Department of Materials Science and Engineering, University of California, Berkeley, CA, United States of America.
Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, CA, United States of America.
Ultramicroscopy. 2023 Aug;250:113732. doi: 10.1016/j.ultramic.2023.113732. Epub 2023 Apr 14.
Nanobeam electron diffraction can probe local structural properties of complex crystalline materials including phase, orientation, tilt, strain, and polarization. Ideally, each diffraction pattern from a projected area of a few unit cells would produce a clear Bragg diffraction pattern, where the reciprocal lattice vectors can be measured from the spacing of the diffracted spots, and the spot intensities are equal to the square of the structure factor amplitudes. However, many samples are too thick for this simple interpretation of their diffraction patterns, as multiple scattering of the electron beam can produce a highly nonlinear relationship between the spot intensities and the underlying structure. Here, we develop a stacked Bloch wave method to model the diffracted intensities from thick samples with structure that varies along the electron beam. Our method reduces the large parameter space of electron scattering to just a few structural variables per probe position, making it fast enough to apply to very large fields of view. We apply our method to SrTiO/PbTiO/SrTiO multilayer samples, and successfully disentangle specimen tilt from the mean polarization of the PbTiO layers. We elucidate the structure of complex vortex topologies in the PbTiO layers, demonstrating the promise of our method to extract material properties from thick samples.
纳米束电子衍射可以探测复杂晶体材料的局部结构特性，包括相、取向、倾斜、应变和极化。理想情况下，从几个单元晶胞的投影区域获得的每个衍射图案都会产生清晰的布拉格衍射图案，其中倒易晶格矢量可以从衍射斑点的间距来测量，并且斑点强度等于结构因子振幅的平方。然而，许多样品太厚，无法对其衍射图案进行简单解释，因为电子束的多次散射会导致斑点强度与基础结构之间产生高度非线性的关系。在这里，我们开发了一种堆叠布洛赫波方法来模拟具有沿电子束变化的结构的厚样品的衍射强度。我们的方法将电子散射的大参数空间减少到每个探针位置仅几个结构变量，使其速度足够快，可以应用于非常大的视场。我们将该方法应用于 SrTiO/PbTiO/SrTiO 多层样品，并成功地将样品倾斜与 PbTiO 层的平均极化区分开来。我们阐明了 PbTiO 层中复杂涡旋拓扑结构的结构，展示了我们的方法从厚样品中提取材料性质的潜力。
