![]() ![]() Hence, in order to procure accurate PDF data with high resolution, it is imperative to collect scattering data with a good signal-to-noise ratio up to a large Q value (scattering vector). Parameters including the completeness and resolution of the collected data will directly affect the quality of the PDF results. The resultant PDF curves can be refined against structural models using specific refining algorithms (Anker et al., 2021 Farrow et al., 2014 Li et al., 2017 ). Data collection is usually carried out by capturing selected-area electron diffraction (SAED) patterns consisting of diffraction rings, followed by further data processing (Tran et al., 2017 Shanmugam et al., 2017 Shi et al., 2019 ). It provides key information in real space that cannot be obtained from X-rays or neutrons.Ī basic ePDF characterization process contains three steps including electron diffraction data collection, data processing and structure refinement. Furthermore, TEM has the capability to observe specimens in real space, including the morphology and size of nanoparticles, as well as atomic resolution images. ![]() Meanwhile, collecting data by TEM will require less sample, which is beneficial in cases where samples are difficult to synthesize in large quantities. High spatial resolution can be also achieved using nanobeam electron diffraction (Mu et al., 2019 ). Because of the strong interaction between electrons and matter, nanosized samples are sufficient for electron pair distribution function (ePDF) (Cowley, 1992 Abeykoon et al., 2012 Mu et al., 2013 ). Compared with high-energy X-rays and neutrons, electrons are easy to access using a transmission electron microscope (TEM) available in many laboratories. PDF analysis is typically conducted with three sources: high-energy X-rays (Billinge & Kanatzidisb, 2004 Tyrsted et al., 2012 Grangeon et al., 2017 Anker et al., 2021 ), neutrons (Frandsen et al., 2014 ) and electrons (Gorelik, 2018 Gorelik et al., 2019 Corrêa et al., 2021 Souza et al., 2021 Schmidt et al., 2023 ). Over the years of its development, PDF has mostly been applied to organic crystals (Castillo-Blas et al., 2020 Prill et al., 2016 ), nanomaterials (Kodama et al., 2006 Willinger et al., 2017 ) and molecular materials (Terban et al., 2016 Terban & Billinge, 2022 ). Pair distribution function (PDF) (Egami & Billinge, 2012 Warren, 1990 Billinge, 2008 Masadeh et al., 2007 ) serves as a robust method in the realm of crystallography, facilitating a rather powerful elucidation of the atomic structures of these materials. For some amorphous materials, polycrystalline materials and extremely tiny nanoparticles, the above-mentioned methods exhibit their respective limitations in revealing accurate structure parameters. For some well crystallized nanocrystals, structural information can be obtained by single-crystal/powder X-ray diffraction (Hauptman, 1986 David & Shankland, 2008 ), 3D electron diffraction (Zhang et al., 2010 Gemmi et al., 2019 ) or high-resolution electron microscopic imaging (Zhang et al., 2018 ). The precise determination of the atomic structure of nanomaterials is one of the most important underlying scientific challenges in materials science (Billinge & Levin, 2007 Egami & Billinge, 2012 Jadzinsky et al., 2007 ) it is significant in the elucidation of structure–property correlations, the exploration of formation mechanisms and the guidance of new functional material synthesis. This method provides a new way of utilizing ePDF to obtain accurate local structure information from nanoparticles. As a result, compared with conventional ePDF data, tilt-ePDF data provide structure parameters with a better accuracy and lower residual factors in the refinement against the crystal structure. The results show that tilt-ePDF can not only enhance the continuity of diffraction rings, but can also improve the signal-to-noise ratio in the high scattering angle range. In the present work, a tilt-series of electron diffraction patterns was collected from gold nanoparticles with three different sizes and a standard sample polycrystalline aluminium film for ePDF analysis. Herein, a new method – tilt-ePDF – is proposed to improve the data quality and compatibility of ePDF by a combination of electron diffraction and specimen tilting. However, current conventional electron diffraction experiments using PDF (ePDF) are limited in their ability to acquire continuous diffraction rings for large nanoparticles. The collection of scattering signals with good statistics is necessary for a reliable structural analysis. As an important characterization method, pair distribution function (PDF) has been extensively used in structural analysis of nanomaterials, providing key insights into the degree of crystallinity, atomic structure, local disorder etc.
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