Research paper

Research on the Thermal Conductivity of Metals Based on First Principles

  • Yang CUI ,
  • Shouhang LI ,
  • Tao YING ,
  • Hua BAO ,
  • Xiaoqin ZENG
Expand
  • 1.School of Materials Science and Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
    2.University of Michigan-Shanghai Jiao Tong University Joint Institute, Shanghai Jiao Tong University, Shanghai 200240, China

Received date: 2020-07-09

  Revised date: 2020-10-09

  Online published: 2020-12-02

Supported by

National Natural Science Foundation of China(51601111);Science and Technology Commission of Shanghai Municipality(18511109302);Joint Fund for Equipment Pre Research and Aerospace Science and Technology(6141B061304);Inner Mongolia Autonomous Region Major Project(ZDZX2016022)

Abstract

Metals are widely used for heat sink and thermal management products, and their thermal conductivities are critical in determining the cooling performance. An efficient method to calculate the thermal conductivity of pure metal is proposed based on the first principles. By introducing the constant relaxation time approximation, density functional theory (DFT) and maximum localized Wannier function (MLWFs) are used to solve the electronic thermal conductivity of metal materials, the calculation procedure of electronic thermal conductivity can be simplified. Regarding the phonon thermal conductivity calculation part, the combination of Slack equation, Birch-Murnaghan equation and Debye model is capable of improving the calculation efficiency. The electrical and thermal conductivities of Al, Mg and Zn in the temperature range of 300-700 K are calculated by the up-mentioned new method. The calculated thermal conductivity was consistent with the measured values, which confirmed the accuracy of the calculation method. The calculation results show that the electronic and phonon structures were essential parameters in thermal conduction of metals. With the increase of temperature, the ratio of the electronic thermal conductivity to the total thermal conductivity increased gradually.

Cite this article

Yang CUI , Shouhang LI , Tao YING , Hua BAO , Xiaoqin ZENG . Research on the Thermal Conductivity of Metals Based on First Principles[J]. Acta Metall Sin, 2021 , 57(3) : 375 -384 . DOI: 10.11900/0412.1961.2020.00250

