title={Fast grain mapping with sub-nanometer resolution using {4D-STEM} with grain classification by principal component analysis and non-negative matrix factorization},
author={Allen, Frances I and Pekin, Thomas C and Persaud, Arun and Rozeveld, Steven J and Meyers, Gregory F and Ciston, Jim and Ophus, Colin and Minor, Andrew M},
journal={Microscopy and microanalysis},
volume={27},
number={4},
pages={794--803},
year={2021},
publisher={Oxford University Press},
url={https://doi.org/10.1017/S1431927621011946},
}
@article{structure_determination,
title={Structure determination of superatom metallic clusters using rapid scanning electron diffraction},
author={Bruma, Alina and Santiago, Ulises and Alducin, Diego and Plascencia Villa, German and Whetten, Robert L and Ponce, Arturo and Mariscal, Marcelo and José-Yacamán, Miguel},
journal={The Journal of Physical Chemistry C},
volume={120},
number={3},
pages={1902--1908},
year={2016},
publisher={ACS Publications},
url={https://doi.org/10.1021/acs.jpcc.5b09524},
}
@article{pyxel_4dstem,
title={Free, flexible and fast: Orientation mapping using the multi-core and {GPU}-accelerated template matching capabilities in the Python-based open source {4D-STEM} analysis toolbox {Pyxem}},
author={Cautaerts, Niels and Crout, Phillip and {\AA}nes, H{\aa}kon W and Prestat, Eric and Jeong, Jiwon and Dehm, Gerhard and Liebscher, Christian H},
title={Unravelling stacking order in epitaxial bilayer \ce{MX2} using {4D-STEM} with unsupervised learning},
author={Mehta, Ankit Nalin and Gauquelin, Nicolas and Nord, Magnus and Orekhov, Andrey and Bender, Hugo and Cerbu, Dorin and Verbeeck, Johan and Vandervorst, Wilfried},
journal={Nanotechnology},
volume={31},
number={44},
pages={445702},
year={2020},
publisher={IOP Publishing},
url={https://doi.org/10.1088/1361-6528/aba5b6},
}
@article{4dstem_organic_films,
title={Diffraction imaging of nanocrystalline structures in organic semiconductor molecular thin films},
author={Panova, Ouliana and Ophus, Colin and Takacs, Christopher J and Bustillo, Karen C and Balhorn, Luke and Salleo, Alberto and Balsara, Nitash and Minor, Andrew M},
journal={Nature Materials},
volume={18},
number={8},
pages={860--865},
year={2019},
publisher={Nature Publishing Group},
url={https://doi.org/10.1038/s41563-019-0387-3},
}
@article{nanodiffraction_review,
title={Advances in the electron diffraction characterization of atomic clusters and nanoparticles},
author={Ponce, Arturo and Aguilar, Jeffery A and Tate, Jess and Yacam{\'a}n, Miguel Jos{\'e}},
journal={Nanoscale Advances},
volume={3},
number={2},
pages={311--325},
year={2021},
publisher={Royal Society of Chemistry},
url={https://doi.org/10.1039/D0NA00590H},
}
@article{4dstem_orientation,
title={Methods for orientation and phase identification of nano-sized embedded secondary phase particles by {4D} scanning precession electron diffraction},
author={Rauch, E F and V{\'e}ron, M},
journal={Acta Crystallographica Section B: Structural Science, Crystal Engineering and Materials},
volume={75},
number={4},
pages={505--511},
year={2019},
publisher={International Union of Crystallography},
url={https://doi.org/10.1107/S2052520619007583},
}
@article{4dstem_amorphous,
title={Nanoscale characterization of crystalline and amorphous phases in silicon oxycarbide ceramics using {4D-STEM}},
author={Yang, Ni and Ophus, Colin and Savitzky, Benjamin H and Scott, Mary C and Bustillo, Karen and Lu, Kathy},
Thus, there has a significant research effort to decrease the PGM content of catalyst materials. Among such systems, platinum-cobalt alloys offer performance close to pure PGM metal catalysts while reducing the PGM loading \cite{core_shell_ordered_np,ultralow_ptco}.
%
Such systems have been observed to demonstrate high mass activity that is maintained for over 25,000 cycles\cite{the_joule_paper}.
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Additionally, since catalysis is a surface reaction-driven phenomenon, there has been a push for making smaller particles to increase the available surface area per unit mass, going all the way down to single-digit-sized nanoparticles.
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While ordered particles' catalytic activity has been shown to exceed disordered particles, essential questions still remain about the exact surface composition and lattice strain in both ordered and disordered platinum-cobalt alloy nanoparticle systems \cite{core_shell_ordered_np,the_joule_paper,structured_ptco,core_shell_ptco,random_vs_structured}. %
\subsection{\label{ssec:how_strain}Measuring strain with electron microscopy}
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Transmission Electron microscopy (TEM), especially in the scanning (STEM) mode, is a potent tool for studying nanoparticles' chemical composition and lattice structure.
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Multiple STEM studies have been performed on nanoparticles, including catalyst systems \cite{strain_tem_vs_stem, original_gpa, gpa_strain, hrem_strain,ef_cbed_strain}.
@@ -117,6 +118,7 @@
While advancements in stage design and post-acquisition drift correction algorithms have mitigated this problem to some extent, it's still non-negligible \cite{revstem, colin_drift,lewys_drift,kevin_drift}.
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\subsection{\label{ssec:why_4dstem}Why 4D-STEM?}
%
One proposed solution for this issue has been 4D-STEM, where the entire convergent beam electron diffraction (CBED) pattern is collected at every single scan position.
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This results in a four-dimensional dataset, where two of the data dimensions correspond to a grid of scan positions, and two of the dimensions correspond to the CBED pattern collected at that particular position\cite{colin_review}.
@@ -147,6 +149,8 @@
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Precession electron diffraction has also been applied to 4D-STEM datasets to perform orientation mapping\cite{4dstem_precession}.
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4D-STEM has been used to map point defect concentrations\cite{4dstem_point_defects}, and map crystallization mechanisms of amorphous materials on graphene\cite{4dstem_graphene}.
%
However, both these works were performed on bulk TEM samples, and as per the authors' knowledge no study has used 4D-STEM to look at catalyst nanoparticle clusters.
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In this work, we present an approach to compare the unit cell size of nanoparticles even when they are not oriented along a low-index crystallographic axis.
