# Electron Channeling Contrast Tomography (ECCT):
## Dislocation Tomography Enabled by ECCI

Timmo Weidner, Romain Gautier, Antoine Guitton, Alexandre Mussi

<figure><img src="image_1.png" /></figure>

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Timmo Weidner, Romain Gautier, Antoine Guitton, Alexandre Mussi. Electron Channeling Contrast Tomography (ECCT): Dislocation Tomography Enabled by ECCI. 2025. hal-05303689v2

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# Electron Channeling Contrast Tomography: Dislocation Tomography Enabled by ECCI

Timmo Weidner<sup>a</sup>, Romain Gautier<sup>b</sup>, Antoine Guitton<sup>c</sup>, Alexandre Mussi<sup>a</sup>

<sup>a</sup>Univ. Lille, CNRS, INRAE, Centrale Lille, UMR 8207 – UMET – Unité Matériaux et Transformations, F-59000 Lille, France,

<sup>b</sup>IMT Nord Europe, Institut Mines-Télécom, Univ. Lille, Centre for Materials and Processes, F-59000 Lille, France,

<sup>c</sup>Université de Lorraine, CNRS, Arts et Métiers Institute of Technology, LEM3, F-57000 Metz, France,

## Abstract

3D characterization of dislocations is critical for understanding plastic deformation in crystalline materials but remains experimentally challenging. Transmission electron microscopy (TEM) provides 3D reconstructions of dislocations but the necessity to use thin-foils, which are difficult to prepare and are small in scale, restricts statistical applicability. Here, we present a proof-of-concept for reconstructing the 3D dislocation microstructure using electron channeling contrast imaging (ECCI) in a scanning electron microscope (SEM). Unlike previous SEM-based approaches relying on serial sectioning, which is time-consuming and remove the material under study, our approach is non-destructive. Two electron channeling contrast micrographs of a single-crystal Ni specimen, acquired at distinct tilt-angles, were used to reconstruct six dislocations via stereomicroscopy. The reconstructed dislocation microstructure reveals glide behavior and instances of cross-slip. This method offers a fast, and non-destructive path to 3D dislocation analyses in bulk materials using standard SEM equipment, extending tomography concepts beyond TEM to accessible SEM-based workflows.

**Keywords:** dislocations, three-dimensional tomography, scanning electron microscopy (SEM), electron channeling contrast imaging (ECCI), plasticity

## 1. Introduction

Dislocations are line defects that govern plastic deformation and control the mechanical behavior of crystalline materials [1]. Their interactions drive the evolution of complex dislocation networks and play a critical role in strain hardening and microstructural evolution during deformation. To fully understand such mechanisms, three-dimensional (3D) characterization is essential. While two-dimensional (2D) projections reveal the approximate density of dislocations [2], their orientations, and simple slip and climb systems, they make it difficult to reveal important aspects such as curvature, connectivity, and spatial correlations.

These limitations become particularly severe in systems where dislocations interact in complex geometries, such as in olivine [3, 4], or where mixed climb, collinear interactions, or cross-slip are involved [5–7]. Notably, these insights were obtained through a combination of transmission electron microscopy (TEM) techniques, including tomography, which enabled the 3D visualization of such complex dislocation behaviors that cannot be captured in projection, and even allowed their use as input data for field dislocation mechanics simulations [8].

TEM has long been the method of choice for high-resolution dislocation imaging, capable of resolving Burgers vectors, slip planes, and defect cores [9–13].

However, its application to mesoscale or bulk studies is constrained by limited field of view of a few square micrometers, thin-foil requirements (typically < 200 nm), and complex sample preparation. TEM-based tomography offers access to full 3D dislocation geometry [14, 15], but typically requires large tilt ranges (up to ±80°), dedicated holders, and time-intensive acquisition and alignment workflows. These factors limit its use in broader screening or dynamic studies.

A simpler alternative is stereo reconstruction, which infers depth from two projections at moderate tilt angles (e.g., ±20°). First demonstrated in TEM by McCabe *et al.* [16], this method has since been used to reconstruct dislocation configurations with reduced experimental burden [17–20], but remains unexplored in scanning electron microscopy (SEM).

