证明晶体物理性能张量对称性的热力学方法  

The Thermodynamics Methodfor Proving the Symmetry of Tensors for Cystal Physical Properties

作　　者：李树清[1,2] 张岩[2] 李国华[1] 

机构地区：[1]曲阜师范大学激光所,273165 [2]济宁学院物理系,山东省曲阜市273155

出　　处：《曲阜师范大学学报（自然科学版）》2009年第2期70-73,共4页Journal of Qufu Normal University(Natural Science)

摘　　要：考虑了晶体宏观对称性及晶体内部热力学对称性对物理性能的影响,先用热力学方法,以晶体的介电常数张量为例,证明二阶张量的对称性,使其张量的独立分量数目由9个减少为6个;再次将其张量主轴化后,得到3个独立分量.并以此方法推导了晶体处于电场中时描述晶体物理性能各阶张量对称性.证明结果表明,三阶对称张量的独立分量数目由27个减少到18个,四阶对称张量的独立分量数目由81个减少到21个,并且将表征晶体物理性能的物理常数表示成为(10×10)矩阵.用热力学方法证明晶体物理性能张量的对称性,优越于根据诺埃曼原则用点群方法证明晶体物理性能张量的对称性,是一种简单、直观的新方法.The infulences of crystal macroscopic symmetry and thermodynamics symmetry to the physical performance are considered in this paper. Two order tensor＇ s symmetry is proved by the use of the dielectric coefficient tensor and its independent components decrease from 9 to 6. After the principle axis transformation 3 independent components can be gained. The symmetry of all the tensors which can discribe the physical properties of the crystal are deduced by the same method when the crystal is in the electric field. The results show that the independent components of the three order tensor decrease from 27 to 18 and the independent components of the four order tensor decrease from 81 to 21. The physical constant which can diseribe the physical properties are shown as a （1010） matrix. Method of proving the symmetry of the tensors which can discribe the physical properties of the crystal by the use of the thermodynamics method is better than the point group method from the Neumann＇ s principle. Furthermore, this method is very simple and intuitive.

关 键 词：晶体对称性 张量 热力学方法 

分 类 号：O436.3[机械工程—光学工程]