Linear And Nonlinear Elastic Properties Of Pentagonal Quasicrystals

Quasicrystals have both positional and orientational long-range order. Thus, they are essentially anisotropic. However, both theory and experiment show that ordinary linear elastic property (linear phonon elasticity) is isotropic for quasicrystals. To detect the quasicrystal anisotropy the nonlinear elasticity should be discussed.In this paper, the independent components of nonlinear (third-order) elastic constants for five-fold quasicrystals are determined with the group theory .Results show that there are 72 independent third-order elastic constants (12 due to phonon field, 10 due to phason field,24 due to phonon- phonon- phason coupling,26 due to phonon- phason -phason coupling) for Laue 11 and 41 independent third-order elastic constants (10 due to phonon field,5 due to phason field, 12 due to phonon- phonon- phason coupling, 16 due to phonon- phason - phason coupling) for Laue 12,respectively.Conclusions are that the nonlinear phonon , phason and phonon- phason coupling elastic properties are expected to be anisotropic for five-fold quasicrystals.