Mechanical, electronic properties and deformation mechanisms of Ti<sub>3</sub>B<sub>4</sub> under uniaxial compressions: a first-principles calculation

Li Jun; Liu Li-Sheng; Xu Shuang; Zhang Jin-Yong

doi:10.7498/aps.69.20191194

Abstract

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.

Keywords:

Authors and contacts

1.
Hubei Key Laboratory of Theory and Application of Advanced Materials Mechanics, Wuhan University of Technology, Wuhan 430070, China
2.
State Key Laboratory of Advanced Technology for Materials Synthesis and Processing, Wuhan University of Technology, Wuhan 430070, China
3.
Institute of Advanced Material Manufacturing Equipment and Technology, Wuhan University of Technology, Wuhan 430070, China

Corresponding author: Xu Shuang, xu_shuang@whut.edu.cn

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References

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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

Figure 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.

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图 2 Ti₃B₄晶体在单轴压缩载荷下的应力-应变曲线

Figure 2. The stress-strain relationship of Ti₃B₄ under uniaxial compressions.

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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

Figure 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.

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图 4 Ti₃B₄晶体在a轴压缩下化学键长度变化

Figure 4. Variation of bond lengths as a function of a-axis uniaxial compressive strain.

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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

Figure 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.

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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

Figure 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.

DownLoad: Full-Size Img PowerPoint

图 7 Ti₃B₄晶体在b轴压缩下化学键长度变化

Figure 7. Variation of bond lengths as a function of b-axis uniaxial compressive strain.

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

图 10 Ti₃B₄晶体在c轴压缩下化学键长度变化

Figure 10. Variation of bond lengths in Ti₃B₄ as a function of c-axis uniaxial compressive strain.

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图 11 Ti₃B₄初始结构的TDOS和PDOS分布

Figure 11. TDOS and PDOS for undeformed Ti₃B₄.

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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)

Figure 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).

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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

DownLoad: CSV

[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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Mechanical, electronic properties and deformation mechanisms of Ti₃B₄ under uniaxial compressions: a first-principles calculation

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	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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Mechanical, electronic properties and deformation mechanisms of Ti3B4 under uniaxial compressions: a first-principles calculation

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Corresponding author: Xu Shuang, xu_shuang@whut.edu.cn

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Mechanical, electronic properties and deformation mechanisms of Ti₃B₄ under uniaxial compressions: a first-principles calculation