准晶理论的新进展

准晶的高分辨电子显微像常显示为直径为2nm、呈十重对称的圆盘，它们还经常重叠。据此，Gummelt在1995年设计出一种内部涂有两种颜色的正十边形，并且证明只要在覆盖时两个十边形中同一颜色的部分相重，就会给出准周期的Penrose图。这种覆盖理论只需要一种正十边形的“准单胞”，覆盖部分是相邻“准单胞”生长的核。覆盖越多，结构越稳定。Gummelt在1999年将正十边形中的两种颜色去掉，既可给出准周期结构，也可给出周期结构，以及介于它们两者之间的各种中间结构。

RECENT PROGRESS OF QUASICRYSTAL THEORY

The high-resolution electron microscopic images of quasicrystals very often show overlapped decagonal discs of about 2nm in diam eter.Based on this observation,Gummelt in 1995 designed a two-coloured decagon which can be overlapped with neighbouring ones.If the covering region of two dec agons has the same coloured parts,it can be proven that this covered pattern,li ke Penrose pattern,is a quasiperiodic one.Such a quasiperiodic covering requires only one “quasi-unit cell” and the covered region serves as a nucleus of the formation of the neighbouring “quasi-unit cell”.Gummelt in 1999 removed the colour in the decagon,and such a covered pattern could be periodic,quasi-period ic,or something intermediate between them.