## 3 Results and Discussion
### Far-Field Neutron Imaging at NIST  
This section and the following section describe neutron grating interferometry experiments. Since neutron imaging is more sensitive than X-rays to lighter atomic elements like Li, neutron interferometry was anticipated to reveal unique battery component degradation for a lithium-based battery. For the neutron experiments, the Talbot-Lau interferometer gives good spatial resolution, but at a fixed interferometer autocorrelation length. The far-field interferometer has poor spatial resolution, but scans a wide range of autocorrelation lengths. Thicker batteries (larger than 1 mm) resulted in high amounts of scattering with the far-field neutron interferometer. The 43 mAh and 90 mAh batteries exhibited the largest changes between charged and discharged, fresh and worn samples. The highest capacity batteries of 90 mAh are shown first. While these batteries are not the thickest of the group of four battery sets (1.6 mm), it was anticipated that the multiple electrode layers would provide a strong scattering signal. The worn battery had 1780 charge/discharge cycles while the fresh battery had one previous cycle to build up the solid electrolyte interface. In Figure 2 we observe a large difference in the scattering signal between a fresh and worn battery at various autocorrelation lengths. The dark-field signal in the worn battery averages around 0.40 while the fresh battery is homogeneous around 0.80 when \(\xi=1.12\). With air having a value of 0.0 and a highly scattering material having a value of 1.0, this indicates a higher amount of scattering in the fresh battery versus the worn battery. Of interest in the worn battery is the left edge,  
Figure 2: Neutron scattering images of charged and discharged, fresh and worn 90 mAh batteries. In the top row images, \(\xi=2.25\). In the middle row images, \(\xi=2.81\). At the bottom, plots show scattering values across the batteries. The color bar represents the dark-field signal acquired through each battery. The reported uncertainty is the one-sigma root mean square uncertainty of the nonlinear least squares fit. which has a high scattering signal of 0.75. With this region not in the folds of the battery (located at the top and bottom of each battery), it is important to observe that the scattering signal is high on just one side of the battery. When \(\xi\) is increased from 1.12 \(\upmu\)m to 1.69 \(\upmu\)m, the scattering signal increases for both batteries. Upon increasing the autocorrelation length to 2.25 \(\upmu\)m, the worn battery appears to gain uniformity across the right side of the sample while the fresh battery remains homogeneous (Figure 2 top). When the autocorrelation length is increased to 2.81 \(\upmu\)m, the highly intense scattering centers in the worn battery diminish (Figure 2 middle row). The fresh battery also has a small reduction in signal, however it is not as noticeable as in the worn battery. One possible explanation for this decrease in signal is that 2.81 \(\upmu\)m sized particles are more prevalent in the fresh battery than the worn battery. While this could be related to battery degradation within the cell of smaller components, it is challenging to specify which component would cause this phenomenon without known particle size or porosity information in these commercially available batteries. The dark-field signal is shown in Figure 2 as a function of \(\xi\). When focused on the worn battery, a major difference can be observed in the dark-field signal between the left and right regions (Figure 2 bottom right). The left region behaves as if there are many particles up to 2.5 \(\upmu\)m in size while the right region appears to have a more even distribution of particles yielding scattering for autocorrelation lengths in the range from 788 nm to 3.0 \(\upmu\)m. This could be indicative of the right half of the battery becoming less involved in the worn battery chemistry where lithium is less able to intercalate in graphite, thus leaving only the left side of the battery active.