# Dislocation substructures and networks induced by compression test in polycrystalline UO2 at 1550 °C

Claire Onofri, Xaviere Iltis, Jean Philippe Monchoux, Jonathan Amodeo, Ronan Madec, Daniel Caillard, Catherine Sabathier-Devals, Herve Palancher, Julie Fouet, Doris Drouan, et al.

► To cite this version:

Claire Onofri, Xaviere Iltis, Jean Philippe Monchoux, Jonathan Amodeo, Ronan Madec, et al. Dislocation substructures and networks induced by compression test in polycrystalline UO2 at 1550 °C. Acta Materialia, 2025, 304, pp.121827. cea-05419850

HAL Id: cea-05419850

https://cea.hal.science/cea-05419850v1

Submitted on 16 Dec 2025

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# Dislocation substructures and networks induced by compression test in polycrystalline UO₂ at 1550 °C

C. Onofriª, X. Iltisª, J.P. Monchouxᵇ, J. Amodeoᶜ, R. Madecᵈ,ᵉ, D. Caillardᵇ, C. Sabathierª, H. Palancherª, J. Fouetª, D. Drouanª, M. Legrosᵇ

ª CEA, DES, IRESNE, DEC, Cadarache, F-13108 Saint Paul Lez Durance, France

ᵇ CEMES, CNRS, 29 rue Jeanne Marvig, 31055 Toulouse Cedex 4, France

ᶜ Aix Marseille Université, Université de Toulon, CNRS, IM2NP, 13397 Marseille, France

ᵈ CEA, DAM, DIF, F-91297 Arpajon, France

ᵉ Université Paris-Saclay, CEA, Laboratoire Matière en Conditions Extrêmes, F-91680 Bruyères-le-Châtel, France

**Keywords**

Nuclear ceramics, plasticity, sub-grain boundary, EBSD, TEM

**Abstract**

Understanding the plastic behavior of UO₂ fuel pellets is a major challenge for nuclear safety, particularly during off-normal operating conditions of pressurized water reactors. This study provides insights into dislocation interactions and sub-grain boundary formation under load at high temperatures. Characterizations using transmission electron microscopy and electron backscattered diffraction are performed on polycrystalline UO₂ pellets deformed using uniaxial compression tests at 1550 °C with a constant strain rate. For the first time, a detailed characterization of various sub-grain boundaries is conducted in UO₂, including dislocation networks composed of one to three independent dislocation populations with various types of dislocation junctions. Experiments are interpreted using dislocation dynamics simulations and theoretical models, both relying on the elastic theory. This study helps at improving our understanding of high-temperature plastic deformation mechanisms in nuclear fuel at the nanoscale.

## 1. Introduction

Uranium dioxide (UO₂), the nuclear fuel most commonly used in pressurized water reactors (PWRs), undergoes significant microstructural changes during in-pile irradiation, affecting its mechanical and thermal properties, ultimately limiting its in-reactor lifetime. During operation and beyond a burn-up of about 40 GWd/t_u, at the fuel pellet periphery, where the temperature is the lowest and the concentration of fission products is particularly high, the original fuel grains (typically about 10 µm in diameter) are subdivided into finer grains of about 0.2 µm in size. This microstructure is known as the high burn-up structure (HBS) [1][2][3]. At higher burn-ups, sub-grains with low misorientation appear near the center of the pellets, where the temperature is the highest [4]. Such microstructural changes are due to the combined action of various factors throughout the irradiation process. Indeed, energetic fission products dissipate their energy through various processes, initially mainly via inelastic interactions and later mainly through elastic collisions, causing significant damages along their paths
before coming to rest in the UO₂ matrix, thereby contributing to pellet swelling. The fuel is also subjected to various mechanical stresses during irradiation. Also, due to their low thermal conductivity, pellets are subjected to significant radial temperature gradients: temperatures at the center and periphery of the pellets are of the order of 1000-1100 °C and 400-500 °C, respectively. In the early stages of irradiation, a differential expansion between the pellet center and its periphery induces tangential tensile stresses. In this temperature range, the fuel pellets are also subjected to irradiation-induced creep under the combined effect of fission spikes, moderate temperatures, and stresses. Then, above 30 GWd/t_u, fuel swelling associated with irradiation-induced creep in the cladding leads to contact and interaction with the cladding. Subsequently, this pellet-to-cladding interaction may be accentuated during off-normal power transients, characterized by a high-power rise within a time frame of about a few tens of milliseconds to several minutes (depending on the exact scenario). During such power transients, the pellet center temperature increases sharply, from 1200 to more than 2000 °C. These extreme conditions and temperature gradients strongly modify the fuel pellet mechanical behaviour by inducing compressive loads at the center of the pellet (up to c.a. 100 MPa) and tensile stresses within the cladding.

