关键词: 晶粒尺寸, 介观效应, Formi统计

Abstract: The existence of optimum grain size examined theoretically is a mesoscopic effect, which comes from the failure of Fermic statistical formula describing negative oxygen ion concentrationns when grain size reduces to a certain range. According to Kubo's theory, when the grain size reduces to a characteristic length rm, the grain will exhibit neutrality. The Fermi statistics must be corrected to give the optimum grain size r*0=2rm theoretically. Using the Kubo's formula of electron work function, the numbers of rm and r*0 are estimated, which are consistent with experimental results.

Key words: mesoscopic effect, fermi statistic , grain size