晶体和准晶旋声性质的旋转不变性

Invariance under Rotation for Acoustic Activity of Crystals and Quasicrystals

依据群论原理对计算张量的群论方法作了改进,采用非对称化基函数取代对称化基函数,以便于编程。用MATLAB编制了用于计算属于SO(2)群各阶张量的软件。借助于该软件得到了具有SO(2)群对称性的旋声张量的形式。指出晶体中属于六角系的6、6mm和622晶类和准晶中属于五角系的5、52、5m晶类的旋声性质具有围绕晶体或准晶中唯一高次轴的任意旋转不变性。该结果对于旋声性的应用有重要意义。

The group theoretical methods for calculating tensors were improved on the basis of group theory,that is,instead of the symmetrized basis functions,the nonsymmetrized ones came into use,which convenienced programming.A software for getting all-rank tensors which belong to the group SO（2） was programmed by means of MATLAB.The form of acoustic activity tensor having the symmetry of the group SO（2） was got with the help of the software.It was indicated that the acoustic activity tensor for classes 6,6mm and 622 that belong to hexagonal crystal system,as well as for classes 5,52 and 5m that belong to pentagonal quasicrystal system,have invariance under arbitrary rotation about the unique higher-fold axis in the classes.The result was of importance to application of the acoustic activity.