updated equation for strain

Selected_SEM_Images/Electrolyzers/.DS_Store

Selected_SEM_Images/Fuel_Cells/.DS_Store

Selected_SEM_Images/Fuel_Cells/Non-PGM/.DS_Store

.qodo

				\end{bmatrix}

				= 

				\begin{bmatrix}

					1 + \epsilon_{xx} & \frac{\epsilon_{xy} - \epsilon_{\theta}}{2} \\

					\frac{\epsilon_{yx} + \epsilon_{\theta}}{2} & 1 + \epsilon_{yy}

					1 + \epsilon_{yy} & \frac{\epsilon_{\theta} - \epsilon_{xy}}{2} \\

					-\left(\frac{\epsilon_{yx} + \epsilon_{\theta}}{2}\right) & 1 + \epsilon_{xx}

				\end{bmatrix}

				\times

				\begin{bmatrix}

		\subsection{\label{ssec:aberration_correction}Common Referencing to Quantify Strains Across Particles}

		\begin{figure*}

			\centering

			\includegraphics[width=\textwidth]{GeneratedFigures/Montage_Figure.pdf}

			\caption{\label{fig:montage} \textbf{Volumetric Strain across all nanoparticles. a,} 

			\includegraphics[width=\textwidth]{GeneratedFigures/Corrected_Median_Spots.pdf}

			\caption{\label{fig:diff_correction} \textbf{Correcting median spots to known PtCo pattern. a,} 

			The theoretically calculated diffraction pattern for PtCo alloy, with the peak positions and the corresponding Miller indices in red.

			\textbf{b,} Original median spots for \textit{beginning-of-life (BOL)} nanoparticles in red, with the corrected spots shown in blue.

			\textbf{c,} NOriginal median spots for \textit{end-of-life (EOL)} nanoparticles in red, with the corrected spots shown in blue.}

		\end{figure*}

		To generate the corrected strain maps, after the aberration correction, we also need to get corrected median spots. 

		This is because our strain is calculated with respected to the median diffraction position in each nanoparticle.

		Thus, first we apply our aberration correction parameters to the median positions. 

		\subsection{\label{ssec:montage_strain}Volumetric Strain across all nanoparticles}

		\begin{figure*}

			\centering

			\includegraphics[width=\textwidth]{GeneratedFigures/Corrected_Median_Spots.pdf}

			\caption{\label{fig:diff_correction} \textbf{Correcting median spots to known PtCo pattern. a,} 

			\includegraphics[width=\textwidth]{GeneratedFigures/Montage_Figure.pdf}

			\caption{\label{fig:montage} \textbf{Volumetric Strain across all nanoparticles. a,} 

			The theoretically calculated diffraction pattern for PtCo alloy, with the peak positions and the corresponding Miller indices in red.

			\textbf{b,} Original median spots for \textit{beginning-of-life (BOL)} nanoparticles in red, with the corrected spots shown in blue.

			\textbf{c,} NOriginal median spots for \textit{end-of-life (EOL)} nanoparticles in red, with the corrected spots shown in blue.}