Acta mathematica scientia,Series A ›› 2005, Vol. 25 ›› Issue (4): 522-537.

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The Base Function of the Irreducible Representation for Point Groups in the Expansion of Free Energy

 ZHOU Guo-Xiang, HE Wen-Chen, GUO Ge-Xin, LI Jia-   

  • Online:2005-08-25 Published:2005-08-25

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Abstract:

There are many choices for the selection of the base functions (BF) of the irreducible representations for point groups. The different BF corresponds to the different representative matrix. Although under the same matrix, there are different choices for BF. The expansion of the free energy can be constructed by BF when the phenomenological phase transition theory is used. So the table of the BF of the irreducible representations is significant.In the literatures before, the BF is up to the second order. Furthermore, in some literature, the different BF for the same irreducible representations corresponds to different representative matrix. It is wrong by using such BF toobtain the invariant. The thirdorder BF was supplemented in this paper. The table of BF given in this paper is very helpful for obtaining he expansion of the free energy correctly and rapidly. Eighteen kinds of pointgroups were found having thirdorder invariant. If the group of the hightemperature crystal structure is one of these points groups, then the ferroelectrics undertake the first order phase transition when temperature is lowed.

Key words: Irreducible representation, Base function Invariant, Expansion of free energy, , Landau theory

CLC Number: 

  • 20C35
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