During creep tests at high temperatures, two deformation domains are usually defined for UO₂ polycrystals, depending on the level of applied stress. The transition from one to the other takes place at a transition stress value στ [5][6]. While the secondary creep rate regime is usually described using a power-law, the nature of the elementary mechanisms governing the plastic deformation of nuclear fuel in the two regimes are poorly known. Moreover, some of the conclusions drawn in the literature are flawed by the insufficient characterization of dislocation substructures and the wide dispersion of self-diffusion measurements. Thus, from our knowledge, there is no study where the characterization of complete deformation processes of UO₂ polycrystal deformed at high-temperature has been properly addressed. Still, it is generally accepted that UO₂ polycrystal deformation at high-temperature is governed by a diffusion creep mechanism (such as Nabarro-Herring or Coble mechanisms [7]) for stresses below the transition stress. Above the transition stress, a dislocation creep mechanism is supposed to operate [8][9]. Depending on temperature and strain rate, deformation is induced by dislocation glide, which may be controlled by climbing over obstacles. But again, the exact nature of the mechanisms involved remains speculative. Finally, grain boundary (GB) sliding is often cited as the reason for high stress exponent values [10][11][12][13]. Different mechanisms can be implemented to accommodate the incompatibilities generated during sliding [14][15]: Rachinger gliding, in which dislocation movement occurs within the grains, and Lifshitz gliding, which is based on diffusion processes. Dherbey *et al.* [12] observe hexagonal dislocation networks showing irregularities after creep tests between 10 and 80 MPa at 1465 °C, using transmission electron microscopy (TEM). They assume that this is due to GB sliding assisted by dislocation insertions and extractions. Other studies, using TEM [16][17] or accurate electron channeling contrast imaging (accurate-ECCI) [18][19][20], report sub-grain boundaries (sGB) made of various networks. Mainly hexagonal networks are described in the literature and are attributed to dislocation cross slip in {111} crystallographic planes while double slip conditions in {100} or {110} are gathered [17]. More complex networks are also reported at the highest temperatures, with parallel dislocations or square network parts, possibly involving climb [18][20]. Unfortunately, no more details on these complex sGBs can be found so far in the literature. It is therefore necessary to provide a more comprehensive description of the complex dislocation microstructure obtained under thermo-mechanical conditions representative of off-normal operating conditions to better assess and predict the fuel mechanical integrity.
This work focuses on sGBs obtained after constant strain rate uniaxial compression tests conducted at 1550 °C on polycrystalline UO₂ pellets, using TEM and electron backscattered diffraction (EBSD). Experimental observations are compared to theoretical models and dislocation dynamics (DD) simulations, both relying on the elastic theory. A detailed characterization of the dislocation networks will help us to define the features of the sGBs generated during these tests, thereby providing deeper insights into the high temperature plastic deformation mechanisms of UO₂ polycrystals at small-scales.

## 2. Materials and methods

All the technical details about the characteristics of UO₂ pellets investigated in this study can be found in [13] and [21]. Three pellets were subjected to uniaxial compression tests at 1550 °C, with a constant strain rate ($\dot{\epsilon} = 1 \times 10^{-4} s^{-1}$) up to final strain values of 1.7%, 8.1%, and 22%. These tests were conducted using an Instron 1185 compression test machine under a reducing atmosphere (95% Ar, 5% H₂) to prevent any stoichiometry changes.

For TEM and EBSD characterizations, parallel sections were extracted from the center of the strained pellets, where deformation is maximal [13], with the loading axis perpendicular to the samples. Before preparing thin foils, these sections were polished. EBSD maps were acquired using a FEI NovaNano SEM 430 equipped with a Symmetry camera from Oxford Instruments, under conditions similar to those described in [18]. The acquisition step size was set to 0.26 µm, and the indexing rate of EBSD maps exceeded 98% (non-indexed pixels primarily corresponded to manufacturing porosities). The EBSD maps were then post-processed and analyzed using Channel 5 and AZTEC Crystal software to reliably quantify low-angle GBs, following the optimized protocol presented in [19]. The critical misorientation angle chosen to define a GB in UO₂ was set at 10°. Consequently, the term 'sGB' used in the following only refers to lines with angular misorientations ranging between 0.3° and 10°. It is worth noting that sGBs with misorientations lower than 0.3° may be present in such deformed UO₂ pellets [18] but could not be accurately detected by EBSD under the current acquisition conditions.

TEM samples were prepared by mechanical polishing and chemical etching. Further details can be found in [21]. TEM observations were performed using a 200 kV TALOS F200X microscope at CEA Cadarache (France), with a single tilt sample holder allowing ± 45° tilting around the holder's axis (α). Complementary TEM examinations were also conducted at the CEMES laboratory (Toulouse, France) using a 200 kV JEOL 2010 microscope, equipped with a double tilt sample holder (α, β) for 3D reconstruction of a grain part, allowing ± 60° tilting around the holder's axis (α). As described in more detail in [22], a diffraction vector **g** was placed along the holder's axis, and images were acquired every 1° by maintaining the same diffraction vector (using **β** tilt). The ImageJ plug-in TomoJ was used for tomographic reconstruction, and TomViz was employed to visualize the 3D tomographic data.

For the dislocation analysis, Burgers vectors **b** are determined using the extinction criterion $g \cdot b = 0$ (where **g** represents various diffraction vectors). The line direction, which is crucial for network analysis and the study of line character, is established using the tangent method. This method involves obtaining tangents at a specific point on the studied line, imaged under two different and spaced diffraction vectors. The intersection of these tangents corresponds to the line direction (see Supplementary Materials-2). The sGB plane corresponding to the dislocation network viewed edge-on is determined using the tilt method, as described in more detail in [23]. This method involves studying the dislocation network using various diffraction vectors **g** by tilting the sample. As the sample
is tilted, the projected width of the sGB changes. When the sGB plane is parallel to the electron beam, the projection of the sGB appears edge-on (rectilinear). When it is not possible to tilt the sample sufficiently to observe the sGB edge-on, a sinusoidal function can be used to fit the variation in the projection width of the sGB as a function of the tilt angle $α$ and extrapolate the edge-on position.

