关键词: 倒易点阵, 晶面间距, 晶胞, 体心立方晶胞

Abstract: Using the properties of reciprocal lattice，a general formula for calculating the crystal interplanar spacing is derived，which can be simplified when calculating the interplanar spacing of some crystals with special lattice constants. However，this formula cannot be directly used to calculate the interplanar spacing of complex unit cells. When the general formula derived from the reciprocal lattice properties is used to calculate the interplanar spacing of complex unit cells，either a representative crystal plane that meets the constraint conditions for the appearance of reciprocal points in that plane orientation should be considered，or the primitive cell corresponding to the complex unit cell should be found. Then，new basis vectors are constructed using the three edges of the primitive cell，and the basis vectors of the reciprocal lattice are obtained. Furthermore，the interplanar spacing of the original complex unit cell can be obtained by taking the reciprocal of the modulus length of the reciprocal basis vector with the same indices. Nevertheless，in the new basis vector system，the indices of the crystal planes marked in the original unit cell often change accordingly，which is often overlooked by students when calculating interplanar spacing，leading to incorrect results. In this paper，we first briefly describe the constraints for the appearance of reciprocal points on crystal planes of complex unit cell. Then，combining a specific example of a body-centered cubic unit cell，we present the process of calculating interplanar spacing using representative crystal planes or constructing new basis vectors，aiming to deepen students' understanding of these knowledge points through specific calculations and adopt them in practical applications.

Key words: reciprocal lattice, interplanar spacing, unit cell, body-centered cubic unit cell