基于金属价电子占据 k 空间体积与布里渊区体积之间的关系，求出费米球半径，导出电子平均自由程的计算公式。 以 Ag 和 Cu 为例计算出电子平均自由程，与其他方法计算结果一致。 当金属材料的几何尺度与电子平均自由程相当时，与之相关的物理性能会发生显著变化，从这个角度出发，用电子平均自由程尺度估算 Ag 和 Cu 的纳米尺寸临界值分别为 52 ｎｍ 和 39 ｎｍ。 这种计算思路同样适用于其他金属纳米材料。
Based on the relationship between the volume of metal valence electrons occupying k space and thevolume of the Brillouin zone , the radius of the Fermi sphere was calculated, and the formula for calculatingelectron mean free path was derived, Taking Ag and Cu as examples, the electron mean free path wascalculated, which was consistent with the results obtained by other methods.When the geometric scale of metalmaterials was equivalent to the electron mean firee path , the physical properties related to it would undergo significant changes, From this perspective ,the critical values of Ag and Cu nano size were estimated using theaverage free path seale of electrons to be 52 nm and 39 nm , respectively.This caleulation approach was alsoapplicable to other metal nanomaterials.
