4.067 | 419 | 303 | 169 | 252 | 232 | 533 | 0.148 | 1.850 | ||||||
BN | F$\bar{4}$3m | 3.625 | 766 | 433 | 161 | 363 | 381 | 847 | 0.111 | 1.342 | ||||||
C3N4 | P63/m | 6.448, 2.422 | 822 | 1013 | 283 | 286 | 250 | 120 | 404 | 315 | 750 | 0.191 | 1.233 | |||
C3N4 | Fd$\bar{3}$m | 4.795 | 901 | 200 | 88 | 359 | 283 | 672 | 0.188 | 0.542 | ||||||
CrN | Fm$\bar{3}$m | 4.054 | 573 | 6 | 200 | 324, 325a | 78, 60a | 217 | 0.388 | 0.369 | ||||||
4.150* | 490* | 60* | 141* | 257, 249b | 106, 150b | 279 | 0.319 | 0.534 | ||||||||
Cr2N | P$\bar{3}$1m | 4.784, 4.404 | 472 | 404 | 161 | 156 | 160 | 235 | 290 | 144 | 369 | 0.287 | 0.855 | |||
Fe16N2 | I4/mmm | 5.676, 6.244 | 305 | 320 | 80 | 82 | 115 | 138 | 190 | 85 | 221 | 0.306 | 0.865 | |||
Fe2N | P$\bar{3}$1m | 4.750, 4.317 | 350 | 338 | 103 | 99 | 153 | 210 | 243 | 92 | 245 | 0.331 | 0.965 | |||
Fe3N | P6322 | 4.656, 4.317 | 307 | 315 | 101 | 85 | 137 | 140 | 196 | 91 | 237 | 0.298 | 1.105 | |||
Fe4N | Pm$\bar{3}$m | 3.671 | 385 | 64 | 175 | 245 | 80 | 217 | 0.352 | 0.787 | ||||||
GaN | Fm$\bar{3}$m | 4.277 | 360 | 201 | 161 | 227 | 161 | 390 | 0.214 | 1.565 | ||||||
HfN | Fm$\bar{3}$m | 4.532 | 614 | 116 | 122 | 286, 267c, 306d | 168, 123c, 185d | 422 | 0.254 | 0.576 | ||||||
InN | Fm$\bar{3}$m | 4.723 | 281 | 116 | 115 | 171 | 103 | 257 | 0.249 | 1.233 | ||||||
IrN2 | Pnnm | 4.094, 4.929, 2.781 | 674 | 838 | 482 | 109 | 272 | 169 | 146 | 263 | 79 | 330, 347e | 210 | 520 | 0.237 | 0.560 |
MoN | Fm$\bar{3}$m | 4.347 | 588 | -43 | 224 | |||||||||||
NbN | Fm$\bar{3}$m | 4.453 | 648 | 75 | 134 | 306, 332a, 354d | 148, 176a, 134d | 381 | 0.292 | 0.438 | ||||||
OsN2 | Pmnn | 2.698, 4.955, 4.147 | 576 | 931 | 735 | 173 | 329 | 131 | 90 | 269 | 169 | 366, 362e | 241 | 592 | 0.230 | 0.417 |
Pd2N | Pmnn | 3.157, 5.149, 4.765 | 242 | 227 | 215 | 91 | 36 | 54 | 139 | 130 | 173 | 174 | 52 | 143 | 0.363 | 1.125 |
PtN | F$\bar{4}$3m | 4.780 | 174 | 6 | 202 | |||||||||||
PtN2 | Pmnn | 3.203, 4.872, 3.760 | 477 | 692 | 466 | 143 | 245 | 105 | 86 | 243 | 86 | 274, 286e | 180 | 443 | 0.231 | 0.435 |
RuN2 | Pnnm | 4.110, 4.927, 2.726 | 604 | 762 | 420 | 90 | 258 | 109 | 148 | 210 | 72 | 294 | 182 | 452 | 0.244 | 0.413 |
ScN | Fm$\bar{3}$m | 4.497 | 411 | 168 | 118 | 216, 217a | 159, 153a | 383 | 0.204 | 1.102 | ||||||
