Growth Rules And Molecular Dynamics Simulation Of Two-dimensional Quasicrystal Models

The geometric structure of quasicrystals is usually described by quasi-periodic tiling model.The structural properties and growth rules of quasi-periodic tiling model are the basic problems of quasi-crystal theory.Ammann-Beenker tiling is widely used as geometric model in two-dimensional octagonal symmetric quasicrystals.In this paper,by studying the configuration properties of Ammann-Beenker tiling,based on the local growth rule,the growth method of perfect octagonal quasi-periodic tiling is proposed.In addition,two-dimensional dodecagonal quasicrystals have been obtained by molecular dynamics simulation.According to the previous research background of Ammann-Beenker tiling Oman line drawing method,we put forward a simple Oman line drawing method,and combine the self-similar transformation property of tiling and the theory of Onoda's vertex configuration to construct Penrose tiling.A set of growth methods of Ammann-Beenker tiling and the analysis method of tiling boundary are constructed.Through the analysis of the growth process of Ammann-Beenker tiling,we find that some boundaries have the phenomenon of long-range mutual constraints over long distances,and by comparing the characteristics of various long-range constraints with the Omani line,We get the difference in the distribution of vertices within the boundaries of the tiling,Can lead to the conclusion that perfect Ammann-Beenker tiling growth cannot be achieved with local rules alone.For this reason,we optimize the growth algorithm,select the appropriate growth kernel,and propose a set of local rules to grow the Ammann-Beenker tiling with seamless tiling of the whole plane.Based on the study of the growth process of octagonal quasi-periodic tiling,we also propose a growth method of Ammann-Beenker tiling with periodic arrangement with quartic rotation symmetry.For two-dimensional dodecagonal quasicrystals,on the basis of Engel et al.,we add two Gauss terms to the Lennard-Jones potential function to obtain the pair potential with three potential wells,and the dodecagonal quasicrystal structure is formed by molecular dynamics simulation.The results are analyzed from the point of view of theoretical model,diffractionimage and radial distribution function.