Dislocation dynamics (DD) simulations were performed using the lattice-based code MobiDiC to test the formation and stability of dislocation networks [24]. In particular, MobiDiC was recently used to model dislocation interactions and composite slip processes in $UO_2$ [25][26]. Both isotropic ($μ = 93.8$ GPa, $ν = 0.35$, with $μ$ the shear modulus and $ν$ the Poisson's ratio) and anisotropic elastic theories were used for comparison when necessary. Anisotropic simulations relied on anisotropic line tension computed using Disdi [27], dislocation fields computed using the Willis method [28] and room temperature elastic constants ($C_{11} = 396$ GPa, $C_{12} = 121$ GPa, $C_{44} = 64$ GPa) [29]. The DD simulations of dislocation networks were inspired by interaction cartography simulations [25], in which initially intersecting straight dislocations belonging to various slip systems are allowed to relax. Specific boundary conditions were employed to simulate intersecting stacks of parallel dislocations, with Burgers vectors derived from TEM observations. Indeed, the midpoints of the parallelogram pattern sides formed by the initial dislocation networks before relaxation are symmetrical and represent stable points of the configuration. By pinning these points for four adjacent parallelograms (see Supplementary Materials-2 Figure C), the simulation models two intersecting dislocation lines (representative of the substructure of interest) undergoing relaxation. The final network was then obtained through translations. The Burgers and discretization lengths were set to 0.387 nm and 30 nm, respectively. A viscous dislocation mobility law, typical of high-temperature behaviors, $v(τ) = τ.b/B$, with $τ$ is the shear stress and $B$ a damping coefficient set to $4.5 × 10^5$ Pa.s, were used for all simulations. A time step of 0.5 ps, low enough to ensure that the dynamics of the network formation is respected, was employed.

### 3. Results

After deformation, the defect microstructure of the samples is characterized by various dislocation networks at the origin of sGBs as well as isolated dislocation lines, the latter having been thoroughly characterized in a previous study [21]. These dislocations do not exhibit preferred crystallographic line directions and are either connected to porosities or located near GB/sGBs, where they often interact or become entangled. Besides, sGBs are characterized by various dislocation networks, which often exhibit irregularities such as extrinsic dislocations or local mesh distortions. For the rest of the document, the dislocations constituting the ordered patterns of the networks are called intrinsic dislocations. In contrast, dislocations originating from the grain, i.e., from outside the grain boundary, are called extrinsic dislocations. Extrinsic dislocations can disrupt the equilibrium structure of the grain boundary by destroying the periodicity of the intrinsic dislocation arrangement. This section first presents EBSD statistical data, followed by a detailed analysis of network geometry using conventional TEM. Additionally, DD simulations are presented to better elucidate the formation of some of the dislocation networks. Finally, examples of irregularities due to dislocation line interactions with the networks are presented.

#### 3.1. EBSD results
At the lowest strain value (1.7%), the EBSD map (Figure 1(a)) reveals very few sGBs. Figure 2 shows that only 3% of the boundaries have a misorientation angle $\theta < 10^\circ$, indicating that almost only original GBs are present. Notably, the highest linear fraction of sGBs (1.1%) has a misorientation angle between 0.3° and 0.5°, suggesting that few sGBs form and their misorientation is low. In contrast, samples strained at medium (8.1%) and highest (22%) strain values exhibit numerous sGBs (Figure 1(b) and (c)). The linear fractions of sGBs with $\theta < 10^\circ$ are 26.7% and 43.2%, respectively (Figure 2). The corresponding linear densities (in total length with respect to the map surface) are $6.1 \times 10^2 \text{ cm/cm}^2$ and $1.4 \times 10^3 \text{ cm/cm}^2$, respectively, indicating a factor of two when comparing 8.1% and 22% of strain. For the sample strained up to 8.1%, nearly all sGBs have misorientation angles $< 2^\circ$. At 22% strain, the linear fraction remains relatively constant for $\theta < 1^\circ$ but increases significantly for $\theta$ between 1° and 5°. These findings align with previous observations by Ben Saada et al. [30], in which both the linear fraction and misorientation of sGBs increase with strain level. We can also suppose that between 8.1% and 22% strain, new low-misoriented sGBs (some undetectable by EBSD due to misorientation $< 0.3^\circ$) have continuously formed, while existing boundaries became increasingly misoriented.

<figure><img src="image_2.png" /><figcaption>Figure 1. EBSD misorientation maps obtained from samples strained at 1550 °C with a constant strain rate up to: (a) 1.7%, (b) 8.1% and (c) 22%. The background gray levels correspond to the Kikuchi pattern quality index. The compression directions are normal to the maps. Colors are available online.</figcaption></figure>
<figure><img src="image_3.png" /></figure>

Figure 2. Linear fraction of GBs and sGBs as a function of the misorientation angle θ, measured by EBSD on samples strained at 1550 °C with a constant strain rate up to three different strain values. Colors are available online.

## 3.2. Dislocation network characteristics – TEM and DD results

Various types of sGBs are identified in the three samples, dividing the grains into misoriented sub-grains involving different numbers of dislocation populations. Only sGBs with low misorientation angles ( (< 1°) are studied in detail using conventional bright field (BF) TEM. Five different types of sGBs are encountered and are described first. In **Supplementary Materials-1**, the Frank formula is applied [31] as used in the Bollmann model [32] to estimate whether or not the different sGBs induce a long-range stress field and are therefore stable. We found that this is generally the case.

### 3.2.1. Sub-grain boundaries with one dislocation group

These sGBs are characterized by parallel edge dislocation lines with the same Burgers vector **b**, what corresponds to symmetrical tilt sGBs. An example is shown in **Figure 3**. In this case, parallel dislocation lines with the same contrast across different TEM images are predominantly observed. Their Burgers vector (b//) is found to be parallel to [101]. In **Figure 3(b)**, the sGB is viewed edge on (only the emergence points of the dislocation lines at the lamella surface are visible). It appears to lie on the (202) plane, as determined by stereographic analysis (**Figure 3(c)**). Since the Burgers vector is perpendicular to the sGB plane, dislocation rearrangement within this sGB can only occur by pure climb.

The misorientation angle θ was calculated using the following formula [32]:
$$h = \frac{\|b\|}{2\sin\frac{\theta}{2}}$$

Where h is the distance between two dislocations.