Electron channeling contrast imaging (ECCI) is a SEM technique that enables direct, non-destructive imaging of lattice defects on bulk samples under controlled diffraction conditions [21–25]. With sub-micron resolution and strong
defect contrast [22, 26], ECCI has been used to visualize
single dislocations, stacking faults, nanotwins, and com-
plex dislocation patterns [27, 28]. Furthermore, ECCI fa-
cilitates complementary approaches with mechanical test-
ing [29–32] or with artificial intelligence [33], offering in-
sights that go beyond those accessible by TEM.

Despite these advantages, conventional ECCI yields
inherently 2D information. Initial efforts to extract 3D
dislocation data in SEM have relied on destructive serial
sectioning methods [34], which remove material and pre-
clude further analysis. A non-destructive 3D approach us-
ing stereo reconstruction would thus significantly enhance
ECCI's utility for defect characterization. In this study,
we present the first proof-of-concept for electron chan-
neling contrast tomography (ECCT), a non-destructive
SEM-based method for 3D dislocation reconstruction us-
ing stereo ECCI. By acquiring two ECC micrographs at
distinct tilt angles from the same region of a single-crystal
Ni specimen and applying geometric triangulation, we re-
cover the spatial morphology of individual dislocations.
This approach provides a rapid and accessible pathway
for 3D defect analysis in bulk crystalline materials using
standard SEM instrumentation.

**2. Materials and Methods**

2.1. Material

The specimen used in this study was a high-purity
single-crystal nickel (Ni) sample with a surface orienta-
tion close to (111), grown by *Goodfellow* with a purity
level of 99.999 %. The dislocations analyzed here were
pre-existing, formed during the crystal growth process. A
nanoindentation network was introduced prior to imaging
to facilitate precise localization of the region of interest; it
was placed sufficiently far from the imaged area to avoid in-
teractions between deformation-induced and grown-in dis-
locations. Nickel was selected due to its face-centered cu-
bic (FCC) crystal structure and relatively high Z value,
which provides multiple slip systems, well-understood dis-
location behavior, and favorable conditions for electron
channeling contrast. In FCC metals, dislocations have
usually Burgers vectors of the type $\frac{1}{2}\langle 110 \rangle$ and glide pri-
marily on $\{111\}$ planes [35]. The use of a single crys-
tal offers a well-defined orientation and defect structure,
as well as simplifying electron channeling pattern (ECP)
alignment and interpretation.

2.2. Imaging

ECCI was performed using a Zeiss (Carl Zeiss AG,
Oberkochen, Germany) Gemini field emission SEM (FE-
SEM) equipped with a Crytur REBEKA backscattered
electron (BSE) detector (Crytur, Turnov, Czech Repub-
lic). The imaging parameters were set to an acceleration
voltage of 20 kV and a working distance of approximately
10 mm, optimized for ECC.

To determine the crystal orientation, an electron
backscatter diffraction (EBSD) map of the region of in-
terest was acquired using the *AZtecCrystal 3.0* software.
From this dataset, the local Euler angles were extracted
and used to simulate the expected Kikuchi pattern at 0°
tilt using the *Bruker ESPRIT 2.2.0* software package. The
simulated Kikuchi pattern was then directly compared to
the experimentally recorded electron channeling pattern
(ECP), acquired via the BSE detector under channeling
conditions (i.e., near-Bragg condition). This comparison
enabled fine-tuning of the specimen alignment and verifi-
cation of channeling conditions with a high degree of accu-
racy (Fig. 1) [22]. The diffracting vector **g**₁ = (220) was
selected for its high structure factor, experimental acces-
sibility, and its ability to reveal dislocations with different
Burgers vectors.

Once the orientation was confirmed, the specimen was
rotated such that the selected diffraction vector (g₁ =
(220)) was aligned parallel to the SEM stage tilt axis. This
geometry ensures that the same channeling conditions are
maintained during stage tilting, allowing dislocations to
remain in contrast across projections and enabling consis-
tent 3D reconstruction.

A stereo image pair was acquired from the same sur-
face region at tilt angles of +1° and +20° (Fig. 2a,b). Ad-
ditional ECC micrographs were recorded at intermediate
and higher tilt angles to verify reconstruction quality at
a later stage and validate spatial accuracy. To determine
the Burgers vectors (**b**), an invisibility criterion analysis
was performed based on the condition **g** ⋅ **b** = 0. ECC mi-
crographs were acquired under several suitable diffraction
vectors belonging to the {220} and {113} families, a list
for the diffraction conditions is given in table 1. Disloca-
tions that became out of contrast under specific conditions
were systematically matched to those in the stereo pair.
This allowed unambiguous assignment of Burgers vectors
for each reconstructed dislocation. An in-depth study on
<figure><img src="image_2.png" /><figcaption>Figure 1: Comparison between simulated Kikuchi patterns and experimental electron channeling patterns (ECPs) used for orientation alignment. (a) Experimental ECPs acquired along the diffraction vector $\mathbf{g}_1 = (\bar{2}20)$ at various tilt angles; conditions suitable for stereo imaging are highlighted in green. (b) Corresponding simulated ECPs generated using Bruker ESPRIT, highlighting the diffraction band used for the stereo reconstruction, as well as the bands used to identify the Burgers vectors.</figcaption></figure>

