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声子是石墨烯导热过程中的主要载体，而声子的弛豫时间又是其中最基本、最重要的物理量. 本文采用简正模式分解法研究了石墨烯声子的弛豫时间，并且借此分析了不同声子在导热过程中的贡献. 该方法通过平衡分子动力学模拟实现，首先通过模拟得到单个声子的能量自相关函数衰减曲线，并进一步采用拟合和积分两种方法得到单个声子的弛豫时间. 然后，研究了弛豫时间与波矢、频率和温度的关系. 结果发现，弛豫时间随波矢的变化与对应的色散关系相近，弛豫时间与频率和温度的关系符合理论模型：1/=nTm，其中声学支的n 为1.56，而光学支结果较为发散，指数m对于不同声子支结果略有不同. 最后，还研究了不同频率声子对导热的贡献，发现低频声子在态密度上占有绝对优势，并且其弛豫时间整体高于高频声子，所以低频声子对导热的贡献占据主导地位.Phonons are the main energy carriers for heat conduction in graphene. One of the most important and basic thermal properties is the relaxation time. In this paper, phonon relaxation times are investigated by a normal mode decomposition method to reveal the distinctions of the different phonon modes. The method is based on equilibrium molecular dynamics simulation. In the simulations, the heat current autocorrelation functions are obtained for each single phonon, and the relaxation times are extracted by fitting the functions. In addition, the relations among relaxation time, wave vector, frequency, and temperature are examined. It is found that the variation tendency of the relaxation time with wave vector is close to that of the dispersion with wave vector. For frequency and temperature, they are in agreement with the theoretical model: 1/=nTm. It is shown thatn is 1.56 for acoustic phonons, while for optical phonons, it varies slightly with frequencies; and m is slightly different for each mode. Finally, the contributions of different phonon modes to thermal conductivity are investigated. It is found that low frequency phonons dominate the heat conduction process because of the relatively high relaxation time and density of states.
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Keywords:
- graphene /
- phonon relaxation time /
- normal mode decomposition /
- molecular dynamics
[1] Novoselov K S, Geim A K, Morozov S V, Jiang D, Zhang Y, Dubonos S, Grigorieva I V 2004 Science 306 666
[2] [3] [4] Nika D L, Pokatilov E P, Askerov A S, Balandin A A 2009 Phys. Rev. B 79 155413
[5] [6] Balandin A A 2011 Nat. Mater. 10 569
[7] [8] Sevinçi H, Cuniberti G 2010 Phys. Rev. B 81 113401
[9] [10] Hu J, Ruan X, Chen Y P 2009 Nano Lett. 9 2730
[11] [12] Hu J N, Schiffli S, Vallabhaneni A, Ruan X L, Chen Y P 2010 Appl. Phys. Lett. 97 133107
[13] Xu X D, Gabor N M, Alden J S, van der Zande A M, McEuen P L 2010 Nano Lett. 10 562
[14] [15] [16] Zheng B Y, Dong H L, Chen F F 2014 Acta Phys. Sin. 63 076501 (in Chinese) [郑伯昱, 董慧龙, 陈非凡 2014 63 076501]
[17] [18] Kang K, Abdula D, Cahill D G, Shim M 2010 Phys. Rev. B 81 165405
[19] [20] Lindsay L, Broido D A, Mingo N 2011 Phys. Rev. B 83 235428
[21] Bonini N, Lazzeri M, Marzari N, Mauri F 2007 Phys. Rev. Lett. 99 176802
[22] [23] [24] Ladd A J C, Moran B, Hoover W G 1986 Phys. Rev. B 34 5058
[25] McGaughey A J H, Kaviany M 2004 Phys. Rev. B 69 094303
[26] [27] Kaviany M 2008 Heat Transfer Physics (Cambridge: Cambridge University Press) p175
[28] [29] Bao H J 2013 Acta Phys. Sin. 62 186302 (in Chinese) [鲍华 2013 62 186302]
[30] [31] Henry A S, Chen G 2008 J. Comput. Theor. Nanosci. 5 141
[32] [33] Henry A S, Chen G 2009 Phys. Rev. B 79 144305.
