一维Fibonacci类准晶的衍射性质

利用傅里叶变换方法推导了一维Fibonacci类(FC(n))准晶衍射的结构因子方程,讨论了该系统的衍射峰和系统消光规则.在此基础上,计算了FC(1)和FC(3)准点阵的衍射谱.另外,把所得方程进行推广使之能用来研究FC(n)准周期超晶格的衍射性质.通过把FC(1)准周期超晶格衍射相对强度的计算结果与Merlin等人的实验结果进行比较,发现大多数衍射谱符合得较好,但有一条谱不一致.理论计算表明Merlin等人标定的谱(4,2)应该是一个次强峰.     

Diffraction properties of one-dimensional finite size fibonacci quasilattice

The diffraction patterns from Fibonacci quasilattices have been calculated. Finite-size effects are evaluated for weak and strong peaks. For a smaller number of scatterers (<100) there are fluctuations in the intensities of weak and strong peaks. The fluctuations in weak peaks are greater than that in strong peaks. The fluctuations in intensities of weak and strong peaks near the origin are larger than in the corresponding cases of weak and strong peaks far away from the origin. Small shifts in peak-positions are unexpectedly found, the shifts being proportional toN ^−3/2 for a large number of scatterers. The diffraction pattern of a one-dimensional crystal and random structure is compared with that of the Fibonacci quasilattice. The strong peaks observed in the diffraction pattern of 1-d crystal show negligible peak-shifts, they being comparable with computational errors even when the number of scatterers is as small as 5. The implications for analysing the experiments are briefly indicated.     

一维Fibonacci类准晶的衍射性质

利用傅里叶变换方法推导了一维Fibonacci类(FC(n))准晶衍射的结构因子方程,讨论了该系统的衍射峰和系统消光规则.在此基础上,计算了FC(1)和FC(3)准点阵的衍射谱.另外,把所得方程进行推广使之能用来研究FC(n)准周期超晶格的衍射性质.通过把FC(1)准周期超晶格衍射相对强度的计算结果与Merlin等人的实验结果进行比较,发现大多数衍射谱符合得较好,但有一条谱不一致.理论计算表明Merlin等人标定的谱(4,2)应该是一个次强峰.