In Figure 3(b), the distance measured between two dislocation lines (averaged over 16 lines) is 106 nm. The misorientation angle is thus 0.2°. These very low misoriented sGBs are likely to be undetectable by EBSD under the acquisition conditions used in this study. It is therefore important to emphasize that there are likely more very low misoriented sGBs (with misorientation angles less than 0.3°) than those evidenced by EBSD.

<figure><img src="image_4.png" /><figcaption>Figure 3. Symmetrical tilt sGB involving one dislocation group generated during compression test at 1550 °C with a constant strain rate (10⁻⁴ s⁻¹) up to a strain of 1.7%. (a, b) BF TEM images showing the parallel dislocations forming the sGB under different diffraction conditions. In image (b), the sGB is seen edge on. (c) Stereographic representation corresponding to image (b) obtained using the Stereoproj software [33]. The Burgers vector **b**// is circled in blue and is parallel to the diffraction vector **g** = [202]. The trace of the sGB, seen edge on, is reported in blue and corresponds to the trace of the (202) plane. Colors are available online.</figcaption></figure>
3.2.2. Sub-grain boundaries with two parallel independent dislocation populations

These sGBs are made of parallel dislocation lines (with the same direction **x**) with two distinct Burgers vectors (**b**₁ and **b**₂), what corresponds to asymmetrical tilt sGBs. Figure 4 illustrates an example of this sGB type. As shown in the different TEM images (Figure 4(a-e)), three dislocation populations are involved in this sGB. While being all parallel, they exhibit different contrasts/extinctions for a same diffraction vector. However, the dislocations indicated by the blue arrows are in the minority compared to the other two, indicated respectively by green and red arrows. Therefore, we can consider that this sGB is primarily made of those dislocations coloured in green and red. The Burgers vectors of the green (**b**₁) and red (**b**₂) dislocations were found to be parallel to [011] and [011], respectively. In Figure 4(b), the sGB appears nearly edge on. A reversal of the tilt of the dislocation lines is observed when comparing Figure 4(a) with the others. Thus, the sGB plane is parallel to the electron beam for a tilt angle α between -39° and -20°. Using the corresponding stereographic representation (Figure 4(f)), we can see that the trace of the sGB is close to the trace of the (014) plane, which is parallel to the electron beam at -25°. Since both Burgers vectors, **b**₁ and **b**₂, are not perpendicular to the sGB plane, the rearrangement of the dislocations is likely to occur by mixed climb [23][34].
<figure><img src="image_5.png" /><figcaption>Figure 4. Asymmetrical tilt sGB primarily involving two parallel dislocation populations (indicated by green and red arrows), induced by a compression test at 1550 °C with a constant strain rate (10⁻⁴ s⁻¹) up to a strain of 8.1%. (a-e) BF TEM images showing the parallel dislocations forming the sGB under different diffraction conditions. In image (a), dislocations pointed by green and red arrows are out of contrast. The dislocations indicated by blue arrows are in the minority compared to the other two. In image (b), the sGB is almost seen edge on. (f) Stereographic representation corresponding to image</figcaption></figure>
(b). The Burgers vectors $b_1$ and $b_2$ are circled in green and red. The trace of the sGB is reported in dark grey and is close to the trace of the $(0\bar{1}4)$ plane. Colors are available online.

### 3.2.3. Sub-grain boundaries with two independent dislocation populations and Burgers vectors oriented at 120° to each other

These sGBs consist of two independent dislocation populations with Burgers vectors along <110> directions, oriented at 120° to each other. In some cases, the dislocations react to form a junction with a Burgers vector along a third <110> direction, what leads to the formation of hexagonal dislocation networks, as shown in Figure 5. If the sGB plane contains the three Burgers vectors (i.e., if it is a {111} type plane), the sGB is of twist character. If the sGB plane does not contain the three Burgers vectors, the sGB is of mixed character.

In Figure 5, one can identify three dislocation populations labelled $d_1$, $d_2$ and $d_3$. They are characterized by $(x_1^l, x_1^f, b_1)$ (in green), $(x_2^l, x_2^f, b_2)$ (in red) and $(x_3^l, x_3^f, b_3)$ (in blue) with $x_l^l$ and $x_l^f$ the dislocation direction before/after relaxation of the boundary and $b_l$ the Burgers vectors along [011], $[\bar{1}\bar{1}0]$ and $[\bar{1}01]$, respectively. In the lower part of the network, two intersecting (but not yet reacting) dislocation lines can be observed (circled in white in Figure 5). These dislocations should allow the identification of initial reacting dislocations (before any contact reaction and junction formation). The two dislocation segments have Burgers vectors $b_1$ and $b_3$ and thus belong to groups 1 and 3, respectively.

These two dislocations can form a junction according to the following reaction:

$$ \frac{1}{2}[0\bar{1}\bar{1}] + \frac{1}{2}[\bar{1}01] \rightarrow \frac{1}{2}[\bar{1}\bar{1}0] $$

As shown in the stereographic representation (cf. Figure 5(c)), the three Burgers vectors belong to the same $(\bar{1}\bar{1}1)$ plane (normal to this plane circled in black) and $-b_1$ and $b_3$ are oriented at 120° to each other. In this example, the network width varies non-uniformly along the sGB as the sample is tilted. In Figure 6(a), only the middle part of the sGB is seen edge on, the upper part is close of being edge on, whereas the lower part is still far from it. This indicates that this sGB belongs to different planes. The associated stereographic representation (Figure 6(b)) shows that the middle part lies on a high-index plane close to (718) (orange trace). By fitting the upper part width variation as a function of $\alpha$ tilt using a sinusoidal function, we predict the upper part should be edge on for $\alpha = -41°$ with a trace corresponding to a plane close to (318) (dark green trace). This sGB does not lie on the $(\bar{1}\bar{1}1)$ plane (containing the three Burgers vectors) and is therefore of mixed character. Additionally, the hexagonal network characterized here is only planar by portions. The forming dislocation lines seem to be coplanar within a given portion (their ends lying along a single straight line), while the three $b_i$ vectors do not belong to the different network planes.