Si3N4 | P63/m | 7.660, 2.925 | 400 | 521 | 99 | 112 | 176 | 103 | 232 | 125 | 317 | 0.272 | 1.302 | |||
Si3N4 | Fd$\bar{3}$m | 5.506 | 692 | 233 | 84 | 286 | 261 | 601 | 0.150 | 0.793 | ||||||
TaN | Fm$\bar{3}$m | 4.414 | 762 | 59 | 138 | 346, 320c, 372d | 160, 84d | 417 | 0.299 | 0.335 | ||||||
TiN | Fm$\bar{3}$m | 4.255 | 595 | 159 | 137 | 290, 269a, 283c | 187, 189a, 109c | 462 | 0.234 | 0.764 | ||||||
VN | Fm$\bar{3}$m | 4.118 | 609 | 124 | 186 | 327, 325a, 317c | 159, 185a, 109c | 411 | 0.291 | 0.712 | ||||||
V2N | P$\bar{3}$1m | 4.901, 4.534 | 451 | 441 | 149 | 144 | 164 | 194 | 272 | 141 | 360 | 0.279 | 0.976 | |||
WN | P$\bar{6}$m2 | 2.864, 2.900 | 649 | 706 | 114 | 226 | 196 | 277 | 389 | 175 | 456 | 0.305 | 1.087 | |||
YN | Fm$\bar{3}$m | 4.919 | 311 | 124 | 83 | 159 | 120 | 288 | 0.198 | 1.061 | ||||||
ZrN | Fm$\bar{3}$m | 4.608 | 564 | 116 | 114 | 264, 263a, 283d | 159, 150a, 169d | 398 | 0.249 | 0.613 |
Table 3 LCs (in ?) and elastic properties (Cij, B, G and E in GPa) of nitrides at zero pressure
SG | LCs | C 11 | C 22 | C 33 | C 44 | C 55 | C 66 | C 12 | C 13 | C 23 | B | G | E | v | A | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
AlN | Fm$\bar{3}$m | 4.067 | 419 | 303 | 169 | 252 | 232 | 533 | 0.148 | 1.850 | ||||||
BN | F$\bar{4}$3m | 3.625 | 766 | 433 | 161 | 363 | 381 | 847 | 0.111 | 1.342 | ||||||
C3N4 | P63/m | 6.448, 2.422 | 822 | 1013 | 283 | 286 | 250 | 120 | 404 | 315 | 750 | 0.191 | 1.233 | |||
C3N4 | Fd$\bar{3}$m | 4.795 | 901 | 200 | 88 | 359 | 283 | 672 | 0.188 | 0.542 | ||||||
CrN | Fm$\bar{3}$m | 4.054 | 573 | 6 | 200 | 324, 325a | 78, 60a | 217 | 0.388 | 0.369 | ||||||
4.150* | 490* | 60* | 141* | 257, 249b | 106, 150b | 279 | 0.319 | 0.534 | ||||||||
Cr2N | P$\bar{3}$1m | 4.784, 4.404 | 472 | 404 | 161 | 156 | 160 | 235 | 290 | 144 | 369 | 0.287 | 0.855 | |||
Fe16N2 | I4/mmm | 5.676, 6.244 | 305 | 320 | 80 | 82 | 115 | 138 | 190 | 85 | 221 | 0.306 | 0.865 | |||
Fe2N | P$\bar{3}$1m | 4.750, 4.317 | 350 | 338 | 103 | 99 | 153 | 210 | 243 | 92 | 245 | 0.331 | 0.965 | |||
Fe3N | P6322 | 4.656, 4.317 | 307 | 315 | 101 | 85 | 137 | 140 | 196 | 91 | 237 | 0.298 | 1.105 | |||
Fe4N | Pm$\bar{3}$m | 3.671 | 385 | 64 | 175 | 245 | 80 | 217 | 0.352 | 0.787 | ||||||
GaN | Fm$\bar{3}$m | 4.277 | 360 | 201 | 161 | 227 | 161 | 390 | 0.214 | 1.565 | ||||||
HfN | Fm$\bar{3}$m | 4.532 | 614 | 116 | 122 | 286, 267c, 306d | 168, 123c, 185d | 422 | 0.254 | 0.576 | ||||||
