正格子与倒格子基矢关系的矩阵形式

Matrix relationship of the basic vectors between direct and reciprocal lattices

本文基于晶轴矢量坐标系,构建了正空间点阵基矢ai(i=1,2,3)的互易矢量bj^*(j=1,2,3).如果在互易矢量关系中引入常数2π,可以证明互易矢量bj=2πbj^*为倒空间点阵的基矢.这样引入的第3种基矢关系(矩阵形式)等价于"固体物理"中定义的其它两种形式.该结果说明正格子和倒格子的对偶性体现在基矢关系上就是它们的互易性.

Based on the coordinates of crystal axis,a reciprocal vector bj^*(j=1,2,3)of a vector ai(i=1,2,3)is presented.By introducing the relatioanship bj=2πbj^*,it is proved that bjis the basic vector of the reciprocal lattice,which is related to the direct lattice with basic vector ai.The matrix relationship of the basic vectors between the direct and the reciprocal lattices is equivalent to that definedin the textbook.This result indicates that the reciprocity of the basic vectors bjand ai embody in the duality property between the direct and the reciprocal lattices.