一维纳米复合结构内部能量传输的分子动力学模拟
|
摘要
随着全球经济的迅猛发展,世界能源危机日益严峻,能源的有效利用已经成为当今社会的重大挑战之一。废热回收利用和电子器件散热问题是两个急需解决的能源问题。热电材料能够直接将废热转换为电能,从而提高能源利用效率；热界面材料可以提高电子器件中界面处的散热效率。纳米材料在能源有效利用和可持续发展方面展示了其独特的潜力,尤其是一维纳米材料在热电转换和电子器件散热方面具有广阔的应用前景。由于声子边界散射增强,Si纳米线具有非常低的热导率,是一种潜在的纳米热电材料；而由于独特的结构,碳纳米管中几乎不存在声子边界散射,使其具有非常高的热导率,成为潜在的热界面材料。尽管存在以上优势,Si纳米线热电材料的热电转换效率还不足以大规模应用,而由于界面热阻的存在,碳纳米管热界面材料的散热效率也比较低。由于声子散射增强,经过修饰的si纳米线复合结构的热导率可以进一步降低,从而获得更大的热电转换效率。因此,有必要对这两种一维纳米复合结构中的能量输运进行进一步的研究。
本论文进行了三方面的工作,分别对Si纳米线修饰结构的热输运性质,碳纳米管和Si基体之间的界面热导以及端部约束碳纳米管中低频机械波的热激发机理进行了研究,总体采用非平衡态分子动力学模拟方法。
为了进一步提高Si纳米线热电材料的能量转换效率,对三种Si纳米线修饰结构的热导率进行了研究,这三种修饰结构分别为：(1)表面分散纳米粒子的si纳米线;(2)内部填充纳米粒子的Si纳米线；以及(3)核壳结构的Si纳米线。能量转换效率的提高用Si纳米线修饰结构热导率的降低来表征。论文研究了表面分散纳米粒子的面积覆盖率和布置方式,内部填充纳米粒子的类型以及壳层结构的类型对Si纳米线热导率的影响。结果表明,相对于纯的Si纳米线,经过修饰的纳米复合结构具有非常低的热导率(最大降低了82%),这就意味着热电转换效率提高了5倍。论文将热导率的大大降低归因于两个方面：(1)声子边界散射的增强；(2)界面声子干涉的发生。计算结果为纳米热电材料中能量转换效率的提高提出了实验上可行的新方式。
分别对垂直和水平布置的(10,10)单壁碳纳米管和si基体之间的界面热导进行了研究。论文研究了界面能,热流方向,碳纳米管长度和系统温度对界面热导的影响以及不同方向的晶格振动对界面总热流密度的相对贡献。通过比较碳纳米管到Si基体和Si基体到碳纳米管两种热流方向下的界面热导,结果表明界面热导存在热整流效应,尤其对于水平布置的碳纳米管,当热流密度达到60W/m时,热整流效应高达184%,说明碳纳米管水平放置在Si基体上的结构是一种潜在的热整流器。通过声子相关的分析可以说明,对于热流由Si流向碳纳米管,界面热导随着热流密度的增加而增加是由于热流密度增加使碳纳米管和Si基体之间的晶格振动更加匹配；而对于热流由碳纳米管流向Si,大热流密度下激发出的低频声子模式对界面热输运起主导作用,是热整流效应产生的主要原因。此外,论文提出了一种简单有效的方法来定量地描述各个方向的晶格振动对总界面热流密度的相对贡献。无论是热流由碳纳米管流向Si还是由Si流向碳纳米管,碳纳米管-Si界面处的面外晶格振动都对总热流密度起主要贡献,面内晶格振动贡献较小。这种方法可以用来分析不同声子支对热流的相对贡献,从而识别纳米尺度能量传递的机理。
研究了夹在两个si基体之间的单壁碳纳米管在定常的高热流密度下的热输运行为。观察到一个异常的波状总动能分布,并首次对这种高热流密度下碳纳米管中激发出的低频横向声学机械波主导的能量输运机理进行了研究。这种一维低频机械波传递的能量被定量地表示为施加的总热流密度的函数,并和传统的傅立叶热传导传递的能量进行了对比。结果表明,在低热流密度下,傅立叶热传导在能量输运中占主导,低频机械波的贡献可以忽略；然而,随着热流密度的增加,低频机械波被激发出来,并在能量输运中占主导,使碳纳米管能够有效地传递更多的能量。论文提出了高热流密度下低维纳米结构(如一维纳米管和纳米线)中一种新的能量输运机理,这种机理可以用于研究微／纳米电子器件在高热流密度下的散热问题。
With rapid development of the global economy the world's energy crisis is increasing severe, the efficient utilization of energy has become one of the greatest challenges in modern society. Waste heat recovery and heat dissipation in electronics are the two very urgent energy issues. Thermoelectric materials can directly convert waste heat to electricity for improving the efficiency of energy utilization, and thermal interface materials can improve the efficiency of heat dissipation across the interfaces of electronics. Nanomaterials have demonstrated their unique potential in effective utilization and sustainable development of energy, and especially one-dimensional materials have broad prospects for applications of thermoelectric conversion and heat dissipation in electronics. Si nanowires have extremely low thermal conductivity due to increased phonon boundary scattering, making them promising thermoelectric materials; and due to the unique structure, phonon boundary scattering is nearly absent in carbon nanotubes, making them possessing ultra high thermal conductivity, expected to be promising thermal interface materials. Despite of the advantages above, the thermoelectric conversion efficiency of Si nanowire thermoelectric materials is not enough for widespread applications and the efficiency of heat dissipation in carbon nanotube thermal interface materials is also not high enough due to existence of interfacial thermal resistance. Due to increased phonon scattering, the Si nanowire nanocomposites with modification are expected to achieve lower thermal conductivity and larger thermoelectric conversion efficiency. So, it's necessary to furtherly investigate the energy transport in the two one-dimensional nanocomposites.
Using non-equilibrium molecular dynamics, the thesis investigated thermal transport in modified Si nanowires, interfacial thermal conductance between carbon nanotubes and Si substrate, and thermal transport in a single-walled carbon nanotube bridging two Si slabs under constant high heat flux, respectively.
To improve the energy conversion efficiency of Si nanowire thermoelectric materials, the thesis investigated the thermal conductivity of three types of modified Si nanowires, including:(1) Si nanowire decorated with nanoparticles,(2) Si nanowire with nanoparticle inclusions, and (3) Si-based core-shell nanowire. The enhancement in energy conversion efficiency was inferred from the reduction in thermal conductivity of the modified Si nanowires. The effects of the surface coverage and configuration of external particles, the different types of internal inclusions, and the different shell coatings on the thermal conductivity of Si nanowire are investigated. Compared to pristine Si nanowires, it was found that the modified nanocomposite structures have considerably lower thermal conductivity (up to82%reduction), implying～5X enhancement in the ZT coefficient. This significant effect appears to have two origins:(1) increase in phonon-boundary scattering and (2) onset of interfacial interference. The results suggest new fundamental-yet realizable ways to improve markedly the energy conversion efficiency of nanostructured thermoelectrics.
The thesis investigated the interfacial thermal conductance between vertically and horizontally aligned single-walled (10,10) carbon nanotubes and Si substrate. Effects of interfacial energy, the direction of heat flux, length of carbon nanotube, temperature of model system on the interfacial thermal conductance, and relative contributions of lattice vibrations in different directions to total interfacial heat flux were investigated. Compared with the results with heat flowing from the carbon nanotube to Si substrate and vice versa, the thesis found that there exists a thermal rectification for the interfacial thermal conductance, especially for the horizontally aligned carbon nanotube, the maximum thermal rectification is up to184%with a critical heat flux of60W/m, which is promising for thermal rectifier applications. By phonon-related analysis, the thesis found that for heat flowing from Si to carbon nanotube the increase of the interfacial thermal conductance with heat flux is due to the better match of phonon density of states between carbon nanotube and Si substrate, while for heat flowing from carbon nanotube to Si the low-frequency phonon modes excited at large heat fluxes dominate the interfacial heat transfer and such low-frequency phonon mode mechanism is responsible for the thermal rectification effect. Moreover, the thesis proposed a simple yet very useful method to quantify the directional contributions of lattice vibrations to the total interfacial heat flux and demonstrated that the out-of-plane lattice vibrations at the interface dominate the heat transfer across the silicon/horizontally aligned carbon nanotube interfaces. This method could be helpful in identifying mechanism in nanoscale heat transfer by analyzing the relative contributions from different phonon branches.
The thesis investigated thermal transport in a single-walled carbon nanotube bridging two Si slabs under constant high heat flux. An anomalous wave-like kinetic energy profile was observed and a previously unexplored, wave-dominated energy transport mechanism is identified for high heat fluxes in carbon nanotubes, originated from excited low frequency transverse acoustic waves. The transported energy, in terms of a one-dimensional low frequency mechanical wave, is quantified as a function of the total heat flux applied and is compared to the energy transported by traditional Fourier heat conduction. The results suggest that at low heat fluxes Fourier heat conduction is dominant and the contribution of low frequency waves is negligible; however, as the heat flux exceeds a critical value, low frequency waves are excited and the wave transport energy mechanism overtakes the traditional Fourier conduction, rendering the carbon nanotube significantly more energy conductive. The results reveal an important new mechanism for high heat flux energy transport in low-dimensional nanostructures, such as1-D nanotubes and nanowires, which could be very relevant to high heat flux dissipation such as in micro/nanoelectronics applications.
