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Ti3B4作为一种重要的钛硼化合物, 被广泛应用于工业生产和国防军事中. 但是有关Ti3B4在外载荷下的变形行为却鲜有报道, 这在很大程度上限制了它的应用. 本文采用基于密度泛函理论的第一性原理方法研究了Ti3B4在不同方向单轴压缩下的力学行为、电子结构以及变形机制. 结果表明, 在不同方向单轴压缩下, Ti3B4的变形行为表现出很强的各向异性. a轴压缩下, 层内Ti- Ti键减弱使Ti3B4承载能力降低, 最终层间Ti-Ti键和沿b轴B-B键断裂造成压缩应力突降; b轴压缩下, 层内Ti-B键减弱和层间Ti-B键增强导致Ti3B4承载能力逐渐降低, B-B键断裂导致结构破坏; c轴压缩下, 层内Ti-B键断裂和层间Ti-B键形成使结构稳定性降低. 由态密度分布可知, 在单轴压缩下, 变形后的Ti3B4仍然呈现金属性, 但是其共价性能降低. 通过讨论Ti3B4在不同方向单轴压缩下的力学行为与微观变形机制可以为改善其宏观性能提供一定的理论指导.As an important Ti-B component, Ti3B4 has been widely used in industry and military applications. However, its deformation behaviors are not clear, which greatly limits its applications. First-principles methods based on density function theory were employed to investigate the mechanical, electronic properties and deformation mechanisms of Ti3B4 under uniaxial compressions along different axis. The results show that the structure underwent a massive change under different axial compressions. Strong anisotropic of deformation behaviors in Ti3B4 was observed. The compressive strength along b-axis is the highest in Ti3B4 structure. Under a-axis compression, the interaction between intralayer Ti—Ti bonds becomes weaker as the compressive strain increases, causing the partly damage of Ti3B4. However, in this process, the structure is not destroyed and can sustain the stress continuously. After that, the interlayer Ti—Ti bonds and the intralyer B—B bonds which are along b-axis, are broken and then it causes the sudden drop in stress, implying that the Ti3B4 structure is fully destroyed. Under b-axis compression, the changes of Ti—B bonds in Ti3B4 structure lead to the decrease of stress. Similarly, the structure can sustain the stress continuously in the process. Then, the B—B bonds which are along b-axis are broken, resulting in the sudden drop in stress. Under c-axis compression, the formation of interlayer Ti—B bonds and the breakage of intralayer Ti—B bonds result in structural instability of Ti3B4. Meanwhile, the deformed Ti3B4 still exhibits a metallic feature in the crystalline state after uniaxial compressions. However, there is no noticeable pseudogap in DOS spectra for a-axis and b-axis compressions. While for c-axis compression, there still exists a pseudogap around the Fermi energy, but it moves to the lower energy. And the pseudogap becomes narrower than that of the initial structure, which means that the covalent properties of Ti3B4 are reduced after deformations. The present work provides necessary insights in understanding the mechanical behaviors and deformation mechanisms of Ti3B4, which is the basis for improving the mechanical performance of Ti3B4 at macroscale.
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Keywords:
- Ti3B4 /
- First-principles methods /
- mechanical properties /
- deformation mechanisms
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图 1 Ti3B4的晶体结构 (a) 单晶胞结构; (b) 超晶胞结构. 其中蓝色原子为Ti原子, 绿色原子为B原子
Fig. 1. The crystal structure of Ti3B4: (a) The unit cell; (b) the supercell. The blue balls in the figure denote the Ti atoms, and the green balls refer to the B atoms.
图 2 Ti3B4晶体在单轴压缩载荷下的应力-应变曲线
Fig. 2. The stress-strain relationship of Ti3B4 under uniaxial compressions.
图 3 a轴压缩时不同应变下Ti3B4晶体的结构和ELF分布图 (a) ε = 0.00; (b) ε = 0.10; (c) ε = 0.15; (d) ε = 0.24; (e) ε = 0.242
Fig. 3. The structural and ELF at various strains under a-axis uniaxial compression: (a) ε = 0.00; (b) ε = 0.10; (c) ε = 0.15; (d) ε = 0.24; (e) ε = 0.242.
图 4 Ti3B4晶体在a轴压缩下化学键长度变化
Fig. 4. Variation of bond lengths as a function of a-axis uniaxial compressive strain.
图 5 a轴压缩时临界应变下Ti3B4晶体(100)晶面ELF分布图 (a) ε = 0.24; (b) ε = 0.242
Fig. 5. The ELF at critical strains of (100) crystal plane in Ti3B4 structure under a-axis uniaxial compression: (a) ε = 0.24; (b) ε = 0.242.
