# X-ray computed tomography for 3D crystallization monitoring: A use case with paracetamol

Sébastien Clercq, Jérôme Vicente, Philippe Moulin

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Sébastien Clercq, Jérôme Vicente, Philippe Moulin. X-ray computed tomography for 3D crystallization monitoring: A use case with paracetamol. Journal of Crystal Growth, 2024, 642, pp.127794. 10.1016/j.jcrysgro.2024.127794. hal-05042665

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# X-ray computed tomography for 3D crystallization monitoring: A use case with paracetamol

Sébastien Clercq<sup>a</sup>, Jérôme Vicente<sup>b</sup>, Philippe Moulin<sup>a, *</sup>

<sup>a</sup> Aix Marseille Univ., CNRS, Centrale Marseille, (M2P2 UMR 7340), Equipe Procédés Membranaires (EPM), Europôle de l'Arbois, BP80, Pavillon Laennec, Hall C 13545, Aix en Provence Cedex, France

<sup>b</sup> Aix Marseille Univ., Institut Universitaire des Systèmes Thermiques Industriels (IUSTI-CNRS-UMR 6595), Technopôle de Château-Gombert, 5 rue Enrico Fermi 13453, Marseille Cedex 13, France

## ARTICLE INFO

Communicated by Alexander van Driessche

**Keywords:**

3D crystallization

Xray tomography

Crystal habit

Polymorphic form

Crystallization monitoring

## ABSTRACT

This work highlights the capabilities and limits of X-ray computed tomography in crystallization monitoring through a use case involving paracetamol as the solute, recrystallized from ethanol, methanol, or a mixture of both. The cooling crystallization operation was set up in two different containers, prepared with cotton yarns stretched vertically, acting as linear nucleation sites that immobilize the grown crystals in the recording area. The largest container (10 mL test tubes) allowed the acquisition of a larger number of crystals (up to 300 particles) for a more appropriate bulk analysis. The smallest container (5 mL pipette tips) allowed for a finer resolution of the recorded solid phase at the expense of a reduced recording volume. Crystallization was monitored in terms of the number of individual crystals, their size, and the overall volume, thus leading to the nucleation and growth rates, and solid-phase production rate. The main benefit of X-ray computed tomography is in the 3D analysis of the reconstructed solid phase. The crystal habit of paracetamol form I was predicted using force-field modeling. The predicted habit was in great accordance with the reconstructed solids, confirming the polymorphic form. Furthermore, face-specific growth rates of reconstructed crystals were measured, paving the way for a novel approach to the investigation of crystal-solvent interactions.

## 1. Introduction

X-Ray computed tomography (XCT) is an imagery technology that allows the investigation of solids morphology, non-destructively and with an in-depth analysis of the confined volume of a material. It is well known for its implication in medical imaging [1], but also has applications in material science, either for characterization [2–4] or stability control [5–7]. An SCT scan creates a 3D reconstruction of an object, by projecting X-rays into different radiographic projections of the object [8]. Each projection creates, at the surface of the detector, a negative 2D image of the object as it absorbs X-rays. A reconstruction algorithm processes the 2D negatives into a digitalized 3D object. Thanks to the penetrability of X-rays through the matter, the projected image is grayscale rather than binary, allowing the reconstruction of details in the internal volume of the object.

In this work, micro-XCT was applied to crystallization monitoring. Crystal properties highly depend on their size, size distribution, morphology, and, even more importantly, on their polymorphic form.

Those physical properties arise from the nucleation and growth rate, as well as from the influence of the growth environment (solvent, growth inhibitors) on growing crystals. When an advanced material is involved, for instance in the pharmaceutical field, controlling these mechanisms is key to obtaining the desired properties. In this regard, in-situ SCT imagery is appropriate to monitor a crystallization operation, without influence on its kinetics or equilibrium thanks to being contactless and non-destructive. The added benefit, unique to this approach, is the 3D morphological analysis. Using micro-XCT, Liang et al. [9] proposed a method for the measurement of the reaction rate constant of gas hydrates forming a shell at the surface of a water droplet. The method is based on the joint measurement of the water volume decrease (inner shell diameter), and the shell growth (outer shell diameter) with a control of the sphericity and the uniform thickness that allow the use of the shell growth model. Turner et al. used micro-XCT to investigate the effect of the crystal morphology of L-Glutamic acid polymorphic form α (prismatic shape) and β (needle-like shape), on powder flowability, packing and tablet tensile strength through in-depth cartography of the

