Matthiessen’s rule has been applied to analyze the simultaneously measured electrical and thermal conductivities of polycrystalline platinum nanofilms. The results show that the greatly reduced conductivities are mainly attributed to the grain boundary scatterings. By taking into account the background scattering and the grain boundary scattering, Mathienssen’s rule slightly underestimates the thermal conductivity, but obviously overestimates the electrical conductivity. By introducing an additional parameter characterizing electron scattering on the grain boundary in Matthiessen’s rule, the agreement between the theoretical predictions and the observed results are greatly improved. Further studies show that when the mean grain size is much smaller than the corresponding mean free path, the electrons’ behavior inside the grains becomes affected by the grain boundaries and the underlying assumption of independent scattering processes for Mathiessen’s rule will become invalid.
- Nanotechnology Institute
Matthienssen’s Rule in Polycrystalline Metallic Nanofilms
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Zhang, Q, Cao, B, Zhang, X, Takahashi, K, Fujii, M, & Zhu, L. "Matthienssen’s Rule in Polycrystalline Metallic Nanofilms." Proceedings of the 2007 First International Conference on Integration and Commercialization of Micro and Nanosystems. First International Conference on Integration and Commercialization of Micro and Nanosystems, Parts A and B. Sanya, Hainan, China. January 10–13, 2007. pp. 761-768. ASME. https://doi.org/10.1115/MNC2007-21092
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