搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

超晶格和层状结构传热特性的连续模型及其在能源材料设计中的应用

李柱松 朱泰山

引用本文:
Citation:

超晶格和层状结构传热特性的连续模型及其在能源材料设计中的应用

李柱松, 朱泰山

Continuum modeling of thermal transport in superlattices and layered materials for new energy matierlas

Li Zhu-Song, Steven Zhu
PDF
导出引用
  • 层状材料和超晶格结构为提高热电材料和隔热涂层提供了新的设计思路, 并成为最近的研究热点. 应用连续波动方程和线性阻尼理论, 本文研究了此类材料中的声子输运特性. 给出了在整个相空间里的界面调制和声子局域化效应, 得出了超晶格材料热导率的上极限和下极限; 同时, 分析表明界面锐化加强了声子带隙, 使得部分模态的声子局域化加强. 最后, 通过对石墨烯/氮化硼超晶格(G/hBN)和硅/锗超晶格的分子模拟(Si/Ge), 验证了该理论模型. 该方法适用于所有的层状材料和超晶格结构, 对此类新能源材料的设计提供了普适的设计思路.
    Both high-efficient thermoelectric materials and thermal insulating coatings requiring low thermal conductivities, layered materials and superlattices prove to be an efficient multiscale material design for such requirements. The interfaces are artificially introduced to scatter thermal phonons, thus hindering thermal transport. Very recently, it has been found that interface modulation can further reduce the thermal conductivity. All of the recent advances originate from highly demanding numerical computations. An efficient estimate of the thermal properties is important for fast and/or high-throughput calculations. In this article, the phonon transport on layered material is studied theoretically for general purposes, based on the fact that long-wavelength phonons contribute dominantly in general. According to the Debye hypothesis, the classical wave equation can describe phonon transport very well. This fact has been very recently used to model phonon transport carbon nanotubes, which justifies the applicability of continuum mechanics for nanomaterials. Furthermore, Kronig and Penny have solved the electron transport on periodic lattices. In a very similar way, for the periodic layered materials and superlattices, with Floquet and linear attenuation theory, the wave equations with and without damping are solved analytically. The wave equation decouples to Helmholtz equations in each direction with periodic excitation functions. In this paper, we propose to model the phonon transport by using Matthew-Hill equation, with which we can obtain the phonon spectrum (i.e. phonon dispersion relation). The proposed theory is justified by two-dimensional (2D) graphene/hexagon boron nitride superlattice and three-dimensional (3D) silicon/germanium superlattices. Like the carbon nanotube cases, using this continuum-mechanics method, we can reproduce the previous numerical results very quickly compared with using published molecular dynamics and density functional theory The effects of interface modulation and phonon localization are shown over full phase space, which further enables the calculating of both high and low bounds of thermal conductivity for all possible superlattices and layered materials. In order to model real interfaces, with considering possible mixing and transition due to other mechanisms, we use the smooth transition function, which is further modeled via sinusoidal series. Very interestingly, interface grading is shown to erase band gaps and delocalize modes. This fact has been seldom reported and can be helpful for designing real materials. Likewise, we take phonon damping (equivalent to inter-phonon scattering) into account by adding damping into the wave equation. It is observed that phonon damping smears the originally sharp boundaries of phonon phase space. In this way, evanescent phonons and transporting phonons can be treated simultaneously on the same footing. The proposed method can be used for modeling the efficient and general thermal materials
      通信作者: 李柱松, zhusongli922@gmail.com
    • 基金项目: 国家自然科学基金(批准号: DMR-0934206)资助的课题.
      Corresponding author: Li Zhu-Song, zhusongli922@gmail.com
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. DMR-0934206).
    [1]

    Dresselhaus M S, Chen G, Tang M Y, Yang R G, Lee H, Wang D Z, Ren Z F, Fleurial J P, Gogna P 2007 Adv. Mater. 19 1043

    [2]

    Heremans J P, Dresselhaus M S, Bell L E, Morelli D T 2013 Nat. Nanotechnol. 8 471

    [3]

