Lattice vibration and thermodynamical properties of a single-layergraphene in the presence of vacancy defects

doi:10.1088/1674-1056/26/3/036303

中国物理B ›› 2017, Vol. 26 ›› Issue (3): 36303-036303.doi: 10.1088/1674-1056/26/3/036303

• CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES • 上一篇下一篇

Lattice vibration and thermodynamical properties of a single-layergraphene in the presence of vacancy defects

Sha Li(黎莎), Zeng-Tao Lv(吕增涛)

1 School of Physics, Beijing Institute of Technology, Beijing 100081, China;
2 School of Physical Science and Information Engineering, Liaocheng University, Liaocheng 252059, China

收稿日期:2016-09-13 修回日期:2016-12-11 出版日期:2017-03-05 发布日期:2017-03-05
通讯作者: Zeng-Tao Lv E-mail:lvzengtao@lcu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11404155 and 11274040).

Lattice vibration and thermodynamical properties of a single-layergraphene in the presence of vacancy defects

Sha Li(黎莎)¹, Zeng-Tao Lv(吕增涛)^1,2

1 School of Physics, Beijing Institute of Technology, Beijing 100081, China;
2 School of Physical Science and Information Engineering, Liaocheng University, Liaocheng 252059, China

Received:2016-09-13 Revised:2016-12-11 Online:2017-03-05 Published:2017-03-05
Contact: Zeng-Tao Lv E-mail:lvzengtao@lcu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11404155 and 11274040).

摘要/Abstract

摘要： The phonon density of states (PDOS) and the thermodynamical properties including the heat capacity, the free energy, and the entropy of a single-layer graphene with vacancy defects have been studied theoretically. We first analytically derive the general formula of the lattice vibration frequency, and then numerically discuss the effect of the defects on the PDOS. Our results suggest that the vacancy defects will induce the sawtooth-like oscillation of the PDOS and the specific oscillation patterns depend on the concentration and the spatial distribution of the vacancies. In addition, it is verified that the vacancy defects will cause the increase of the heat capacity because of the vacancy-induced low-frequency resonant peak. Moreover, the influences of the vacancies on the free energy and the entropy are investigated.

关键词: phonons in graphene, thermal properties, defects

Abstract: The phonon density of states (PDOS) and the thermodynamical properties including the heat capacity, the free energy, and the entropy of a single-layer graphene with vacancy defects have been studied theoretically. We first analytically derive the general formula of the lattice vibration frequency, and then numerically discuss the effect of the defects on the PDOS. Our results suggest that the vacancy defects will induce the sawtooth-like oscillation of the PDOS and the specific oscillation patterns depend on the concentration and the spatial distribution of the vacancies. In addition, it is verified that the vacancy defects will cause the increase of the heat capacity because of the vacancy-induced low-frequency resonant peak. Moreover, the influences of the vacancies on the free energy and the entropy are investigated.

Key words: phonons in graphene, thermal properties, defects

中图分类号: (Phonons in graphene)

63.22.Rc

65.80.Ck (Thermal properties of graphene) 61.72.-y (Defects and impurities in crystals; microstructure)

黎莎, 吕增涛. Lattice vibration and thermodynamical properties of a single-layergraphene in the presence of vacancy defects[J]. 中国物理B, 2017, 26(3): 36303-036303.

Sha Li(黎莎), Zeng-Tao Lv(吕增涛). Lattice vibration and thermodynamical properties of a single-layergraphene in the presence of vacancy defects[J]. Chin. Phys. B, 2017, 26(3): 36303-036303.

