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One-dimensional (1D) carbyne chain has the potential applications in the nanoelectronic devices due to its unique properties. Although some progress of the mechanical and thermal properties of 1D carbyne chain has been made, the physical mechanism of the strain modulation of atomic bond nature remains unclear. In order to explore the strain effects on the mechanical and related physical properties of 1D carbyne chain, we systematically investigate the strain-dependent bond nature of 1D carbyne chain based on the first-principles calculations of density functional theory and generalized gradient approximation. It is found that when the compressive strain is 16%, the bonding nature of 1D carbyne chain is changed, and the bond length alternation of single and triple bonds in 1D carbyne chain tends to zero, which originates from the difference in bond strength between single bond and triple bond. Moreover, 1D carbyne chain can change from semiconductor into metal when the compressive strain is 16% indicated by analyzing the band structure and related differential charge density. When the strain is 17%, the phonon spectrum has an imaginary frequency. Besides, when the ambient temperature is less than 510 K, the heat capacity of 1D carbyne chain decreases with strain increasing. However, more phonon modes will be activated at larger strains when the temperature is higher than 510 K, and the heat capacity is enhanced gradually with strain increasing. Also, the stiffness coefficient of 1D carbyne chain is larger than that of graphene and carbon nanotube. These results conduce to the fundamental understanding of atomic bond nature in 1D carbyne chain under different strains.
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Keywords:
- carbyne /
- first-principles calculations /
- electronic structure /
- heat capacity
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图 1 (a) Carbyne链结构示意图; (b) 差分电荷密度图
Figure 1. (a) Schematic diagram of a carbyne unit cell structure; (b) diagram of the related differential charge density.
图 2 (a) Carbyne链单位应变能(两个原子)与应变之间的关系; (b), (c) 分别为拉伸应变和压缩应变所对应的carbyne链键长差值的变化; (d) carbyne链差分电荷密度在拉伸和压缩应变下的变化图
Figure 2. (a) Density functional theory calculations of stretching energy per unit cell (two atoms) as a function of strain
$\varepsilon $ ; (b) tensile strain and (c) compressive strain dependence of bond length difference; (d) the charge density of carbyne under the condition of tensile and compressive strains.
图 3 Carbyne链原胞的能带结构 (a) 未施加应变; (b) 压缩应变为16%.
Figure 3. Band structures of carbyne chain: (a) Without strain; (b) under compressive strain of 16%.
图 4 (a), (b), (c) 分别为碳-碳单键、碳-碳三键和carbyne链在拉伸应变下外力与c方向长度改变量之间的关系
Figure 4. Force of (a) single bond, (b) triple bonds and (c) carbyne chain as a function of length change in the c direction under tensile strain.
图 5 Carbyne链原胞的声子谱 (a)—(f) 分别是轴向拉伸应变为0%, 3%, 6%, 9%, 12%, 17%时对应的声子谱.
Figure 5. Phonon spectrum of carbyne unit cell. Panels (a)–(f) are the corresponding phonon spectra when the axial tensile strains are 0%, 3%, 6%, 9%, 12% and 17%, respectively.
