1.10 Tensors in quasiperiodic structures

This chapter is devoted to the symmetry-related physical properties of quasiperiodic crystals. In the first part the symmetry properties are described: point groups, superspace groups and the action of symmetry groups. The second part concerns the properties of tensors in higher-dimensional spaces, with emphasis on the particular cases of the piezoelectric, elastic and electric field gradient tensors. The last section gives tables of characters of some point groups for quasicrystals and of the matrices of the corresponding irreducible representations. Keywords: Fourier module; compensating gauge transformations; elastic constants; electric field gradient; icosahedral quasicrystals; incommensurate structures; irreducible representations; metric tensor; modulation wavevector; octagonal quasicrystals; piezoelectric tensor; quasicrystals; quasiperiodic structures; superspace; superspace groups; tensors