参考文献 53

[1]	Novoselov K S, Geim A K, Morozov S V, Jiang D, Katsnelson M I, Grigorieva I V, Dubonos S V and Firsov A A 2005 Nature 438 197
[2]	Geim A K and Novoselov K S 2007 Nat. Mater. 6 183
[3]	Zhang Y B, Tan Y, Stormer H L and Kim P 2005 Nature 438 201
[4]	Stankovich S, Dikin D A, Dommett G H B, Kohlhaas K M, Zimney E J, Stach E A, Piner R D, Nguyen S T and Ruoff R S 2006 Nature 442 282
[5]	Pereira V M, Guinea F, Lopes dos Santos J M B, Peres N M R and Castro Neto A H 2006 Phys. Rev. Lett. 96 036801
[6]	Calizo I, Miao F, Bao W, Lau C N and Balandin A A 2007 Appl. Phys. Lett. 91 071913
[7]	Balandin A A, Ghosh S, Bao W Z, Calizo I, Teweldebrhan D, Miao F and Lau C N 2008 Nano Lett. 8 902
[8]	Wang Z, Xie R, Bui C T, Liu D, Ni X, Li B and Thong J T L 2011 Nano Lett. 11 113
[9]	Pop E, Varshney V and Roy A K 2012 MRS Bull. 37 1273
[10]	Jang W, Bao W, Jing L, Lau C N and Dames C 2013 Appl. Phys. Lett. 103 113102
[11]	Nair R R, Blake P, Grigorenko A N, Novoselov K S, Booth T J, Stauber T, Peres N M R and Geim A K 2008 Science 320 1308
[12]	Mak K F, Shan J and Heinz T F 2011 Phys. Rev. Lett. 106 046401
[13]	Yan J, Ruan W Y and Chou M Y 2008 Phys. Rev. B 77 125401
[14]	Saha S K, Waghmare U V, Krishnamurthy H R and Sood A K 2008 Phys. Rev. B 78 165421
[15]	Ma F, Zheng H B, Sun Y J, Yang D, Xu K W and Chu P K 2012 Appl. Phys. Lett. 101 111904
[16]	Cocemasov A I, Nika D L and Balandin A A 2013 Phys. Rev. B 88 035428
[17]	Kim K S, Zhao Y, Jang H, Lee S Y, Kim K S, Ahn J, Kim P, Choin J and Hong B H 2009 Nature 457 706
[18]	Bae S, Kim H, Lee Y, Xu X, Park J, Zheng Y, Balakrishnan J, Lei T, Kim H R, Song Y, Kim Y, Kim K S, Özyilmaz B, Ahn J, Hong B H and Lijima S 2010 Nat. Nanotechnol. 5 574
[19]	Sutter P W, Flege J and Sutter E A 2008 Nat. Mater. 7 406
[20]	Pan B Y, Zhang H, Shi D, Sun J, Du S, Liu F and Gao H 2009 Adv. Mater. 21 2777
[21]	Stankovich S, Dikin D A, Domentt G H B, Kohlhaas K M, Zimney E J, Stach E A, Piner R D, Nguyen S T and Ruoff R S 2006 Nature 442 282
[22]	Wang H, Robinson J T, Li X and Dai H 2009 J. Am. Chem. Soc. 131 9910
[23]	Jiang J W, Wang J S and Li B 2009 Phys. Rev. B 79 205418
[24]	Savic I, Mingo N and Stewart D A 2008 Phys. Rev. Lett. 101 165502
[25]	Jiang J W, Lan J, Wang J S and Li B 2010 J. Appl. Phys. 107 054314
[26]	Mingo N, Esfarjani K, Broido D A and Stewart D A 2010 Phys. Rev. B 81 045408
[27]	Zhang H, Lee G and Cho K 2011 Phys. Rev. B 84 115460
[28]	Hao F, Fang D and Xu Z 2011 Appl. Phys. Lett. 99 041901
[29]	Jiang J W, Wang B S and Wang J S 2011 Appl. Phys. Lett. 98 113114
[30]	Adamyan V and Zavalniuk V 2011 J. Phys.:Condens. Matter 23 015402
[31]	Sgouros A, Sigalas M M, Kalosakas G, Papagelis K and Papanicolaou N I 2012 J. Appl. Phys. 112 094307
[32]	Gass M H, Bangert U, Bleloch A L, Wang P, Nair R R and Geim A K 2008 Nat. Nanotechnol. 3 676
[33]	Meyer J C, Kisielowski C, Erni R, Rossell M D, Crommie M F and Zettl A 2008 Nano Lett. 8 3582
[34]	Ugeda M M, Brihuega I, Guinea F and Gómez-Rodríguez G M 2010 Phys. Rev. Lett. 104 096804
[35]	Banhart F, Kotakoski J and Krasheninnikov A V 2011 ACS Nano 5 26
[36]	Saito R, Dresselhaus G and Dresselhaus M S 1998 Physical Properties of Carbon Nanotubes (Singapore:Imperial College Press) p. 169
[37]	Dubay O and Kresse G 2003 Phys. Rev. B 67 035401
[38]	Maultzsch J, Reich S, Thomsen C, Requardt H and Ordejón 2004 Phys.Rev. Lett. 92 075501
[39]	Wirtz L and Rubio A 2004 Solid State Commun. 131 141
[40]	Oshima C, Aizawa T, Souda R, Lshizawa Y and Sumiyoshi Y 1988 Solid State Commun. 65 1601
[41]	Mohr M, Maultzsch J, Dobardižić E, Reich S, Milošević I, Dammn-janović M, Bosak A, Krisch M and Thomsen C 2007 Phys. Rev. B 76 035439
[42]	Perdew J P, Burke K and Ernzerhof M 1996 Phys. Rev. Lett. 77 3865
[43]	Amara H, Latil S, Meunier V, Lambin P and Charlier J C 2007 Phys. Rev. B 76 115423
[44]	Roy R S 1968 J. Phys. B 1 445
[45]	Jain K P and Prabhakaran A K 1962 Phys. Rev. Lett. 9 54
[46]	Brout R and Visscher W M 1972 Phys. Rev. B 6 596
[47]	Liang W, Xiao Y and Ding J W 2008 Acta Phys. Sin. 57 3714
[48]	Sharmila S N and Waghmare U V 2012 Phys. Rev. B 86 165401
[49]	Nihira T and Iwata T 2003 Phys. Rev. B 68 134305
[50]	Lu D, Jiang P and Xu Z Z 2010 Solid State Physics (Shanghai:Shanghai Scientific and Technical Publishers) p. 76
[51]	Aizawa T, Souda R, Ishizawa Y, Hirano H, Yamada T, Tanaka K and Oshima C 1990 Surf. Sci. 237 194
[52]	Shikin A M, Farias D and Rieder K H 1998 Europhys. Lett. 44 44
[53]	Ong Z Y and Pop E 2011 Phys. Rev. B 84 075471