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: philippe.moulin@univ-amu.fr (P. Moulin).</footnote>
<table><caption>**Table 1**
Crystallization solutions.</caption><thead><tr><td>Solvent</td><td>Paracetamol mass fraction (%wt.)</td><td>Starting temperature</td><td>Expected solubility at 20 °C (mass fraction in %wt.) [30]</td></tr></thead><tbody><tr><td>Ethanol</td><td>32.7</td><td>79 °C</td><td>16.0</td></tr><tr><td>Methanol</td><td>30.8</td><td>65 °C</td><td>22.9</td></tr><tr><td>95 %wt. ethanol + 5 %wt. methanol</td><td>31.9</td><td>78 °C</td><td>—</td></tr></tbody></table>

<figure><img src="image_2.png" /><figcaption>**Fig. 1.** (a) Test tubes and (b) pipette tips used as containers for crystallization under micro-XCT acquisition.</figcaption></figure>

respective powder beds. Achermann *et al.* [10] correlated the spatial variations of the gray scale of time-average X-Ray tomograms with the density of crystals (Al particles) in differently mixed reactors, which confirmed the particle spatial distribution obtained by CFD simulations. Lately, Hypolite *et al.* [11,12] developed a method to monitor crystal growth using micro-XCT with automated crystal segmentation. Those primer tests, conducted with case study solutes namely potassium alum, chromium alum, and copper sulfate, highlighted the feasibility to count the number of individual crystals, measure their growth and observe the time-dependent evolution of their respective morphology.

This paper presents a follow-up study that aims to demonstrate a real use-case of micro-XCT application for crystal growth monitoring. Different well-described solutes with rich crystallographic behavior were investigated, namely L-Glutamic acid, Ibuprophen (2-(4-isobutylphenyl) propionic acid) and Paracetamol (N-acetyl-para-aminophenol).

Crystallization of L-Glutamic acid was performed in water, as it rather easily crystallized into either form α or β using L-phenylalanine as an additive [13–15] with distinctive crystal habits due to different – and quantified – water-crystal interactions [16]. However, the SCT imagery was not suited for this crystallization operation: to work, it is mandatory for the solute to absorb significantly more X-rays than the solvent does, to become detectable as X-Rays hit the detector. Water and L-Glutamic acid were on the same range in terms of X-Ray absorption, which prevents the observation of grown crystals in solution.

Ibuprofen was chosen for its wide range of solvents in which it can be solubilized [17]. Furthermore, its crystal habit can differ greatly depending on the solvent in which it was grown [18] most likely due to the complexity of its morphologically dominant crystal faces [19]. However, within our apparatus and methodology, crystallization of

ibuprofen was poorly controlled and went through a high nucleation-low growth pathway, leading to particle size too close to the resolution of the micro-XCT device. Indeed, the resolution not only depends on the volume that is recorded, but also on the time interval between each individual radiographic projection. To reduce the acquisition duration, the detector pixel size is increased to gather a sufficient X-Rays flux to generate contrasted projections. The resolution is therefore a compromise between the sample size and the acquisition duration, and a balance could not be found for Ibuprofen-solvent mixtures. It was therefore considered less suitable for the development of the micro-XCT observation methodology and was discarded for potential future work.

<figure><img src="image_3.png" /></figure>

<figure><img src="image_4.png" /></figure>

<figure><img src="image_5.png" /><figcaption>**Fig. 2.** Temperature evolution in (a) Ethanol-PCM, (b) Methanol-PCM and (c) Ethanol-Methanol-PCM mixtures, (Δ) in test tube and (+) in pipette tips.</figcaption></figure>
<figure><img src="image_6.png" /><figcaption>Fig. 3. Image of a slice (left) unprocessed, (middle) denoised and binarized, and (right) fully processed.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>Fig. 4. Gray-scale levels of the slice presented in the precedent figure, (left) before and (right) after the non-local mean denoising algorithm.</figcaption></figure>

<table><caption>**Table 2**

Calculated attachment energy and lattice spacing for PCM form I.</caption><thead><tr><td>Face (hkl)</td><td>Attachment energy (kcal.mol<sup>-1</sup>)</td><td>D<sub>hkl</sub> (Å)</td></tr></thead><tbody><tr><td>(101)</td><td>-1.7</td><td>5.90</td></tr><tr><td>(011)</td><td>-3.9</td><td>7.51</td></tr><tr><td>(002)</td><td>-4.5</td><td>5.99</td></tr></tbody></table>

<figure><img src="image_8.png" /><figcaption>Fig. 5. Theoretical PCM form I crystal habit at the thermodynamic equilibrium.</figcaption></figure>

Finally, paracetamol (PCM), also known as acetaminophen, was selected as the case study solute. PCM is a widely used painkiller and fever-reliever drug that is of great interest to the crystallography community as well. It is known to have at two stable polymorphic forms with remarkable morphological differences: the form I, the monoclinic form, generally grow in a prismatic habit, while the form II, the orthorhombic form, generally grow in a rod-like or needle-like habit [20]. A solvent-mediated polymorphic transition from form II to form I was observed in an ethanol + 5 % methanol mixture [20–22], in batch cooling crystallization. Furthermore, slight habit modifications [23] and different nucleation and growth rates [24,25] are expected for PCM crystals grown in either ethanol or methanol solutions. The present study aims to challenge the micro-XCT technology to be able to provide the information necessary for highlighting such phenomenon, demonstrate the validity of the approach and how it can benefit research, but also its intrinsic limitations for crystal growth monitoring.

