Theoretical study of atomic relaxation, surface energy, electronic structure and properties of B2- and B19'-NiTi surfaces

Chen Lu; Li Ye-Fei; Zheng Qiao-Ling; Liu Qing-Kun; Gao Yi-Min; Li Bo; Zhou Chang-Meng

doi:10.7498/aps.68.20181944

Abstract

NiTi shape memory alloy has been widely used in industrial and biological fields due to its excellent mechanical properties, unique shape memory effect and superelasticity. In this paper, the atomic relaxation, thermodynamic energy, structural stability, electronic structures and other properties of all low-index surfaces of B2- and B19'-NiTi alloys are systematically studied by using the first principles calculations based on density functional theory. The calculated results show that the atomic relaxations on all low-index surfaces of both B2- and B19'-NiTi alloys are mainly concentrated in 2−3 atomic layers on the surface, which means that the surface effect is mainly confined in two or three layers on the surface configuration. In addition, the atomic relaxation of Ti-terminated surface is most remarkable, and followed by Ni-terminated surface, while the atomic relaxation of Ni&Ti-terminated surface is insignificant. Furthermore, the valence charge density decays rapidly from the surface configuration to the vacuum layer.　　The calculation results of surface energy show that surface energy is inversely related to the coordinate number, and surface stability increases with the coordination number increasing. For B2- and B19'-NiTi, the surface energy of non-dense and non-stoichiometric surface depend on the chemical potential of Ti, and the surface energy is high. Therefore, the stabilities of these surfaces change with the chemical potential of Ti increasing. However, the surface energy values of dense surface configurations with stoichiometric ratio for B2-NiTi (101) and B19'-NiTi (010) are 1.81 J/m² and 1.93 J/m², respectively, which are both lower than those for other non-dense surfaces in the most Ti chemical potentials range, showing excellent structural stability. Moreover, the electron density analysis indicates that the dominant bonding for B2-NiTi (101) surface is the chained Ni-Ti-Ni metallic bond, the distribution of electrons and the distance between Ni and Ti atoms on the B2-NiTi (101) surface are more uniform and smaller, respectively, than those for B19'-NiTi (010) surface. In summary, the B2-NiTi (101) surface shows the high stability.

Keywords:

Authors and contacts

1.
State Key Laboratory for Mechanical Behavior of Materials, Xi'an Jiaotong University, Xi'an 710049, China
2.
Shandong Huifeng Casting Technology Co., Ltd., Ji'nan 250000, China

Corresponding author: Li Ye-Fei, liyefei@xjtu.edu.cn

Funds: Projects supported by the National Natural Science Foundation of China (Grant No. 51501139), the Natural Science Foundation of Shaanxi Province, China (Grant No. 2018JM5002), the Guangxi Innovation Driven Development Project, China (Grant No. GUIKEAA18242001), the Science and Technology Project Fund of Guangdong Province, China (Grant No. 2015B010122003), the Guangzhou Science and Technology Project Fund, China (Grant No.201604046009), and the China Postdoctoral Science Foundation (Grant Nos. 2018M631152, 2018T111051).