[34] [35] [36] Brenner D W 1990 Phys. Rev. B 42 9458
[37] Hu G J, Cao B Y 2012 Mol. Simul. 38 823
[38] [39] [40] Ye Z Q, Cao B Y, Guo Z Y 2014 Carbon 66 567
[41] [42] Hu G J, Cao B Y 2013 J. Appl. Phys. 114 224308
[43] Hui Z X, He P F, Dai Y, W A H 2014 Acta Phys. Sin. 63 074401 (in Chinese) [惠治鑫, 贺鹏飞, 戴瑛, 吴艾辉 2014 63 074401]
[44] [45] [46] Born M, Huang K 2011 Dynamical Theory of Crystal Lattices (Beijing: Peking University Press) p32 (in Chinese) [玻恩, 黄昆 2011 晶格动力学理论 (北京: 北京大学出版社) 第32页]
[47] Tohei T, Kuwabara A, Oba F, Tanaka I 2006 Phys. Rev. B 73 064304
[48] [49] Goicochea J V, Madrid M, Amon C 2010 J. Heat Transf-Trans ASME 132 012401
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[1] Novoselov K S, Geim A K, Morozov S V, Jiang D, Zhang Y, Dubonos S, Grigorieva I V 2004 Science 306 666
[2] [3] [4] Nika D L, Pokatilov E P, Askerov A S, Balandin A A 2009 Phys. Rev. B 79 155413
[5] [6] Balandin A A 2011 Nat. Mater. 10 569
[7] [8] Sevinçi H, Cuniberti G 2010 Phys. Rev. B 81 113401
[9] [10] Hu J, Ruan X, Chen Y P 2009 Nano Lett. 9 2730
[11] [12] Hu J N, Schiffli S, Vallabhaneni A, Ruan X L, Chen Y P 2010 Appl. Phys. Lett. 97 133107
[13] Xu X D, Gabor N M, Alden J S, van der Zande A M, McEuen P L 2010 Nano Lett. 10 562
[14] [15] [16] Zheng B Y, Dong H L, Chen F F 2014 Acta Phys. Sin. 63 076501 (in Chinese) [郑伯昱, 董慧龙, 陈非凡 2014 63 076501]
[17] [18] Kang K, Abdula D, Cahill D G, Shim M 2010 Phys. Rev. B 81 165405
[19] [20] Lindsay L, Broido D A, Mingo N 2011 Phys. Rev. B 83 235428
[21] Bonini N, Lazzeri M, Marzari N, Mauri F 2007 Phys. Rev. Lett. 99 176802
[22] [23] [24] Ladd A J C, Moran B, Hoover W G 1986 Phys. Rev. B 34 5058
[25] McGaughey A J H, Kaviany M 2004 Phys. Rev. B 69 094303
[26] [27] Kaviany M 2008 Heat Transfer Physics (Cambridge: Cambridge University Press) p175
[28] [29] Bao H J 2013 Acta Phys. Sin. 62 186302 (in Chinese) [鲍华 2013 62 186302]
[30] [31] Henry A S, Chen G 2008 J. Comput. Theor. Nanosci. 5 141
[32] [33] Henry A S, Chen G 2009 Phys. Rev. B 79 144305.
[34] [35] [36] Brenner D W 1990 Phys. Rev. B 42 9458
[37] Hu G J, Cao B Y 2012 Mol. Simul. 38 823
[38] [39] [40] Ye Z Q, Cao B Y, Guo Z Y 2014 Carbon 66 567
[41] [42] Hu G J, Cao B Y 2013 J. Appl. Phys. 114 224308
[43] Hui Z X, He P F, Dai Y, W A H 2014 Acta Phys. Sin. 63 074401 (in Chinese) [惠治鑫, 贺鹏飞, 戴瑛, 吴艾辉 2014 63 074401]
[44] [45] [46] Born M, Huang K 2011 Dynamical Theory of Crystal Lattices (Beijing: Peking University Press) p32 (in Chinese) [玻恩, 黄昆 2011 晶格动力学理论 (北京: 北京大学出版社) 第32页]
[47] Tohei T, Kuwabara A, Oba F, Tanaka I 2006 Phys. Rev. B 73 064304
[48] [49] Goicochea J V, Madrid M, Amon C 2010 J. Heat Transf-Trans ASME 132 012401
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