## 2. Materials and methods

### 2.1. Chemicals

Paracetamol (4-acetamidophenol, CAS number 103–90-2) > 97.5 % purity was purchased at Fischer Scientific (France) in sealed plastic container. The content was used as received without further purification. Absolute ethanol (CAS number 64–17-5) and absolute methanol (CAS number 67–56-1) were purchased at Fischer Scientific (France) in glass bottle conditioning.

### 2.2. Paracetamol crystallography and modelling

The crystal structure of PCM form-I was retrieved from the Cambridge Crystallographic Data Centre under the reference HXACAN58 [26]. It belongs to the $P2_1/n$ monoclinic space group ($Z = 4$ molecules per unit cell) with crystal lattice parameters $a = 7.344$ Å, $b = 9.645$ Å, c
= 12.087 Å and β = 97.37°. The file also contains the molecular conformation of PCM in the crystal lattice, obtained by electron diffraction. Hydrogen atoms positioning was conserved, as election diffraction is sensitive enough to localize hydrogen atom [27]. GenMol force field [28] was used to model the PCM form I crystal habit using the attachment energy model [29].

## 2.3. Crystallization solution preparation

Three crystallization solutions were produced, consisting in solubilized PCM (close to saturation) in heated solvents. Details of the three solutions are provided in Table 1.

Solutions were prepared the day before JACK acquisition and stored at room temperature in glass bottles. It was observed for both methanol-containing solution that the initially colorless solution turns pink about an hour into being mixed and heated. It also occurs for the ethanol solution after about 12 h. It is known that PCM is sensitive to hydrolysis upon exposure to light and at high temperature [31], reportedly leading to the formation of 4-Aminophenol, then quinone imine through oxidation, responsible for the pink coloration. To the author's knowledge, PCM degradation in pure ethanol or methanol was not reported. Therefore, the observed degradation is likely due to hydrolysis by atmospheric moisture only, which is significantly accelerated in the presence of methanol. The crystallization operation was initially performed in a test tube following the method of Hypolite et al. [11]. Test

tubes (13.5 mm in inner diameter) were prepared with three cotton yarns stretched from the bottom (trapped with epoxy glue) to the tube's cap at the opposite end. Cotton yarns create a linear nucleation site on which crystals can grow with an ideal disposition for JACK imagery. Crystals also have a fixed position for the duration of the experiment, easing the image acquisition and post-processing of individual crystals. Test tubes are presented in Fig. 1-a.

A second type of crystallization container was built, using a 5 mL pipette tip. With a reduced diameter (8 mm), the acquisition volume was lowered and therefore the resolution and contrast were increased. Only one cotton yarn was used in pipette tips. To ensure that the cotton yarn was centered and as vertical as possible, a cap and a base to hold the pipette tip were 3D printed. The cotton yarn length per volume is halved in pipette tips, hence reducing the nucleation site density: there is 21 and 11.4 mm of submerged yarn per milliliter of solution, respectively in test tubes and in pipette tips.

Once fully dissolved, about 6 mL (test tubes) or 3 mL (pipette tips) of solution is introduced in the container that is placed in the JACK acquisition chamber. Temperature evolution in solutions were monitored in replicated experiments to avoid the presence of the thermocouple in recorded images, measurements are plotted in Fig. 2. Due to a larger surface/volume ratio, pipette tip mixtures temperature decreases more rapidly, reaching a plateau in around 10 to 15 min. In test tubes, the lowest temperature is reached after 20 min.