A detailed analysis of the dislocation line characteristics and junction geometry is performed for the upper part of the dislocation network and compared to DD simulation results. Details about the initial $(x_i^l)$ and final $(x_i^f)$ dislocation direction determination are provided in the Supplementary Materials-2. The different directions are reported in Figure 5 and Table 1 for the upper part of the sGB. The angles between $x_i^l$ and $x_i^f$ with Burgers vectors $b_i$ (referred as $\beta_i^l$ and $\beta_i^f$, respectively) and the lengths of the different dislocations ($L_i^l$ and $L_i^f$) are also indicated in Table 1. The two initial dislocations have mixed characters with a dominant screw component for $d_3$. The plane which contains the direction of
the initial dislocation line $x_1^I$ and the Burgers vector $b_1$ is close (13° off) to the (200) slip plane (referred as $n_1^I$ in Table 1). The direction of the initial dislocation line $x_3^I$ belongs to the (111) slip plane. Note that the final dislocation line directions, obtained by the tangent method, belong to the same (318) plane determined by fitting the width change of the upper part with the α tilt (see Supplementary Materials-2). Following the simulation protocol described in the method section, the formation of this junction is studied by DD using both isotropic and anisotropic elasticity. The two cases only present very slight differences (cf. Table 1). The dislocations $d_1$ ($b_1 = 1/2[011]$) and $d_3$ ($b_3 = 1/2[10\bar{1}]$), which react to form the junction $d_2$ ($b_2 = 1/2[110]$), are positioned on a {100}, {110}, or {111} crystallographic plane. The plane is chosen as close as possible to the dislocation's initial slip plane observed in the experiment, i.e., (200) for $d_1$ and (111) for $d_3$. The dislocation line length is set to 150 nm to match the average dislocation line length measured experimentally. This rigorous crystallographic approach implies that the junction $d_2$ forms along the $[0\bar{1}1]$ direction in a $(\bar{1}11)$ plane, which also contains the final direction $x_2^F$. To remain in crystallographic planes, the initial dislocation line directions of $d_1$ and $d_3$ may differ significantly from those identified experimentally. This is particularly the case for dislocation $d_1$. In this case, the dislocation character in the simulation is maintained very close to the experimental one, preserving comparable line energies between reacting dislocations. Concerning the junction direction, the character characterized in the experiment differs markedly from the character imposed by crystallography. This leads to a junction with larger line energy. Junction dislocation network simulations rely on ideal slip planes as imposed by the lattice-based DD formalism, whereas experiments shown here often exhibit planar distortions. While this assumption has consequences on the spatial orientation of the dislocation networks and thus the detail of dislocation line energy, we believe it does not impact heavily the reaction which is at the roots of the network shape. Still, the formation of junctions of about 50 nm length is observed in the experiment and in the DD simulations (both isotropic and anisotropic). Indeed, the overall energetics of this junction (cf. [25]: $A_{11}$ reacting with $B_{1114}$ to form a $^{III}_{1/IIIa}$ gliding junction) is among the most favourable of all junctions in the fluorite structure. As shown by Portelette et al. [25], the recombination rate for this reaction is about 44%, leading to one of the highest junction coefficients (of the order of 0.4). In this case, the elastic energy diminution comes mainly from the Burgers vector norms involved and is only modulated by the effect of dislocation characters. On the other hand, the reaction geometry is quite different between the simulations and the experimental case. In the simulations, a three-dimensional junction is formed (Figure 5(d)). It is formed solely by slip on crystallographic planes, without changing these planes. Note that the two dislocation lines remain quite far from the screw orientation, which *a priori* precludes the activation of cross-slip-type mechanisms. On the other hand, there is an evolution in the experiment from a three-dimensional configuration (initial common plane can be defined but different from the final plane) towards a common habit plane between the two dislocations and the junction formed. Note that this final habit plane (318) does not contain any of the Burgers vectors involved and is therefore not a slip plane for any of these dislocations. The resulting junction is therefore, in the strict crystallographic sense, not coplanar. Even if the junction direction (($x_2^F$ ≈ $[\bar{7} \bar{1}14]$) lies in its crystallographic slip plane and has clearly slipped from the intersection of the initial slip planes ($[0\bar{1}1]$), this is not the case for $d_1$, which has moved further away from its slip plane (200), while $d_3$ appears to have changed its slip plane from (111) to (020). Such behaviour cannot be assessed by slip or cross-slip, but requires much complex processes such as climb or mixed climb, perhaps combined with cross-slip.
<figure><img src="image_6.png" /></figure>