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References

[1]	马蕾, 王旭, 尚家香 2014 63 233103 Google Scholar Ma L, Wang X, Shang J X 2014 Acta Phys. Sin. 63 233103 Google Scholar
[2]	吴红丽, 赵新青, 宫声凯 2010 59 515 Google Scholar Wu H L, Zhao X Q, Gong S K 2010 Acta Phys. Sin. 59 515 Google Scholar
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[4]	Huang X Y, Bungaro C, Godlevsky V, Rabe K M 2001 Phys. Rev. B 65 014108 Google Scholar
[5]	Fukuda T, Kakeshita T, Houjoh H, Shiraishi S, Saburi T 1999 Mater. Sci. Eng. A 273−275 166
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[12]	孔祥确, 金学军, 刘剑楠 2016 功能材料 47 1007 Google Scholar Kong X Q, Jin X J, Liu J N 2016 Func. Mater. 47 1007 Google Scholar
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[14]	杨贤金, 朱胜利, 崔振铎, 姚康德 2001 功能材料 32 154 Google Scholar Yang X J, Zhu S L, Cui Z D, Yao K D 2001 Func. Mater. 32 154 Google Scholar
[15]	Qiu D L, Wang A P, Yin Y S 2010 Appl. Surf. Sci. 257 1774 Google Scholar
[16]	Li Y F, Tang S L, Gao Y M, Ma S Q, Zheng Q L, Cheng Y H 2017 Int. J. Mod. Phys. B 31 1750161 Google Scholar
[17]	Nigussa K N, Støvneng J A 2011 Comput. Phys. Commun. 182 1979 Google Scholar
[18]	Vishnu K G, Strachan A 2012 Phys. Rev. B 85 014114 Google Scholar
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[20]	Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865 Google Scholar
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图 1 NiTi合金的低指数表面原子构型　(a) B2-NiTi(101)_NiTi; (b) B2-NiTi_Ni; (100); (c) B2-NiTi(111)_Ni; (d) B19’-NiTi(010)_NiTi; (e) B19'-NiTi(001)_Ni; (f) B19'-NiTi(110)_Ni; 绿色球和黑色球分别代表Ni, Ti原子

Figure 1. Atomic low-index surface configurations of NiTi alloy: (a) B2-NiTi(101)_NiTi; (b) B2-NiTi(100)_Ni; (c) B2-NiTi(111)_Ni; (d) B19’-NiTi(010)_NiTi; (e) B19'-NiTi(001)_Ni; (f) B19'-NiTi(110)_Ni.

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图 2 NiTi合金的DOS曲线　(a)B2-NiTi; (b)B19'-NiTi

Figure 2. DOS curves for NiTi alloys: (a) B2-NiTi; (b) B19'-NiTi.

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图 3 富Ti条件下表面能随表面构型原子层数目变化曲线　(a) B2-NiTi; (b) B19'-NiTi

Figure 3. Under the condition of Ti-rich, the surface energy varies with the number of atomic layers of the surface configuration: (a) B2-NiTi; (b) B19'-NiTi.

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图 4 B2-NiTi和B19'-NiTi体相密排面的电荷密度分布　(a) B2-NiTi (101); (b) B19'-NiTi (010)

Figure 4. Charge density distribution of dense plane of bulk B2-NiTi and B19'-NiTi: (a) B2-NiTi (101); (b) B19'-NiTi (010).

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图 5 非化学计量比表面的表面能随Ti化学势的变化　(a) B2-NiTi; (b) B19'-NiTi

Figure 5. Surface energies of non-stoichiometric surface versus Ti chemical potentials: (a) B2-NiTi; (b) B19'-NiTi.

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图 6 B2-和B19'-NiTi体相总DOS和表面构型层投影DOS曲线　(a) B2-NiTi (100)_Ni; (b) B19'-NiTi (010)_NiTi; (c) B2-NiTi (101)_NiTi; (d) B19'-NiTi (101)_Ni; (e) B2-NiTi (111)_Ni; (f) B19'-NiTi (111)_Ni

Figure 6. Total DOS of B2 and B19'-NiTi body phase and surface configurations layer projected DOS curves: (a) B2-NiTi (100)_Ni; (b) B19'-NiTi (010)_NiTi; (c) B2-NiTi (101)_NiTi; (d) B19'-NiTi (101)_Ni; (e) B2-NiTi (111)_Ni; (f) B19'-NiTi (111)_Ni.

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图 7 B2-和B19'-NiTi表面构型总电子密度分布　(a) B2-NiTi (101)_NiTi; (b) B2-NiTi (111)_Ni; (c) B19'-NiTi (010)_NiTi; (d) B19'-NiTi (101)_Ni

Figure 7. Total electron density distribution of B2- and B19'-NiTi surface configurations: (a) B2-NiTi (101)_NiTi; (b) B2-NiTi (111)_Ni; (c) B19'-NiTi (010)_NiTi; (d) B19'-NiTi (101)_Ni.