本论文进行了三方面的工作,分别对Si纳米线修饰结构的热输运性质,碳纳米管和Si基体之间的界面热导以及端部约束碳纳米管中低频机械波的热激发机理进行了研究,总体采用非平衡态分子动力学模拟方法。
为了进一步提高Si纳米线热电材料的能量转换效率,对三种Si纳米线修饰结构的热导率进行了研究,这三种修饰结构分别为：(1)表面分散纳米粒子的si纳米线;(2)内部填充纳米粒子的Si纳米线；以及(3)核壳结构的Si纳米线。能量转换效率的提高用Si纳米线修饰结构热导率的降低来表征。论文研究了表面分散纳米粒子的面积覆盖率和布置方式,内部填充纳米粒子的类型以及壳层结构的类型对Si纳米线热导率的影响。结果表明,相对于纯的Si纳米线,经过修饰的纳米复合结构具有非常低的热导率(最大降低了82%),这就意味着热电转换效率提高了5倍。论文将热导率的大大降低归因于两个方面：(1)声子边界散射的增强；(2)界面声子干涉的发生。计算结果为纳米热电材料中能量转换效率的提高提出了实验上可行的新方式。
分别对垂直和水平布置的(10,10)单壁碳纳米管和si基体之间的界面热导进行了研究。论文研究了界面能,热流方向,碳纳米管长度和系统温度对界面热导的影响以及不同方向的晶格振动对界面总热流密度的相对贡献。通过比较碳纳米管到Si基体和Si基体到碳纳米管两种热流方向下的界面热导,结果表明界面热导存在热整流效应,尤其对于水平布置的碳纳米管,当热流密度达到60W/m时,热整流效应高达184%,说明碳纳米管水平放置在Si基体上的结构是一种潜在的热整流器。通过声子相关的分析可以说明,对于热流由Si流向碳纳米管,界面热导随着热流密度的增加而增加是由于热流密度增加使碳纳米管和Si基体之间的晶格振动更加匹配；而对于热流由碳纳米管流向Si,大热流密度下激发出的低频声子模式对界面热输运起主导作用,是热整流效应产生的主要原因。此外,论文提出了一种简单有效的方法来定量地描述各个方向的晶格振动对总界面热流密度的相对贡献。无论是热流由碳纳米管流向Si还是由Si流向碳纳米管,碳纳米管-Si界面处的面外晶格振动都对总热流密度起主要贡献,面内晶格振动贡献较小。这种方法可以用来分析不同声子支对热流的相对贡献,从而识别纳米尺度能量传递的机理。
研究了夹在两个si基体之间的单壁碳纳米管在定常的高热流密度下的热输运行为。观察到一个异常的波状总动能分布,并首次对这种高热流密度下碳纳米管中激发出的低频横向声学机械波主导的能量输运机理进行了研究。这种一维低频机械波传递的能量被定量地表示为施加的总热流密度的函数,并和传统的傅立叶热传导传递的能量进行了对比。结果表明,在低热流密度下,傅立叶热传导在能量输运中占主导,低频机械波的贡献可以忽略；然而,随着热流密度的增加,低频机械波被激发出来,并在能量输运中占主导,使碳纳米管能够有效地传递更多的能量。论文提出了高热流密度下低维纳米结构(如一维纳米管和纳米线)中一种新的能量输运机理,这种机理可以用于研究微／纳米电子器件在高热流密度下的散热问题。
With rapid development of the global economy the world's energy crisis is increasing severe, the efficient utilization of energy has become one of the greatest challenges in modern society. Waste heat recovery and heat dissipation in electronics are the two very urgent energy issues. Thermoelectric materials can directly convert waste heat to electricity for improving the efficiency of energy utilization, and thermal interface materials can improve the efficiency of heat dissipation across the interfaces of electronics. Nanomaterials have demonstrated their unique potential in effective utilization and sustainable development of energy, and especially one-dimensional materials have broad prospects for applications of thermoelectric conversion and heat dissipation in electronics. Si nanowires have extremely low thermal conductivity due to increased phonon boundary scattering, making them promising thermoelectric materials; and due to the unique structure, phonon boundary scattering is nearly absent in carbon nanotubes, making them possessing ultra high thermal conductivity, expected to be promising thermal interface materials. Despite of the advantages above, the thermoelectric conversion efficiency of Si nanowire thermoelectric materials is not enough for widespread applications and the efficiency of heat dissipation in carbon nanotube thermal interface materials is also not high enough due to existence of interfacial thermal resistance. Due to increased phonon scattering, the Si nanowire nanocomposites with modification are expected to achieve lower thermal conductivity and larger thermoelectric conversion efficiency. So, it's necessary to furtherly investigate the energy transport in the two one-dimensional nanocomposites.
Using non-equilibrium molecular dynamics, the thesis investigated thermal transport in modified Si nanowires, interfacial thermal conductance between carbon nanotubes and Si substrate, and thermal transport in a single-walled carbon nanotube bridging two Si slabs under constant high heat flux, respectively.
To improve the energy conversion efficiency of Si nanowire thermoelectric materials, the thesis investigated the thermal conductivity of three types of modified Si nanowires, including:(1) Si nanowire decorated with nanoparticles,(2) Si nanowire with nanoparticle inclusions, and (3) Si-based core-shell nanowire. The enhancement in energy conversion efficiency was inferred from the reduction in thermal conductivity of the modified Si nanowires. The effects of the surface coverage and configuration of external particles, the different types of internal inclusions, and the different shell coatings on the thermal conductivity of Si nanowire are investigated. Compared to pristine Si nanowires, it was found that the modified nanocomposite structures have considerably lower thermal conductivity (up to82%reduction), implying～5X enhancement in the ZT coefficient. This significant effect appears to have two origins:(1) increase in phonon-boundary scattering and (2) onset of interfacial interference. The results suggest new fundamental-yet realizable ways to improve markedly the energy conversion efficiency of nanostructured thermoelectrics.
The thesis investigated the interfacial thermal conductance between vertically and horizontally aligned single-walled (10,10) carbon nanotubes and Si substrate. Effects of interfacial energy, the direction of heat flux, length of carbon nanotube, temperature of model system on the interfacial thermal conductance, and relative contributions of lattice vibrations in different directions to total interfacial heat flux were investigated. Compared with the results with heat flowing from the carbon nanotube to Si substrate and vice versa, the thesis found that there exists a thermal rectification for the interfacial thermal conductance, especially for the horizontally aligned carbon nanotube, the maximum thermal rectification is up to184%with a critical heat flux of60W/m, which is promising for thermal rectifier applications. By phonon-related analysis, the thesis found that for heat flowing from Si to carbon nanotube the increase of the interfacial thermal conductance with heat flux is due to the better match of phonon density of states between carbon nanotube and Si substrate, while for heat flowing from carbon nanotube to Si the low-frequency phonon modes excited at large heat fluxes dominate the interfacial heat transfer and such low-frequency phonon mode mechanism is responsible for the thermal rectification effect. Moreover, the thesis proposed a simple yet very useful method to quantify the directional contributions of lattice vibrations to the total interfacial heat flux and demonstrated that the out-of-plane lattice vibrations at the interface dominate the heat transfer across the silicon/horizontally aligned carbon nanotube interfaces. This method could be helpful in identifying mechanism in nanoscale heat transfer by analyzing the relative contributions from different phonon branches.
The thesis investigated thermal transport in a single-walled carbon nanotube bridging two Si slabs under constant high heat flux. An anomalous wave-like kinetic energy profile was observed and a previously unexplored, wave-dominated energy transport mechanism is identified for high heat fluxes in carbon nanotubes, originated from excited low frequency transverse acoustic waves. The transported energy, in terms of a one-dimensional low frequency mechanical wave, is quantified as a function of the total heat flux applied and is compared to the energy transported by traditional Fourier heat conduction. The results suggest that at low heat fluxes Fourier heat conduction is dominant and the contribution of low frequency waves is negligible; however, as the heat flux exceeds a critical value, low frequency waves are excited and the wave transport energy mechanism overtakes the traditional Fourier conduction, rendering the carbon nanotube significantly more energy conductive. The results reveal an important new mechanism for high heat flux energy transport in low-dimensional nanostructures, such as1-D nanotubes and nanowires, which could be very relevant to high heat flux dissipation such as in micro/nanoelectronics applications.
引文
[1]McFarland A D, Haynes C L, Mirkin C A, Van Duyne R P, Godwin H A. Color my nanoworld [J]. Journal of Chemical Education,2004,81(4):544 A.
[2]Liang L, Li B. Size-dependent thermal conductivity of nanoscale semiconducting systems [J]. Physical Review B,2006,73(15):153303.
[3]Kulkarni A J, Zhou M. Size-dependent thermal conductivity of zinc oxide nanobelts [J]. Applied Physics Letters,2006,88(14):141921.
[4]Roh J W, Jang S Y, Kang J, Lee S, Noh J-S, Kim W, Park J, Lee W. Size-dependent thermal conductivity of individual single-crystalline PbTe nanowires [J]. Applied Physics Letters,2010, 96(10):103101.
[5]Lu X, Shen W Z, Chu J H. Size effect on the thermal conductivity of nanowires [J]. Journal of Applied Physics,2002,91(3):1542.
[6]Wang Z, Tang D, Zheng X, Zhang W, Zhu Y. Length-dependent thermal conductivity of single-wall carbon nanotubes:prediction and measurements [J]. Nanotechnology,2007,18(47): 475714.
[7]Wang Z, Tang D, Li X, Zheng X, Zhang W, Zheng L, Zhu Y, Jin A, Yang H, Gu C. Length-dependent thermal conductivity of an individual single-wall carbon nano tube [J]. Applied Physics Letters,2007,91(12):123119.
