# Potential of Deep Learning Methods for Deep Level Particle Characterization in Crystallization
## 4 Results
### Application to Crystallization
In Figure 10, the \(\overline{pc/ag}\) in dependency of the agglomeration size is depicted. In the evaluation of the experiments agglomerates smaller than 161 \(\upmu\)m do not obtain the limit of two \(\overline{pc/ag}\) which indicates an underestimation for small crystals in particular and also lead to the low overall \(\overline{pc/ag}\) just above 2. However, regardless of size the agglomerates rarely consist of more than four \(pc/ag\), showing that the material system tends to agglomerate only moderately with few \(pc/ag\) in general. For larger particles, the \(\overline{pc/ag}\) even starts to decrease again, indicating that larger primary crystals do not form stable aggregates, which reduces the formation of agglomerates. Generally, the image analysis possibly underestimates the primary crystals due to the reduction of the spatial crystals to a 2D image. Especially, when small primary crystals are attached to large ones, the probability is high that the small primary crystals are obscured by the orientation of the agglomerate on the image and therefore do not appear in the evaluation. In addition to an averaged number of primary crystals in agglomerates, primary crystals in an agglomerate are characterized in more detail by distributions of size and number of primary crystals in agglomerates (Figure 11). Similar to a PSD, the characteristic value \(pc/ag\) instead of the size can be plotted against the fraction of primary crystals within a specified class of \(pc/ag\)[4]. In Figure 11a, it is shown that 72% (\(\theta_{sat}=40\)\({}^{\circ}\)C) and 57% (\(\theta_{sat}=50\)\({}^{\circ}\)C) of the agglomerates consist of maximally two primary crystals and less than 10% of agglomerates constitute of more than four \(pc/ag\) no matter what saturation temperature and agglomerate size. Again, a slight underestimation can be assumed based on the trends shown in Figure 10. However, in connection with Figure 10 and the exemplary images in Figure 7 it is shown that L-alanine crystallized from aqueous solution appears to form agglomerates containing only a few primary crystals per agglomerate and their number does not vary much, mainly between two to four. \begin{table}
\begin{tabular}{c c c} \hline \hline  & \(Ag\) & \(\overline{pc/ag}\) \\ \hline \(\theta_{sat}=50\)\({}^{\circ}\)C & \(0.697\pm 0.016\) & \(2.78\pm 0.15\) \\ \(\theta_{sat}=40\)\({}^{\circ}\)C & \(0.666\pm 0.009\) & \(2.11\pm 0.04\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Agglomeration degree (\(Ag\)) and number of primary crystals per agglomerate (\(\overline{pc/ag}\)) for different saturation temperatures in batch cooling crystallization. The end temperature is 20 \({}^{\circ}\)C each. The error bars are calculated according to the three replicated crystallizations for each saturation temperature. Besides number of primary crystals per agglomerate, the size of primary crystals in agglomerates are characterized in Figure 11b. All in all, the primary crystals in agglomerates reflect the subpopulation of single crystals, which means that the primary crystals grow equally in solution and in agglomerates, whereas it is still difficult to identify small primary crystals in agglomerates, larger ones are usually fully imaged. The contours can be estimated successfully so that overlapping does not impact the size calculation. Further, segmentation is facilitated by the moderate agglomeration, since the agglomerates are not very clumpy and mostly they only touch each other without much overlapping. We conclude that agglomeration takes place during the entire process and no tendencies can be determined whether there are preferred particle sizes that agglomerate with each other. There are agglomerates which consist of primary crystals of the same size as well as those which are composed of primary crystals of different sizes (see also Figure 7). Here a measurement during the process would be helpful to determine the influences regarding time point and particle size of the agglomeration.