<table><caption>**Table 3**
Reconstructed volume as a function of time of PCM crystals grown in ethanol, in test tube.</caption><thead><tr><th>Time (min)</th><th>14</th><th>16</th><th>20</th><th>24</th></tr></thead><tbody><tr><td>Reconstructed volume</td><td></td><td></td><td></td><td></td></tr><tr><td>Time (min)</td><td>29</td><td>37</td><td>43</td><td>49</td></tr><tr><td>Reconstructed volume</td><td></td><td></td><td></td><td></td></tr></tbody></table>
<table><caption>**Table 4**
Reconstructed volume as a function of time of PCM crystals grown in methanol, in test tube. Crystals grown at the surface of the test tube were removed for visibility.</caption><thead><tr><th>Time (min)</th><th>4</th><th>6</th><th>8</th><th>10</th><th>11</th><th>13</th></tr></thead><tbody><tr><td>Reconstructed volume</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Time (min)</td><td>18</td><td>20</td><td>23</td><td>32</td><td>36</td><td>41</td></tr><tr><td>Reconstructed volume</td><td></td><td></td><td></td><td></td><td></td><td></td></tr></tbody></table>
<table><caption>**Table 5**
Reconstructed volume as a function of time of PCM crystals grown in ethanol-methanol mixtures, in test tube.</caption><thead><tr><th>Time (min)</th><th>6</th><th>8</th><th>10</th><th>12</th><th>14</th><th>16</th></tr></thead><tbody><tr><td>Reconstructed volume</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Time (min)</td><td>19</td><td>21</td><td>23</td><td>26</td><td>28</td><td>30</td></tr><tr><td>Reconstructed volume</td><td></td><td></td><td></td><td></td><td></td><td></td></tr></tbody></table>

(continued on next page)
<table><caption>Table 5 (continued)</caption><thead><tr><th>Time (min)</th><th>Time (min)</th><th>Reconstructed volume</th></tr></thead><tbody><tr><td>6</td><td>8</td><td>34</td></tr><tr><td></td><td>37</td><td></td></tr><tr><td></td><td>41</td><td></td></tr><tr><td></td><td>56</td><td></td></tr><tr><td></td><td>12</td><td></td></tr><tr><td></td><td>14</td><td>59</td></tr><tr><td></td><td>16</td><td>61</td></tr></tbody></table>

<figure><img src="image_9.png" /></figure>

<figure><img src="image_10.png" /></figure>

<figure><img src="image_11.png" /><figcaption>Fig. 6. Evolution of (a) number, (b) mean diameter (considered as spheres of equivalent volume) and (c) cumulated volume of PCM crystals in test tubes and in different mixtures: (◇) PCM-ethanol, (○) PCM-methanol and (×) PCM-ethanol-methanol. Error bars in (b) represent the crystal size standard deviation calculated from the equivalent diameters.</figcaption></figure>

## 2.4. X-ray computed tomography: image acquisition and processing

Acquisition of micro-XCT images was performed by an EasyTom XL "Mechanic Ultra" microtomograph equipped with the "Micro 150" X-Ray generator (RX-Solution, France). For test tube trials, the detector was operated at a voltage of 114 kV and a current 232 mA. For pipette tip trials, the applied settings were: 95 kV and 153 mA. The detection pixels are merged with a binning of 2, which was necessary to increase contrast in projections, at the expense of resolution. To further increase contrast and signal/noise ratio, each tomographic projection was generated by an averaging of 3 frames. Those settings were optimal to keep the acquisition short (about 60 s) compared to the expected crystallization growth rate, while maximizing the image quality. The voxel
<figure><img src="image_12.png" /><figcaption>Fig. 7. View from the top, reconstructed volume of PCM crystals grown in methanol, (a) in test tube and (b) in pipette tip. The outer particles are attached to the container surface.</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>Fig. 8. Close view of reconstructed volumes in test tubes, showing paracetamol crystals grown from: (a)(d)(g) ethanol, (b)(e)(h) methanol or (c)(f)(i) ethanol-methanol mixtures. Images (a)(b)(c) are taken from the first acquisition time. Images (d)(e)(f) are taken at the last acquisition time. Images (g)(h)(i) show the fit of experimental crystals with the modeled paracetamol form I crystal. Crystal length is given by pixel summation and therefore depends on the pixel size (25 µm).</figcaption></figure>
<figure><img src="image_14.png" /><figcaption>**Table 6**
Vertical slice of reconstructed volume as a function of time of PCM crystals grown in ethanol mixtures, in pipette tip. Coloration following the segmentation algorithm. Dashed lines represent the cotton yarn that has been numerically removed for volume analysis.</figcaption></figure>

size was 25 µm for the test tube, the scanned volume was 721 × 721 × 860 voxels, or 18 × 18 × 21.5 mm. Thanks to a lower diameter, the voxel size was reduced to 15 µm for the pipette tips, with a scanned volume equivalent to 713 × 713 × 829 voxels, or 10.7 × 10.7 × 12.4 mm. The recorded inner volume was 21.5×Ø13.5 mm (or 3.1 mL) and 12.4×Ø8 mm (or 1.1 mL) for test tubes and pipette tips respectively. At this size, 544 radiographic projections are performed on a 360° rotation, resulting in 0.66° per successive projections. Those 2D projections are processed by an algorithm provided in "X-ACT" software (RX-Solution, France) to output the 3D model of the scanned object. The 3D output is, in turn, saved into grayscale 2D images consisting of "slices" of the scanned volume, which can be further processed manually. The acquisition process is repeated at different times, with a timestep of a few minutes, to monitor the crystal growth.

