一种求解三维简约布里渊区体积的方法

An approach to calculate the volume of three-dimensional reduced Brillouin zone

简约布里渊区体积的求解是固体物理学中的一个重要知识点,当前,根据不同布里渊区的结构形式,其体积的具体求解方法一般不同,这导致该知识点的教学难度增加.本文提出将简约布里渊区离散为以波矢空间原点为共同顶点的多个棱椎体,使布里渊区体积的求解转化为求各棱椎体积和的形式,并以面心立方和体心立方布里渊区体积的求解为例进行了应用,得到布里渊区体积与倒格子原胞的体积相同.结果表明,该方法具有简单、直观和普适性的优点.

The solution of the volume of reduced Brillouin zone(BZ) is an important knowledge point in solid state physics. At present, the solution methods of BZ volume are generally different because of different BZ forms, which increases the teaching difficulty. In this paper, the reduced BZ is discretized into multiple pyramid with the origin of wave vector space as the common vertex, so that the solution of BZ volume is transformed into the sum of each pyramid. Taking the BZ volume solution of face-centered and body-centered cubic lattice as an example, it is obtained that the reduced BZ volume is the same as that of the reciprocal lattice primitive cell. The results show that the method is simple, intuitive and universal.