[8]Lukes J R, Zhong H L. Thermal conductivity of individual single-wall carbon nanotubes [J]. Journal of Heat Transfer,2007,129(6):705.
[9]Mingo N, Broido D A. Length dependence of carbon nanorube thermal conductivity and the "problem of long waves" [J]. Nano Letters,2005,5(7):1221.
[10]Shi L, Yao D, Zhang G, Li B. Size dependent thermoelectric properties of silicon nanowires [J]. Applied Physics Letters,2009,95(6):063102.
[11]Zhong H, Lukes J R. Interfacial thermal resistance between carbon nanotubes:Molecular dynamics simulations and analytical thermal modeling [J]. Physical Review B,2006,74(12): 125403.
[12]Diao J, Srivastava D, Menon M. Molecular dynamics simulations of carbon nanotube/silicon interfacial thermal conductance [J]. The Journal of Chemical Physics,2008, 128(16):164708.
[13]Ju H, Zhang S, Li Z, Shui X, Kuo P. Size-dependent thermal diffusivity of multilayered thin films deposited on substrates characterized by transient grating technique [J]. Applied Physics Letters,2009,94(3):031902.
[14]Shin H S, Yu J, Song J Y. Size-dependent thermal instability and melting behavior of Sn nanowires [J]. Applied Physics Letters,2007,91(17):173106.
[15]Zhang M, Efremov M Y, Schiettekatte F, Olson E A, Kwan A T, Lai S L, Wisleder T, Greene J E, Allen L H. Size-dependent melting point depression of nanostructures:Nanocalorimetric measurements [J]. Physical Review B,2000,62(15):10548.
[16]Lai S L, Guo J Y, Petrova V, Ramanath G, Allen L H. Size-dependent melting properties of small tin particles:Nanocalorimetric measurements [J]. Physical Review Letters,1996,77(1): 99.
[17]Castro T, Reifenberger R, Choi E, Andres R P. Size-dependent melting temperature of individual nanometer-sized metallic clusters [J]. Physical Review B,1990,42(13):8548.
[18]Dick K, Dhanasekaran T, Zhang Z, Meisel D. Size-dependent melting of silica-encapsulated gold nanoparticles [J]. Journal of the American Chemical Society,2002,124(10):2312.
[19]Li X, Yang R. Size-dependent phonon transmission across dissimilar material interfaces [J]. Journal of Physics:Condensed Matter,2012,24(15):155302.
[20]Liang L, Wei Y, Li B. Size-dependent interface phonon transmission and thermal conductivity of nanolaminates [J]. Journal of Applied Physics,2008,103(8):084314.
[21]Cahill D G, Ford W K, Goodson K E, Mahan G D, Majumdar A, Maris H J, Merlin R, Phillpot S R. Nanoscale thermal transport [J]. Journal of Applied Physics,2003,93(2):793.
[22]Ashby M F, Ferreira P J, Schodek D L. Chapter 6-Nanomaterials:Classes and fundamentals [M]. Nanomaterials, Nanotechnologies and Design. Boston; Butterworth-Heinemann.2009:177.
[23]Iijima S. Helical microtubules of graphitic carbon [J]. Nature,1991,354(6348):56.
[24]Holmes J D, Johnston K P, Doty R C, Korgel B A. Control of thickness and orientation of solution-grown silicon nanowires [J]. Science,2000,287(5457):1471.
[25]Hanrath T, Korgel B A. Supercritical fluid-liquid-solid (SFLS) synthesis of Si and Ge nanowires seeded by colloidal metal nanocrystals [J]. Advanced Materials,2003,15(5):437.
[26]Gyu-Chul Y, Chunrui W, Won Il P. ZnO nanorods:synthesis, characterization and applications [J]. Semiconductor Science and Technology,2005,20(4):S22.
[27]Huang X, Neretina S, El-Sayed M A. Gold nanorods:From synthesis and properties to biological and biomedical applications [J]. Advanced Materials,2009,21(48):4880.
[28]Zhou F-L, Gong R-H. Manufacturing technologies of polymeric nanofibres and nanofibre yarns [J]. Polymer International,2008,57(6):837.
[29]Nakada K, Fujita M, Dresselhaus G, Dresselhaus M S. Edge state in graphene ribbons: Nanometer size effect and edge shape dependence [J]. Physical Review B,1996,54(24):17954.
[30]Khitun A, Balandin A, Wang K L. Modification of the lattice thermal conductivity in silicon quantum wires due to spatial confinement of acoustic phonons [J]. Superlattices and Microstructures,1999,26(3):181.
[31]Volz S G, Chen G Molecular dynamics simulation of thermal conductivity of silicon nanowires [J]. Applied Physics Letters,1999,75(14):2056.
[32]Shi L, Li D, Yu C, Jang W, Kim D, Yao Z, Kim P, Majumdar A. Measuring thermal and thermoelectric properties of one-dimensional nanostructures using a microfabricated device [J]. Journal of Heat Transfer,2003,125(5):881.
[33]Pop E. Energy dissipation and transport in nanoscale devices [J]. Nano Research,2010,3(3): 147.
[34]Hochbaum A I, Chen R, Delgado R D, Liang W, Gamett E C, Najarian M, Majumdar A, Yang P. Enhanced thermoelectric performance of rough silicon nanowires [J]. Nature,2008, 451(7175):163.
[35]Hu X, et. al. Thermal characterisation of aligned carbon nanotubes on silicon [C]. Proceedings of the 21st Semi-Therm, San Jose, CA, F,2005.
[36]Peng K-Q, Wang X, Wu X-L, Lee S-T. Platinum nanoparticle decorated silicon nanowires for efficient solar energy conversion [J]. Nano Letters,2009,9(11):3704.
[37]Yang N, Zhang G, Li B. Ultralow thermal conductivity of isotope-doped silicon nanowires [J]. Nano Letters,2007,8(1):276.
[38]Hu M, Giapis K P, Goicochea J V, Zhang X, Poulikakos D. Significant reduction of thermal conductivity in Si/Ge core-shell nanowires [J]. Nano Letters,2010,11(2):618.
[39]Hu M, Zhang X, Giapis K P, Poulikakos D. Thermal conductivity reduction in core-shell nanowires [J]. Physical Review B,2011,84(8):085442.
[40]Majumdar A. Thermoelectricity in semiconductor nanostructures [J]. Science,2004, 303(5659):777.
[41]Ettenberg M H, Jesser W A, Rosi F D. Proceedings of the 15th International Conference on Thermoelectrics (Ed:T Caillat), Piscataway, F,1996 [C].
[42]Weber L, Gmelin E. Transport properties of silicon [J]. Applied Physics A:Materials Science & Processing,1991,53(2):136.
[43]Li D, Wu Y, Kim P, Shi L, Yang P, Majumdar A. Thermal conductivity of individual silicon nanowires [J]. Applied Physics Letters,2003,83(14):2934.
[44]Chen X, Wang Y, Ma Y, Cui T, Zou G. Origin of the high thermoelectric performance in Si nanowires:A first-principle study [J]. The Journal of Physical Chemistry C,2009,113(31): 14001.
[45]Xu J, Fisher T S. Enhancement of thermal interface materials with carbon nanotube arrays [J]. International Journal of Heat and Mass Transfer,2006,49(9-10):1658.
[46]Zhang K, Chai Y, Yuen M M F, Xiao D G W, Chan P C H. Carbon nanotube thermal interface material for high-brightness light-emitting-diode cooling [J]. Nanotechnology,2008, 19(21):215706.
[47]Shiomi J, Maruyama S. Non-Fourier heat conduction in a single-walled carbon nanotube: Classical molecular dynamics simulations [J]. Physical Review B,2006,73(20):205420.
[48]Greaney P A, Lani G, Cicero G, Grossman J C. Anomalous dissipation in single-walled carbon nanotube resonators [J]. Nano Letters,2009,9(11):3699.
[49]Wang H, Cao B, Guo Z. Non-Fourier heat conduction in carbon nanotubes [J]. Journal of Heat Transfer,2012,134(5):051004.
[50]Wang M, Yang N, Guo Z. Non-Fourier heat conductions in nanomaterials [J]. Journal of Applied Physics,2011,110(6):064310.
[51]Wang H, Liu J, Guo Z, Takahashi K. Non-Fourier heat conduction study for steady states in metallic nanofilms [J]. Chinese Science Bulletin,2012,57(24):3239.
[52]Wright D A. Thermoelectric properties of bismuth telluride and its alloys [J]. Nature,1958, 181(4612):834.
[53]Venkatasubramanian R, Siivola E, Colpitts T, O'Quinn B. Thin-film thermoelectric devices with high room-temperature figures of merit [J]. Nature,2001,413(6856):597.
[54]Harman T C, Taylor P J, Walsh M P, LaForge B E. Quantum dot superlattice thermoelectric materials and devices [J]. Science,2002,297(5590):2229.
[55]Chen J, Zhang G, Li B. Remarkable reduction of thermal conductivity in silicon nanotubes [J]. Nano Letters,2010,10(10):3978.
[56]Kurti N, Rollin B V, Simon F. Preliminary experiments on temperature equilibria at very low temperatures [J]. Physica,1936,3(1-4):266.
[57]Keesom W H, Keesom A P. On the heat conductivity of liquid helium [J]. Physica,1936,3: 359.
[58]Kapitza P L. The study of heat transfer in helium Ⅱ [J]. J Phys-USSR,1941,4(1-6):181.
