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A composite theoretical model for the thermal conductivity of nanocrystalline materials

  • Yingguang Liu
  • Jie Yan
  • Yaru Dan
Research Paper
  • 80 Downloads

Abstract

In order to study the thermal conductivity of nanocrystalline (NC) materials, a two-phase composite model consisting of grain interior (GI) regarded as an ordered crystal phase and plastically softer grain boundary-affected zone (GBAZ) phase was presented. The effects of GI and GBAZ on thermal conduction were considered, respectively. In this work, time independent Schrodinger’s wave equation (TISWE) was used to study the carriers’ transmission in a crystal particle, through which we can get the thermal conductivity of the GBAZ. The thermal conductivity of GI was calculated based on a kinetic theory. The whole effective grain thermal conductivity was simulated by a modified formula for composite materials. The results showed that as the grain size decreases to 80 nm, it has a strong size effect, and the thermal conductivity decreases with the decreasing of grain size.

Keywords

Thermal conductivity Grain size Transmission Composite material Nanoscale modeling and simulation 

Notes

Funding

The authors are grateful for the funding of the National Natural Science Foundation of China (51576066, 51301069), Natural Science Foundation of Hebei Province (E2014502073), and the Fundamental Research Funds for the Central Universities (2017MS123).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interests.

References

  1. Bellanger P, Gorsse S, Bernard-Granger G, Navone C (2015) Effect of microstructure on the thermal conductivity of nanostructured Mg2(Si, Sn) thermoelectric alloys: an experimental and modeling approach. Acta Mater 95:102–110CrossRefGoogle Scholar
  2. Carotenuto G, Hison CL, Capezzuto F (2009) Synthesis and thermoelectric characterisation of bismuth nanoparticles. J Nanopart Res 11:1729–1738CrossRefGoogle Scholar
  3. Chang SL, Chien CS, Jeng BW (2007) Computing wave functions of nonlinear Schrödinger equations: a time-independent approach. J Comput Phys 226:104–130CrossRefGoogle Scholar
  4. Che J, Çağın T, Deng W (2000) Thermal conductivity of diamond and related materials from molecular dynamics simulations. J Chem Phys 113:6888–6900CrossRefGoogle Scholar
  5. Chen G (translated by Zhou HC, Li BS, Huang ZF) (2014) Nanoscale energy transport and conversion: a parallel treatment of electrons, molecules, phonons, and photons, Beijing: Tsinghua University Press (in Chinese), pp 14–15Google Scholar
  6. Cheng Z, Liu L, Xu S, Lu M, Wang X (2015) Temperature dependence of electrical and thermal conduction in single silver nanowire. Sci Rep 5:10718CrossRefGoogle Scholar
  7. Chernatynskiy A, Bai XM, Gan J (2016) Systematic investigation of the misorientation- and temperature-dependent Kapitza resistance in CeO2. Int J Heat Mass Transf 99:461–469CrossRefGoogle Scholar
  8. Cho HJ, Wang S, Zhou Y, Palumbo G, Erb U (2016) Thermal conductivity of bulk electrodeposited nanocrystalline nickel. Int J Heat Mass Transf 100:490–496CrossRefGoogle Scholar
  9. Deng Y, Zhang Z, Wang Y (2012) Preferential growth of BiTe films with a nanolayer structure: enhancement of thermoelectric properties induced by nanocrystal boundaries. J Nanopart Res 14:775CrossRefGoogle Scholar
  10. Dong H, Wen B, Melnik R (2014) Relative importance of grain boundaries and size effects in thermal conductivity of nanocrystalline materials. Sci Rep 4:7037CrossRefGoogle Scholar
  11. Goswami R, Das B (2012) Behavior of transmission probability in a single rectangular potential barrier at constant barrier height–barrier width product. Int J Eng Sci 1:85–94Google Scholar
  12. Hasselman DPH, Johnson LF (1987) Effective thermal conductivity of composites with interfacial thermal barrier resistance. J Compos Mater 21:508–515CrossRefGoogle Scholar
  13. Hochbaum AI, Chen R, Delgado RD (2015) Enhanced thermoelectric performance of rough silicon nanowires. Nature 451:111–115Google Scholar
  14. Hua YC, Cao BY (2017) An efficient two-step Monte Carlo method for heat conduction innanostructures. J Comput Phys 342:253–266CrossRefGoogle Scholar
