A composite theoretical model for the thermal conductivity of nanocrystalline materials
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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.
KeywordsThermal 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).
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Conflict of interest
The authors declare that they have no conflict of interests.
- 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
- 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
- Hochbaum AI, Chen R, Delgado RD (2015) Enhanced thermoelectric performance of rough silicon nanowires. Nature 451:111–115Google Scholar
- Liu Y, Zhang S, Han Z, Zhao Y (2016a) Grain-size-dependent thermal conductivity of nanocrystalline materials. J Nanopart Res 18:18296Google Scholar
- Liu Y, Zhang S, Han Z (2016b) Influence of grain size on the thermal conduction of nanocrystalline copper. Acta Phys Sin 65:104401Google Scholar
- Maxwell JC (2014) A treatise on electricity and magnetism. Nature 7:478–480Google Scholar
- Wu L, Natalio M, Lindsay L (2017) Thermal conductivity of diamond nanowires from first principles. Phys Rev B 85:195436Google Scholar