[59]Khalatnikov I M.*Teploobmen mezhdu tverdym telom Ⅰ geliem-Ⅱ [J]. Zhurnal Eksperimentalnoi Teor Fiz,1952,22(6):687.
[60]Mazo R M. Theoretical studies on low temperature phenomena [D]. Yale University,1955.
[61]Little W A. The transport of heat between dissimilar solids at low temperatures [J]. Canadian Journal of Physics,1959,37(3):334.
[62]Swartz E T, Pohl R O. Thermal boundary resistance [J]. Reviews of Modern Physics,1989, 61(3):605.
[63]Zeng T, Chen G. Phonon heat conduction in thin films:Impacts of thermal boundary resistance and internal heat generation [J]. Journal of Heat Transfer,2001,123(2):340.
[64]Young D A, Maris H J. Lattice-dynamical calculation of the Kapitza resistance between fcc lattices [J]. Physical Review B,1989,40(6):3685.
[65]Cunnington G R, Jr. Thermal conductance of filled aluminium and magnesium joints in a vacuum environment [M]. ASME Winter Annual Meeting. New York.1964.
[66]Getty R C, Tatro R E. Spacecraft thermal joint conduction [M]. AIAA Thermophysics Specialists Conference. New Orleans.1967.
[67]Marotta E E, Fletcher L S. Thermal contact conductance of selected polymeric materials [J]. Journal of Thermophysics and Heat Transfer,1996,10(2):334.
[68]Xu Y, Luo X, Chung D D L. Sodium silicate based thermal interface material for high thermal contact conductance [J]. Journal of Electronic Packaging,2000,122(2):128.
[69]Hachman M. Intel adapting buckyballs for cooling chips [M]. ExtremeTech. http://www.extremetech.com/cxtreme/73118-intel-adapting-buckyballs-for-cooling-chips.2002.
[70]Montgomery S W, Holalkere V R. Carbon nanotube thermal interface structures:US, 6965513 B2 [P/OL].2005-November 2005.
[71]Lee T-M, Chiou K-C, Tseng F-P, Hung C-C. High thermal efficiency carbon nanotube-resin matrix for thermal interface materials [C]. Proceedings of the 55th Electronic components and technology conference, F,2005.
[72]Zhang K, Xiao G-W, Wong C K Y, Gu H-W, Yuen M M F, Chan P C H, Xu B. Study on thermal interface material with carbon nanotubes and carbon black in high-brightness LED packaging with flip-chip technology [C]. Proceedings of the 55th Electronic components and technology conference, F,2005.
[73]Frenkel D, Smit B. Understanding molecular simulation:From algorithms to applications [M]. Orlando, FL, USA:Academic Press,2001.
[74]Schelling P K, Phillpot S R, Keblinski P. Comparison of atomic-level simulation methods for computing thermal conductivity [J]. Physical Review B,2002,65(14):144306.
[75]Stillinger F H, Weber T A. Computer simulation of local order in condensed phases of silicon [J]. Physical Review B,1985,31(8):5262.
[76]Tersoff J. Modeling solid-state chemistry:Interatomic potentials for multicomponent systems [J]. Physical Review B,1989,39(8):5566.
[77]Tersoff J. Erratum:Modeling solid-state chemistry:Interatomic potentials for multicomponent systems [J]. Physical Review B,1990,41(5):3248.
[78]Stuart S J, Tutein A B, Harrison J A. A reactive potential for hydrocarbons with intermolecular interactions [J]. The Journal of Chemical Physics,2000,112(14):6472.
[79]Plimpton S. Fast parallel algorithms for short-range molecular dynamics [J]. Journal of Computational Physics,1995,117(1):1.
[80]Hanley H J M, McCarty R D, Haynes W M. The viscosity and thermal conductivity coefficients for dense gaseous and liquid argon, krypton, xenon, nitrogen, and oxygen [J]. Journal of Physical and Chemical Reference Data,1974,3(4):979.
[81]Muller-Plathe F. A simple nonequilibrium molecular dynamics method for calculating the thermal conductivity [J]. The Journal of Chemical Physics,1997,106(14):6082.
[82]Nieto-Draghi C, Avalos J B. Non-equilibrium momentum exchange algorithm for molecular dynamics simulation of heat flow in multicomponent systems [J]. Molecular Physics,2003, 101(14):2303.
[83]Chen X, Wang Y, Ma Y. High thermoelectric performance of Ge/Si core-shell nanowires: First-principles prediction [J]. The Journal of Physical Chemistry C,2010,114(19):9096.
[84]Yang Z, Guarin F, Tao I W, Wang W I, Iyer S S. Approach to obtain high quality GaN on Si and SiC-on-silicon-on-insulator compliant substrate by molecular-beam epitaxy [J]. Journal of Vacuum Science & Technology B,1995,13(2):789.
[85]Schenk H P D, Kipshidze G D, Lebedev V B, Shokhovets S, Goldhahn R, Krauplich J, Fissel A, Richter W. Epitaxial growth of A1N and GaN on Si(111) by plasma-assisted molecular beam epitaxy [J]. Journal of Crystal Growth,1999,201-202(0):359.
[86]Joblot S, Semond F, Natali F, Vennegues P, Laugt M, Cordier Y, Massies J. Growth of wurtzite-GaN on silicon (100) substrate by molecular beam epitaxy [M]//STUTZMANN M. Physica Status Solidi C-Conferences and Critical Reviews, Vol 2, No 7. Weinheim; Wiley-V C H Verlag Gmbh.2005:2187.
[87]Kumagai T, Izumi S, Hara S, Sakai S. Development of bond-order potentials that can reproduce the elastic constants and melting point of silicon for classical molecular dynamics simulation [J]. Computational Materials Science,2007,39(2):457.
[88]Ramana Murty M V, Atwater H A. Empirical interatomic potential for Si-H interactions [J]. Physical Review B,1995,51(8):4889.
[89]Juslin N, Erhart P, Traskelin P, Nord J, Henriksson K O E, Nordlund K, Salonen E, Albe K. Analytical interatomic potential for modeling nonequilibrium processes in the W-C-H system [J]. Journal of Applied Physics,2005,98(12):123520.
[90]Albe K, Nordlund K, Nord J, Kuronen A. Modeling of compound semiconductors: Analytical bond-order potential for Ga, As, and GaAs [J]. Physical Review B,2002,66(3): 035205.
[91]Brenner D W. Relationship between the embedded-atom method and Tersoff potentials [J]. Physical Review Letters,1989,63(9):1022.
[92]Erhart P, Albe K. Analytical potential for atomistic simulations of silicon, carbon, and silicon carbide [J]. Physical Review B,2005,71(3):035211.
[93]Nord J, Albe K, Erhart P, Nordlund K. Modelling of compound semiconductors:analytical bond-order potential for gallium, nitrogen and gallium nitride [J]. Journal of Physics:Condensed Matter,2003,15(32):5649.
[94]Albe K, Nordlund K, Averback R S. Modeling the metal-semiconductor interaction: Analytical bond-order potential for platinum-carbon [J]. Physical Review B,2002,65(19): 195124.
[95]Ding K, Andersen H C. Molecular-dynamics simulation of amorphous germanium [J]. Physical Review B,1986,34(10):6987.
[96]Karimi M, Kaplan T, Mostoller M, Jesson D E. Ge segregation at Si-Ge (001) stepped surfaces [J]. Physical Review B,1993,47(15):9931.
[97]Zhou X, Jones R E. Effects of cutoff functions of Tersoff potentials on molecular dynamics simulations of thermal transport [J]. Modelling and Simulation in Materials Science and Engineering,2011,19(2):025004.
[98]Benkabou F, Certier M, Aourag H. Elastic properties of zinc-blende GaN, A1N and InN from molecular dynamics [J]. Molecular Simulation,2003,29(3):201.
[99]Goumri-Said S, Kanoun M B, Merad A E, Merad G, Aourag H. Prediction of structural and thermodynamic properties of zinc-blende A1N:molecular dynamics simulation [J]. Chemical Physics,2004,302(1-3):135.
[100]Munetoh S, Motooka T, Moriguchi K, Shintani A. Interatomic potential for Si-O systems using Tersoff parameterization [J]. Computational Materials Science,2007,39(2):334.
[101]Billeter S R, Curioni A, Fischer D, Andreoni W. Ab initio derived augmented Tersoff potential for silicon oxynitride compounds and their interfaces with silicon [J]. Physical Review B,2006,73(15):155329.
[102]Billeter S R, Curioni A, Fischer D, Andreoni W. Erratum:Ab initio derived augmented Tersoff potential for silicon oxynitride compounds and their interfaces with silicon [Phys. Rev. B 73,155329 (2006)] [J]. Physical Review B,2009,79(16):169904.
[103]Ippolito M, Meloni S. Atomistic structure of amorphous silicon nitride from classical molecular dynamics simulations [J]. Physical Review B,2011,83(16):165209.
[104]Nose S. A unified formulation of the constant temperature molecular dynamics methods [J]. The Journal of Chemical Physics,1984,81(1):511.
[105]Hoover W G Canonical dynamics:Equilibrium phase-space distributions [J]. Physical Review A,1985,31(3):1695.
[106]Jund P, Jullien R. Molecular-dynamics calculation of the thermal conductivity of vitreous silica [J]. Physical Review B,1999,59(21):13707.
[107]Pan L, Lew K-K, Redwing J M, Dickey E C. Stranski-krastanow growth of germanium on silicon nanowires [J]. Nano Letters,2005,5(6):1081.
[108]Dickey J M, Paskin A. Computer simulation of the lattice dynamics of solids [J]. Physical Review,1969,188(3):1407.