For this study, the treatment of “slice” images consisted in obtaining binary images where 0 (black) represents the liquid phase and 1 (white) represents the solid phase. Firstly, 16-bit images are converted to 8-bit images whose gray-scale values ranges from 0 (black) to 255 (white) (see Fig. 3 left). Then, a non-local means noise filtering algorithm is applied to all slices with a smoothing factor of 2 and a sigma value ranging from 16 to 20, depending on the solution. Histograms in Fig. 4 shows the evolution of the distribution of gray-scale values before and after the non-local means noise filtering algorithm, for the slice presented in Fig. 3: the “fluid area” and “solid area” are well separated, and the binarization is simply obtained by a threshold conversion, where the threshold limits were put between the two peaks, in the range of 119 to 126 depending on the solution, leading to the denoised and binarized image (Fig. 3-middle). Then, a cylinder is cut (pixel switched to black) to remove the yarn. This is done to ensure that measuring the solid phase growth only accounts for the crystallization. The cylinder’s extremities are manually positioned on both the first and the last image of an acquisition stack, then a script cut holes on the rest of the sample slices accordingly. The manual positioning is only done once per sample, as the yarn stays still between acquisitions. Next, the “impurities” passing through the previous filters are removed by removing all solids of volume lower than 100 connected voxels. Finally, a “dilatation-erosion” algorithm is applied, in which a layer (3 pixels width) of white pixels is added at the surface of the solid phase, then a layer of same width is removed, resulting in filling holes and smoothing planes while maintaining the morphology and angles of solids (see Fig. 3 right).

## 2.5. Volume analysis

The pixels of 2D images are actually volumetric elements called voxels because the images represent a section of the volume with a thickness corresponding to the size of the pixels. Solid voxels are summed to provide the overall crystals volume ($V_{tot}$), and volume growth over time ($\frac{dV_{tot}}{dt}$). Further analysis of the crystal phase requires the segmentation of connected crystals, which is performed by the “Automatic 3D Segmentation” algorithm developed by Hypolite et al. [12]. In short, it breaks the solid phase into small fragments (over-segmentation) based on an augmented watershed segmentation method [32], that are merged if connected to a given face, hence most likely belonging to the same crystal. Tuning of a few parameters (coplanarity criterion for face identification, convexity of recognizable particles, ...) adapts the algorithm to the studied solid phase.

The splitting process uses a threshold for some concavities on the particle surfaces to be tolerated. Isolated crystals with surface irregularities or elongated shapes, which could generate over-segmentation with the usual watershed techniques, are then directly identified as a single crystal by the segmented watershed. At the same time, the aggregates or overlapping crystals need to be fragmented, and in this case over-segmentation is preferable. Even though it easily segments isolated crystals, a too high concavity threshold is unable to separate aggregates or small crystals in contact with larger ones. In a second phase, an
<caption>**Table 7**</caption>

Vertical slice of reconstructed volume as a function of time of PCM crystals grown in methanol mixtures, in pipette tip. Coloration following the segmentation algorithm. Surface crystals are not displayed. Dashed lines represent the cotton yarn that has been numerically removed for volume analysis.

<figure><img src="image_15.png" /></figure>

algorithm identifies the different flat faces on the surface of aggregates and crystals. The parameters for the planar face detection are adjusted depending on image quality, surface irregularities and resolution. The final phase consists in bringing together the fractionated elements that share a previously identified face. If the faces are well identified and the split objects belong to the same crystal, then the segmentation technique is guaranteed to work. It is not necessary to detect all the faces of a crystal, because a single face in contact with fractionated objects is enough to merge them. On the other hand, it is necessary to properly subdivide the aggregates which implies using a low concavity threshold. Moreover, the segmentation method could suffer from the indivisibility of small crystals in contact with large crystals or more generally when the contact surface between two crystals presents no constrictions i.e. when the characteristic dimension of the contact surface is higher than the characteristic dimension of one of the two crystals.

Once correctly segmented, crystals can be counted to calculate the nucleation rate or the mean size of crystals, given below as the diameter of the sphere of equal volume V:

$$d_{eq} = \sqrt[3]{\frac{6V}{\pi}} \qquad (1)$$

Finally, crystals are individually analyzed in terms of shape, size, growth rate ($\frac{dV}{dt}$) and individual volume growth ($\frac{dV}{dt}$).

# 3. Results and discussion

## 3.1. Paracetamol crystal modelling

Crystal habit at the thermodynamic equilibrium (in vacuo) of PCM form-I was modeled using the attachment energy model calculated with the GenMol force field. Calculated attachment energy and lattice spacing ($D_{hkl}$) of predominant faces are given in Table 2, and the equilibrium habit is given in Fig. 5.