    Mahan G D, Sofo J O 1996 Proc. Natl. Acad. Sci. USA 93 7436

    [4]

    Snyder G J, Toberer E S 2008 Nat. Mater. 7 105

    [5]

    Nolas G S, Sharp J, Goldsmid H J 2001 Thermoelectrics: Basic Principles and New Materials Developments (Berlin: Springer) pp12-23

    [6]

    Tsu R 2011 Superlattice to Nanoelectronics (Boston: Elsevier) pp1-7

    [7]

    Chen G 1997 J. Heat Trans. 119 220

    [8]

    Chen G 1999 J. Heat Trans. 121 945

    [9]

    Hicks L D, Dresselhaus M S 1993 Phys. Rev. B 47 12727

    [10]

    Hicks L D, Harman T C, Dresselhaus M S 1993 Appl. Phys. Lett. 63 3230

    [11]

    Zhu T, Ertekin E 2014 Phys. Rev. B 90 195209

    [12]

    Li X D, Yu S, Wu S Q, Wen Y H, Zhou S, Zhu Z Z 2013 J. Phys. Chem. C 117 15347

    [13]

    Lindsay L, Broido D A 2010 Phys. Rev. B 81 205441

    [14]

    Lindsay L, Broido D A 2011 Phys. Rev. B 84 155421

    [15]

    Zhu T, Ye W 2010 Phys. Rev. E 82 036308

    [16]

    Zhu T, Ye W 2011 Phys. Rev. E 84 056316

    [17]

    Zhu T, Ye W 2010 Num. Heat Trans. B 57 203

    [18]

    Zhu T, Ye W 2012 J. Heat Trans. 134 051013

    [19]

    Guo Z, Xu K 2016 arXiv:1602.01680v1

    [20]

    Liu H, Xu K, Zhu T, Ye W 2012 Comput. Fluids 67 115

    [21]

    Munoz E, Lu H, Yakobson B I 2010 Nano Lett. 10 1652

    [22]

    Hill G W 1886 Acta Math. 8 1

    [23]

    van der Pol B, Strutt M J O 1928 Phil. Mag. 5 18

    [24]

    McLachlan N W 1964 Theory and Applications of Mathieu Functions (New York: Dover) pp11-23

    [25]

    Magnus W, Winkler S 1966 Hill's Equation (New York: Interscience) pp7-13

    [26]

    Lyngby P P 1980 Ingenieur-Archiv. 49 15

    [27]

    Kwong M K, Wong J S W 2006 J. Math. Anal. Appl. 320 37

    [28]

    Ruby L 1996 Am. J. Phys. 64 39

    [29]

    Gutierrez-Vega J C 2003 Am. J. Phys. 71 233

    [30]

    Kittel C 1996 Introduction to Solid State Physics (New York: Wiley) pp180-182

    [31]

    Simkin M V, Mahan G D 2000 Phys. Rev. Lett. 84 927

    [32]

    Zhu T, Ertekin E 2016 arXiv:1602.02419

    [33]

    Savic I, Donadio D, Gygi F, Galli G 2013 Appl. Phys. Lett. 102 073113

    [34]

    Chalopin Y, Esfarjani K, Henry A, Volz S, Chen G 2012 Phys. Rev. B 85 195302

    [35]

    Zhu T, Ertekin E 2015 Phys. Rev. B 91 205429

    [36]

    Taylor J H, Narendra K S 1969 SIAM J. Appl. Math. 17 343

  • [1]

    Dresselhaus M S, Chen G, Tang M Y, Yang R G, Lee H, Wang D Z, Ren Z F, Fleurial J P, Gogna P 2007 Adv. Mater. 19 1043

    [2]

    Heremans J P, Dresselhaus M S, Bell L E, Morelli D T 2013 Nat. Nanotechnol. 8 471

    [3]

    Mahan G D, Sofo J O 1996 Proc. Natl. Acad. Sci. USA 93 7436

    [4]

    Snyder G J, Toberer E S 2008 Nat. Mater. 7 105

    [5]

    Nolas G S, Sharp J, Goldsmid H J 2001 Thermoelectrics: Basic Principles and New Materials Developments (Berlin: Springer) pp12-23