  15. Ju SH, Liang XG (2012) Thermal conductivity of nanocrystalline silicon by direct molecular dynamics simulation. Appl Phys 112:064305CrossRefGoogle Scholar
  16. Kojda D, Mitdank R, Handwerg M, Mogilatenko A, Wang Z (2014) Temperature-dependent thermoelectric properties of individual silver nanowires. Phys Rev B 91:024302CrossRefGoogle Scholar
  17. Limarga AM, Clarke DR (2011) The grain size and temperature dependence of the thermal conductivity of polycrystalline, tetragonal yttria-stabilized zirconia. Appl Phys Lett 98:211906CrossRefGoogle Scholar
  18. Liu Y, Zhang S, Han Z, Zhao Y (2016a) Grain-size-dependent thermal conductivity of nanocrystalline materials. J Nanopart Res 18:18296Google Scholar
  19. Liu Y, Zhang S, Han Z (2016b) Influence of grain size on the thermal conduction of nanocrystalline copper. Acta Phys Sin 65:104401Google Scholar
  20. Maxwell JC (2014) A treatise on electricity and magnetism. Nature 7:478–480Google Scholar
  21. Minnich AJ, Dresselhaus MS, Ren ZF (2009) Bulk nanostructured thermoelectric materials: current research and future prospects. Energy Environ Sci 2:466–479CrossRefGoogle Scholar
  22. Murata M, Yamamoto A, Hasegawa Y (2017) Theoretical modeling of electrical resistivity and Seebeck coefficient of bismuth nanowires by considering carrier mean free path limitation. J Appl Phys 121:014303CrossRefGoogle Scholar
  23. Oudriss A, Creus J, Bouhattate J (2012) Grain size and grain-boundary effects on diffusion and trapping of hydrogen in pure nickel. Acta Mater 60:6814–6828CrossRefGoogle Scholar
  24. Palumbo G, Thorpe SJ, Aust KT (1990) On the contribution of triple junctions to the structure and properties of nanocrystalline materials. Scripta Metall Mater 24:1347–1350CrossRefGoogle Scholar
  25. Pokharel M, Zhao H, Ren Z (2013) Grain boundary Kapitza resistance analysis of nanostructured FeSb2. Int J Therm Sci 71:32–35CrossRefGoogle Scholar
  26. Rayleigh L (1982) On the influence of obstacles arranged in rectangular order upon the properties of a medium. Philos Mag 34:481–502CrossRefGoogle Scholar
  27. Romano G, Grossman JC (2015) Heat conduction in nanostructured materials predicted by phonon bulk mean free path distribution. J Heat Trans 137:071302CrossRefGoogle Scholar
  28. Romano G, Esfarjani K, Strubbe D (2016) Temperature-dependent thermal conductivity in silicon nanostructured materials studied by the Boltzmann transport equation. Phys Rev B 93:035408CrossRefGoogle Scholar
  29. Wang Z, Alaniz JE, Jang W (2011a) Thermal conductivity of nanocrystalline silicon: importance of grain size and frequency-dependent mean free paths. Nano Lett 11:2206–2213CrossRefGoogle Scholar
  30. Wang HD, Liu JH, Zhang X, Guo ZY (2011b) Experimental study on the influences of grain boundary scattering on the charge and heat transport in gold and platinum nanofilms. Heat Mass Transf 47:893–898CrossRefGoogle Scholar
  31. Wu L, Natalio M, Lindsay L (2017) Thermal conductivity of diamond nanowires from first principles. Phys Rev B 85:195436Google Scholar
  32. Yang HS, Bai GR, Thompson LJ (2002) Interfacial thermal resistance in nanocrystalline yttria-stabilized zirconia. Acta Mater 50:2309–2317CrossRefGoogle Scholar
  33. Ye FJ, Zeng ZG, Lin C (2015) The investigation of electron–phonon coupling on thermal transport across metal–semiconductor periodic multilayer films. J Mater Sci 50:833–839CrossRefGoogle Scholar
  34. Yuan SP, Jiang PX (2005) Thermal conductivity of nanoscale thin nickel films. Prog Nat Sci 15:922–929CrossRefGoogle Scholar
  35. Yuan SP, Jiang PX (2006) Thermal conductivity of small nickel particles. Int J Thermo Phys 27:581–595CrossRefGoogle Scholar
  36. Zeng XY, Zhang QK, Yu RM (2010) A new transparent conductor: silver nanowire film buried at the surface of a transparent polymer. Adv Mater 22:4484–4488CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Department of Power Engineering, School of Energy and Power EngineeringNorth China Electric Power UniversityBaodingChina

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