InN | Fm$\bar{3}$m | 4.723 | 281 | 116 | 115 | 171 | 103 | 257 | 0.249 | 1.233 | ||||||
IrN2 | Pnnm | 4.094, 4.929, 2.781 | 674 | 838 | 482 | 109 | 272 | 169 | 146 | 263 | 79 | 330, 347e | 210 | 520 | 0.237 | 0.560 |
MoN | Fm$\bar{3}$m | 4.347 | 588 | -43 | 224 | |||||||||||
NbN | Fm$\bar{3}$m | 4.453 | 648 | 75 | 134 | 306, 332a, 354d | 148, 176a, 134d | 381 | 0.292 | 0.438 | ||||||
OsN2 | Pmnn | 2.698, 4.955, 4.147 | 576 | 931 | 735 | 173 | 329 | 131 | 90 | 269 | 169 | 366, 362e | 241 | 592 | 0.230 | 0.417 |
Pd2N | Pmnn | 3.157, 5.149, 4.765 | 242 | 227 | 215 | 91 | 36 | 54 | 139 | 130 | 173 | 174 | 52 | 143 | 0.363 | 1.125 |
PtN | F$\bar{4}$3m | 4.780 | 174 | 6 | 202 | |||||||||||
PtN2 | Pmnn | 3.203, 4.872, 3.760 | 477 | 692 | 466 | 143 | 245 | 105 | 86 | 243 | 86 | 274, 286e | 180 | 443 | 0.231 | 0.435 |
RuN2 | Pnnm | 4.110, 4.927, 2.726 | 604 | 762 | 420 | 90 | 258 | 109 | 148 | 210 | 72 | 294 | 182 | 452 | 0.244 | 0.413 |
ScN | Fm$\bar{3}$m | 4.497 | 411 | 168 | 118 | 216, 217a | 159, 153a | 383 | 0.204 | 1.102 | ||||||
Si3N4 | P63/m | 7.660, 2.925 | 400 | 521 | 99 | 112 | 176 | 103 | 232 | 125 | 317 | 0.272 | 1.302 | |||
Si3N4 | Fd$\bar{3}$m | 5.506 | 692 | 233 | 84 | 286 | 261 | 601 | 0.150 | 0.793 | ||||||
TaN | Fm$\bar{3}$m | 4.414 | 762 | 59 | 138 | 346, 320c, 372d | 160, 84d | 417 | 0.299 | 0.335 | ||||||
TiN | Fm$\bar{3}$m | 4.255 | 595 | 159 | 137 | 290, 269a, 283c | 187, 189a, 109c | 462 | 0.234 | 0.764 | ||||||
VN | Fm$\bar{3}$m | 4.118 | 609 | 124 | 186 | 327, 325a, 317c | 159, 185a, 109c | 411 | 0.291 | 0.712 | ||||||
V2N | P$\bar{3}$1m | 4.901, 4.534 | 451 | 441 | 149 | 144 | 164 | 194 | 272 | 141 | 360 | 0.279 | 0.976 | |||
WN | P$\bar{6}$m2 | 2.864, 2.900 | 649 | 706 | 114 | 226 | 196 | 277 | 389 | 175 | 456 | 0.305 | 1.087 | |||
YN | Fm$\bar{3}$m | 4.919 | 311 | 124 | 83 | 159 | 120 | 288 | 0.198 | 1.061 | ||||||
ZrN | Fm$\bar{3}$m | 4.608 | 564 | 116 | 114 | 264, 263a, 283d | 159, 150a, 169d | 398 | 0.249 | 0.613 |
Fig. 3 Cross sections of Young’s moduli distribution on the (001) plane (ab plane) for group IV-VI TM carbides a and nitrides b. WC and WN are excluded for hexagonal structure, and MoN for elastic instability. Horizontal and vertical directions correspond to a and b axes of a cubic crystal. Blue circles are contour lines and numbers are values with unit of GPa for Young’s moduli; the increment is 100 GPa