As per the attachment energy model, the growth rate of a given face is inversely proportional to its attachment energy. Therefore, with the lowest attachment energy, the (101) face has the slowest growth, hence the largest surface area of the equilibrium crystal habit. Face (011) is also of great importance as it is the face with the lowest attachment energy bordering the crystal in the y-axis direction. Finally, the (002) face is of lesser importance, because its attachment energy is higher than that of the (101) face, while being in a competition with the latter in the z-axis direction.

## 3.2. Crystallization in test tubes

Reconstructed volumes of XCT acquisitions in test tubes are presented in Table 3, Table 4 and Table 5 respectively for ethanol-PCM, methanol-PCM and ethanol-methanol-PCM mixtures, at different times.

From these reconstructed volumes, different measurements were performed on the solid phase, presented in Fig. 6.

Firstly, the number of individual crystals was counted from the segmentation-merging algorithm presented in the previous section (Fig. 6-a). In ethanol, PCM nucleation is extremely sparse, reaching only 7 individual by the end of the experiment. Interestingly, only one yarn was seeded, the other two remained empty of any crystals. In methanol, PCM nucleation was higher, reaching almost 300 crystals that grew either from cotton yarns, but also from the tube's surface (see Fig. 7 for a view from the top): more than half the crystals are sticked to the tube surface at 17 min and above. Surface crystals were put in transparency for readability in pictures of Table 4. When 95 %wt. ethanol + 5 %wt. methanol mixture was used, the nucleation rate was intermediate, reaching a maximum of 55 individual crystals, including only 4 at the tube's surface. It is interesting to note how a few amount of nucleation-favoring solvent allowed, in this case, to multiply by 10 the nucleation rate.

The growth rate was also monitored; the mean size given in Fig. 6-b corresponds to the mean diameter of spheres of equal volume to that of
<figure><img src="image_16.png" /><figcaption>**Fig. 9.** Inconsistencies and excessive merging observed in the segmentation algorithm.</figcaption></figure>

<figure><img src="image_17.png" /></figure>

crystals. The growth rate of PCM in ethanol and in ethanol-methanol mixtures was almost identical, ranging between $5.4 \times 10^{-7}$ and $6.7 \times 10^{-7}$ m.s$^{-1}$ in the steady growth period (between 10 and 35 min). In methanol, the overall growth rate was lower with an average of $1.8 \times 10^{-7}$ m.s$^{-1}$ calculated from 20 min until the end. The average growth rate of PCM in methanol was partially reduced by the secondary nucleation at the tube's surface: when surface crystals are excluded, the growth rate was $4.4 \times 10^{-7}$ m.s$^{-1}$ on average, which is still lower than in the two other mixtures, mostly because of aggregation and a reduction of crystal growth area.

The cumulated volume of the crystal phase is also measured (Fig. 6-c). Logically, in ethanol, the crystal phase volume is low due to the lack of nucleation. The overall crystallized mass at the end of measurements is evaluated to 17 mg (paracetamol density: $\rho_{PCM} = 1290 \text{ kg.m}^{-3}$). Referring to the expected solubilities given in Table 1, the production yield was only about 5% after 50 min of experiment, highlighting a very slow process. The productivity was higher in methanol than in ethanol-methanol mixture, respectively 122 and 77 mg produced in the recorded 3.1 mL volume at 40 min, but this is mainly due to the ability of PCM crystals in methanol to nucleate from the surface. Referring to the expected solubilities, the crystallization yield reached 67% at 41 min in methanol.

The error bars correspond to the standard deviation of the diameter, also calculated on spheres of equal volume to that of crystals. It increases with time due to the nucleation – mostly for PCM-methanol experiment – and aggregation. Deviation on the number of crystals as well as on the cumulated volume of PCM crystals are not represented as it mainly depends on the quality of the segmentation and merging algorithm with no suitable equation to calculate them. It is important to note, however, that this algorithm is based on binarized images, and therefore depends on the binarization threshold. As recalled from Fig. 4, the two phases are easily identifiable after the non-local mean treatment. The number of crystals and the cumulated volume of PCM crystals are therefore very stable relative to the process variables.

In each sample, crystals exhibited the predicted prismatic morphology, with the (002) face fully developed, hence without a surface. As shown in Fig. 8, faces (101) and (011), the habit-defining faces, are easily distinguishable throughout the latest acquisitions. Furthermore, from image visualization, it can be shown that the growth of the (101) face is larger in the presence of methanol than that of the
theoretical equilibrium crystal: the neighboring faces, namely (011) and its symmetrical equivalents, have a reduced relative growth rate most likely induced by crystal-solvent interactions. However, in test tubes, the observed in acquisitions below 10 min (for PCM-methanol and PCM-ethanol-methanol mixtures) is limited by the resolution. The crystal habit cannot be retrieved at this stage, therefore it is impossible to observe a potential crystal phase transition of PCM from form II to form I [20–22].

