准晶格的推导与准晶体的微粒分数维结构模型

五次对称和准晶态的发现(Shechtmen,1984)不仅是结晶学的新阶段,对包括地质学在内的整个自然科学将产生深远影响(彭志忠,1985)。在准晶体结构中,配位二十面体作长程定向有序,但无平移有序。作者(1985)探讨了准晶体的构筑原理,认为,在准晶体的结构中两个原理在起作用,即二十面体原理和黄金中值原理。

THE DEDUCTION OF QUASICRYSTAL LATTICE AND THE FRACTAL STRUCTURE MODEL OF QUASICRYSTAL

The discovery of fivefold symmetry and quasicrystal state not only is a new stage of crystallography but also has profound influence in all natural sciences including geology.In the structure of quasicrystal, the coordination icosahedron have long range ordering but not have translation ordering. Anther dealt with the building principle of quasicrystal and thought that two principles played a role in the quasicrystal structure, i.e. the icosahedron principle and the golden mean principle. The icosahedron principle indicates that the icosahedron ligand is favour in energy when the arrangement of atoms similar in size forms isolated ligands with the coordination number is twelve. The golden mean principle points out that the arrangement of atoms in quasicrystal accords with the golden mean rule, i.e. according to the arrangement of Fibonacci series. These two principle are suitable for the system composed by few atoms and also for some biological structures. Applying these two principles to quasicrystal particles, we obtained the most simple structure model of quasicrystals, and could explain all details of the high-resolution electron microscopic image of the Al-Mn quasicrystal. This model does not contradict the understanding of regarding quasicrystal as a three dimensions Penrose tiling, but it is unsimilar with Hiraga’s model^5] and Bursill’s model. The Al₁₂Mn icosahedron is not shaving edges in Auther’s model. The Auther’s model has the characteristic of fractal structure, therefore, we call it the particle fractal structure model.