    [6]

    Tsu R 2011 Superlattice to Nanoelectronics (Boston: Elsevier) pp1-7

    [7]

    Chen G 1997 J. Heat Trans. 119 220

    [8]

    Chen G 1999 J. Heat Trans. 121 945

    [9]

    Hicks L D, Dresselhaus M S 1993 Phys. Rev. B 47 12727

    [10]

    Hicks L D, Harman T C, Dresselhaus M S 1993 Appl. Phys. Lett. 63 3230

    [11]

    Zhu T, Ertekin E 2014 Phys. Rev. B 90 195209

    [12]

    Li X D, Yu S, Wu S Q, Wen Y H, Zhou S, Zhu Z Z 2013 J. Phys. Chem. C 117 15347

    [13]

    Lindsay L, Broido D A 2010 Phys. Rev. B 81 205441

    [14]

    Lindsay L, Broido D A 2011 Phys. Rev. B 84 155421

    [15]

    Zhu T, Ye W 2010 Phys. Rev. E 82 036308

    [16]

    Zhu T, Ye W 2011 Phys. Rev. E 84 056316

    [17]

    Zhu T, Ye W 2010 Num. Heat Trans. B 57 203

    [18]

    Zhu T, Ye W 2012 J. Heat Trans. 134 051013

    [19]

    Guo Z, Xu K 2016 arXiv:1602.01680v1

    [20]

    Liu H, Xu K, Zhu T, Ye W 2012 Comput. Fluids 67 115

    [21]

    Munoz E, Lu H, Yakobson B I 2010 Nano Lett. 10 1652

    [22]

    Hill G W 1886 Acta Math. 8 1

    [23]

    van der Pol B, Strutt M J O 1928 Phil. Mag. 5 18

    [24]

    McLachlan N W 1964 Theory and Applications of Mathieu Functions (New York: Dover) pp11-23

    [25]

    Magnus W, Winkler S 1966 Hill's Equation (New York: Interscience) pp7-13

    [26]

    Lyngby P P 1980 Ingenieur-Archiv. 49 15

    [27]

    Kwong M K, Wong J S W 2006 J. Math. Anal. Appl. 320 37

    [28]

    Ruby L 1996 Am. J. Phys. 64 39

    [29]

    Gutierrez-Vega J C 2003 Am. J. Phys. 71 233

    [30]

    Kittel C 1996 Introduction to Solid State Physics (New York: Wiley) pp180-182

    [31]

    Simkin M V, Mahan G D 2000 Phys. Rev. Lett. 84 927

    [32]

    Zhu T, Ertekin E 2016 arXiv:1602.02419

    [33]

    Savic I, Donadio D, Gygi F, Galli G 2013 Appl. Phys. Lett. 102 073113

    [34]

    Chalopin Y, Esfarjani K, Henry A, Volz S, Chen G 2012 Phys. Rev. B 85 195302

    [35]

    Zhu T, Ertekin E 2015 Phys. Rev. B 91 205429

    [36]

