Practical Electron Microscopy and Database

Aperiodic crystals (also named incommensurate phases) lack three-dimensional (3-D) translational symmetry and thus lattice periodicity, while they are still long-range ordered. Aperiodic materials cannot be described by any of the 230 space groups; however, they show another type of long-range ordering. The aperiodic crystals can be categorized by three main classes [1]:
         i)  Incommensurate modulated structures,
         ii)  Incommensurate composite crystals,
         iii)  Quasicrystals.

All aperiodic materials present a discrete diffraction pattern and can be described as a 3-D atomic feature of a n-dimensional (n-D) (n > 3) periodic structure.

[1] Van Smaalen, S. (2007). Incommensurate Crystallography, Oxford University Press, Oxford.