平行四边形晶格结构中布里渊区的研究

A Study on Brillouin Zone in the Lattice Structure of Parallelogram

平行四边形晶格结构是一种宽泛的结构模型,在电子晶体、光子晶体和声子晶体中都广泛存在,研究平行四边形结构的布里渊区图像,是研究这三类晶体能带结构的基础。本文以晶体结构中倒格矢的定义和性质为基础,根据晶体结构正格矢,推导和计算平行四边形晶体结构的倒格矢,利用绘图工具绘制出平行四边形晶体结构的布里渊区图像。研究表明,保持晶格基矢模长比R不变,改变倾斜角,第一布里渊区形状将在矩形和平行六边形间交替变化。同时,利用倒格矢正交临界条件对第一布里渊区的形状和所需的倒格矢进行划分归类。

The parallelogram lattice structure is a kind of broad structure model and is widely used in electronic crystals, photonic crystal and harmonic child. The study of the Brillouin zone image of the parallelogram structure is the basis of studying the band structure of these three kinds of crystals. In this paper, based on the definition and properties of reciprocal lattice vector in crystal structure, the inverted vector of parallelogram crystal structure is deduced and calculated according to the crystal structure MMC, the Brillouin zone image of the parallelogram crystal structure is drawn by using the drawing tool. The study shows that the length ratio of the lattice base to R is constant and the angle θ is changed and the shape of the first Brillouin zone will alternate between the hexagonal shape and the rectangular shape. At the same time, the shape of the first Brillouin zone and the required inverted vector are classified by the reciprocal lattice vector orthogonal critical condition.