### 3.3. Crystallization in pipette tips

A vertical slice of the reconstructed volume of XCT acquisitions in pipette tips are presented in Table 6, Table 7 and Table 8 respectively for ethanol-PCM, methanol-PCM and ethanol-methanol-PCM mixtures, at different times. Individual crystals or segments were colored in accordance with the segmentation algorithm.

The automatic segmentation algorithm is effective with the provided samples. The algorithm settings were varied to minimize the number of “errors”, judged, and counted manually. We noticed two kind of errors, illustrated in Fig. 9, i.e. inconsistencies (when a segment is indexed to a different crystal for different time steps) and excessive merging (fusion of crystals considered different at previous time steps). Indeed, during growth, two or more crystals can share a large contact area and form complex agglomerates, increasing the difficulty for the segmentation algorithm. Nonetheless, those inconsistencies and excessive merging errors are sparse and do not significantly affect the number of crystals and the mean diameter of crystals.

The bulk analysis was applied to PCM crystals grown in pipette tips; the results are provided in Fig. 10.

Unsurprisingly, in ethanol-PCM and ethanol-methanol-PCM mixtures, the nucleation was low: only 5 and 7 crystals respectively grew from those mixtures, but around 85 individual crystals were counted in methanol-PCM solutions (Fig. 10-a). At 17 min, the segmentation algorithm excessively merged some agglomerated crystals together for the PCM-methanol mixture (see Fig. 9), leading to an erroneous decreasing number of particles: no dissolution or crystals falling was observed. In PCM-methanol mixture, crystals also significantly grew from the container surface, as shown with a view from the top in Fig. 7-b. The proportion of crystals grown from the surface peaks at 25 % in number. The fastest crystal growth out of those experiments was observed for ethanol-PCM, with an average growth rate of $6.7 \times 10^{-7}$ m.s$^{-1}$ throughout the experiment. PCM growth in PCM-ethanol-methanol mixture was slightly slower, measured at $4.3 \times 10^{-7}$ m.s$^{-1}$ on average. This slower growth rate is most likely due to a hindrance caused by aggregation. As shown in Table 8, two aggregates form within the acquisition volume: a group of 4 crystals at the top and 2 crystals at the bottom. Comparatively, all 5 crystals are separated in ethanol-PCM mixture (Table 6). With even more aggregation and secondary nucleation, PCM crystals grew the slowest in methanol: $2.0 \times 10^{-7}$ m/s on average. Due to that slow growth, the productivity of the methanol-PCM mixture was lower than that of the ethanol-PCM mixture, with the lowest crystal number, during the 20 first minutes. Then, as the number of crystals rose, the productivity in methanol-PCM mixture became the highest among all mixtures 20 min after the injection. The lowest PCM crystal production was observed in PCM-ethanol-methanol mixture, but, again, this is likely due to aggregation hindrance. The total volume of the crystal phase was 2.4 mm$^3$, or 3.2 mg in PCM-ethanol solution at 26 min, and 5.6 mm$^3$, or 7.2 mg in PCM-methanol solution at 35 min. Referring to the expected solubilities, the crystallization yields were 2 % and 11 % respectively. The lower yields, when compared to test tubes experiments, can be explained by the lower nucleation site density (halved submerged yarn

<figure><img src="image_18.png" /></figure>

<figure><img src="image_19.png" /></figure>

<figure><img src="image_20.png" /><figcaption>**Fig. 10.** Evolution of (a) number, (b) mean diameter (considered as spheres of equivalent volume) and (c) cumulated volume of PCM crystals in pipette tips and in different mixtures: (◇) PCM-ethanol, (○) PCM-methanol and (×) PCM-ethanol-methanol. Error bars in (b) represent the crystal size standard deviation calculated from the equivalent diameters.</figcaption></figure>

length per volume of mixture in pipette tips) as well as the lower number of crystals at the container surface.

In PCM-ethanol and PCM-ethanol-methanol mixtures, the low number of crystals and low aggregation allows a narrow size distribution, hence low standard deviations. In the PCM-methanol mixture, as the crystal count – and inevitably the aggregation – rises, the size distribution widens.