Fig. 4 Correlation between the normalized Cauchy pressures p=(C12-C44)/B and the Pugh’s modulus ratio r=G/B for 86 elastically stable compounds a and group IV-VI TM phases b. Black dash line in a is the fitting curve
SFEs (mJ/m2) | SFEs in studies (mJ/m2) | ||
---|---|---|---|
Cell shape fixed | Cell shape relaxed | ||
Diamond | 277.5, 9167 | 258.1 | 318a, 279b |
cBN | 183.8, 6515 | 176.5 | 191c |
β-SiC | 1.52 | 1.14 | -1.7d |
PtN | 318.0 | 293.7 | |
HfB | -26.2 | -46.6 | |
ZrB | 42.4 | 25.8 | |
CrC | -100.7e, -172.5f | -198.7e, -258.8f | |
HfC | 1609 | 1604 | |
MoC | -929.9 | -1211 | |
NbC | 637.8 | 568.5 | |
ReC | -1021 | -3206 | |
TaC | 772.6 | 633.4 | |
TiC | 1672, 3495 | - | |
VC | 895.5 | 892.6 | |
ZrC | 1367 | - | |
AlN | 4813 | 4453 | |
CrN | 1112e, 2775f | 425.4e, 527.3f | |
GaN | 3544 | - | |
HfN | 234.5 | 297.9 | |
InN | 1821 | - | |
NbN | -130.0 | -677.5 | |
ScN | 1889 | - | |
TaN | -147.7 | -970.8 | |
TiN | 1081, 1509 | - | 1050g |
VN | 91.0 | -329.1 | |
YN | 1217 | - | |
ZrN | 330.3 | 224.2 |
Table 4 Calculated SFEs at 0 K. The SFEs of SF1 are italic
SFEs (mJ/m2) | SFEs in studies (mJ/m2) | ||
---|---|---|---|
Cell shape fixed | Cell shape relaxed | ||
Diamond | 277.5, 9167 | 258.1 | 318a, 279b |
cBN | 183.8, 6515 | 176.5 | 191c |
β-SiC | 1.52 | 1.14 | -1.7d |
PtN | 318.0 | 293.7 | |
HfB | -26.2 | -46.6 | |
ZrB | 42.4 | 25.8 | |
CrC | -100.7e, -172.5f | -198.7e, -258.8f | |
HfC | 1609 | 1604 | |
MoC | -929.9 | -1211 | |
NbC | 637.8 | 568.5 | |
ReC | -1021 | -3206 | |
TaC | 772.6 | 633.4 | |
TiC | 1672, 3495 | - | |
VC | 895.5 | 892.6 | |
ZrC | 1367 | - | |
AlN | 4813 | 4453 | |
CrN | 1112e, 2775f | 425.4e, 527.3f | |
GaN | 3544 | - | |
HfN | 234.5 | 297.9 | |
InN | 1821 | - | |
NbN | -130.0 | -677.5 | |
ScN | 1889 | - | |
TaN | -147.7 | -970.8 | |
TiN | 1081, 1509 | - | 1050g |
VN | 91.0 | -329.1 | |
YN | 1217 | - | |
ZrN | 330.3 | 224.2 |
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[1] | Fushi Jiang, Chang Pang, Zhaoyang Zheng, Qing Wang, Jijun Zhao, Chuang Dong. First-Principles Calculations for Stable β-Ti-Mo Alloys Using Cluster-Plus-Glue-Atom Model [J]. Acta Metallurgica Sinica (English Letters), 2020, 33(7): 968-974. |
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