Author Affiliations
1Institute of Low Dimensional Materials and Technology, College of Science, CivilAviation University of China, Tianjin 300300, China2Sino-European Institute of Aviation Engineering, Civil Aviation University of China, Tianjin 300300, Chinashow less
Fig. 1. Structure models of γ-TiAl: (a) The L10 face-center tetragonal unit cell; (b) the least tetragonal unit cell; (c) the unit of Sp0(Ti8Al8).
γ-TiAl晶胞结构模型 (a) L10型面心四方结构单元; (b)最小结构单元; (c) Sp0(Ti8Al8)结构单元
Fig. 2. Structure models of γ-TiAl including O (Ti8Al8O): (a) Sp0-Oa; (b) Sp0-Ob; (c) Sp0-Oc; (d) Sp0-Od包含O原子的γ-TiAl晶胞结构模型 (a) Sp0-Oa; (b) Sp0-Ob; (c) Sp0-Oc; (d) Sp0-Od
Fig. 3. Typical structure models of γ-TiAl including Ti or Al vacancy: (a) Sp0-□Ti (Ti7□Al8); (b) Sp0-□Al (Ti8Al7□)
包含Ti空位或Al空位的γ-TiAl典型结构模型 (a) Sp0-□Ti (Ti7□Al8); (b) Sp0-□Al (Ti8Al7□)
Fig. 4. Typical structure models of Si and Y co-doping γ-TiAl: (a) Sd1x (Ti6SiYAl8); (b) Sd2 (Ti7YAl7Si); (c)Sd3 (Ti7SiAl7Y); (d) Sd4(Ti8Al6SiY)
Si和Y替位双掺杂γ-TiAl体系的典型结构模型 (a) Sd1x (Ti6SiYAl8); (b) Sd2 (Ti7YAl7Si); (c) Sd3 (Ti7SiAl7Y); (d) Sd4(Ti8Al6SiY)
Fig. 5. Typical structure models of Si and Y co-doping γ-TiAl including O: (a) Sd1x-Od (Ti6SiYAl8O); (b) Sd2x-Od (Ti7YAl7SiO); (c) Sd3x-Od (Ti7SiAl7YO); (d) Sd4x-Od(Ti8Al6SiYO)
Si和Y替位双掺杂γ-TiAl含氧体系的典型结构模型 (a) Sd1x-Od (Ti6SiYAl8O); (b) Sd2x-Od (Ti7YAl7SiO); (c) Sd3x-Od (Ti7SiAl7YO); (d) Sd4x-Od(Ti8Al6SiYO)
Fig. 6. Typical structure models of Si and Y co-doping γ-TiAl including vacancy: (a)Sd1x-□Ti (Ti5SiY□Al8); (b) Sd2x-□Ti (Ti6Y□Al7Si); (c) Sd3x-□Ti(Ti6Si□Al7Y); (d) Sd4x-□Ti(Ti7□Al6SiY); (e) Sd1x-□Al (Ti6SiYAl7□); (f) Sd2x-□Al (Ti7YAl6Si□); (g) Sd3x-□Al(Ti7SiAl6Y□); (h) Sd4x-□Al(Ti8Al5SiY□)
Si和Y替位双掺杂γ-TiAl含空位体系的典型结构模型 (a) Sd1x-□Ti (Ti5SiY□Al8); (b) Sd2x-□Ti (Ti6Y□Al7Si); (c) Sd3x-□Ti(Ti6Si□Al7Y); (d) Sd4x-□Ti(Ti7□Al6SiY); (e) Sd1x-□Al (Ti6SiYAl7□); (f) Sd2x-□Al (Ti7YAl6Si□); (g) Sd3x-□Al(Ti7SiAl6Y□); (h) Sd4x-□Al(Ti8Al5SiY□)
Fig. 7. Formation energies of interstitial O atoms in the Si and Y co-doping γ-TiAl systems.
Si和Y替位双掺杂γ-TiAl含氧体系中间隙O原子的形成能
Fig. 8. Formation energies of Ti and Al vacancies in Si and Y co-doping γ-TiAl systems.
Si和Y双掺杂γ-TiAl含空位体系中Ti空位和Al空位的形成能
体系 | 能量性质 | Et /eV
| Ef/eV
| Sp0 | –13283.2619 | –0.3579 | Sd17 | –10375.5782 | –0.2448 | Sd19 | –10375.3125 | –0.2282 | Sd2 | –11923.1797 | –0.3078 | Sd3 | –11921.0891 | –0.1771 | Sd4 | –13468.5526 | –0.2315 |
|
Table 1. Energy properties of pure γ-TiAl and Si and Y co-doping γ-TiAl systems.
纯γ-TiAl体系与Si和Y替位双掺杂γ-TiAl体系的能量性质
体系 | C11/GPa
| C12/GPa
| C13/GPa
| C33/GPa
| C44/GPa
| C66/GPa
| Sp0 | 232.2438 | 39.8470 | 69.3592 | 196.4413 | 112.3486 | 44.8147 | Sd11 | 130.8671 | 75.6434 | 87.7505 | 134.2535 | 70.0558 | 46.6357 | Sd13 | 136.8296 | 75.1812 | 86.9261 | 134.1158 | 64.9601 | 49.0225 | Sd14 | 180.5075 | 43.1529 | 81.6884 | 138.5193 | 73.0642 | 19.7364 | Sd15 | 136.6952 | 74.6364 | 84.6822 | 128.5797 | 67.3934 | 47.4253 | Sd16 | 160.1225 | 90.0601 | 87.6092 | 137.2518 | 106.8941 | 43.0277 | Sd19 | 130.8850 | 74.3862 | 78.7846 | 125.4646 | 68.9906 | 56.7747 | Sd110 | 132.4566 | 95.9060 | -40.8881 | 351.4524 | 24.8135 | 42.5965 | Sd4 | 174.4526 | 59.4503 | 76.4982 | 151.9303 | 82.9168 | 12.5223 |
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Table 2. Elastic constants of tetragonal systems in pure γ-TiAl and Si and Y co-doping γ-TiAl systems.
