## 3 Results and Discussion
### Far-Field Neutron Imaging at NIST
In the 43 mAh batteries, large differences in the mean scattering values across the batteries were observed. Figure 3 exhibits the drastic change in scattering as a function of state of charge. Here, the fresh battery has undergone a single cycle to generate the solid-electrolyte interface. The slightly worn battery still has the initial capacity. The worn battery after 1790 cycles still has a capacity of 38.6 mAh, close to its advertised capacity of 43 mAh. The first sign of deterioration in the discharged batteries is when \(\xi=2.59\)\(\upmu\)m, where the worn battery begins showing inhomogeneous scattering across the battery image. The slightly worn battery shows small regions that change between the edges and center while the fresh battery still exhibits a homogeneous scattering image. Similar to the case of the 2 mm thick 90 mAh batteries, we observe a large difference in the scattering between charged and discharged 43 mAh batteries at larger autocorrelation lengths. In the charged batteries, the worn battery has low scattering values similar to air, the slightly worn battery has higher signal along the edges, and the fresh battery is still near homogeneous. The worn battery still possesses scattering along the edge, however the middle area of the battery now has scattering values similar to air. In comparing the mean scattering values for charged and discharged cycles, we observe the lower plots in Figure 3.  
Of interest in the scattering images is how the dark-field signal increases up to \(\xi=2.36\)\(\upmu\)m for the fresh battery, \(\xi=1.80\)\(\upmu\)m for the slightly worn battery, and \(\xi=1.69\)\(\upmu\)m for the worn battery before decreasing. This could indicate that the fresh battery has particles of larger size in comparison to the worn battery. As a battery undergoes degradation from its original capacity, larger particles within the battery are breaking down into smaller particles. The difficult challenge is determining whether the degradation is occurring on the solid electrolyte interface or the lithium cobalt oxide or graphite electrodes. Thin batteries (15 mAh and 50 mAh, 0.5 mm thick) had limited scattering value differences between charged and discharged cycles in comparison to the 1.5 mm thick batteries. There is limited difference in the scattering signal between the charged and discharged states at \(\xi\) of 1.12 \(\upmu\)m. One explanation is that the 0.5 mm batteries did not have as much electrolytic material at the 2 mm thick batteries to cause as much scattering of the neutrons. Although the signal is not changing between charged and discharged states, there is a large spatial difference in the dark-field signal when the autocorrelation length is changed. When \(\xi=1.35\)\(\upmu\)m, the fresh battery has a higher scattering signal on the left side of the battery. However, when the autocorrelation length is increased up to 2.81 \(\upmu\)m, the higher scattering signal is located on the opposite, right side of the battery. This is indicative of smaller sized features (up to 1.12 \(\upmu\)m) on the left side of the battery compared to larger sized features around 2.81 \(\upmu\)m on the right side. One challenge with these experiments is that the battery imaging is face-on. This means that both the cathode and anode material is included in the attenuation and dark-field values. Ideally, the battery is separated into cathode and anode components for far-field interferometry to understand which electrode the battery degradation is occurring. While these experiments are able to spatially locate where particle sizes are changing within the Lipo batteries, the chemical mechanisms causing these changes need further understanding.