关键词: 介电常数, 二阶张量, 三次旋转轴, 旋转矩阵, 坐标轴变换

Abstract: Crystals exhibit higher structural symmetry, which influences the macroscopic physical properties of crystals. As an important physical quantity, dielectric constant can be effectively simplified through theoretical calculations. Furthermore, theoretical calculations can simplify experimental measurements. In this work, a method of rotating coordinate system is proposed, basing on the dielectric constant of crystals as a secondorder tensor. To be more intuitive, the dielectric constant of the crystal can be calculated. Taking the regular tetrahedral crystal structure as an example, the symmetry operations on the crystal in the new coordinate system can achieve rotation matrix. Consequently, the degradation of the dielectric tensor is achieved. Compared with the existing methods, this approach substantially mitigates the empirical limitations and mathematical abstraction. The whole derivation visually demonstrates the degradation of the crystal dielectric constant, while simultaneously deepening students comprehension of the physical properties of the dielectric constant and advancing their theoretical calculation ability. 

Key words: dielectric constant, secondorder tensor, threefold rotation axis, rotation matrix, coordinate axis transformation