Figure 5. Mixed sGB mainly characterized by two dislocation populations forming a hexagonal network with junctions, induced by a compression test at 1550 °C with a constant strain rate (10⁻⁴ s⁻¹) up to a strain of 22%. (a, b) BF TEM images showing the hexagonal network under different diffraction conditions. In image (a), *d*₃ is out of contrast. In image (b), *d*₂ is out of contrast. (c) Stereographic representation at 0° where the dislocation line directions *x*₁ and *x*₂ for the upper part of the network and Burgers vectors *b*₁, *b*₂ and *b*₃ are indicated. The plane containing *b*₃ and *x*₁ is indicated in blue. The closest crystallographic plane containing *b*₁ and *x*₁ is indicated in green. The plane which contains *b*₂ and *x*₂ is indicated in red. (d) Glissile junction formed using anisotropic elasticity, view in (3 1 8) plane - the experimental dislocation network plane. Colors online.
<figure><img src="image_7.png" /><figcaption>Figure 6. (a) BF TEM image of the sGB, with the middle part viewed edge on. (b) The corresponding stereographic representation. The trace of this part is reported in orange and is close to the trace of a high index plane (718). The trace of the upper part is reported in dark green and corresponds to the trace of another high index plane (318). The Burgers vectors $b_1$, $b_2$ and $b_3$ are circled. Colors are available online.</figcaption></figure>
<table><caption>Table 1. TEM and DD simulation characteristics of the glissile junction observed in the sGB made of two independent dislocation populations with Burgers vectors oriented at 120° from each other.</caption><thead><tr><th>n<sup>network</sup></th><th>Dislocation line</th><th>d<sub>1</sub></th><th>d<sub>3</sub></th><th>Junction = d<sub>2</sub></th></tr></thead><tbody><tr><td></td><td>b</td><td>1/2 [0 1 1]</td><td>1/2 [1 0 1]</td><td>1/2 [1 1 0]</td></tr><tr><td rowspan="8">TEM<br/>≈ (3 1 8)<br/>final one</td><td>x<sup>I</sup></td><td>≈ [3 18 1]</td><td>≈ [1 1 0]</td><td>-</td></tr><tr><td>β<sup>I</sup></td><td>44°</td><td>60°</td><td>-</td></tr><tr><td>L<sup>I</sup></td><td>120-180 nm</td><td>120-180 nm</td><td>-</td></tr><tr><td>n<sup>I</sup></td><td>13° from (2 0 0)</td><td>(1 1 1)</td><td>-</td></tr><tr><td>x<sup>F</sup></td><td>≈ [6 10 1]</td><td>≈ [8 0 3]</td><td>≈ [7 11 4]</td></tr><tr><td>β<sup>F</sup></td><td>50°</td><td>22°</td><td>22°</td></tr><tr><td>L<sup>F</sup></td><td>90-110 nm</td><td>60 nm</td><td>50-60 nm</td></tr><tr><td>n<sup>F</sup></td><td>40° from (2 0 0)</td><td>4° from (0 2 0)</td><td>(1 1 1)</td></tr><tr><td rowspan="8">DD<br/>≈ (0 0 1)<br/>tridimensional</td><td>x<sup>I</sup></td><td>≈ [0 1 0]</td><td>≈ [1 1 0]</td><td>-</td></tr><tr><td>β<sup>I</sup></td><td>45°</td><td>60°</td><td>-</td></tr><tr><td>L<sup>I</sup></td><td>150 nm</td><td>150 nm</td><td>-</td></tr><tr><td>n<sup>I</sup> = n<sup>F</sup></td><td>(2 0 0)</td><td>(1 1 1)</td><td>(1 1 1)</td></tr><tr><td>x<sup>F</sup><sub>iso</sub></td><td>≈ [0 25 12]</td><td>≈ [52 29 12]</td><td>[0 1 1]</td></tr><tr><td>β<sup>F</sup><sub>iso</sub></td><td>20°</td><td>33°</td><td>60°</td></tr><tr><td>L<sup>F</sup><sub>iso</sub></td><td>112 nm</td><td>130 nm</td><td>68 nm</td></tr><tr><td>x<sup>F</sup><sub>aniso</sub></td><td>≈ [0 54 19]</td><td>≈ [52 33 19]</td><td>[0 1 1]</td></tr><tr><td>β<sup>F</sup><sub>aniso</sub></td><td>26°</td><td>39°</td><td>60°</td></tr><tr><td>L<sup>F</sup><sub>aniso</sub></td><td>118 nm</td><td>132 nm</td><td>55 nm</td></tr></tbody></table>

### 3.2.4. Sub-grain boundaries with two independent dislocation populations, Burgers vectors oriented at 90° to each other

Such sGBs are composed of two independent populations of dislocations with <110> Burgers vectors, oriented at 90° to each other, as illustrated in Figure 7. Depending on their configuration, they can form either a square network without interaction or a hexagonal network with <100> Hirth junctions, which induce a third population of dislocations. If the sGB plane contains the Burgers vectors (i.e., if it is a {100} type plane), the sGB is of twist character; otherwise, it is of mixed character. In Figure 7, three main dislocation populations are highlighted in this sGB: $d_1$ (in green), $d_2$ (in blue), and $d_3$ (in red). Their Burgers vectors are parallel to $[1\overline{1}0]$, $[\overline{1}10]$ and to $[0\overline{1}0]$, respectively. These three dislocations lead to the formation of a Hirth junction following the reaction:

$$ \frac{1}{2}[1\overline{1}0] + \frac{1}{2}[\overline{1}10] \rightarrow [0\overline{1}0] $$

As shown in the stereographic representation (cf. Figure 7(c)), the three Burgers vectors belong to the same (002) plane with $b_1$ and $b_2$ oriented at 90° to each other. They form a hexagonal network, where $d_3$ is shorter than the other dislocation segments, particularly in the lower part of the sGB. The network width varies with sample tilting, reaching a near-maximum for $\alpha = 7^\circ$, suggesting a habit plane close to the lamella plane. For the upper part of the sGB (where $d_3$ is longer), the habit plane is close to $(12\overline{3})$ (cf. Supplementary Materials-2). Therefore, the (002) plane containing the Burgers vectors is unlikely to be the habit plane, indicating a mixed character for this sGB.

This Hirth junction has not been previously observed experimentally in $UO_2$. Considering only the dependence of line energy on $b^2$, a Hirth junction does not reduce the total energy in the first
approximation, as the Burgers vectors are orthogonal and $b_{junction}^2 = b_1^2 + b_2^2$. The energy reduction driving the formation of these junctions must therefore arise from the dependence of the dislocation line energy on their character (i.e., the relative proportion of edge and screw components). In potassium chloride crystals, Amelinckx [35] observe <100> Burgers vector dislocations at the intersecting points of dislocations forming cross-grids, facilitated by the stress field of a third dislocation or a specific initial angle between dislocations. Using the elastic theory and DD simulations, Portelette et al. [25] only barely observed the formation of such junctions in case of non-coplanar dislocations in UO₂, with a particularly small junction lobe on the dislocation reaction map. The partial validation of the Frank formula (see Supplementary Materials-1) indicates that the stability of the network involving Hirth junctions depends on the length of the <100> dislocation.