[109]Hu M, Goicochea J V, Michel B, Poulikakos D. Water nanoconfinement induced thermal enhancement at hydrophilic quartz interfaces [J]. Nano Letters,2009,10(1):279.
[110]Goicochea J V, Hu M, Michel B, Poulikakos D. Surface functionalization mechanisms of enhancing heat transfer at solid-liquid interfaces [J]. Journal of Heat Transfer,2011,133(8): 082401.
[111]Hu M, Zhang X, Poulikakos D, Grigoropoulos C P. Large "near junction" thermal resistance reduction in electronics by interface nanoengineering [J]. International Journal of Heat and Mass Transfer,2011,54(25-26):5183.
[112]Bell R J, Dean P. Atomic vibrations in vitreous silica [J]. Discussions of the Faraday Society,1970,50:55.
[113]Daly B C, Maris H J, Imamura K, Tamura S. Molecular dynamics calculation of the thermal conductivity of superlattices [J]. Physical Review B,2002,66(2):024301.
[114]Landry E S, McGaughey A J H. Effect of interfacial species mixing on phonon transport in semiconductor superlattices [J]. Physical Review B,2009,79(7):075316.
[115]Termentzidis K, Chantrenne P, Keblinski P. Nonequilibrium molecular dynamics simulation of the in-plane thermal conductivity of superlattices with rough interfaces [J]. Physical Review B,2009,79(21):214307.
[116]Termentzidis K, Merabia S, Chantrenne P, Keblinski P. Cross-plane thermal conductivity of superlattices with rough interfaces using equilibrium and non-equilibrium molecular dynamics [J]. International Journal of Heat and Mass Transfer,2011,54(9-10):2014.
[117]Yao Z, Wang J, Li B, Liu G. Thermal conduction of carbon nanotubes using molecular dynamics [J]. Physical Review B,2005,71(8):085417.
[118]Lee J H, Grossman J C, Reed J, Galli G. Lattice thermal conductivity of nanoporous Si: Molecular dynamics study [J]. Applied Physics Letters,2007,91(22):223110.
[119]Donadio D, Galli G. Temperature Dependence of the Thermal conductivity of thin silicon nanowires [J]. Nano Letters,2010,10(3):847.
[120]Schneider T, Stoll E. Molecular-dynamics study of a three-dimensional one-component model for distortive phase transitions [J]. Physical Review B,1978,17(3):1302.
[121]Ong Z, Pop E. Molecular dynamics simulation of thermal boundary conductance between carbon nanotubes and SiO2 [J]. Physical Review B,2010,81(15):155408.
[122]Osman M A, Srivastava D. Temperature dependence of the thermal conductivity of single-wall carbon nanotubes [J]. Nanotechnology,2001,12(1):21.
[123]Padgett C W, Brenner D W. Influence of chemisorption on the thermal conductivity of single-wall carbon nanotubes [J]. Nano Letters,2004,4(6):1051.
[124]Saito Y, Sasaki N, Moriya H, Kagatsume A, Noro S. Parameter optimization of Tersoff interatomic potentials using a genetic algorithm [J]. JSME International Journal Series A-Solid Mechanics and Material Engineering,2001,44(2):207.
[125]Liang Z, Tsai H-L. Reduction of solid-solid thermal boundary resistance by inserting an interlayer [J]. International Journal of Heat and Mass Transfer,2012,55(11-12):2999.
[126]Ju S, Liang X, Wang S. Investigation of interfacial thermal resistance of bi-layer nanofilms by nonequilibrium molecular dynamics [J]. Journal of Physics D:Applied Physics,2010,43(8): 085407.
[127]Cao A, Qu J, Yao M. Atomistic simulations of heat transfer at carbon nanotube/Si interfaces [M]. IEEE Electronics Components and Technology Conference. Las Vegas.2010: 417.
[128]Chang C W, Okawa D, Majumdar A, Zettl A. Solid-state thermal rectifier [J]. Science, 2006,314(5802):1121.
[129]Hu M, Keblinski P, Li B. Thermal rectification at silicon-amorphous polyethylene interface [J]. Applied Physics Letters,2008,92(21):211908.
[130]Hu M, Goicochea J V, Michel B, Poulikakos D. Thermal rectification at water/functionalized silica interfaces [J]. Applied Physics Letters,2009,95(15):151903.
[131]Zhang X, Hu M, Poulikakos D. A Low-frequency wave motion mechanism enables efficient energy transport in carbon nanotubes at high heat fluxes [J]. Nano Letters,2012,12(7): 3410.
[132]Chen J, Zhang G, Li B. Phonon coherent resonance and its effect on thermal transport in core-shell nano wires [J]. The Journal of Chemical Physics,2011,135(10):104508.
[133]Humphrey W, Dalke A, Schulten K. VMD:Visual molecular dynamics [J]. Journal of Molecular Graphics,1996,14(1):33.
[134]Pop E, Mann D, Cao J, Wang Q, Goodson K, Dai H J. Negative differential conductance and hot phonons in suspended nanotube molecular wires [J]. Physical Review Letters,2005, 95(15):155505.
[135]Kim P, Shi L, Majumdar A, McEuen P L. Thermal transport measurements of individual multiwalled nanotubes [J]. Physical Review Letters,2001,87(21):215502.
[136]Fujii M, Zhang X, Xie H Q, Ago H, Takahashi K, Ikuta T, Abe H, Shimizu T. Measuring the thermal conductivity of a single carbon nanotube [J]. Physical Review Letters,2005,95(6): 065502.
[137]Choi T Y, Poulikakos D, Tharian J, Sennhauser U. Measurement of the thermal conductivity of individual carbon nanotubes by the four-point three-omega method [J]. Nano Letters,2006,6(8):1589.
[138]Che J, Cagin T, Goddard W A. Thermal conductivity of carbon nanotubes [J]. Nanotechnology,2000,11(2):65.
[139]Wang J, Wang J. Carbon nanotube thermal transport:Ballistic to diffusive [J]. Applied Physics Letters,2006,88(11):111909.
[140]Donadio D, Galli G. Thermal conductivity of isolated and interacting carbon nanotubes: Comparing results from molecular dynamics and the Boltzmann transport equation [J]. Physical Review Letters,2007,99(25):255502.
[141]Hu M, Keblinski P, Wang J S, Raravikar N. Interfacial thermal conductance between silicon and a vertical carbon nanotube [J]. Journal of Applied Physics,2008,104(8):083503.
[142]Grujicic M, Cao G, Roy W. Computational analysis of the lattice contribution to thermal conductivity of single-walled carbon nanotubes [J]. Journal of Materials Science,2005,40(8): 1943.
[143]Varshney V, Patnaik S S, Roy A K, Froudakis G, Farmer B L. Modeling of thermal transport in pillared-graphene architectures [J]. ACS Nano,2010,4(2):1153.
[144]Muller-Plathe F, Reith D. Cause and effect reversed in non-equilibrium molecular dynamics:An easy route to transport coefficients [J]. Computational and Theoretical Polymer Science,1999,9(3-4):203.
[145]Lee J W, Meade A J, Barrera E V, Templeton J A. Dependencies of the thermal conductivity of individual single-walled carbon nanotubes [J]. Proceedings of the Institution of Mechanical Engineers, Part N:Journal of Nanoengineering and Nanosystems,2010,224(1-2): 41.
[146]Thomas J A, Iutzi R M, McGaughey A J H. Thermal conductivity and phonon transport in empty and water-filled carbon nanotubes [J]. Physical Review B,2010,81(4):045413.
[147]Kumar S, Kamaraju N, Karthikeyan B, Tondusson M, Freysz E, Sood A K. Terahertz spectroscopy of single-walled carbon nanotubes in a polymer film:Observation of low-frequency phonons [J]. The Journal of Physical Chemistry C,2010,114(29):12446.
[148]Jo I, Hsu I K, Lee Y J, Sadeghi M M, Kim S, Cronin S, Tutuc E, Banerjee S K, Yao Z, Shi L. Low-frequency acoustic phonon temperature distribution in electrically biased graphene [J]. Nano Letters,2010,11(1):85.
[149]Fung Y C. Foundations of solid mechanics [M]. Englewood Cliffs, N.J.:Prentice-Hall, 1965.
[150]Togo A, Oba F, Tanaka I. First-principles calculations of the ferroelastic transition between rutile-type and CaCl2-type SiO2 at high pressures [J]. Physical Review B,2008,78(13):134106.
[151]Donald W B, Olga A S, Judith A H, Steven J S, Boris N, Susan B S. A second-generation reactive empirical bond order (REBO) potential energy expression for hydrocarbons [J]. Journal of Physics:Condensed Matter,2002,14(4):783.
[152]Wang H, Cao B, Guo Z. Heat flow choking in carbon nanotubes [J]. International Journal of Heat and Mass Transfer,2010,53(9-10):1796.
[153]Zhang S, Xia M, Zhao S, Xu T, Zhang E. Specific heat of single-walled carbon nanotubes [J]. Physical Review B,2003,68(7):075415.
[2]Liang L, Li B. Size-dependent thermal conductivity of nanoscale semiconducting systems [J]. Physical Review B,2006,73(15):153303.
[3]Kulkarni A J, Zhou M. Size-dependent thermal conductivity of zinc oxide nanobelts [J]. Applied Physics Letters,2006,88(14):141921.
[4]Roh J W, Jang S Y, Kang J, Lee S, Noh J-S, Kim W, Park J, Lee W. Size-dependent thermal conductivity of individual single-crystalline PbTe nanowires [J]. Applied Physics Letters,2010, 96(10):103101.