图 6 b轴压缩时不同应变下Ti3B4晶体的结构和ELF分布图 (a) ε = 0.10; (b) ε = 0.14; (c)ε = 0.26; (d) ε = 0.268
Fig. 6. The structural and ELF at various strains under b-axis uniaxial compression: (a) ε = 0.10; (b) ε = 0.14; (c) ε = 0.26; (d) ε = 0.268.
图 7 Ti3B4晶体在b轴压缩下化学键长度变化
Fig. 7. Variation of bond lengths as a function of b-axis uniaxial compressive strain.
图 8 b轴压缩时临界应变下Ti3B4晶体(100)晶面ELF分布图 (a) ε = 0.14; (b) ε = 0.20; (c) ε = 0.26; (d) ε = 0.268
Fig. 8. The ELF at critical strains of (100) crystal plane in Ti3B4 structure under b-axis uniaxial compression: (a) ε = 0.14; (b) ε = 0.20; (c) ε = 0.26; (d) ε = 0.268.
图 9 c轴压缩时不同应变下Ti3B4晶体的结构和ELF分布图 (a) ε = 0.10; (b) ε = 0.13; (c) ε = 0.18; (d) ε = 0.20; (e) ε = 0.26
Fig. 9. The structural and ELF at various strains under c-axis uniaxial compression: (a) ε = 0.10; (b) ε = 0.13; (c) ε = 0.18; (d) ε = 0.20; (e) ε = 0.26.
图 10 Ti3B4晶体在c轴压缩下化学键长度变化
Fig. 10. Variation of bond lengths in Ti3B4 as a function of c-axis uniaxial compressive strain.
图 12 在单轴压缩下Ti3B4结构在临界压缩应变处的TDOS和PDOS分布 (a) ε = 0.242 (a轴); (b) ε = 0.268 (b轴); (c) ε = 0.19 (c轴)
Fig. 12. TDOS and PDOS for Ti3B4 at critical strains under uniaxial compressions: (a) ε = 0.242 (a-axis); (b) ε = 0.268 (b-axis); (c) ε = 0.19 (c-axis).
表 1 峰值A和谷值B处的Ti原子和B原子的PDOS和Ti3B4的TDOS (states/eV)
Table 1. The PDOS of a Ti and a B atom and TDOS of Ti3B4 at Peak A and Bottom B (states/eV).
D(Ti-s) D(Ti-3p) D(Ti-3d) D(B-2s) D(B-2p) D(Total) 峰值A 0.0137 0.0959 0.5610 0.0308 0.527 13.0945 谷值B 0.0001 0.0007 0.1996 0.0010 0.019 2.2669 
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[1] Li P F, Zhou R L, Zeng X C 2015 ACS Appl. Mater. Interfaces 7 15607
Google Scholar
[2] Munro R G 2000 J. Res. Nat. Inst. Stand. Technol. 105 709
Google Scholar
[3] 黎军军, 赵学坪, 陶强, 黄晓庆, 朱品文, 崔田, 王欣 2013 物理学报 62 026202
Google Scholar
Li J J, Zhao X P, Tao Q, Huang X Q, Zhu P W, Cui T, Wang X 2013 Acta Phys. Sin. 62 026202
Google Scholar
[4] Murray J L, Liao P K, Spear K E 1986 Bull. Alloy Phase Diagrams 7 550
Google Scholar
[5] Spear K E, Mcdowell P, Mcmahon F 1986 J. Am. Ceram. Soc. 69 C-4
Google Scholar
[6] Huang F, Fu Z Y, Yan A H, Wang W M, Wang H, Zhang J Y, Zhang Q J 2010 Powder Technol. 197 83
Google Scholar
[7] Panda K B, Ravi Chandran K S 2006 Comput. Mater. Sci. 35 134
Google Scholar
[8] Ma X Y, Li C R, Du Z M, Zhang W J 2004 J. Alloys Compd. 370 149
Google Scholar
[9] Yan H Y, Wei Q, Chang S M, Guo P 2011 Trans. Nonferrous Met. Soc. China (English Ed.) 21 1627
Google Scholar
[10] Tian J Z, Zhao Y H, Wang B, Hou H, Zhang Y M 2018 Mater. Chem. Phys. 209 200
Google Scholar
[11] Sun L, Gao Y M, Xiao B, Li Y F, Wang G L 2013 J. Alloys Compd. 579 457
Google Scholar
[12] Zhang X H, Luo X G, Li J P, Hu P, Han J C 2010 Scr. Mater. 62 625
Google Scholar
[13] Cheng T B, Li W G 2015 J. Am. Ceram. Soc. 98 190
Google Scholar