A detailed analysis of the dislocation line and junction geometry is conducted for the upper part of the network and compared with DD results. The determination of the initial ($x_i^I$) and final ($x_i^F$) dislocation line directions are provided in Supplementary Materials-2. Figure 7 and Table 2 present the different directions for the upper part of the sGB. Table 2 also lists the angles between initial and final dislocation line directions with Burgers vectors $b_i$ (referred as $\beta_i^I$ and $\beta_i^F$, respectively) and the lengths of the different dislocations ($L_i^I$ and $L_i^F$). The two initial dislocations exhibit mixed characters, with a dominant screw component for $d_1$.

For the upper part, the plane containing the initial dislocation direction $x_1^I$ and the Burgers vector $b_1$ is significantly misaligned with the crystallographic slip planes, being 15° out from (11̄1) and 20° from (220). In contrast, the plane containing $x_2^I$ and $b_2$ is closely aligned with the slip plane (11̄1), with only 8° deviation (see Figure 7(c)). The formation of this Hirth junction is investigated using DD simulation using the previously mentioned protocol (cf. Section 3.2.3). The dislocations length is set to 110 nm and additional details are summarized in Table 2. Considering initial planes (11̄1) for $d_1$ dislocations and (11̄1) for $d_2$ dislocations, the intersection direction is along [011], and the plane containing $b_3$ and [011] is thus (2̄00). The initial dislocation line directions of $d_1$ and $d_2$, which belong to a crystallographic plane in the simulation, differ by a few degrees from those experimentally identified. Moreover, the junction character observed experimentally differs significantly from the character imposed by the crystallography in the simulation, resulting in a higher junction line energy. The simulation using the isotropic elasticity leads to a very short junction (<10 nm), while the anisotropic elasticity yields to a 50 nm junction, comparable to the experimental measurement for the sGB upper part. For the Hirth<sub>III/III</sub> junction (cf. [25]), the line energy reduction is attributed to the dislocation characters involved, highlighting the importance of an accurate description based on the anisotropic elasticity. This Hirth junction, made of {111} dislocations, is the only one with a non-negligible recombination rate (albeit below 10%). Other configurations potentially leading to Hirth junctions mostly result in crossed- and repulsive states, as shown by Portelette et al. [25]. However, some discrepancies arise when comparing reaction geometry details between simulations and experiments. Simulations predict a three-dimensional junction formed by slip (see Figure 7(d) and (e)), whereas experiments reveal a common habit plane for the two dislocations and the junction. Once again, the final habit plane (123̄) does not contain any of the involved Burgers vectors. It is thus not a slip plane for the dislocations, and the resulting junction is not initially coplanar. Experimentally, $d_1$ remains close to a screw orientation throughout the junction formation process and appears to cross-slip from the (11̄1) slip plane to the (111) slip plane. The resulting junction is also close to a screw orientation, allowing it to move away from the (200) crystallographic slip plane. A very easy cross slip [26] could therefore more significantly
contribute to the formation of the observed configuration than in the previous case, while being coupled to other mechanisms of movement outside the slip plane.

<figure><img src="image_8.png" /></figure>

Figure 7. Mixed sGB primarily involving two dislocation populations forming Hirth junctions and a hexagonal network, induced by a compression test at 1550 °C with a constant strain rate of 10⁻⁴ s⁻¹ up to a strain of 22%. (a, b) BF TEM images showing the sGB under different diffraction conditions. In image (a), *d*₂ presents a residual contrast. In image (b), *d*₃ is out of contrast. (c) Stereographic representation at α = 0° where the dislocation directions *x*ᵢ and *x*ᵢ² for the upper part of the network and Burgers vectors *b*₁, *b*₂ and *b*₃ are indicated. The closest crystallographic plane containing *b*₁ and *x*₁ is indicated in green. The closest crystallographic plane containing *b*₂ and *x*₂ is indicated in blue. The closest crystallographic plane containing *b*₃ and *x*₃ is indicated in red. (d, e) Hirth junction formed using anisotropic elasticity. In (d), the view is in (12*3*) plane - the experimental dislocation network plane. In (e), the view is in (200) plane – theoretical plane of the junctions. Colors online.
<table><caption>Table 2. The long Hirth junction geometry: TEM versus DD simulations.</caption><thead><tr><th>n<sup>network</sup></th><th>Dislocation line</th><th>d<sub>1</sub></th><th>d<sub>2</sub></th><th>Junction = d<sub>3</sub></th></tr></thead><tbody><tr><td></td><td>b</td><td>1/2 [1 1 0]</td><td>1/2 [1 1 0]</td><td>[0 1 0]</td></tr><tr><td rowspan="8">TEM<br/>≈ (1 2 3)</td><td>x<sup>I</sup></td><td>≈ [9 12 5]</td><td>≈ [2 8 5]</td><td>-</td></tr><tr><td>β<sup>I</sup></td><td>22°</td><td>44°</td><td>-</td></tr><tr><td>L<sup>I</sup></td><td>110 nm</td><td>70-110 nm</td><td>-</td></tr><tr><td>n<sup>I</sup></td><td>15° from (1 1 1)</td><td>8° from (1 1 1)</td><td>-</td></tr><tr><td>x<sup>F</sup></td><td>≈ [12 9 2]</td><td>≈ [6 9 8]</td><td>≈ [1 8 4]</td></tr><tr><td>β<sup>F</sup></td><td>9°</td><td>37°</td><td>26°</td></tr><tr><td>L<sup>F</sup></td><td>70-80 nm</td><td>70-80 nm</td><td>50 nm</td></tr><tr><td>n<sup>F</sup></td><td>17° from (1 1 1)</td><td>17° from (1 1 1)</td><td>20° from (2 0 0)</td></tr><tr><td rowspan="8">DD<br/>≈ (5 1 4)</td><td>x<sup>I</sup></td><td>≈ [8 15 7]</td><td>≈ [8 29 21]</td><td>-</td></tr><tr><td>β<sup>I</sup></td><td>28°</td><td>45°</td><td>-</td></tr><tr><td>L<sup>I</sup></td><td>110 nm</td><td>110 nm</td><td>-</td></tr><tr><td>n<sup>I</sup> = n<sup>F</sup></td><td>(1 1 1)</td><td>(1 1 1)</td><td>(2 0 0)</td></tr><tr><td>x<sup>F</sup><sub>iso</sub></td><td>≈ [8 13 6]</td><td>≈ [8 27 19]</td><td>[0 1 1]</td></tr><tr><td>β<sup>F</sup><sub>iso</sub></td><td>26°</td><td>44°</td><td>45°</td></tr><tr><td>L<sup>F</sup><sub>iso</sub></td><td>106 nm</td><td>102 nm</td><td>7 nm</td></tr><tr><td>x<sup>F</sup><sub>aniso</sub></td><td>≈ [31 29 3]</td><td>≈ [8 13 6]</td><td>[0 1 1]</td></tr><tr><td>β<sup>F</sup><sub>aniso</sub></td><td>87°</td><td>76°</td><td>45°</td></tr><tr><td>L<sup>F</sup><sub>aniso</sub></td><td>64 nm</td><td>50 nm</td><td>66 nm</td></tr></tbody></table>