Lattice vibration and thermodynamical properties of a single-layergraphene in the presence of vacancy defects

Lattice vibration and thermodynamical properties of a single-layergraphene in the presence of vacancy defects

RichHTML

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 53

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	Yadong Wang(王亚东), Fujie Zhang(张富界), Xuri Rao(饶旭日), Haoran Feng(冯皓然),Liwei Lin(林黎蔚), Ding Ren(任丁), Bo Liu(刘波), and Ran Ang(昂然). Advancing thermoelectrics by suppressing deep-level defects in Pb-doped AgCrSe₂ alloys[J]. 中国物理B, 2023, 32(4): 47202-047202.
[2]	Tao-Wen Xiong(熊涛文), Xiao-Ping Chen(陈小平), Ye-Ping Lin(林也平), Xin-Fu He(贺新福), Wen Yang(杨文), Wang-Yu Hu(胡望宇), Fei Gao(高飞), and Hui-Qiu Deng(邓辉球). Molecular dynamics study of interactions between edge dislocation and irradiation-induced defects in Fe–10Ni–20Cr alloy[J]. 中国物理B, 2023, 32(2): 20206-020206.
[3]	Zhiqiang Ye(叶志强), Yawei Lei(雷亚威), Jingdan Zhang(张静丹), Yange Zhang(张艳革), Xiangyan Li(李祥艳), Yichun Xu(许依春), Xuebang Wu(吴学邦), C. S. Liu(刘长松), Ting Hao(郝汀), and Zhiguang Wang(王志光). Effects of oxygen concentration and irradiation defects on the oxidation corrosion of body-centered-cubic iron surfaces: A first-principles study[J]. 中国物理B, 2022, 31(8): 86802-086802.
[4]	Yutuo Guo(郭玉拓), Qinqin Wang(王琴琴), Xiaomei Li(李晓梅), Zheng Wei(魏争), Lu Li(李璐), Yalin Peng(彭雅琳), Wei Yang(杨威), Rong Yang(杨蓉), Dongxia Shi(时东霞), Xuedong Bai(白雪冬), Luojun Du(杜罗军), and Guangyu Zhang(张广宇). Direct visualization of structural defects in 2D semiconductors[J]. 中国物理B, 2022, 31(7): 76105-076105.
[5]	Shan Feng(冯山), Ming Jiang(姜明), Qi-Hang Qiu(邱启航), Xiang-Hua Peng(彭祥花), Hai-Yan Xiao(肖海燕), Zi-Jiang Liu(刘子江), Xiao-Tao Zu(祖小涛), and Liang Qiao(乔梁). First-principles study of stability of point defects and their effects on electronic properties of GaAs/AlGaAs superlattice[J]. 中国物理B, 2022, 31(3): 36104-036104.
[6]	Zheng-Zhao Lin(林正兆), Ling Lü(吕玲), Xue-Feng Zheng(郑雪峰), Yan-Rong Cao(曹艳荣), Pei-Pei Hu(胡培培), Xin Fang(房鑫), and Xiao-Hua Ma(马晓华). Effect of heavy ion irradiation on the interface traps of AlGaN/GaN high electron mobility transistors[J]. 中国物理B, 2022, 31(3): 36103-036103.