The prismatic morphology of the form I of PCM crystals was retrieved using the predicted crystal with the (002) face fully developed, as shown in Fig. 11. The better resolution achieved by using a thinner container allowed to distinguish more details out of the smallest observed crystals. In Fig. 12, some instances of such small particles are shown. These crystals exhibit an acicular formation at opposed
<figure><img src="image_21.png" /><figcaption>**Fig. 11.** Close view of reconstructed volumes in pipette tips, showing paracetamol crystals grown from: (a)(d)(g) ethanol, (b)(e)(h) methanol or (c)(f)(i) ethanol-methanol mixtures. Images (a)(b)(c) are taken from the first acquisition time. Images (d)(e)(f) are taken at the last acquisition time. Images (g)(h)(i) show the fit of experimental crystals with the modeled paracetamol form I crystal. Crystal length is given by pixel summation and therefore depends on the pixel size (15 µm).</figcaption></figure>

extremities, which was not observed in any other sample. It occurred to about half of the unaggregated particles that grew in the solution, i.e. ignoring those in contact with the pipette tip surface. This acicular formation is not observed as consistently in the second acquisition (13 min), and completely disappears at the third acquisition (15 min): it typically occurs on smaller crystals ranging from 150 to 300 µm. It is hypothetically the expected metastable form II, rapidly transitioning into the most stable form I. The acquisition with the applied settings is, however, not sufficient to further investigate this crystallization pathway dynamically.

An important benefit of the XCT technology when it comes to crystallization monitoring is the ability to dynamically measure and characterize individual crystals. For instance, the volume of each individual crystals of PCM grown from the PCM-ethanol solution is plotted against the time in the Fig. 13.

More importantly, the 3D reconstitution allows the calculation of the linear growth rate of each crystal face. An illustration of this measurement is given in Fig. 14, for a PCM crystal grown from ethanol (shown in Fig. 11). The measured linear growth rates were: $V_{011} = 5.7 \times 10^{-7} \text{ m.s}^{-1}$ and $V_{101} = 4.7 \times 10^{-7} \text{ m.s}^{-1}$.

According to the attachment energy model [29], the linear growth rate is proportional to the attachment energy, which can be interpreted as the energy released when the crystal grow one slice in the

considered direction. If the attachment energy is rather easy to estimate [33], the thermodynamical contribution of the growth environment does not make consensus. XCT allows an accurate measurement of the face-specific growth rates of multiple crystals in one recording, dynamically and in 3D, in a large volume. Therefore, this novel approach can be used to better understand crystal-solvent interactions from mono-crystal growth and study the effect of growth inhibitors.

## 4. Conclusion

X-ray computed tomography was used to study the cooling crystallization of paracetamol in three solutions: ethanol, methanol, and a 95 % wt. ethanol + 5 % wt. methanol mixture. The operation was set up in two containers. The image samples generated from the larger container (10 mL test tube) allowed to tune the image acquisition, the post-treatment, the volume reconstruction processes, as well as the segmentation algorithm for this use case. The method allowed the monitoring of the crystallization operation through the calculation of the number of single crystals, their individual and the average growth rates, as well as the overall crystal production. A force-field modeling with habit calculation also confirmed that the observed paracetamol crystals belong to the polymorphic form I. No evidence of form II was found at the smaller resolution deriving from the larger container.
<figure><img src="image_22.png" /><figcaption>**Fig. 12.** Close view of reconstructed volumes of PCM-methanol mixture in pipette tips. Crystal length is given by pixel summation and therefore depends on the pixel size (15 µm).</figcaption></figure>

<figure><img src="image_23.png" /><figcaption>**Fig. 13.** Volume growth of individual crystals in PCM-ethanol mixture, in pipette tip. Different colors are arbitrary attributed to each individual crystal.</figcaption></figure>

The smaller container (a 5 mL pipette tip) allowed a finer resolution of the recorded volumes, thus a more in-depth post-treatment. Smaller particles were observed, from which the elusive form II may have been identified from acicular formations. Furthermore, with finer details, more advanced post-treatments were made possible, such as the measurement of face-specific growth rates of mono-crystals in all directions at once. This novel approach has potential uses as a tool to quantify the thermodynamic contribution of crystal-solvent (or growth inhibitors) interactions on crystal habit. More generally, this technical approach is a new way to investigate, understand and optimize transformation operations on solids, such as a crystallization process, through a non-invasive, real-time acquisition and automated post-treatment of the reaction volume in desired conditions.

<figure><img src="image_24.png" /><figcaption>**Fig. 14.** Measurement from 3D reconstructions of linear growth rate of a crystal grown from PCM-ethanol solution, in pipette tip.</figcaption></figure>

### CRediT authorship contribution statement

**Sébastien Clercq:** Writing – original draft, Visualization, Validation, Software, Methodology, Investigation, Formal analysis. **Jérôme Vice-**
**nte:** Writing – review & editing, Visualization, Supervision, Software, Methodology, Investigation. **Philippe Moulin:** Writing – review &
editing, Validation, Supervision, Methodology, Funding acquisition.

### Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

### Data availability

Data will be made available on request.

### Acknowledgement

The project leading to this publication has received funding from the IMI (Institut Mécanique et Ingénierie, Aix Marseille University).

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