A composite theoretical model for the thermal conductivity of nanocrystalline materials

  • Yingguang LiuEmail author
  • Jie Yan
  • Yaru Dan
Research Paper


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.


Thermal conductivity Grain size Transmission Composite material Nanoscale modeling and simulation 



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.


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© 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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