the identification of Burgers vectors is developed further in the document.

<table><caption>Table 1: Tested diffraction conditions for Burgers vector identification. Each cell lists the scalar product $\mathbf{g} \cdot \mathbf{b}$. Highlighting the two extinction conditions displayed in Fig. 4 a,b.</caption><thead><tr><th rowspan="2">b</th><th colspan="6">g</th></tr><tr><th>(220)</th><th>(202)</th><th>(022)</th><th>(113)</th><th>(131)</th><th>(311)</th></tr></thead><tbody><tr><td>1/2 [110]</td><td>0</td><td>1</td><td>1</td><td>1</td><td>-1</td><td>1</td></tr><tr><td>1/2 [101]</td><td>-1</td><td>0</td><td>-1</td><td>-1</td><td>1</td><td>1</td></tr><tr><td>1/2 [011]</td><td>1</td><td>-1</td><td>0</td><td>-1</td><td>-1</td><td>-1</td></tr><tr><td>1/2 [110]</td><td>-2</td><td>1</td><td>-1</td><td>0</td><td>2</td><td>2</td></tr><tr><td>1/2 [101]</td><td>-1</td><td>2</td><td>1</td><td>2</td><td>0</td><td>2</td></tr><tr><td>1/2 [011]</td><td>1</td><td>1</td><td>2</td><td>2</td><td>-2</td><td>0</td></tr></tbody></table>

### 2.3. Stereo Tracing

To ensure consistency between the two stereo images, distinct surface features such as scratches and inherent topographic features were used as markers. Manual alignment of the image pair was then performed to correct for tilt-induced rotation and ensure that the tilt axis was

placed in a perfectly horizontal position. Since the tilt was applied around the x-direction, only a y-parallax was introduced between projections, simplifying the triangulation geometry.

Dislocation lines were manually traced in both images using Inkscape (Version 1.4.2) with sub-pixel precision (Fig. 2c,d). Traced dislocation lines were exported as point sequences, and nodes with identical x-coordinates were automatically matched across the two projections for 3D reconstruction.

Manual tracing was favored over automated methods due to the limited number of dislocations in this proof-of-concept and the presence of surface artifacts, such as debris or polishing-induced features, that exhibited contrast similar to dislocations. These features could mislead automated algorithms but were distinguishable through visual inspection. The resulting dislocation traces and node assignments served as direct input for the stereo reconstruction process described in the following section.

### 2.4. 3D Stereo Reconstruction

A Python script was developed to perform 3D reconstruction of stereo images using two viewing angles $\alpha_1$ and $\alpha_2$. With specimen rotation around the x-axis, the projections are displaced only in the y direction. This implies that corresponding points in both images share the same x-coordinate. Each dislocation is represented as a sequence of nodes $k$, whose coordinates $(x_k, y_k, z_k)$ can be reconstructed using the projected y-positions from each image, denoted $y_{k1}$ and $y_{k2}$.

The mathematical framework underlying this triangulation is illustrated in Fig. 3. If the tilt axis (indicated with the index $R$), oriented along $\mathbf{u}_x$, is at the origin of the coordinate system $(0, \mathbf{u}_y, \mathbf{u}_z)$, i.e. $y_R = z_R = 0$, the vector $\mathbf{v}$ (Fig. 3) takes the following expression, for $\alpha_j = 0^\circ$:

$$ \mathbf{v} = \begin{bmatrix} y_k \\ z_k \end{bmatrix} \qquad (1) $$

Which transforms under tilt angle $\alpha_j$ into the rotated coordinate frame $\mathbf{u}'$, with:

$$ \mathbf{u}'_y = \cos(\alpha_j) \mathbf{u}_y + \sin(\alpha_j) \mathbf{u}_z \qquad (2) $$

