Added some refs

  publisher={Cambridge University Press},

  url={https://doi.org/10.1017/S1551929522001286},

}

@article{many_4dstem,

  title={{Analysis of Interpretable Data Representations for 4D-STEM Using Unsupervised Learning}},

  author={Bruefach, Alexandra and Ophus, Colin and Scott, Mary C},

  journal={Microscopy and Microanalysis},

  volume={28},

  number={6},

  pages={1998--2008},

  year={2022},

  publisher={Cambridge University Press},

  url={https://doi.org/10.1017/S1431927622012259},

}

@article{4dstem_precession,

  title={{High Precision Orientation Mapping from 4D-STEM Precession Electron Diffraction data through Quantitative Analysis of Diffracted Intensities}},

  author={Corr{\^e}a, Leonardo and Ortega, Eduardo and Ponce, Arturo and Cotta, M{\^o}nica and Ugarte, Daniel},

  journal={arXiv preprint arXiv:2301.10286},

  year={2023},

  url={https://arxiv.org/abs/2301.10286},

}

@article{4dstem_graphene,

  title={4D scanning transmission electron microscopy {(4D-STEM)} reveals crystallization mechanisms of organic semiconductors on graphene},

  author={Guo, Zixuan and Ophus, Colin and Bustillo, Karen C and Fair, Ryan and Mannsfeld, Stefan C B and Briseno, Alejandro L and Gomez, Enrique D},

  journal={MRS Communications},

  pages={1--8},

  year={2023},

  publisher={Springer},

  url={https://doi.org/10.1557/s43579-022-00310-5},

}

 No newline at end of file

		%

		However, quantification of surface strain in nanoparticles remains a challenging endeavor, as the only technique that can reach the resolution needed to probe strain on a unit cell by unit cell basis, with the precision needed to track minute distortions is transmission electron microscopy. 

		%

		However, such techniques proposed till date can only visualize a single, or a few nanoparticles. This is because strain quantification needs the nanoparticles to be oriented on-axis. 

		However, such techniques proposed till date can only visualize a single, or a few nanoparticles, since strain quantification needs the nanoparticles to be oriented on-axis. 

		%

		Here we demonstrate 4D-STEM based quantification techniques that can \emph{simultaneously} quantify strain across hundreds of nanoparticles, even if none of those particles are on a low-index crystallographic zone axis. 

		%

		Furthermore, we show that combining the diffraction information from all the nanoparticle datasets can be used to generate diffraction space datasets that can track the evolution of strain across individual lattice planes.

		%

		Our results thus demonstrate that 4D-STEM can bridge between traditional imaging and diffractometry techniques, and generate crystallographic information at a spatial resolution unavailable to any other technique.

	\end{abstract}

    \maketitle

		%

		The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (\url{http://energy.gov/downloads/doe-public-access-plan})}}

		%

		Over the past two centuries, anthropogenic activities have increased greenhouse gas (GHG) concentrations in the Earth's atmosphere as a byproduct of fossil fuel combustion \cite{ghg, humidity_temp}. 

		%

		The adverse effects of increasing GHGs are well studied and are already starting to be felt globally\cite{economic_climate_change}. 

		%

		In a fuel cell, hydrogen undergoes a redox reaction with oxygen with water as the byproduct. However, the oxygen reduction reaction (ORR) component of this redox reaction needs to be catalyzed \cite{strain_np_surface,HP_Pt_ORR,PEMFC_review}. Among the commonly used catalysis systems, platinum group metals (PGMs) are the most widely used system commercially. 

		%

		\subsection{\label{ssec:why_strain}The importance of measuring strain in catalyst nanoparticles}

		The problem with PGM catalysts is that such elements have low crustal abundance and are finite resources\cite{pt_abundance}. 

		%

		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}. 

		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. 

		%

		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}

		Transmission Electron microscopy (TEM), especially in the scanning (STEM) mode, is a potent tool for studying nanoparticles' chemical composition and lattice structure. 

		%

		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}. 

		%

		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}. 

		%

		\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. 

		%

		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}. 

		%

		Two recent works have proposed methods to break this logjam -- strain measurements from multiple zone axes, and using cepstrum functions to process CBED datasets, and both of them have shown promising results\cite{elliot_strain,strain_tensor}. 

		%

		Yet another recent work has demonstrated that using unsupervised approaches, complicated microstructures can be reconstructed and identified from each other from 4D-STEM datasets\cite{many_4dstem}.

		%

		Precession electron diffraction has also been applied to 4D-STEM datasets to perform orientation mapping\cite{4dstem_precession}.

		%

		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. 

		%

		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. 

		%

		Using this approach, we demonstrate that multiple nanoparticles' unit cell size variations can be visualized from a single 4D-STEM dataset. 

	\begin{acknowledgments}

		The authors acknowledge DOE.

	\end{acknowledgments}

	\section*{\label{sec:methods}{Materials \& Methods}}

		\subsection{\label{sec:sample_prep}Sample Preparation}

		\subsection{\label{sec:microscopy}Electron Microscopy}

		\subsection{\label{sec:analysis}Data Analysis}

	\bibliography{Combined_4DSTEM}

	%%%%%%%%%% Merge with supplemental materials %%%%%%%%%%