## 4 Conclusions  
The first spatially resolved scattering images for 19 mAh to 93 mAh Li-po batteries are shown using neutron Talbot-Lau and far-field interferometry. This is one of the first applications of neutron far-field interferometry to battery chemistry, and the first for a set of commercial batteries. In the 43 mAh batteries, neutron attenuation and dark-field images clearly show differences between charged and discharged states, and between fresh and worn batteries. Moreover, wear induces inhomogeneities in the 2D images, obtained with high resolution--25.7 \(\upmu\)m effective pixel size--along one dimension.  
Relative to Talbot-Lau, the far-field interferometry is able to scan a wide range of autocorrelation lengths, which enables tuning the imaging experiment to features within the battery most sensitive to state of charge and wear. When the same battery was imaged at a charged and a discharged state, the dark-field image was found to evolve unevenly, with significant differences at the edges of the batteries.  
On the basis of the range of batteries sizes studied, from 19 mAh to 300 mAh, and the various neutron imaging and diffraction experiments performed, we suggest the combination of far-field imaging and neutron diffraction as a productive path for the characterization of small, commercial batteries.  
Figure 6: Time-of-flight neutron diffraction plots for fresh (**left**) and worn, 25% of original capacity (**right**) 300 mAh Li-ion batteries where the blue trace (with vertical offset) indicates charged battery and the black trace is for the discharged battery. A few diffraction peaks are tentatively assigned in (**C**). The Cu (002) diffraction peak is cropped from figures (**C,D**).  
**Author Contributions:** Conceptualization, A.J.B., D.S.H., D.L.J., N.K., L.G.B.; methodology, A.J.B., D.S.H., K.H., I.M., N.K., L.G.B.; software, A.J.B., D.S.H., K.H., N.K., L.G.B.; validation, D.S.H., D.L.J. and L.G.B.; formal analysis, D.S.H., K.H., L.G.B.; investigation, A.J.B., K.H., N.K., L.G.B.; resources, D.S.H., K.H., D.L.J., I.M., N.K.; data curation, I.M., L.G.B.; writing--original draft preparation, A.J.B.; writing--review and editing, K.H., D.L.J., L.G.B.; visualization, A.J.B., L.G.B.; supervision, L.G.B.; project administration, D.L.J., I.M., L.G.B.; funding acquisition, D.S.H., D.L.J., I.M., N.K., L.G.B. All authors have read and agreed to the published version of the manuscript.  
The lithium battery neutron imaging and spectroscopy research at LSU was supported by the U.S. Department of Energy (DOE) under EPSCoR Grant No. DE-SC0012432 with additional support from the Louisiana Board of Regents. A.J.B. also thanks the Charles E. Coates Memorial Fund for research travel support. We acknowledge the support of the National Institute of Standards and Technology, U.S. Department of Commerce, in providing the neutron research facilities used in this work. Measurements were carried out at the CONRAD-2 beamline operated by the Helmholtz-Zentrum Berlin fur Materialien und Energie. A portion of this research used resources at the Spallation Neutron Source a DOE Office of Science User Facility operated by the Oak Ridge National Laboratory. We gratefully acknowledge the support of [PERSON], lead instrument scientist at the VULCAN beamline. Certain trade names and company products are mentioned in the text or identified in an illustration in order to adequately specify the experimental procedure and equipment used. In no case does such identification imply recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply that the products are necessarily the best available for the purpose.  
The data presented in this study are available on request from the corresponding author.  
The authors declare no conflict of interest.