Therefore, the projection of $\mathbf{v}$ onto $(O, \mathbf{u}'_y, \mathbf{u}'_z)$ is simply
<figure><img src="image_3.png" /><figcaption>Figure 2: ECC micrographs used for stereo reconstruction. (a) Micrograph acquired at an inclination angle of 1°; (b) micrograph at 20°. (c) Manual tracing of dislocations in *Inkscape* (Version 1.4.2) over the micrograph with an inclination angle of 1°, with labeled dislocations; (d) same for 20°. (e,f) Superimposition of the stereo reconstruction with the corresponding micrographs, the coloring correspond to their respective Burgers vector, see Fig.4.</figcaption></figure>

the scalar product $\mathbf{v} \cdot \mathbf{u}'_y$:

$$y_k^j = z_k \sin(\alpha_j) + y_k \cos(\alpha_j) \quad (3)$$

The least squares method allows us to find the coordinates of each node that delimit the dislocations in space $(O, x, y, z)$. It takes the form:

$$\gamma = \sum_k \sum_j (x_k^j - x_{k,\text{exp}}^j)^2 + \sum_k \sum_j (y_k^j - y_{k,\text{exp}}^j)^2 \quad (4)$$

where $x_k^j$ and $y_k^j$ are the simulated projected coordinates of each node $k$ and projection angle $j$, and $x_{k,\text{exp}}^j$, $y_{k,\text{exp}}^j$ are the experimental projected coordinates.

Consequently:

$$y_k^j(x_k, z_k, x_R) = z_k \sin(\alpha_j) + y_k \cos(\alpha_j) \quad (5)$$

and

$$x_k^j = x_k = x_{k,\text{exp}}^j \quad (6)$$

To find the simulated 3D coordinates of each node $k$, we minimize $\gamma$ with respect to all coordinates:

$$\left. \frac{\partial \gamma}{\partial x_k} \right|_{y_k, z_k} = \left. \frac{\partial \gamma}{\partial y_k} \right|_{x_k, z_k} = \left. \frac{\partial \gamma}{\partial z_k} \right|_{x_k, y_k} = 0 \quad (7)$$
Finally, for only two tilt angles, $\alpha_1$ and $\alpha_2$:

$$ \left\{ \begin{aligned} x_k &= x_{k,\text{exp}}^1 = x_{k,\text{exp}}^2 \\ y_k &= \frac{\sin(\alpha_1) \cdot y_{k,\text{exp}}^2 - \sin(\alpha_2) \cdot y_{k,\text{exp}}^1}{\sin(\alpha_1 - \alpha_2)} \\ z_k &= \frac{\cos(\alpha_2) \cdot y_{k,\text{exp}}^1 - \cos(\alpha_1) \cdot y_{k,\text{exp}}^2}{\sin(\alpha_1 - \alpha_2)} \end{aligned} \right. \quad (8) $$

Each projected dislocation was traced manually and parameterized using spline interpolation via Python's SciPy package [36]. This approach enables smooth representation of dislocation lines, including those with strong curvature that result in multiple y-values for the same x-coordinate. To ensure consistent triangulation, node pairs were automatically assigned by first ensuring an identical count of nodes between the two projections and by attributing nodes with multiple matching solution (i.e multiple y-values for the same x-coordinate) to the corresponding closest one. A separate study on the semi-automation of this 3D stereoscopic reconstruction workflow is currently in preparation. The 3D reconstructions of the dislocations were qualitatively validated by projecting them onto additional ECC micrographs acquired at different tilt angles. The consistency of these overlays confirmed the reliability of the stereo triangulation process. Further refinement involved cross-verifying the reconstructed dislocation segments with ECC at intermediate tilts to ensure the geometry remained consistent across the entire tilt range (Fig. 2e,f).

### 3. Results and Discussion

A total of six dislocations were successfully reconstructed in 3D from stereo ECC micrographs of a single-crystal Ni specimen. These dislocations are labeled 1 to 6 as seen in Fig. 2. Burgers vectors were assigned knowing that the Burgers vectors of perfect dislocations in FCC structures are of the type $\mathbf{b} = \pm \frac{1}{2} \langle 110 \rangle$ and based on inviscibility criteria under specific diffraction conditions: dislocations 1–3, located in the upper part of the reconstructed volume, became out of contrast under $\mathbf{g}_2 = (11\bar{3})$, indicating $\mathbf{b}_1 = \pm \frac{1}{2} [1\bar{1}0]$. Dislocations 4–6, in the lower part, were out of contrast under $\mathbf{g}_3 = (\bar{3}11)$, corresponding to $\mathbf{b}_2 = \pm \frac{1}{2} [01\bar{1}]$ (Fig. 4a,b). These two groups are hereafter color-coded by their respective Burgers vectors or-ange for $\mathbf{b}_1 = \pm \frac{1}{2} [1\bar{1}0]$ and green for $\mathbf{b}_2 = \pm \frac{1}{2} [01\bar{1}]$ as seen

a)