[14] Sun M, Wang C Y, Liu J P 2018 Chin. Phys. B 27 077103
Google Scholar
[15] Arpita Aparajita A N, Sanjay Kumar N R, Chandra Shekar N V, Kalavathi S 2017 Mater. Res. Express 4 096508
Google Scholar
[16] Tian D C, Wang X B 1992 J. Phys. Condens. Matter 4 8765
Google Scholar
[17] Mouffok B, Feraoun H, Aourag H 2006 Mater. Lett. 60 1433
Google Scholar
[18] Vajeeston P, Ravindran P, Ravi C, Asokamani R 2001 Phys. Rev. B 63 045115
Google Scholar
[19] Wang C L, Yu B H, Huo H L, Chen D, Sun H B 2009 Chin. Phys. B 18 1248
Google Scholar
[20] Peng F, Fu H Z, Cheng X L 2007 Phys. B Condens. Matter 400 83
Google Scholar
[21] Xiang H M, Feng Z H, Li Z P, Zhou Y C 2015 J. Appl. Phys. 117 225902
Google Scholar
[22] Wang M L 2014 Phys. Scr. 89 115702
Google Scholar
[23] Lu J Q, Qin J N, Chen Y F, Zhang Z W, Lu W J, Zhang D 2010 J. Alloys Compd. 490 118
Google Scholar
[24] Zhang R, Wang D J, Yuan S J 2017 Mater. Des. 134 250
Google Scholar
[25] Chen D, Chen Z, Wu Y, Wang M L, Ma N H, Wang H W 2014 Intermetallics 52 64
Google Scholar
[26] Panda K B, Ravi Chandran K S 2006 Acta Mater. 54 1641
Google Scholar
[27] Rou S, Ravi Chandran K S 2018 J. Am. Ceram. Soc. 101 4308
Google Scholar
[28] Wang G L, Li Y F, Gao Y M, Cheng Y H, Ma S Q 2015 Comput. Mater. Sci. 104 29
Google Scholar
[29] Li J, Liu L S, Xu S, Zhang J Y and She W C 2019 J. Appl. Phys. A 125 222
Google Scholar
[30] 房玉真, 孔祥晋, 王东亭, 崔守鑫, 刘军海 2018 物理学报 67 117101
Google Scholar
Fang Y Z, Kong X J, Wang D T, Cui S X, Liu J H 2018 Acta Phys. Sin. 67 117101
Google Scholar
[31] 丁超, 李卫, 刘菊燕, 王琳琳, 蔡云, 潘沛锋 2018 物理学报 67 213102
Google Scholar
Ding C, Li W, Liu J Y, Wang L L, Cai Y, Pan P F 2018 Acta Phys. Sin. 67 213102
Google Scholar
[32] 刘琪, 管鹏飞 2018 物理学报 67 178101
Google Scholar
Liu Q, Guan P F 2018 Acta Phys. Sin. 67 178101
Google Scholar
[33] He X, Li J B 2019 Chin. Phys. B 28 037301
Google Scholar
[34] 吕常伟, 王臣菊, 顾建兵 2019 物理学报 68 077102
Google Scholar
Lv C W, Wang C J, Gu J P 2019 Acta Phys. Sin. 68 077102
Google Scholar
[35] Lu B K, Wang C Y 2018 Chin. Phys. B 27 077104
Google Scholar
[36] Kresse G 1999 Phys. Rev. B 59 1758
Google Scholar
[37] Kresse G, Furthmüller J 1996 Comput. Mater. Sci. 6 15
Google Scholar
[38] Kresse G, Furthmüller J 1996 Phys. Rev. B 54 11169
Google Scholar
[39] Becke A D, Edgecombe K E 1990 J. Chem. Phys. 92 5397
Google Scholar
[40] Momma K, Izumi F 2011 J. Appl. Crystallogr. (International Union Crystallogr.-IUCr) 44 1272
Google Scholar
[41] Segall M, Shah R, Pickard C 1996 Phys. Rev. B 54 16317
Google Scholar
[42] Gull E, Parcollet O, Millis A J 2013 Phys. Rev. Lett. 110 216405
Google Scholar
[43] 王欣, 王发展, 雷哲锋, 王博, 马姗, 王哲, 吴振 2013 物理学报 62 123101
Google Scholar
Wang X, Wang F Z, Lei Z F, Wang B, Ma S, Wang Z, Wu Z 2013 Acta Phys. Sin. 62 123101
Google Scholar
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