References

1 Watanabe H, Fukusumi M, Somekawa H, et al. Texture and mechanical properties of superplastically deformed magnesium alloy rod [J]. Mater. Sci. Eng., 2010, A527: 6350
2 Shaeri M R, Yaghoubi M. Thermal enhancement from heat sinks by using perforated fins [J]. Energy Conv. Manag., 2009, 50: 1264
3 Liang X B, Jia C C, Chu K, et al. Predicted interfacial thermal conductance and thermal conductivity of diamond/Al composites with various interfacial coatings [J]. Rare Met., 2011, 30: 544
4 Wang R G. Research on the extrusion technology of magnesium alloy radiator [J]. China Met. Bull., 2009, (46): 42
4 王荣贵. 镁合金散热器挤压工艺研究 [J]. 中国金属通报, 2009, (46): 42
5 Klemens P G, Williams R K. Thermal conductivity of metals and alloys [J]. Int. Met. Rev., 1986, 31: 197
6 Liu J. First principal study of thermal conductivity of Cu/Fe/Al and their alloys [D]. Harbin: Harbin Institute of Technology, 2014
6 刘 金. 关于金属Cu、Fe、Al及其合金热导率的第一性原理研究 [D]. 哈尔滨: 哈尔滨工业大学, 2014
7 Wen B, Feng X. Thermal conductivity of metal from first principles calculations and its application in aluminum [J]. J. Yanshan Univ., 2015, 39: 298
7 温 斌, 冯 幸. 金属热导率的第一性原理计算方法在铝中的应用 [J]. 燕山大学学报, 2015, 39: 298
8 Tong Z, Bao H. Decompose the electron and phonon thermal transport of intermetallic compounds NiAl and Ni3Al by first-principles calculations [J]. Int. J. Heat Mass Trans., 2018, 117: 972
9 Ma H, Yang C L, Wang M S, et al. Effects of transport direction and carrier concentration on the thermoelectric properties of AgIn5Te8: A first-principles study [J]. Mater. Res. Bull., 2019, 113: 77
10 Den E V. Influence of the relaxation time approximation on first principle study of transport coefficients in thermoelectric material PbTe [D]. Louvain-la-Neuve: Université catholique de Louvain, 2016
11 Berman R. Thermal Conduction in Solids [M]. Oxford: Oxford University Press, 1976: 10
12 Tritt T M. Thermal Conductivity: Theory, Properties, and Applications [M]. New York: Kluwer Academic/Plenum Publishers, 2004: 21
13 Ziman J M. Electrons and Phonons [M]. Oxford: Oxford University Press, 1960: 12
14 Madsen G K H, Singh D J. BoltzTraP. A code for calculating band-structure dependent quantities [J]. Comput. Phys. Commun., 2006, 175: 67
15 Motta C, El-Mellouhi F, Sanvito S. Charge carrier mobility in hybrid halide perovskites [J]. Sci. Rep., 2015, 5: 12746
16 Souza I, Marzari N, Vanderbilt D. Maximally localized Wannier functions for entangled energy bands [J]. Phys. Rev., 2001, 65B: 035109
17 Nath P, Plata J J, Usanmaz D, et al. High throughput combinatorial method for fast and robust prediction of lattice thermal conductivity [J]. Scr. Mater., 2017, 129: 88
18 Slack G A. The thermal conductivity of nonmetallic crystals [J]. Solid State Phys., 1979, 34: 1
19 Poirier J P. Introduction to the Physics of the Earth's Interior [M]. Cambridge: Cambridge University Press, 1991: 66
20 Toher C, Plata J J, Levy O, et al. High-throughput computational screening of thermal conductivity, Debye temperature, and Grüneisen parameter using a quasiharmonic Debye model [J]. Phys. Rev., 2014, 90B: 174107
21 Birch F. Finite elastic strain of cubic crystals [J]. Phys. Rev., 1947, 71: 809
22 Murnaghan F D. The compressibility of media under extreme pressures [J]. Proc. Natl. Acad. Sci. USA, 1944, 30: 244
23 Wang Z, Wang S D, Obukhov S, et al. Thermoelectric transport properties of silicon: Toward an ab initio approach [J]. Phys. Rev., 2011, 83B: 205208
24 Deinzer G, Birner G, Strauch D. Ab initio calculation of the linewidth of various phonon modes in germanium and silicon [J]. Phys. Rev., 2003, 67B: 144304
25 Curtarolo S, Setyawan W, Wang S D, et al. AFLOWLIB.ORG: A distributed materials properties repository from high-throughput ab initio calculations [J]. Comput. Mater. Sci., 2012, 58: 227
26 Bai S J. Effect of Zr content on the structure and properties of commercial aluminum [D]. Shenyang: Northeastern University, 2015
26 白嗣俊. Zr含量对工业纯铝组织性能的影响 [D]. 沈阳: 东北大学, 2015
27 Tong X, You G Q, Ding Y H, et al. Effect of grain size on low-temperature electrical resistivity and thermal conductivity of pure magnesium [J]. Mater. Lett., 2018, 229: 261
28 Tyndall E P T, Hoyem A G. Resistivity of single crystal zinc [J]. Phys. Rev., 1931, 38: 820
29 Blakemore J S. Solid State Physics [M]. Cambridge: Cambridge University Press, 1985: 87
30 Wang Y, Liu Z K, Chen L Q. Thermodynamic properties of Al, Ni, NiAl, and Ni3Al from first-principles calculations [J]. Acta Mater., 2004, 52: 2665
31 Yamagishi H, Fukuhara M, Chiba A. Determination of the mechanical properties of extruded pure magnesium during tension-tension low-cycle fatigue using ultrasonic testing [J]. Mater. Trans., 2010, 51: 2025
32 Weiss R J. The absolute X-ray scattering factor of magnesium [J]. Philos. Mag., 1967, 16: 141
33 Siebke W. Considerations on the bulk modulus of pure metals [J]. Phys. Status Solidi, 1981, 64: 577
34 Madelung O, White G K. Landolt-Bo¨rnstein—Group III Condensed Matter. Metals: Electronic Transport Phenomena?Thermal Conductivity of Pure Metals and Alloys[M]. Berlin: Springer, 1991: 12
35 Franz R, Wiedemann G. Ueber die W?rme-Leitungsf?higkeit der Metalle [J]. Ann. Phys., 1853, 165: 497
36 Ying T. Thermal behavior of pure magnesium and binary magnesium alloys [D]. Harbin: Harbin Institute of Technology, 2015
36 应 韬. 纯镁和二元镁合金的导热行为研究 [D]. 哈尔滨: 哈尔滨工业大学, 2015
37 Seitz F, Turnbull D. Solid State Physics [M]. New York: Academic Press, 1958: 255
38 Yang J, Morelli D T, Meisner G P, et al. Influence of electron-phonon interaction on the lattice thermal conductivity of Co1-xNixSb3 [J]. Phys. Rev., 2002, 65B: 094115
Outlines

/