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表 1 NiTi合金的晶格常数、密度、剪切模量、体模量及生成焓

Table 1. Calculated cell parameters, density, shear modulus, bulk modulus and formation enthalpy.

Compounds	a/Å	b/Å	c/Å	V/Å³	G/MPa	B/MPa	${\Delta _{\rm{r}}}H$/eV·atom^–1
B2-NiTi	3.015 (3.033^a, 3.016^b, 3.01^c)	—	—	27.402 (27.901^a, 27.434^b, 27.27^c)	69.0 (73^d)	155.5 (142.3^a, 150.0^b, 142^e)	–0.374 (–0.35^f)
B19'-NiTi	4.646 (4.685^g, 4.813^h, 4.631ⁱ)	4.108 (4.035^g, 4.121^h, 4.10ⁱ)	2.898 (2.941^g, 3.007^h, 2.885ⁱ)	55.705 (55.080^g, 58.610^h, 54.84ⁱ)	26.2 (23^j)	148.9 (147^k, 158^f)	–0.328
注: a, b, d, g, h, j, k为理论参考值, Ref.[21-22,23,3,26,27-28]; c, 实验参考值, Inorganic Crystal Structure Database (ICSD) #105413; e, 实验参考值Ref.[24]; f, 实验参考值, Ref.[25]; i, 实验参考值, ICSD #240195.

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表 2 B2-NiTi表面原子层位移相对体相间距的变化率随切片厚度的变化 (%)

Table 2. Relaxations of B2-NiTi surfaces with different terminations and slab thickness given in terms of the change of interlayer spacing in percent of the bulk spacing (%).

Surface	Termination	Interlayer	Slab thickness
Surface	Termination	Interlayer	3	5	7	9	11
(101)	Ni, Ti	${\varDelta _{12}}$	–9.67	–10.42	–9.99	–9.88	–9.91
		${\varDelta _{23}}$		–0.19	1.18	1.99	1.78
		${\varDelta _{34}}$			–0.83	–0.65	–0.47
		${\varDelta _{45}}$				0.43	1.15
		${\varDelta _{56}}$					0.57
(100)	Ni	${\varDelta _{12}}$	–1.77	–8.13	–8.89	–8.78	–8.93
		${\varDelta _{23}}$		3.85	3.48	2.79	2.76
		${\varDelta _{34}}$			–0.72	–0.41	0.17
		${\varDelta _{45}}$				1.11	–0.37
		${\varDelta _{56}}$					2.18
	Ti	${\varDelta _{12}}$	–2.24	–21.68	–17.08	–15.16	–16.68
		${\varDelta _{23}}$		15.42	12.14	7.11	10.78
		${\varDelta _{34}}$			0.01	4.03	2.82
		${\varDelta _{45}}$				–5.72	–1.93
		${\varDelta _{56}}$					1.53