[5]Lu X, Shen W Z, Chu J H. Size effect on the thermal conductivity of nanowires [J]. Journal of Applied Physics,2002,91(3):1542.
[6]Wang Z, Tang D, Zheng X, Zhang W, Zhu Y. Length-dependent thermal conductivity of single-wall carbon nanotubes:prediction and measurements [J]. Nanotechnology,2007,18(47): 475714.
[7]Wang Z, Tang D, Li X, Zheng X, Zhang W, Zheng L, Zhu Y, Jin A, Yang H, Gu C. Length-dependent thermal conductivity of an individual single-wall carbon nano tube [J]. Applied Physics Letters,2007,91(12):123119.
[8]Lukes J R, Zhong H L. Thermal conductivity of individual single-wall carbon nanotubes [J]. Journal of Heat Transfer,2007,129(6):705.
[9]Mingo N, Broido D A. Length dependence of carbon nanorube thermal conductivity and the "problem of long waves" [J]. Nano Letters,2005,5(7):1221.
[10]Shi L, Yao D, Zhang G, Li B. Size dependent thermoelectric properties of silicon nanowires [J]. Applied Physics Letters,2009,95(6):063102.
[11]Zhong H, Lukes J R. Interfacial thermal resistance between carbon nanotubes:Molecular dynamics simulations and analytical thermal modeling [J]. Physical Review B,2006,74(12): 125403.
[12]Diao J, Srivastava D, Menon M. Molecular dynamics simulations of carbon nanotube/silicon interfacial thermal conductance [J]. The Journal of Chemical Physics,2008, 128(16):164708.
[13]Ju H, Zhang S, Li Z, Shui X, Kuo P. Size-dependent thermal diffusivity of multilayered thin films deposited on substrates characterized by transient grating technique [J]. Applied Physics Letters,2009,94(3):031902.
[14]Shin H S, Yu J, Song J Y. Size-dependent thermal instability and melting behavior of Sn nanowires [J]. Applied Physics Letters,2007,91(17):173106.
[15]Zhang M, Efremov M Y, Schiettekatte F, Olson E A, Kwan A T, Lai S L, Wisleder T, Greene J E, Allen L H. Size-dependent melting point depression of nanostructures:Nanocalorimetric measurements [J]. Physical Review B,2000,62(15):10548.
[16]Lai S L, Guo J Y, Petrova V, Ramanath G, Allen L H. Size-dependent melting properties of small tin particles:Nanocalorimetric measurements [J]. Physical Review Letters,1996,77(1): 99.
[17]Castro T, Reifenberger R, Choi E, Andres R P. Size-dependent melting temperature of individual nanometer-sized metallic clusters [J]. Physical Review B,1990,42(13):8548.
[18]Dick K, Dhanasekaran T, Zhang Z, Meisel D. Size-dependent melting of silica-encapsulated gold nanoparticles [J]. Journal of the American Chemical Society,2002,124(10):2312.
[19]Li X, Yang R. Size-dependent phonon transmission across dissimilar material interfaces [J]. Journal of Physics:Condensed Matter,2012,24(15):155302.
[20]Liang L, Wei Y, Li B. Size-dependent interface phonon transmission and thermal conductivity of nanolaminates [J]. Journal of Applied Physics,2008,103(8):084314.
[21]Cahill D G, Ford W K, Goodson K E, Mahan G D, Majumdar A, Maris H J, Merlin R, Phillpot S R. Nanoscale thermal transport [J]. Journal of Applied Physics,2003,93(2):793.
[22]Ashby M F, Ferreira P J, Schodek D L. Chapter 6-Nanomaterials:Classes and fundamentals [M]. Nanomaterials, Nanotechnologies and Design. Boston; Butterworth-Heinemann.2009:177.
[23]Iijima S. Helical microtubules of graphitic carbon [J]. Nature,1991,354(6348):56.
[24]Holmes J D, Johnston K P, Doty R C, Korgel B A. Control of thickness and orientation of solution-grown silicon nanowires [J]. Science,2000,287(5457):1471.
[25]Hanrath T, Korgel B A. Supercritical fluid-liquid-solid (SFLS) synthesis of Si and Ge nanowires seeded by colloidal metal nanocrystals [J]. Advanced Materials,2003,15(5):437.
[26]Gyu-Chul Y, Chunrui W, Won Il P. ZnO nanorods:synthesis, characterization and applications [J]. Semiconductor Science and Technology,2005,20(4):S22.
[27]Huang X, Neretina S, El-Sayed M A. Gold nanorods:From synthesis and properties to biological and biomedical applications [J]. Advanced Materials,2009,21(48):4880.
[28]Zhou F-L, Gong R-H. Manufacturing technologies of polymeric nanofibres and nanofibre yarns [J]. Polymer International,2008,57(6):837.
[29]Nakada K, Fujita M, Dresselhaus G, Dresselhaus M S. Edge state in graphene ribbons: Nanometer size effect and edge shape dependence [J]. Physical Review B,1996,54(24):17954.
[30]Khitun A, Balandin A, Wang K L. Modification of the lattice thermal conductivity in silicon quantum wires due to spatial confinement of acoustic phonons [J]. Superlattices and Microstructures,1999,26(3):181.
[31]Volz S G, Chen G Molecular dynamics simulation of thermal conductivity of silicon nanowires [J]. Applied Physics Letters,1999,75(14):2056.
[32]Shi L, Li D, Yu C, Jang W, Kim D, Yao Z, Kim P, Majumdar A. Measuring thermal and thermoelectric properties of one-dimensional nanostructures using a microfabricated device [J]. Journal of Heat Transfer,2003,125(5):881.
[33]Pop E. Energy dissipation and transport in nanoscale devices [J]. Nano Research,2010,3(3): 147.
[34]Hochbaum A I, Chen R, Delgado R D, Liang W, Gamett E C, Najarian M, Majumdar A, Yang P. Enhanced thermoelectric performance of rough silicon nanowires [J]. Nature,2008, 451(7175):163.
[35]Hu X, et. al. Thermal characterisation of aligned carbon nanotubes on silicon [C]. Proceedings of the 21st Semi-Therm, San Jose, CA, F,2005.
[36]Peng K-Q, Wang X, Wu X-L, Lee S-T. Platinum nanoparticle decorated silicon nanowires for efficient solar energy conversion [J]. Nano Letters,2009,9(11):3704.
[37]Yang N, Zhang G, Li B. Ultralow thermal conductivity of isotope-doped silicon nanowires [J]. Nano Letters,2007,8(1):276.
[38]Hu M, Giapis K P, Goicochea J V, Zhang X, Poulikakos D. Significant reduction of thermal conductivity in Si/Ge core-shell nanowires [J]. Nano Letters,2010,11(2):618.
[39]Hu M, Zhang X, Giapis K P, Poulikakos D. Thermal conductivity reduction in core-shell nanowires [J]. Physical Review B,2011,84(8):085442.
[40]Majumdar A. Thermoelectricity in semiconductor nanostructures [J]. Science,2004, 303(5659):777.
[41]Ettenberg M H, Jesser W A, Rosi F D. Proceedings of the 15th International Conference on Thermoelectrics (Ed:T Caillat), Piscataway, F,1996 [C].
[42]Weber L, Gmelin E. Transport properties of silicon [J]. Applied Physics A:Materials Science & Processing,1991,53(2):136.
[43]Li D, Wu Y, Kim P, Shi L, Yang P, Majumdar A. Thermal conductivity of individual silicon nanowires [J]. Applied Physics Letters,2003,83(14):2934.
[44]Chen X, Wang Y, Ma Y, Cui T, Zou G. Origin of the high thermoelectric performance in Si nanowires:A first-principle study [J]. The Journal of Physical Chemistry C,2009,113(31): 14001.
[45]Xu J, Fisher T S. Enhancement of thermal interface materials with carbon nanotube arrays [J]. International Journal of Heat and Mass Transfer,2006,49(9-10):1658.
[46]Zhang K, Chai Y, Yuen M M F, Xiao D G W, Chan P C H. Carbon nanotube thermal interface material for high-brightness light-emitting-diode cooling [J]. Nanotechnology,2008, 19(21):215706.
[47]Shiomi J, Maruyama S. Non-Fourier heat conduction in a single-walled carbon nanotube: Classical molecular dynamics simulations [J]. Physical Review B,2006,73(20):205420.
[48]Greaney P A, Lani G, Cicero G, Grossman J C. Anomalous dissipation in single-walled carbon nanotube resonators [J]. Nano Letters,2009,9(11):3699.
[49]Wang H, Cao B, Guo Z. Non-Fourier heat conduction in carbon nanotubes [J]. Journal of Heat Transfer,2012,134(5):051004.
[50]Wang M, Yang N, Guo Z. Non-Fourier heat conductions in nanomaterials [J]. Journal of Applied Physics,2011,110(6):064310.
[51]Wang H, Liu J, Guo Z, Takahashi K. Non-Fourier heat conduction study for steady states in metallic nanofilms [J]. Chinese Science Bulletin,2012,57(24):3239.
[52]Wright D A. Thermoelectric properties of bismuth telluride and its alloys [J]. Nature,1958, 181(4612):834.
[53]Venkatasubramanian R, Siivola E, Colpitts T, O'Quinn B. Thin-film thermoelectric devices with high room-temperature figures of merit [J]. Nature,2001,413(6856):597.
[54]Harman T C, Taylor P J, Walsh M P, LaForge B E. Quantum dot superlattice thermoelectric materials and devices [J]. Science,2002,297(5590):2229.