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

b)

<figure><img src="image_5.png" /><figcaption>Figure 3: Representative sketch used to determine the 3D coordinates of nodes k: (a) Thin foil represented with projection angle $\alpha_j = 0^{\circ}$; the point of interest has coordinates $[x_k \ y_k \ z_k]$; the tilt axis follows the direction $\mathbf{u}_x$ and has coordinates $[y_R \ z_R]$ on the plane $(O, \mathbf{u}_y, \mathbf{u}_z)$; (b) same representation for any angle $\alpha_j$, where the projection of the point of interest on the axis $(O, \mathbf{u}_y)$ gives $y_k^j$.</figcaption></figure>

in Fig. 4c. Note that the orange dislocations are practically screw dislocations and the green dislocations are practically edge dislocations (which explains their residual contrasts in Fig. 4a).

The reconstructed dislocation network is visualized in Fig. 5. Dislocation 1 lies entirely within the (111) glide plane and runs nearly parallel to the specimen surface (Fig. 5a,c,e). In the lower region, dislocations 5 and 6 also glide in the (111) plane. While their appearance in 2D projections might suggest a dipole configuration the 3D reconstruction reveals parallel alignment and similar curvatures, indicating that they more likely form a dislocation pair undergoing correlated motion. Such behavior has been reported for dislocations interacting with short-range order (SRO) obstacles, nanoscale precipitates, or ordered nanodomains, as seen in particular in a medium-entropy Ni alloy [37] and in Ni-based superalloys [38–41]. However,
<figure><img src="image_6.png" /><figcaption>Figure 4: Burgers vector characterization: (a) Extinction of dislocations in the lower region under $g_3 = (\bar{3}11)$, corresponding to $b_2 = \pm \frac{1}{2}[01\bar{1}]$, while dislocations in the upper region remain in contrast. (b) Extinction of dislocations in the upper region under $g_2 = (11\bar{3})$, indicating $b_1 = \pm \frac{1}{2}[1\bar{1}0]$, with other dislocations remain in contrast. (c) ECC micrograph from the tilt series with the reconstructed dislocations superimposed and color-coded: green for $\frac{1}{2}[01\bar{1}]$ and orange for $\frac{1}{2}[1\bar{1}0]$. Dotted lines indicate slight surface contamination.</figcaption></figure>

in this study, our material is pure. This behavior could perhaps result from interaction with small obstacles, such as an ordered group of point defects, which acts as a barrier to dislocation. Dislocation 4 could not be fully traced due to reduced channeling contrast in its lower segment. However, overlays with additional tilt images confirm its continuity and suggest that it too glides in the (111) plane. Dislocations 2 and 3, close to screw dislocations, deviate from a single glide plane, indicative of cross-slip. Dislocation 2, in particular, shows a pronounced curvature, where the deviated slip is very clearly identified. Edge-on views of the cross-slip planes—(110) and (11$\bar{1}$)—confirm this interpretation (Fig. 5b,d,f,g), which corresponds to the known cross-slip behavior. Even though deviated slip in Ni is known [42], these characteristics would be ambiguous or invisible in 2D projections, highlighting the value of 3D reconstruction.

The reconstructed microstructure spans approximately 3 µm × 2.5 µm × 100 nm. This depth is consistent with ECCI's effective signal range under the employed conditions and aligns with previous estimates based on the extinction distance [43]. Mori and his co-workers estimated an analysis depth of 5 extinction distances. For pure Ni at 20 kV and for the diffracting vector $g_1 = (\bar{2}20)$, the extinction distance is approximately 21 nm.