纯γ-TiAl体系与Si和Y替位双掺杂γ-TiAl体系中四方晶系的弹性常数
体系 | C11/GPa
| C12/GPa
| C13/GPa
| C15/GPa
| C22/GPa
| C23/GPa
| C25/GPa
| Sd17 | 174.0489 | 51.0128 | 78.8477 | – | 178.6799 | 73.6936 | – | Sd2 | 177.5408 | 69.1504 | 69.7969 | –3.6774 | 172.7134 | 65.2400 | –1.6610 | Sd3 | 158.9597 | 58.6004 | 72.7099 | –10.1161 | 160.3606 | 73.2300 | –0.1101 | 体系 | C33/GPa
| C35/GPa
| C44/GPa
| C46/GPa
| C55/GPa
| C66/GPa
| | Sd17 | 117.2748 | – | 59.8220 | – | 64.1452 | 10.4758 | | Sd2 | 170.8100 | –1.4732 | 77.8416 | –1.2719 | 78.4798 | 38.6156 | | Sd3 | 139.6061 | –1.4377 | 67.2411 | 0.7657 | 67.6317 | 26.4129 | |
|
Table 3. Elastic constants of Si and Y co-doping γ-TiAl systems Sd17, Sd2 and Sd3.
Si和Y替位双掺杂γ-TiAl体系Sd17, Sd2和Sd3的弹性常数
体系 | 能量性质 | Et /eV
| Ef /eV
| Sp0 | –13283.2619 | –0.3579 | Sp0-Oa | –13718.1429 | –0.0716 | Sp0-Ob | –13720.0413 | –0.1832 | Sp0-Oc | –13720.6086 | –0.2166 | Sp0-Od | –13720.9863 | –0.2388 |
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Table 4. Energy properties of pure γ-TiAl and the systems including O.
纯γ-TiAl体系及其含氧体系的能量性质
体系 | 能量性质 | Et(SdO)/eV
| Et (Sd)/eV
| Ef(O)/eV
| Sp0-Od | –13720.9863 | –13283.2619 | 1.6665 | Sd11-Od | –10812.9929 | –10375.4180 | 1.8160 | Sd13-Od | –10813.0355 | –10375.3811 | 1.7365 | Sd14-Od | –10813.1059 | –10375.4175 | 1.7025 | Sd15-Od | –10813.0129 | –10375.3988 | 1.7768 | Sd16-Od | –10813.0989 | –10375.3983 | 1.6903 | Sd17-Od | –10813.1600 | –10375.5782 | 1.8091 | Sd19-Od | –10813.0084 | –10375.3125 | 1.6950 | Sd110-Od | –10813.0341 | –10375.3121 | 1.6689 | Sd21-Od | –12361.2419 | –11923.1797 | 1.3287 | Sd22-Od | –12361.1930 | –11923.1797 | 1.3776 | Sd23-Od | –12361.2834 | –11923.1797 | 1.2872 | Sd31-Od | –12359.6285 | –11921.0891 | 0.8515 | Sd32-Od | –12360.0430 | –11921.0891 | 0.4370 | Sd33-Od | –12359.9518 | –11921.0891 | 0.5282 | Sd41-Od | –13907.6183 | –13468.5526 | 0.3252 | Sd42-Od | –13906.9550 | –13468.5526 | 0.9885 | Sd43-Od | –13906.7798 | –13468.5526 | 1.1637 |
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Table 5. Formation energies of interstitial O atoms in Si and Y co-doping γ-TiAl systems.
Si和Y替位双掺杂γ-TiAl含氧体系中间隙O原子的形成能
体系 | Et (Sd)/eV
| Et (Sd□Al)/eV
| Et (Sd□Ti)/eV
| Ef (□Al)/eV
| Ef (□Ti)/eV
| Sp0-□ | –13283.2619 | –13224.0362 | –11678.3061 | 2.6764 | 1.8132 | Sd11-□ | –10375.4180 | –10317.9824 | –8770.2288 | 0.8863 | 2.0466 | Sd13-□ | –10375.3811 | –10317.9645 | –8770.1941 | 0.8673 | 2.0444 | Sd14-□ | –10375.4175 | –10317.9637 | –8770.2884 | 0.9045 | 1.9865 | Sd15-□ | –10375.3988 | –10317.9620 | –8770.2113 | 0.8875 | 2.0449 | Sd16-□ | –10375.3983 | –10317.9032 | –8770.2649 | 0.9098 | 1.9908 | Sd17-□ | –10375.5782 | –10317.4973 | –8770.0900 | 1.5316 | 2.3456 | Sd19-□ | –10375.3125 | –10318.4246 | –8770.2557 | 0.3386 | 1.9143 | Sd110-□ | –10375.3121 | –10318.0212 | –8770.2609 | 0.7416 | 1.9086 | Sd2-□ | –11923.1797 | –11865.3646 | –10317.9810 | 1.2658 | 2.0561 | Sd3-□ | –11921.0891 | –11865.3095 | –10317.6100 | –0.7697 | 0.3365 | Sd4-□ | –13468.5526 | –13409.4369 | –11865.3562 | 2.5664 | 0.0538 |
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Table 6. Formation energies of Ti and Al vacancies in Si and Y co-doping γ-TiAl systems.
Si和Y双掺杂γ-TiAl含空位体系中Ti空位和Al空位的形成能