[7]	Yuan-Ting Huang(黄垣婷), Xiu-Hai Cui(崔秀海), Jian-Qun Yang(杨剑群), Tao Ying(应涛), Xue-Qiang Yu(余雪强), Lei Dong(董磊), Wei-Qi Li(李伟奇), and Xing-Ji Li(李兴冀). Radiation effects of 50-MeV protons on PNP bipolar junction transistors[J]. 中国物理B, 2022, 31(2): 28502-028502.
[8]	Lin Lang(稂林), Huiqiu Deng(邓辉球), Jiayou Tao(陶家友), Tengfei Yang(杨腾飞), Yeping Lin(林也平), and Wangyu Hu(胡望宇). Comparison of formation and evolution of radiation-induced defects in pure Ni and Ni-Co-Fe medium-entropy alloy[J]. 中国物理B, 2022, 31(12): 126102-126102.
[9]	Jijun Huang(黄及军), and Xueling Lei(雷雪玲). Identification of the phosphorus-doping defect in MgS as a potential qubit[J]. 中国物理B, 2022, 31(10): 106102-106102.
[10]	Zhenghao Cai(蔡正浩), Bowei Li(李博维), Liangchao Chen(陈良超), Zhiwen Wang(王志文), Shuai Fang(房帅), Yongkui Wang(王永奎), Hongan Ma(马红安), and Xiaopeng Jia(贾晓鹏). Effect of the codoping of N—H—O on the growth characteristics and defects of diamonds under high temperature and high pressure[J]. 中国物理B, 2022, 31(10): 108104-108104.
[11]	Xue-Hua Liu(刘雪华), Wei-Feng Xie(谢伟锋), Yang Liu(刘杨), and Xu Zuo(左旭). Passivation and dissociation of P_b-type defects at a-SiO₂/Si interface[J]. 中国物理B, 2021, 30(9): 97101-097101.
[12]	Jintao Hong(洪锦涛), Fengyuan Zhang(张丰源), Zheng Liu(刘峥), Jie Jiang(蒋杰), Zhangting Wu(吴章婷), Peng Zheng(郑鹏), Hui Zheng(郑辉), Liang Zheng(郑梁), Dexuan Huo(霍德璇), Zhenhua Ni(倪振华), and Yang Zhang(张阳). Achieving high-performance multilayer MoSe₂ photodetectors by defect engineering[J]. 中国物理B, 2021, 30(8): 87801-087801.
[13]	Qian Yin(尹倩), Ye-Da Lian(连业达), Rong-Hai Wu(巫荣海), Li-Qiang Gao(高利强), Shu-Qun Chen(陈树群), and Zhi-Xun Wen(温志勋). Effect of the potential function and strain rate on mechanical behavior of the single crystal Ni-based alloys: A molecular dynamics study[J]. 中国物理B, 2021, 30(8): 80204-080204.
[14]	Ligang Song(宋力刚), Bo Huang(黄波), Jianghua Li(李江华), Xianfeng Ma(马显锋), Yang Li(李阳), Zehua Fang(方泽华), Min Liu(刘敏), Jishen Jiang(蒋季伸), and Yanying Hu(胡琰莹). Microstructure evolution of T91 steel after heavy ion irradiation at 550 ℃[J]. 中国物理B, 2021, 30(8): 86103-086103.
[15]	Peng-Wei Hou(侯鹏伟), Yu-Hao Li(李宇浩), Zhong-Zhu Li(李中柱), Li-Fang Wang(王丽芳), Xingyu Gao(高兴誉), Hong-Bo Zhou(周洪波), Haifeng Song(宋海峰), and Guang-Hong Lu(吕广宏). Influence of helium on the evolution of irradiation-induced defects in tungsten: An object kinetic Monte Carlo simulation[J]. 中国物理B, 2021, 30(8): 86108-086108.