# Potential of Deep Learning Methods for Deep Level Particle Characterization in Crystallization
## 4 Results
### Application to Crystallization  
As described in Section 3.1 crystallization experiments with different saturation temperatures (\(\theta_{sat}=40\)\({}^{\circ}\)C/50 \({}^{\circ}\)C) are performed. After crystallization, the product crystals are recorded by dynamic image acquisition and a detailed crystal characterization of the product crystals is performed by image processing. According to the image processing methods developed, the two-net variant consisting of one Mask-RCNN for single crystals and agglomerates and an additional one for primary crystals in agglomerates with post-processing (M3_2 PP) is chosen for image processing. Additionally, a size threshold for single crystals and agglomerates of \(d_{eq}\geq 50.8\)\(\upmu\)m is set. Below this size limit, no appropriate differentiation of particle shapes is ensured and artifacts further complicate the analysis (see Figure 5). Nevertheless, no size threshold is assigned for the primary crystals in agglomerates because even an agglomerate of \(d_{eq}=50.8\)\(\upmu\)m must consist of at least two primary crystals in theory. As the result of image analysis, every crystal on the images is detected pixel-wise and classified into single crystals, agglomerates and primary crystals in agglomerates. This allows for the determination of characteristic measures to describe and quantify agglomeration. In Figure 9, the particle size distributions (PSD) of the performed experiments with different saturation temperatures are shown. By classifying single crystals and agglomerates, as shown in Figure 7a, besides the overall number density distribution \(q_{0}\) of all crystals, the total crystals can also be split into the subpopulations of single crystals and agglomerates. When calculating the PSD for the given subpopulation, e.g., single crystals, the single crystals in a given size class are considered in relation to the total crystals. If the subpopulations of the single crystals and the agglomerates are combined, the PSD of the total crystals is obtained again [57]. As expected, the increased saturation temperature shifts the PSD to larger particles. On the one hand, this is due to concentration difference from the beginning to the end of crystallization promoting growth. This is also indicated by the shift of the subpopulation of single crystals to the right. On the other hand, the tailing for bigger crystals is due to the subpopulation of agglomerates. Therefore, the dominant phenomenon for large crystals exceeding 250 \(\upmu\)m is agglomeration. Figure 9: PSD including total crystals (black) and subpopulations of single crystals (green) and agglomerates (magenta) after crystallization for \(\theta_{sat}=40\)\({}^{\circ}\)C on the left (**a**) and \(\theta_{sat}=50\)\({}^{\circ}\)C on the right (**b**). The error bars are calculated according to the three replicated crystallizations for each saturation temperature. The probability for agglomeration at the higher saturation temperature is increased because the formed crystals remain longer in the system due to the same end temperature. Thus, by continuing agglomeration, crystals exceed to larger sizes and the \(Ag\) is increased as well (see Table 3). In addition, the raising solid content promotes the particle collisions. This observation of a higher degree of agglomerated products has also been reported in the literature [7]. The progression of agglomeration is not only depicted by the agglomeration degree but can also be traced on a more detailed level of primary crystals in agglomerates. A first measure is the average number of primary crystals per agglomerate (\(\overline{pc/ag}\)) in Table 3. For the saturation temperature of \(\theta_{sat}=40\)\({}^{\circ}\)C, \(\overline{pc/ag}\) slightly exceeds the minimum limit of two and increases to 2.8 for \(\theta_{sat}=50\)\({}^{\circ}\)C. Based on the size-dependent accuracy of the method, but also due to the wide range of agglomerate sizes, a size-dependent evaluation is useful.