Group-theoretical method for physical property tensors of quasicrystals |
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Authors: | Gong Ping Hu Cheng-Zheng Zhou Xiang Wang Ai-Jun and Miao Ling |
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Institution: | Department of Physics, Wuhan University, Wuhan 430072, China |
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Abstract: | In addition to the phonon variable there is the phason variable in
hydrodynamics for quasicrystals. These two kinds of hydrodynamic
variables have different transformation properties. The phonon
variable transforms under the vector representation, whereas the
phason variable transforms under another related representation.
Thus, a basis (or a set of basis functions) in the representation
space should include such two kinds of variables. This makes it more
difficult to determine the physical property tensors of
quasicrystals. In this paper the group-theoretical method is given
to determine the physical property tensors of quasicrystals. As an
illustration of this method we calculate the third-order elasticity
tensors of quasicrystals with five-fold symmetry by means of basis
functions. It follows that the linear phonon elasticity is
isotropic, but the nonlinear phonon elasticity is anisotropic for
pentagonal quasicrystals. Meanwhile, the basis functions are
constructed for all noncrystallographic point groups of
quasicrystals. |
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Keywords: | quasicrystals elastic constants basis functions |
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