General periodic average structures of decagonal quasicrystals

The concept of periodic average structure is mutated from the theory of incommensurately modulated structures. For quasicrystals, this concept (up to now explored only in few cases) is becoming increasingly useful to understand their properties and to interpret some important structural features. The peculiar property of quasicrystals is that they admit not one but many (infinite) possible different average structures. Few of them, however, will be meaningful. Here are given a simple method (based on reciprocal space) for generating all the possible periodic average structures of decagonal quasicrystals and some new ideas about their meaning. By this method, the most significant average structures can be recognized from the diffraction pattern.