Correlative x-ray/electron beam imaging and analysis of LFP

Overview

This directory contains data, code, and visualizations deriving from a study of LixFeO4 nanoplatelets at three stages of charge cycling: fully lithiated (LFP), partially delithiated (LFP50), and fully delithiated (FP). At each stage, several nanoplatelets - diamond shaped particles ~2-3 um in length by ~1 um in width by ~200-400 nm in thickness - were imaged in both an electron and x-ray beam. Ten particles were imaged: 3 FP particles, 5 LFP particles, and 2 FP particles.

Experiments and processing

In the electron beam, four-dimensional scanning transmission electron microscopy (4D-STEM) was performed, yielding data consisting of a 2D real space grid of 2D diffraction images. By localizing Bragg scattering and fitting lattice vectors in each scan position, the local lattice parameters and infinitesimal strain matrices were computed for every beam position from this data. The 4D-STEM data was also used to produce virtual bright- and dark-field images, and a high-angle annular dark-field image was simultaneously collected with each 4D-STEM scan.

In the x-ray beam, scanning transmission x-ray microscopy (STXM) was performed, yielding 3D data consisting of a 2D real space grid of 1D energy spectra. Using the Fe L_3 edge and FP/LFP reference samples, the local composition was determined at every beam position from this data. The STXM data was used to generate images of the FP, LFP and total optical densities, as well as of the percent lithiation.

The image data generated for each particle from the two beams were then aligned using an affine transformation optimized by gradient descent for the best pixel-by-pixel alignment.

Included are the following data, code, and visualizations:

data/ :

This directory includes

• FP-LFP50-LFPxray-electronbeampixelbypixelcorrelated__10particles16imagechannels.h5: Final processed data for all 10 particles, with 16 image-like information channels associated with each particle. Further description and visualization of this data can be found in show_particles.ipynb.
• 4DSTEM_LFP50P2_1024x1024x225x125_ss16nm_alpha0p48mrad_dt0p08s_spot8_cl600mm_300kV_bin8.dm4: Downsampled 4D-STEM data for one LFP50 nanoplatelet. This 6 GB dataset is a (256,256,225,115)-shaped 4D-array. Processing of this dataset to generate the electron-beam derived information channels is demonstrated in code/compute_strainmaps_from_raw_4DSTEM/.
• 4DSTEM_Alcalibrationdata_1024x1024x25x25_ss16nm_alpha0p48mrad_dt0p01s_spot8_cl600mm_300kV_bin2.dm4: A 4D-STEM scan of an Aluminum standard sample taken in conjunction with the LFP50 nanoplatelet 4D-STEM scan and used to calibrate that dataset. See code/compute_strainmaps_from_raw_4DSTEM/.
• strainmapping_processing.h5: A file containing intermediate processing data when generating strain maps from raw 4D-STEM data. This file is generated by the notebook files in code/compute_strainmaps_from_raw_4DSTEM/, and is provided here for convenience and comparison.

code/ :

The Python analysis and visualization code included here is provided in the form of Jupyter notebooks. With the exception of the compute_strain_from_raw_4DSTEM/ directory, this code operates on the final processed .h5 dataset. A sampling of the output plots are included in the visualizations/ directory. This code makes use of the py4DSTEM analysis package, which is free and open source software available on the Python Package Index. See the package’s github repository or documentation pages for more information.

This directory includes

• show_particles.ipynb: loads and visualizes all 16 information channels from each of the 10 particles
• show_strain.ipynb: visualizes the oriented infinitesimal strain matrix
• custom_colormap_images: generates images of the a- and c- lattice parameters and percent lithiation using custom colormaps designed to identify behavior relative to the nominal FP/LFP structures.
• means_percentiles_popdensities: compute and visualize the means and percentiles of the a- and c- lattice parameters by lithiation content for each particle, and the fraction of the population represented by each lithiation percentage. This notebook also demonstrates computation of the linear coefficients of chemical expansion.
• error_analysis_systematic_v_random: estimates the systematic and random error in the a-/c-lattice parameter measurements
• error_analysis_CV_and_fitting: estimates the error in the lattice vectors identified at each pixel with two methods
• compute_strainmaps_from_raw_4DSTEM/: a directory containing 3 notebooks, which calibrate and analyze the provided raw 4D-STEM dataset to calculate the local infinitesimal strain matrices

visualizations/ :

This directory contains .pdf files showing plots generated by the data and code provided here. These files are provided for convenience and comparison, and can all be generated directly from the files provided here.

References

If using this dataset in a publication, please cite:

L.A. Hughes, Benjamin H. Savitzky, Haitao D. Deng, Norman L. Jin, Eder G. Lomeli, Young-Sang Yu, David A. Shapiro, Patrick Herring, Abraham Anapolsky, William C. Chueh, Colin Ophus, Andrew M. Minor, Correlative analysis of structure and chemistry of LixFePO4 platelets using 4D-STEM and X-ray ptychography, Materials Today, Volume 52, Pages 102-111 (2022).

Pre-print