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}. As a result, alternative energy sources are being looked at, and of the multitude of candidates - hydrogen fuel cells have shown enormous promise for clean, compact energy generation systems\cite{hydrogen_fuel_cells}. 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. 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}. Such systems have been observed to demonstrate high mass activity that is maintained for over 25,000 cycles\cite{the_joule_paper}.
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}. 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}. However, there are two shortcomings with the STEM metrology of nanoparticles. The first is that strain measurements, even with aberration-corrected STEM, are highly susceptible to drift distortions, which arise from mechanical vibrations, thermal instabilities, and so on \cite{original_gpa, gpa_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}. 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}. With advancements in computational hardware and high-speed electron detectors, 4D-STEM experiments are becoming increasingly common, with applications in strain metrology, phase reconstruction, and symmetry quantification \cite{nbed_strain, neg_capacitance, ptycho_deep,ncem_camera}.
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}. 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}. However, there are two shortcomings with the STEM metrology of nanoparticles. The first is that strain measurements, even with aberration-corrected STEM, are highly susceptible to drift distortions, which arise from mechanical vibrations, thermal instabilities, and so on \cite{original_gpa, gpa_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}. 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}. With advancements in computational hardware and high-speed electron detectors, 4D-STEM experiments are becoming increasingly common, with applications in strain metrology, phase reconstruction, and symmetry quantification \cite{nbed_strain1, neg_capacitance, ptycho_deep,ncem_camera}.
When operated in the nanobeam diffraction mode, where the Bragg diffraction disks do not overlap in the resultant CBED pattern, the relative position of the diffraction disks can be used to quantify the lattice parameter of the section of the TEM sample being illuminated by the electron beam\cite{colin_review}. Since this quantification is being performed at every single individual scan position, this quantification is thus free from drift distortion effects. When extended across the entire field of view, this quantification thus tracks the lattice parameter variations, aka strain, with the precision that cannot be beaten by conventional STEM imaging. Indeed, 4D-STEM has been used for picometer precision strain quantification in two-dimensional crystals, semiconductor heterojunctions, and catalyst nanoparticles \cite{nbed_strain1,nbed_strain2, 4dstem_nanoparticles,yimo_strain,holo_strain}. Most notably, it has been demonstrated that the errors in 4D-STEM measurement are significantly lower than the errors from even drift-corrected annular dark field (ADF) STEM imaging, even when looking at the same particle\cite{4dstem_nanoparticles}.
