周期结构与非周期结构像模拟计算中相光栅准备的实空间算法

Real space algorithm of phase grating preparation in high-resolution electron microscopy image for periodic and non-periodic structure

利用数学上一积分公式推导出了一个求晶体电势分布函数U(r→)的解析表达式 :U(r→) =(1 VC) ∑Nn =1 ∑5j=1anj(4π (bnj+Bn) ) 3 2 exp(- 4π2 (r→n -r→) 2 (bnj +Bn) )。将它运用到实空间多层法像模拟中计算相光栅 ,可大大缩短相光栅的计算时间。文中先介绍了解析表达式的推导过程 ,然后以Mg4 4Rh7和C6 0 为例详细说明了相光栅的计算过程 。

Based on a definitely integral formula, an analytical expression for calculating atomic potential distribution function U(r→) was derived as follows:U(r→)=(1/V C)∑Nn=1∑5j=1a nj (4π/(b nj +B n)) 3/2 exp (-4π 2(r→ n-r→) 2/(b nj +B n)).According to the above analytical expression, the phase grating for periodic crystal (Mg 44 Rh 7) as well as non periodic (C 60 ) structure can be calculated in real space and the computation time can be reduced greatly. In the paper, the analytical expression was derived firstly, and then the calculation procedure was described in details. Finally, the comparison was carried out between the analytical method in real space and the digitized method i.e. fast Fourier transformation method in reciprocal space.