Invariance Under Rotation For Acoustic Activity Of Crystals And Quasicrystals

In this thesis, the axial rotation symmetry of acoustic activity was researched with the help of group theoretical methods. According to group representation theory, the former group theoretical methods for calculating tensors were improved. Instead of the symmetrized basis functions, the nonsymmetrized ones came into use. Based on the characteristics of irreducible representation of group SO(2), the program for calculating the basis functions of irreducible representation and the independent components of acoustic activity was compiled with MATLAB. The calculation result was checked.In this program, the higher-order basis functions of group SO(2) were constructed with the lower-order basis functions. The arbitrary order basis function can be derived with the help of the program. Then, in view of the relations of character, a set of linearly independent basis functions of identity representation was picked out.With the program running, 51 linearly independent fifth-order basis functions of identity representation of group SO(2) were got in accordance with group representation theory. And the relations between components of fifth-order tensor having the symmetry of the group SO(2) were obtained as well. It was indicated that, in the fifth-order tensor having the symmetry of the group SO(2), 122 components were zero. Among the 121 non-zero ones, 51 components were independent and other 70 components were dependent.Letting the above fifth-order tensor have the symmetry of acoustic activity tensor, the general form of the acoustic activity tensor having the symmetry of the group SO(2) was obtained. It was indicated that, there were 21 non-zero tensor components, 9 of those were independent.Contrasting the form of the known acoustic activity tensors for variety of crystals and quasi-crystals with that general form obtained, it was found that the acoustic activity tensors for classes 6,6mm and 622 that should belong to hexagonal crystal system, as well as for classes 5,52 and 5m that should belong to pentagonal quasicrystal system met the requirement of that general form. So it can be predicted that the acoustic activity of these classes should have invariance under arbitrary rotation about the unique higher-fold axis in the classes.