The superposition of reconstructed dislocations onto ECC micrographs at various tilt angles confirmed geometric consistency with the real microstructure. All reconstructed dislocations exhibit pronounced curvature and multiple apparent pinning points, likely reflecting interactions with point defects formed during high-temperature crystal growth. Such features are likely introduced dur-

ing solidification and are consistent with the expected microstructure of as-grown single-crystal Ni [44]. In contrast, additional ECC micrographs taken near the nanoindentation site (not shown here) revealed straighter, more planar dislocations, consistent with deformation-induced plasticity. The quality of reconstruction strongly depended on surface condition and contrast. Surface debris and polishing artifacts presented the main sources of error during tracing, especially in regions where contrast was weak. While manual tracing enabled high-fidelity reconstructions in this study, it is time-consuming and subject to user variability. Automated tracing could be viable in the future if contrast quality allows for robust edge detection.

The resolution could be improved by increasing the angular separation of stereo pairs. However, this comes at the cost of reduced channeling contrast at high tilt angles due to increasing topographic contributions and the inherently low channeling signal fraction, estimated at less than 5% of the total BSE yield [45]. Use of high-Z materials and polished, low-relief surfaces are therefore critical for optimal results.

## 4. Conclusion

This study presents the first successful application of ECCT by reconstructing a 3D dislocation microstructure in a single-crystal of pure nickel. Using a stereo image pair acquired at moderate tilt angles, six dislocations were reconstructed via geometric triangulation. The resulting 3D microstructure reveals clear glide behavior, dislocation pairing, and cross-slip, features difficult to infer from 2D projections alone.
<figure><img src="image_7.png" /><figcaption>Figure 5: Reconstructed dislocation microstructure viewed at different tilt angles, visualized using UCSF Chimera [46]. (a) Total reconstructed tomographic volume viewed at an inclination angle of -5°, showing most dislocations in plane; dislocations are labeled and color-coded according to their Burgers vectors as seen in Fig. 4. (b,d) Isolated views of dislocation 2, showing the cross-slip plane (110) edge-on at an inclination angle of -60° and (111) edge-on at an inclination angle of 85°. (c) Total reconstructed volume viewed at a projection angle of 40°. (e) Total reconstructed volume with the major slip plane (111) edge-on; dotted lines indicate habit planes in edge-on orientation. (f,g) Isolated views of dislocation 3, showing the cross-slip plane (111̄) edge-on at an inclination angle of -25° and (111) edge-on at an inclination angle of 85°.</figcaption></figure>

Unlike previous SEM-based 3D approaches that rely on destructive serial sectioning, ECCT is non-destructive, however the depth of the reconstruction is limited by the extinction distance. Compared to TEM-based stereo reconstruction, ECCT is faster, requires simpler alignment, and relies only on conventional SEM instrumentation. While TEM offers superior resolution and coherence, its use is constrained by limited sample size and preparation demands. ECCT, by contrast, is compatible with bulk samples and can be readily integrated into multimodal or *in-situ* experimental setups.

Nonetheless, this proof-of-concept highlights current limitations. Manual tracing remains labor-intensive and prone to subjective error. Dislocations with weak contrast or located in highly curved regions are challenging to reconstruct reliably. Limited tilt angles restrict depth resolution, and the degradation of channeling contrast at

high tilts, due to both topographic effects and weak signal, poses additional challenges.

Future work focus on automating tracing through improved image processing.

Furthermore, combining ECCT with *in-situ* deformation or heating experiments opens a pathway to pseudo-4D studies. As the method matures, ECCT has the potential to become a tool for mesoscale 3D defect analysis in crystalline materials.

## Acknowledgments

The authors would like to thank F. Houlmont for his help with aligning and manually retracing the dislocations. The authors acknowledge financial support from the French National Research Agency (ANR) through grants ANR-PRC-2022-MAMIE-NOVA (ANR-22-CE08-
20018). The TEM national facility in Lille (France) is sup-
ported by the Conseil Regional du Nord-Pas de Calais, the
European Regional Development Fund (ERDF), and the
Institut National des Sciences de l'Univers (INSU, CNRS).

Author contributions

CRediT authorship contribution statement

**T. Weidner:** Conceptualization; Data curation; Formal analysis; Investigation; Methodology; Visualization; Roles/Writing – original draft; and Writing – review & editing. **R. Gautier:** Conceptualization; Formal analysis; Investigation; Methodology; Visualization; and Writing – review & editing. **A. Guitton:** Conceptualization; Funding acquisition; Validation; Visualization; and Writing – review & editing. **A. Mussi:** Conceptualization; Formal analysis; Investigation; Methodology; Validation; Visualization; Writing – review & editing; and Supervision.

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.

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