[55]Chen J, Zhang G, Li B. Remarkable reduction of thermal conductivity in silicon nanotubes [J]. Nano Letters,2010,10(10):3978.
[56]Kurti N, Rollin B V, Simon F. Preliminary experiments on temperature equilibria at very low temperatures [J]. Physica,1936,3(1-4):266.
[57]Keesom W H, Keesom A P. On the heat conductivity of liquid helium [J]. Physica,1936,3: 359.
[58]Kapitza P L. The study of heat transfer in helium Ⅱ [J]. J Phys-USSR,1941,4(1-6):181.
[59]Khalatnikov I M.*Teploobmen mezhdu tverdym telom Ⅰ geliem-Ⅱ [J]. Zhurnal Eksperimentalnoi Teor Fiz,1952,22(6):687.
[60]Mazo R M. Theoretical studies on low temperature phenomena [D]. Yale University,1955.
[61]Little W A. The transport of heat between dissimilar solids at low temperatures [J]. Canadian Journal of Physics,1959,37(3):334.
[62]Swartz E T, Pohl R O. Thermal boundary resistance [J]. Reviews of Modern Physics,1989, 61(3):605.
[63]Zeng T, Chen G. Phonon heat conduction in thin films:Impacts of thermal boundary resistance and internal heat generation [J]. Journal of Heat Transfer,2001,123(2):340.
[64]Young D A, Maris H J. Lattice-dynamical calculation of the Kapitza resistance between fcc lattices [J]. Physical Review B,1989,40(6):3685.
[65]Cunnington G R, Jr. Thermal conductance of filled aluminium and magnesium joints in a vacuum environment [M]. ASME Winter Annual Meeting. New York.1964.
[66]Getty R C, Tatro R E. Spacecraft thermal joint conduction [M]. AIAA Thermophysics Specialists Conference. New Orleans.1967.
[67]Marotta E E, Fletcher L S. Thermal contact conductance of selected polymeric materials [J]. Journal of Thermophysics and Heat Transfer,1996,10(2):334.
[68]Xu Y, Luo X, Chung D D L. Sodium silicate based thermal interface material for high thermal contact conductance [J]. Journal of Electronic Packaging,2000,122(2):128.
[69]Hachman M. Intel adapting buckyballs for cooling chips [M]. ExtremeTech. http://www.extremetech.com/cxtreme/73118-intel-adapting-buckyballs-for-cooling-chips.2002.
[70]Montgomery S W, Holalkere V R. Carbon nanotube thermal interface structures:US, 6965513 B2 [P/OL].2005-November 2005.
[71]Lee T-M, Chiou K-C, Tseng F-P, Hung C-C. High thermal efficiency carbon nanotube-resin matrix for thermal interface materials [C]. Proceedings of the 55th Electronic components and technology conference, F,2005.
[72]Zhang K, Xiao G-W, Wong C K Y, Gu H-W, Yuen M M F, Chan P C H, Xu B. Study on thermal interface material with carbon nanotubes and carbon black in high-brightness LED packaging with flip-chip technology [C]. Proceedings of the 55th Electronic components and technology conference, F,2005.
[73]Frenkel D, Smit B. Understanding molecular simulation:From algorithms to applications [M]. Orlando, FL, USA:Academic Press,2001.
[74]Schelling P K, Phillpot S R, Keblinski P. Comparison of atomic-level simulation methods for computing thermal conductivity [J]. Physical Review B,2002,65(14):144306.
[75]Stillinger F H, Weber T A. Computer simulation of local order in condensed phases of silicon [J]. Physical Review B,1985,31(8):5262.
[76]Tersoff J. Modeling solid-state chemistry:Interatomic potentials for multicomponent systems [J]. Physical Review B,1989,39(8):5566.
[77]Tersoff J. Erratum:Modeling solid-state chemistry:Interatomic potentials for multicomponent systems [J]. Physical Review B,1990,41(5):3248.
[78]Stuart S J, Tutein A B, Harrison J A. A reactive potential for hydrocarbons with intermolecular interactions [J]. The Journal of Chemical Physics,2000,112(14):6472.
[79]Plimpton S. Fast parallel algorithms for short-range molecular dynamics [J]. Journal of Computational Physics,1995,117(1):1.
[80]Hanley H J M, McCarty R D, Haynes W M. The viscosity and thermal conductivity coefficients for dense gaseous and liquid argon, krypton, xenon, nitrogen, and oxygen [J]. Journal of Physical and Chemical Reference Data,1974,3(4):979.
[81]Muller-Plathe F. A simple nonequilibrium molecular dynamics method for calculating the thermal conductivity [J]. The Journal of Chemical Physics,1997,106(14):6082.
[82]Nieto-Draghi C, Avalos J B. Non-equilibrium momentum exchange algorithm for molecular dynamics simulation of heat flow in multicomponent systems [J]. Molecular Physics,2003, 101(14):2303.
[83]Chen X, Wang Y, Ma Y. High thermoelectric performance of Ge/Si core-shell nanowires: First-principles prediction [J]. The Journal of Physical Chemistry C,2010,114(19):9096.
[84]Yang Z, Guarin F, Tao I W, Wang W I, Iyer S S. Approach to obtain high quality GaN on Si and SiC-on-silicon-on-insulator compliant substrate by molecular-beam epitaxy [J]. Journal of Vacuum Science & Technology B,1995,13(2):789.
[85]Schenk H P D, Kipshidze G D, Lebedev V B, Shokhovets S, Goldhahn R, Krauplich J, Fissel A, Richter W. Epitaxial growth of A1N and GaN on Si(111) by plasma-assisted molecular beam epitaxy [J]. Journal of Crystal Growth,1999,201-202(0):359.
[86]Joblot S, Semond F, Natali F, Vennegues P, Laugt M, Cordier Y, Massies J. Growth of wurtzite-GaN on silicon (100) substrate by molecular beam epitaxy [M]//STUTZMANN M. Physica Status Solidi C-Conferences and Critical Reviews, Vol 2, No 7. Weinheim; Wiley-V C H Verlag Gmbh.2005:2187.
[87]Kumagai T, Izumi S, Hara S, Sakai S. Development of bond-order potentials that can reproduce the elastic constants and melting point of silicon for classical molecular dynamics simulation [J]. Computational Materials Science,2007,39(2):457.
[88]Ramana Murty M V, Atwater H A. Empirical interatomic potential for Si-H interactions [J]. Physical Review B,1995,51(8):4889.
[89]Juslin N, Erhart P, Traskelin P, Nord J, Henriksson K O E, Nordlund K, Salonen E, Albe K. Analytical interatomic potential for modeling nonequilibrium processes in the W-C-H system [J]. Journal of Applied Physics,2005,98(12):123520.
[90]Albe K, Nordlund K, Nord J, Kuronen A. Modeling of compound semiconductors: Analytical bond-order potential for Ga, As, and GaAs [J]. Physical Review B,2002,66(3): 035205.
[91]Brenner D W. Relationship between the embedded-atom method and Tersoff potentials [J]. Physical Review Letters,1989,63(9):1022.
[92]Erhart P, Albe K. Analytical potential for atomistic simulations of silicon, carbon, and silicon carbide [J]. Physical Review B,2005,71(3):035211.
[93]Nord J, Albe K, Erhart P, Nordlund K. Modelling of compound semiconductors:analytical bond-order potential for gallium, nitrogen and gallium nitride [J]. Journal of Physics:Condensed Matter,2003,15(32):5649.
[94]Albe K, Nordlund K, Averback R S. Modeling the metal-semiconductor interaction: Analytical bond-order potential for platinum-carbon [J]. Physical Review B,2002,65(19): 195124.
[95]Ding K, Andersen H C. Molecular-dynamics simulation of amorphous germanium [J]. Physical Review B,1986,34(10):6987.
[96]Karimi M, Kaplan T, Mostoller M, Jesson D E. Ge segregation at Si-Ge (001) stepped surfaces [J]. Physical Review B,1993,47(15):9931.
[97]Zhou X, Jones R E. Effects of cutoff functions of Tersoff potentials on molecular dynamics simulations of thermal transport [J]. Modelling and Simulation in Materials Science and Engineering,2011,19(2):025004.
[98]Benkabou F, Certier M, Aourag H. Elastic properties of zinc-blende GaN, A1N and InN from molecular dynamics [J]. Molecular Simulation,2003,29(3):201.
[99]Goumri-Said S, Kanoun M B, Merad A E, Merad G, Aourag H. Prediction of structural and thermodynamic properties of zinc-blende A1N:molecular dynamics simulation [J]. Chemical Physics,2004,302(1-3):135.
[100]Munetoh S, Motooka T, Moriguchi K, Shintani A. Interatomic potential for Si-O systems using Tersoff parameterization [J]. Computational Materials Science,2007,39(2):334.
[101]Billeter S R, Curioni A, Fischer D, Andreoni W. Ab initio derived augmented Tersoff potential for silicon oxynitride compounds and their interfaces with silicon [J]. Physical Review B,2006,73(15):155329.
[102]Billeter S R, Curioni A, Fischer D, Andreoni W. Erratum:Ab initio derived augmented Tersoff potential for silicon oxynitride compounds and their interfaces with silicon [Phys. Rev. B 73,155329 (2006)] [J]. Physical Review B,2009,79(16):169904.
[103]Ippolito M, Meloni S. Atomistic structure of amorphous silicon nitride from classical molecular dynamics simulations [J]. Physical Review B,2011,83(16):165209.
[104]Nose S. A unified formulation of the constant temperature molecular dynamics methods [J]. The Journal of Chemical Physics,1984,81(1):511.
