Guo Yueming, Nakashima Philip N H, Etheridge Joanne
Department of Materials Science and Engineering, Monash University, Victoria 3800, Australia.
Monash Centre for Electron Microscopy, Monash University, Victoria 3800, Australia.
IUCrJ. 2018 Oct 8;5(Pt 6):753-764. doi: 10.1107/S2052252518012216. eCollection 2018 Nov 1.
Under almost all circumstances, electron diffraction patterns contain information about the phases of structure factors, a consequence of the short wavelength of an electron and its strong Coulombic interaction with matter. However, extracting this information remains a challenge and no generic method exists. In this work, a set of simple analytical expressions is derived for the intensity distribution in convergent-beam electron diffraction (CBED) patterns recorded under three-beam conditions. It is shown that these expressions can be used to identify features in three-beam CBED patterns from which three-phase invariants can be extracted directly, without any iterative refinement processes. The octant, in which the three-phase invariant lies, can be determined simply by inspection of the indexed CBED patterns ( the uncertainty of the phase measurement is ±22.5°). This approach is demonstrated with the experimental measurement of three-phase invariants in two simple test cases: centrosymmetric Si and non-centrosymmetric GaAs. This method may complement existing structure determination methods by providing direct measurements of three-phase invariants to replace 'guessed' invariants in phasing methods and hence provide more stringent constraints to the structure solution.
在几乎所有情况下，电子衍射图案都包含有关结构因子相位的信息，这是电子短波长及其与物质强烈库仑相互作用的结果。然而，提取这些信息仍然是一项挑战，并且不存在通用方法。在这项工作中，针对在三束条件下记录的会聚束电子衍射（CBED）图案中的强度分布，推导了一组简单的解析表达式。结果表明，这些表达式可用于识别三束CBED图案中的特征，从中可以直接提取三相不变量，而无需任何迭代细化过程。三相不变量所在的卦限可以通过检查索引后的CBED图案简单确定（相位测量的不确定性为±22.5°）。在两个简单测试案例（中心对称的Si和非中心对称的GaAs）中对三相不变量进行实验测量，证明了这种方法。该方法可以通过提供三相不变量的直接测量来补充现有的结构确定方法，以取代相位法中“猜测”的不变量，从而为结构解析提供更严格的约束。