图 6 轴向拉伸应变下carbyne链热容量随温度的变化
Figure 6. Temperature-dependent heat capacity of carbyne chain under the approach of axial tensile strain
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[1] Novoselov K S, Geim A K, Morozov S V, Jiang D, Zhang Y, Dubonos S V, Grigorieva I V, Firsov A A 2004 Science 306 666
Google Scholar
[2] Bolotin K I, Sikes K J, Jiang Z, Klima M, Fudenberg G, Hone J, Kim P, Stormer H L 2008 Solid State Commun. 146 351
Google Scholar
[3] Cao A Y, Dickrell P L, Sawyer W G, Ghasemi-Nejhad M N, Ajayan P M 2005 Science 310 1307
Google Scholar
[4] Boyd A, Dube I, Fedorov G, Paranjape M, Barbara P 2014 Carbon 69 417
Google Scholar
[5] Dillon A C, Jones K M, Bekkendahl T A, Kiang C H, Bethune D S, Heben M J 1997 Nature 386 377
Google Scholar
[6] Chen P, Wu X, Lin J, Tan K L 1999 Science 285 91
Google Scholar
[7] Baughman R H, Zakhidov A A, De Heer W A 2002 Science 297 787
Google Scholar
[8] Liu M J, Artyukhov V I, Lee H, Xu F, Yakobson B I 2013 ACS Nano 7 10075
Google Scholar
[9] Zhang Y Z, Su Y J, Wang L, Kong E S W, Chen X S, Zhang Y F 2011 Nanoscale Res. Lett. 6 577
Google Scholar
[10] Pan B, Xiao J, Li J, Liu P, Wang C, Yang G 2015 Sci. Adv. 1 e1500857
Google Scholar
[11] Kotrechko S, Timoshevskii A, Kolyvoshko E, Matviychuk Y, Stetsenko N 2017 Nanoscale Res. Lett. 12 327
Google Scholar
[12] Akdim B, Pachter R 2011 ACS Nano 5 1769
Google Scholar
[13] 周艳红, 许英, 郑小宏 2007 物理学报 56 1093
Google Scholar
Zhou Y H, Xu Y, Zheng X H 2007 Acta Phys. Sin. 56 1093
Google Scholar
[14] Sorokin P B, Lee H, Antipina L Y, Singh A K, Yakobson B I 2011 Nano Lett. 11 2660
Google Scholar
[15] Cannella C B, Goldman N 2015 J. Phys. Chem. C 119 21605
Google Scholar
[16] Andrade N F, Aguiar A L, Kim Y A, Endo M, Freire P T C, Brunetto G, Galvao D S, Dresselhaus M S, Souza Filho A G 2015 J. Phys. Chem. C 119 10669
Google Scholar
[17] Wang M, Lin S 2015 Sci. Rep. 5 18122
Google Scholar
[18] Liu F, Ming P, Li J 2007 Phys. Rev. B 76 064120
Google Scholar
[19] Lu J P 1997 Phys. Rev. Lett. 79 1297
Google Scholar
[20] Nair A K, Cranford S W, Buehler M J 2011 Eurphys. Lett. 95 16002
Google Scholar
[21] Artyukhov V I, Liu M, Yakobson B I 2014 Nano Lett. 14 4224
Google Scholar
[22] Yang X G, Lv C F, Yao Z, Yao M G, Qin J X, Li X, Shi L, Du M R, Liu B B, Shan C X 2020 Carbon 159 266
Google Scholar
[23] Zhang Z, Zhao Y P, Ouyang G 2017 J. Phys. Chem. C 121 19296
Google Scholar
[24] Dong J S, Ouyang G 2019 ACS Omega 4 8641
Google Scholar
[25] Kresse G, Furthmüller J 1996 Phys. Rev. B 54 11169
Google Scholar
[26] Kresse G, Furthmüller J 1996 Comput. Mater. Sci. 6 15
Google Scholar
[27] Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865
Google Scholar
[28] Blöchl P E 1994 Phys. Rev. B 50 17953
Google Scholar
[29] Monkhorst H J, Pack J D 1976 Phys. Rev. B 13 5188
Google Scholar
[30] Togo A, Tanaka I 2015 Scr. Mater. 108 1
Google Scholar
[31] Ma F, Zheng H B, Sun Y J, Yang D, Xu K W, Chu P K 2012 Appl. Phys. Lett. 101 111904
Google Scholar
[32] La Torre A, Botello-Mendez A, Baaziz W, Charlier J C, Banhart F 2015 Nat. Commun. 6 6636
Google Scholar
[33] Li J P, Meng S H, Lu H T, Tohyama T 2018 Chin. Phys. B 27 117101
Google Scholar
[34] Cretu O, Botello-Mendez A R, Janowska I, Pham-Huu C, Charlier J C, Banhart F 2013 Nano Lett. 13 3487
Google Scholar
[35] Kudryavtsev Y P, Evsyukov S E, Guseva M B, Babaev V G, Khvostov V V 1993 Russ. Chem. Bull. 42 399
Google Scholar
[36] Heimann R B, Evsyukov S E, Kavan L 1999 Carbyne and Carbynoid Structures (Dordrecht: Kluwer Academic Press) p317
[37] Liu X J, Zhang G, Zhang Y W 2015 J. Phys. Chem. C 119 24156
Google Scholar
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