[105]Hoover W G Canonical dynamics:Equilibrium phase-space distributions [J]. Physical Review A,1985,31(3):1695.
[106]Jund P, Jullien R. Molecular-dynamics calculation of the thermal conductivity of vitreous silica [J]. Physical Review B,1999,59(21):13707.
[107]Pan L, Lew K-K, Redwing J M, Dickey E C. Stranski-krastanow growth of germanium on silicon nanowires [J]. Nano Letters,2005,5(6):1081.
[108]Dickey J M, Paskin A. Computer simulation of the lattice dynamics of solids [J]. Physical Review,1969,188(3):1407.
[109]Hu M, Goicochea J V, Michel B, Poulikakos D. Water nanoconfinement induced thermal enhancement at hydrophilic quartz interfaces [J]. Nano Letters,2009,10(1):279.
[110]Goicochea J V, Hu M, Michel B, Poulikakos D. Surface functionalization mechanisms of enhancing heat transfer at solid-liquid interfaces [J]. Journal of Heat Transfer,2011,133(8): 082401.
[111]Hu M, Zhang X, Poulikakos D, Grigoropoulos C P. Large "near junction" thermal resistance reduction in electronics by interface nanoengineering [J]. International Journal of Heat and Mass Transfer,2011,54(25-26):5183.
[112]Bell R J, Dean P. Atomic vibrations in vitreous silica [J]. Discussions of the Faraday Society,1970,50:55.
[113]Daly B C, Maris H J, Imamura K, Tamura S. Molecular dynamics calculation of the thermal conductivity of superlattices [J]. Physical Review B,2002,66(2):024301.
[114]Landry E S, McGaughey A J H. Effect of interfacial species mixing on phonon transport in semiconductor superlattices [J]. Physical Review B,2009,79(7):075316.
[115]Termentzidis K, Chantrenne P, Keblinski P. Nonequilibrium molecular dynamics simulation of the in-plane thermal conductivity of superlattices with rough interfaces [J]. Physical Review B,2009,79(21):214307.
[116]Termentzidis K, Merabia S, Chantrenne P, Keblinski P. Cross-plane thermal conductivity of superlattices with rough interfaces using equilibrium and non-equilibrium molecular dynamics [J]. International Journal of Heat and Mass Transfer,2011,54(9-10):2014.
[117]Yao Z, Wang J, Li B, Liu G. Thermal conduction of carbon nanotubes using molecular dynamics [J]. Physical Review B,2005,71(8):085417.
[118]Lee J H, Grossman J C, Reed J, Galli G. Lattice thermal conductivity of nanoporous Si: Molecular dynamics study [J]. Applied Physics Letters,2007,91(22):223110.
[119]Donadio D, Galli G. Temperature Dependence of the Thermal conductivity of thin silicon nanowires [J]. Nano Letters,2010,10(3):847.
[120]Schneider T, Stoll E. Molecular-dynamics study of a three-dimensional one-component model for distortive phase transitions [J]. Physical Review B,1978,17(3):1302.
[121]Ong Z, Pop E. Molecular dynamics simulation of thermal boundary conductance between carbon nanotubes and SiO2 [J]. Physical Review B,2010,81(15):155408.
[122]Osman M A, Srivastava D. Temperature dependence of the thermal conductivity of single-wall carbon nanotubes [J]. Nanotechnology,2001,12(1):21.
[123]Padgett C W, Brenner D W. Influence of chemisorption on the thermal conductivity of single-wall carbon nanotubes [J]. Nano Letters,2004,4(6):1051.
[124]Saito Y, Sasaki N, Moriya H, Kagatsume A, Noro S. Parameter optimization of Tersoff interatomic potentials using a genetic algorithm [J]. JSME International Journal Series A-Solid Mechanics and Material Engineering,2001,44(2):207.
[125]Liang Z, Tsai H-L. Reduction of solid-solid thermal boundary resistance by inserting an interlayer [J]. International Journal of Heat and Mass Transfer,2012,55(11-12):2999.
[126]Ju S, Liang X, Wang S. Investigation of interfacial thermal resistance of bi-layer nanofilms by nonequilibrium molecular dynamics [J]. Journal of Physics D:Applied Physics,2010,43(8): 085407.
[127]Cao A, Qu J, Yao M. Atomistic simulations of heat transfer at carbon nanotube/Si interfaces [M]. IEEE Electronics Components and Technology Conference. Las Vegas.2010: 417.
[128]Chang C W, Okawa D, Majumdar A, Zettl A. Solid-state thermal rectifier [J]. Science, 2006,314(5802):1121.
[129]Hu M, Keblinski P, Li B. Thermal rectification at silicon-amorphous polyethylene interface [J]. Applied Physics Letters,2008,92(21):211908.
[130]Hu M, Goicochea J V, Michel B, Poulikakos D. Thermal rectification at water/functionalized silica interfaces [J]. Applied Physics Letters,2009,95(15):151903.
[131]Zhang X, Hu M, Poulikakos D. A Low-frequency wave motion mechanism enables efficient energy transport in carbon nanotubes at high heat fluxes [J]. Nano Letters,2012,12(7): 3410.
[132]Chen J, Zhang G, Li B. Phonon coherent resonance and its effect on thermal transport in core-shell nano wires [J]. The Journal of Chemical Physics,2011,135(10):104508.
[133]Humphrey W, Dalke A, Schulten K. VMD:Visual molecular dynamics [J]. Journal of Molecular Graphics,1996,14(1):33.
[134]Pop E, Mann D, Cao J, Wang Q, Goodson K, Dai H J. Negative differential conductance and hot phonons in suspended nanotube molecular wires [J]. Physical Review Letters,2005, 95(15):155505.
[135]Kim P, Shi L, Majumdar A, McEuen P L. Thermal transport measurements of individual multiwalled nanotubes [J]. Physical Review Letters,2001,87(21):215502.
[136]Fujii M, Zhang X, Xie H Q, Ago H, Takahashi K, Ikuta T, Abe H, Shimizu T. Measuring the thermal conductivity of a single carbon nanotube [J]. Physical Review Letters,2005,95(6): 065502.
[137]Choi T Y, Poulikakos D, Tharian J, Sennhauser U. Measurement of the thermal conductivity of individual carbon nanotubes by the four-point three-omega method [J]. Nano Letters,2006,6(8):1589.
[138]Che J, Cagin T, Goddard W A. Thermal conductivity of carbon nanotubes [J]. Nanotechnology,2000,11(2):65.
[139]Wang J, Wang J. Carbon nanotube thermal transport:Ballistic to diffusive [J]. Applied Physics Letters,2006,88(11):111909.
[140]Donadio D, Galli G. Thermal conductivity of isolated and interacting carbon nanotubes: Comparing results from molecular dynamics and the Boltzmann transport equation [J]. Physical Review Letters,2007,99(25):255502.
[141]Hu M, Keblinski P, Wang J S, Raravikar N. Interfacial thermal conductance between silicon and a vertical carbon nanotube [J]. Journal of Applied Physics,2008,104(8):083503.
[142]Grujicic M, Cao G, Roy W. Computational analysis of the lattice contribution to thermal conductivity of single-walled carbon nanotubes [J]. Journal of Materials Science,2005,40(8): 1943.
[143]Varshney V, Patnaik S S, Roy A K, Froudakis G, Farmer B L. Modeling of thermal transport in pillared-graphene architectures [J]. ACS Nano,2010,4(2):1153.
[144]Muller-Plathe F, Reith D. Cause and effect reversed in non-equilibrium molecular dynamics:An easy route to transport coefficients [J]. Computational and Theoretical Polymer Science,1999,9(3-4):203.
[145]Lee J W, Meade A J, Barrera E V, Templeton J A. Dependencies of the thermal conductivity of individual single-walled carbon nanotubes [J]. Proceedings of the Institution of Mechanical Engineers, Part N:Journal of Nanoengineering and Nanosystems,2010,224(1-2): 41.
[146]Thomas J A, Iutzi R M, McGaughey A J H. Thermal conductivity and phonon transport in empty and water-filled carbon nanotubes [J]. Physical Review B,2010,81(4):045413.
[147]Kumar S, Kamaraju N, Karthikeyan B, Tondusson M, Freysz E, Sood A K. Terahertz spectroscopy of single-walled carbon nanotubes in a polymer film:Observation of low-frequency phonons [J]. The Journal of Physical Chemistry C,2010,114(29):12446.
[148]Jo I, Hsu I K, Lee Y J, Sadeghi M M, Kim S, Cronin S, Tutuc E, Banerjee S K, Yao Z, Shi L. Low-frequency acoustic phonon temperature distribution in electrically biased graphene [J]. Nano Letters,2010,11(1):85.
[149]Fung Y C. Foundations of solid mechanics [M]. Englewood Cliffs, N.J.:Prentice-Hall, 1965.
[150]Togo A, Oba F, Tanaka I. First-principles calculations of the ferroelastic transition between rutile-type and CaCl2-type SiO2 at high pressures [J]. Physical Review B,2008,78(13):134106.
[151]Donald W B, Olga A S, Judith A H, Steven J S, Boris N, Susan B S. A second-generation reactive empirical bond order (REBO) potential energy expression for hydrocarbons [J]. Journal of Physics:Condensed Matter,2002,14(4):783.
[152]Wang H, Cao B, Guo Z. Heat flow choking in carbon nanotubes [J]. International Journal of Heat and Mass Transfer,2010,53(9-10):1796.
[153]Zhang S, Xia M, Zhao S, Xu T, Zhang E. Specific heat of single-walled carbon nanotubes [J]. Physical Review B,2003,68(7):075415.