    Taylor J H, Narendra K S 1969 SIAM J. Appl. Math. 17 343

  • [1] 王继光, 李珑玲, 邱嘉图, 陈许敏, 曹东兴. 钙钛矿超晶格材料界面二维电子气的调控. 物理学报, 2023, 72(17): 176801. doi: 10.7498/aps.72.20230573
    [2] 郑建军, 张丽萍. 单层Cu2X(X=S,Se):具有低晶格热导率的优秀热电材料. 物理学报, 2023, 0(0): 0-0. doi: 10.7498/aps.72.20220015
    [3] 刘英光, 薛新强, 张静文, 任国梁. 基于界面原子混合的材料导热性能. 物理学报, 2022, 71(9): 093102. doi: 10.7498/aps.71.20211451
    [4] 蒋小红, 秦泗晨, 幸子越, 邹星宇, 邓一帆, 王伟, 王琳. 二维磁性材料的物性研究及性能调控. 物理学报, 2021, 70(12): 127801. doi: 10.7498/aps.70.20202146
    [5] 郭宇, 周思, 赵纪军. 新型层状Bi2Se3的第一性原理研究. 物理学报, 2021, 70(2): 027102. doi: 10.7498/aps.70.20201434
    [6] 唐道胜, 华钰超, 周艳光, 曹炳阳. GaN薄膜的热导率模型研究. 物理学报, 2021, 70(4): 045101. doi: 10.7498/aps.70.20201611
    [7] 刘英光, 任国梁, 郝将帅, 张静文, 薛新强. 含有倾斜界面硅/锗超晶格的导热性能. 物理学报, 2021, 70(11): 113101. doi: 10.7498/aps.70.20201807
    [8] 刘英光, 郝将帅, 任国梁, 张静文. 不同周期结构硅锗超晶格导热性能研究. 物理学报, 2021, 70(7): 073101. doi: 10.7498/aps.70.20201789
    [9] 许宏, 苑争一, 黄彤飞, 王啸, 陈正先, 韦进, 张翔, 黄元. 层状材料褶皱对几种地质活动机理研究的启示. 物理学报, 2020, 69(2): 026101. doi: 10.7498/aps.69.20190122
    [10] 王鹏程, 曹亦, 谢红光, 殷垚, 王伟, 王泽蓥, 马欣辰, 王琳, 黄维. 层状手性拓扑磁材料Cr1/3NbS2的磁学特性. 物理学报, 2020, 69(11): 117501. doi: 10.7498/aps.69.20200007
    [11] 骆军委, 李树深. 半导体材料基因组计划:硅基发光材料. 物理学报, 2015, 64(20): 207803. doi: 10.7498/aps.64.207803
    [12] 张程宾, 程启坤, 陈永平. 分形结构纳米复合材料热导率的分子动力学模拟研究. 物理学报, 2014, 63(23): 236601. doi: 10.7498/aps.63.236601
    [13] 黄丛亮, 冯妍卉, 张欣欣, 李静, 王戈, 侴爱辉. 金属纳米颗粒的热导率. 物理学报, 2013, 62(2): 026501. doi: 10.7498/aps.62.026501
    [14] 鲍华. 固体氩的晶格热导率的非简谐晶格动力学计算. 物理学报, 2013, 62(18): 186302. doi: 10.7498/aps.62.186302
    [15] 冯现徉, 逯瑶, 蒋雷, 张国莲, 张昌文, 王培吉. In掺杂ZnO超晶格光学性质的研究. 物理学报, 2012, 61(5): 057101. doi: 10.7498/aps.61.057101
    [16] 黄丛亮, 冯妍卉, 张欣欣, 李威, 杨穆, 李静, 王戈. 介孔二氧化硅基导电聚合物复合材料热导率的实验研究. 物理学报, 2012, 61(15): 154402. doi: 10.7498/aps.61.154402
    [17] 王建立, 熊国平, 顾明, 张兴, 梁吉. 多壁碳纳米管/聚丙烯复合材料热导率研究. 物理学报, 2009, 58(7): 4536-4541. doi: 10.7498/aps.58.4536
    [18] 李志华, 王文新, 刘林生, 蒋中伟, 高汉超, 周均铭. As保护下的生长中断时间对AlSb/InAs超晶格界面粗糙度的影响. 物理学报, 2007, 56(3): 1785-1789. doi: 10.7498/aps.56.1785
    [19] 邓成良, 邵明珠, 罗诗裕. 带电粒子同超晶格的相互作用与系统的混沌行为. 物理学报, 2006, 55(5): 2422-2426. doi: 10.7498/aps.55.2422
    [20] 顾培夫, 陈海星, 秦小芸, 刘 旭. 基于薄膜光子晶体超晶格理论的偏振带通滤波器. 物理学报, 2005, 54(2): 773-776. doi: 10.7498/aps.54.773
计量
  • 文章访问数:  5983
  • PDF下载量:  1244
  • 被引次数: 0
出版历程
  • 收稿日期:  2016-02-22
  • 修回日期:  2016-03-25
  • 刊出日期:  2016-06-05

/

返回文章
返回