The convergent beam electron diffraction (CBED) patterns of twisted bilayer samples exhibit interference patterns in their CBED spots. Such interference patterns can be treated as off-axis holograms and the phase of the scattered waves, meaning the interlayer distance can be reconstructed. A detailed protocol of the reconstruction procedure is provided in this study. In addition, we derive an exact formula for reconstructing the interlayer distance from the recovered phase distribution, which takes into account the different chemical compositions of the individual monolayers. It is shown that one interference fringe in a CBED spot is sufficient to reconstruct the distance between the layers, which can be practical for imaging samples with a relatively small twist angle or when probing small sample regions. The quality of the reconstructed interlayer distance is studied as a function of the twist angle. At smaller twist angles, the reconstructed interlayer distance distribution is more precise and artefact free. At larger twist angles, artefacts due to the moiré structure appear in the reconstruction. A method for the reconstruction of the average interlayer distance is presented. As for resolution, the interlayer distance can be reconstructed by the holographic approach at an accuracy of ±0.5 Å, which is a few hundred times better than the intrinsic z-resolution of diffraction limited resolution, as expressed through the spread of the measured k-values. Moreover, we show that holographic CBED imaging can detect variations as small as 0.1 Å in the interlayer distance, though the quantitative reconstruction of such variations suffers from large errors.

中文翻译：

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从会聚束电子衍射图案全息重建双层二维晶体样品的层间距离

扭曲双层样品的会聚束电子衍射 (CBED) 图案在其 CBED 斑点中表现出干涉图案。这种干涉图案可以被视为离轴全息图和散射波的相位，这意味着可以重建层间距离。本研究提供了重建程序的详细协议。此外，我们推导出了一个精确的公式，用于从恢复的相分布重建层间距离，该公式考虑了各个单层的不同化学成分。结果表明，CBED 光斑中的一个干涉条纹足以重建层之间的距离，这对于具有相对较小扭曲角的样品成像或探测小样品区域时非常实用。重构层间距离的质量被研究为扭曲角的函数。在较小的扭转角下，重建的层间距离分布更精确且无伪影。在较大的扭曲角下，由于莫尔结构造成的伪影出现在重建中。提出了一种重建平均层间距离的方法。至于分辨率，可以通过全息方法以±0.5 Å 的精度重建层间距离，这比衍射极限分辨率的固有 z 分辨率好几百倍，如通过测量 k-值。此外，我们表明全息 CBED 成像可以检测到层间距离小至 0.1 Å 的变化，