Foundations of the quasicrystalline structure description in the statistical approach

13th International Conference on Quasicrystals

Wolny, Janusz^1 ; Buganski, Ireneusz^1 ; Chodyn, Maciej^1 ; Strzalka, Radoslaw^1

Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, Krakow, Poland^1

关键词: Fibonacci chain;    Higher-dimensional;    Mathematical formalism;    Quasi-crystalline structure;    Statistical approach;    Structure factors;    Unified description;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/809/1/012006/pdf
DOI  :  10.1088/1742-6596/809/1/012006

来源: IOP

【 摘 要 】

The statistical approach was in constant development since it was first applied to calculate the structure factor for Fibonacci chain being the model of 1D quasicrystal. Its pertinence was investigated throughout years resulting in fully developed mathematical formalism finally ready to be exploited in its full potential. First serving as an alternative to higher-dimensional description of quasicrystals it proved to be even more general. Structures without nD representation can be investigated within statistical approach as well. Unified description of the variety of structures is possible based on the distribution function constructed upon the reference lattice concept. Furthermore, the distribution is sensitive to disturbances in the structure and reflects them by deformation occurring in the shape of the distribution. Therefore, disorder such as phononic or even phasonic, out of reach for nD approach, can be represented and incorporated in the structural analysis. In the paper we briefly introduce the concept standing behind the statistical approach and discuss the most important achievements of the approach.