Numerical Methods of Quasicrystals and Applications

開催日時
2016/11/11 金 16:30 - 18:00
場所
6号館809号室
講演者
張 平文
講演者所属
北京大学
概要

In this talk, we will introduce a high-precision numerical method for studying quasicrystals, i.e., the projection method. This method is based on the philosophy that a continuous distributed quasicrystal is a continuous function over a quasilattice. It can be used to study the soft quasicrystals. In particular, the projection method decomposes the quasiperiodic structure by a combination of the almost periodic functions, and provides an efficient algorithm to calculate the combinational coefficients in the higher-dimensional space. At the same time, the projection method provides a unified computational framework for the periodic crystals and quasicrystals. The free energies of the two kinds of ordered structures can be obtained with the same accuracy. Therefore, it can be used to determine the thermodynamic stability of periodic and quasiperiodic crystals in theory. We have applied the algorithm to a series of coarse-grained density functional theories, and obtained 2-dimensional 8-, 10, 12-fold symmetric quasicrystals (computed in the 4-dimensional space), and 3-dimensional icosahedral quasicrystals (calculated in the 6-dimensional space). The corresponding phase diagrams, including periodic crystals and quasicrystals, have been constructed.