菲波那契类准晶结构马德隆常数的研究

Study of the Madelung Constant of Fibonacci-class Quasicrystals

利用马德隆常数的定义,计算了一维、二维单原子FC(2),FC(3)4种菲波那契(Fibonac-ci)类准晶的马德隆常数.结果表明:准周期晶体的马德隆常数随着原子离参考点的距离的增加呈振荡式快速收敛,证实了一维、二维Fibonacci准晶的电子能谱是套层结构,得到准晶原子间的结合能随着维数的增加而增大、比同维数的晶体间的结合能弱的结论.其结果对于研究含离子键成份的准晶态物质有非常重要的理论意义.

The Madelung constant of four kinds of Fibonacci-class quasicrystals FC（n） including one and two-dimensional FC（2） and FC（3） was calculated according to its original definition. The results show that the Madelung constant of Fibonacci-class quasicrystals converge at certain points rapidly as the distance from the reference points increases. Oscillatory changes of the Madelung constant demonstrate that electronic energy spectrums for one and two-dimensional Fibonacci-class quasicrystals have some hierarchical structures, the binding energy of Fibonacci-class quasicrystals increases with the increase of the dimension, while is lower than that of the crystals corresponding to the same dimension. These theoretical results are very important to study the quasi-crystalline matters which includes ionic bonds.