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[1]	马蕾, 王旭, 尚家香 2014 63 233103 Google Scholar Ma L, Wang X, Shang J X 2014 Acta Phys. Sin. 63 233103 Google Scholar
[2]	吴红丽, 赵新青, 宫声凯 2010 59 515 Google Scholar Wu H L, Zhao X Q, Gong S K 2010 Acta Phys. Sin. 59 515 Google Scholar
[3]	Wagner M F X, Windl W 2008 Acta. Mater. 56 6232 Google Scholar
[4]	Huang X Y, Bungaro C, Godlevsky V, Rabe K M 2001 Phys. Rev. B 65 014108 Google Scholar
[5]	Fukuda T, Kakeshita T, Houjoh H, Shiraishi S, Saburi T 1999 Mater. Sci. Eng. A 273−275 166
[6]	贾堤, 董治中, 于申军, 刘文西 1998 原子与分子 15 421 Jia D, Dong Z Z, Yu S J, Liu W X 1998 J. Atom. Mol. Phys. Sin. 15 421
[7]	姜振益, 李盛涛 2006 55 6032 Google Scholar Jiang Z Y, Li S T 2006 Acta Phys. Sin. 55 6032 Google Scholar
[8]	Hua Y J, Liu X, Meng C G, Yang D Z 2003 J. Wuhan. Univ. Technol. 18 6
[9]	朱建新, 李永华, 孟繁玲, 刘常升, 郑伟涛, 王煜明 2008 57 7204 Google Scholar Zhu J X, Li Y H, Meng F L, Liu C S, Zheng W T, Wang Y M 2008 Acta Phys. Sin. 57 7204 Google Scholar
[10]	单迪, 何鑫玉, 方长青, 邵晖 2015 材料导报A: 综述篇 29 28 Shan D, He X Y, Fang C Q, Shao H 2015 Mater. Rev. A 29 28
[11]	尹大宇, 朱锦宇, 段永宏, 李矛, 韩建业, 朱庆生 2011 华南国防医学杂志 25 52 Yin D Y, Zhu J Y, Duan Y H, Li M, Han J Y, Zhu Q S 2011 Milit. Medi. J. Sou. China 25 52
[12]	孔祥确, 金学军, 刘剑楠 2016 功能材料 47 1007 Google Scholar Kong X Q, Jin X J, Liu J N 2016 Func. Mater. 47 1007 Google Scholar
[13]	邵明增, 崔春娟, 杨洪波 2018 材料导报A: 综述篇 32 1181 Shao M Z, Cui C J, Yang H B 2018 Mater. Rev. A 32 1181
[14]	杨贤金, 朱胜利, 崔振铎, 姚康德 2001 功能材料 32 154 Google Scholar Yang X J, Zhu S L, Cui Z D, Yao K D 2001 Func. Mater. 32 154 Google Scholar
[15]	Qiu D L, Wang A P, Yin Y S 2010 Appl. Surf. Sci. 257 1774 Google Scholar
[16]	Li Y F, Tang S L, Gao Y M, Ma S Q, Zheng Q L, Cheng Y H 2017 Int. J. Mod. Phys. B 31 1750161 Google Scholar
[17]	Nigussa K N, Støvneng J A 2011 Comput. Phys. Commun. 182 1979 Google Scholar
[18]	Vishnu K G, Strachan A 2012 Phys. Rev. B 85 014114 Google Scholar
[19]	Sandoval L, Haskins J B, Lawson J W 2018 Acta Mater. 154 182 Google Scholar
[20]	Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865 Google Scholar
[21]	Fischer T H, Almlof J 1992 J. Phys. Chem. 96 9768 Google Scholar
[22]	Li G F, Zheng H Z, Shu X Y, Peng P 2016 Met. Mater. Int. 22 69 Google Scholar
[23]	Pfetzing-Micklich J, Somsen C, Dlouhy A, Begau C, Hartmaier A, Wagner M F X, Eggeler G 2013 Acta Mater. 61 602 Google Scholar
[24]	Mercier O, Melton K N, Gremaud G, Häji J 1980 J. Appl. Phys. 51 1833 Google Scholar
[25]	Hatcher N, Kontsevoi O Y, Freeman A J 2009 Phys. Rev. B 80 144203 Google Scholar
[26]	Sestak P, Cerny M, Pokluda J 2008 Strength. Mater. 40 12 Google Scholar
[27]	Sedlak P, Frost M, Kruisova A, Hirmanova K, Heller L, Sittner P 2014 J.Mater. Eng. Perf. 23 2591 Google Scholar
[28]	Zeng Z Y, Hu C E, Cai L C, Chen X R, Jing F Q 2010 Physica B 405 3665 Google Scholar
[29]	Fiorentini V, Methfessel M 1996 J. Phys-Condens. Mat. 8 6525 Google Scholar
[30]	Monkhorst H J, Pack J D 1976 Phys. Rev. B 13 5188 Google Scholar
[31]	Lazzeri M, Vittadini A, Selloni A 2001 Phys. Rev. B 63 155409 Google Scholar

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