Electron movement grain size

In metals, the electron can move freely along any direction in three dimensions. However, when the grain size of the metal is in nanoscale and is smaller than the electron mean free path, the electron movement is restricted by GB. The electron quantum effect which resulted from the scatter of GBs appears in NC metal. Therefore, for NC metal the electron mean free path can be influenced by the grain size. In this case, the electron mean free path Ip in Eq. 3.5 can be replaced by the effective electron mean free path namely. 

Relation of effective electronic mean free path, 1, and grain size (average grain radius R) at different temperatures (corresponding to Eq. 3.7). Effective electronic mean free path is about several tens of nanometers, indicating that grain size of NC metals can restrict electron movement. 

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