Symmetry and phase transitions in decagonal quasicrystals

The possible non-crystallographic point group of the decagonal quasicrystal phase of Al-Mn alloys has been shown by Bendersky (1986) to be either D _10h or C_10h. For the physically irreducible representations of these groups, the authors derive the Clebsch-Gordan products extended integrity bases, stability spaces and tensorial covariants. The point groups which can arise in phase transitions are determined along with corresponding tensorial parameters which could drive the transition. It is shown that equilibrium tensorial properties whose components transform as the components of the electrogyration or elasto-optic tensors can distinguish between the D_10h and C_10h point group symmetry of the decagonal phase.