### 3.2.5. Sub-grain boundaries with three independent dislocation populations

As described by Caillard et al. [36], these sGBs involve the superposition of previously described networks. In Figure 8(b-d), a sGB with different interlinked networks can be observed. Five dislocation groups are reported. $d_1$ (in blue) and $d_2$ (in green) have Burgers vectors oriented at 90° to each other in a {100} type plane, parallel to [011] and to [011], respectively. They interact to form a Hirth junction and dislocation $d_3$ (in red), with a Burgers vector parallel to [001] (out of contrast in Figure 8(c)). They form locally a hexagonal network (with $d_3$ shorter than the other two). $d_4$ (in yellow), with a Burgers vector parallel to [110], does not react with $d_3$ whose Burgers vectors are orthogonal in a {110} type plane. They form locally a square network. $d_4$ also reacts with $d_1$, whose Burgers vectors are oriented at 120° to each other, in a {111} type plane. They form $d_5$ with a Burgers vector parallel to [101] and locally another hexagonal network. $d_1$, $d_2$ and $d_3$ have a dominant screw character, whereas $d_4$ and $d_5$ are of mixed type. Three different networks involving five dislocation populations therefore constitute this complex sGB. We did not attempt to verify the Frank formula in such complex structure. In Figure 8(a), only the upper part of the sGB is seen edge on. This indicates that this sGB lies on several planes. The trace of the upper part, using the corresponding stereographic representation (Figure 8(e)), is very close to the trace of the (200) plane, containing $b_1$, $b_2$ and $b_3$. Perhaps, this sGB was initially of twist character and mainly constituted by $d_1$, $d_2$ and $d_3$. With increasing strain, new dislocations were introduced; the rearrangement of the network was allowed by climb and glide in the three different slip systems of $UO_2$, but the complexity of the network increased, changing its character to mixed type.
<figure><img src="image_9.png" /><figcaption>a) **g** = [200]
α = -29°</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>b) **g** = [002]
α = 2°</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>c) **g** = [220]
α = 28°</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>d) **g** = [022]
α = 45°</figcaption></figure>

<figure><img src="image_13.png" /></figure>

Trace of the upper part
of the GB plane (seen
edge on)
Figure 8. Mixed sGB involving three independent dislocation populations, induced by a compression test at 1550 °C with a constant strain rate of 10⁻⁴ s⁻¹ up to a strain of 8.1%. (a - d) BF TEM images showing the sGB under different diffraction conditions. In image (b), *d*₄ has a residual contrast and *d*₃, a double contrast. In image (c), *d*₃ is out of contrast. In image (d), *d*₁ is out of contrast or has a residual contrast. (e) Stereographic representation corresponding to image (a), where the upper part is seen edge on. The Burgers vectors *b*₁ to *b*₅ are circled. The trace of the upper part of the sGB is reported in black and is close to the trace of (200). Colors are available online.

The following section presents a few examples about how dislocation lines and networks can interact and increase the microstructure complexity.

### 3.3. Evidences of dislocation lines and network interactions

Three examples, detailed below, illustrate the interaction of dislocations with already-existing networks.

The first example involves the tilt sGB discussed in Section 3.2.1, where additional dislocation lines, located between manufacturing porosities, are observed (see Figure 3). As highlighted in Figure 9(a), which is a close-up of one of those lines, the dislocation line interacts with the parallel lines constituting the sGB to form very locally junctions (Burgers vectors are oriented at 120° to each other), as observed by Whelan in the case of a dislocation intersecting a pile-up [44]. The line direction is not the same near the porosity (line colored in orange) and between two junctions (line colored in red). Near the porosity, the line direction ([861]) does not belong to the boundary plane, as also visible in Figure 3(b). In contrast, between two junctions, the line direction ([373]) belongs to the boundary plane, indicating that this segment of the line has been integrated into the network (see Figure 9(b)). If additional dislocations were to move towards this sGB, it could induce the formation of a more complex and misoriented sGB, involving two independent dislocation populations, as observed in hexagonal networks.
<figure><img src="image_14.png" /><figcaption>Figure 9. (a) BF TEM image showing parallel dislocations forming a tilt sGB and interacting with another dislocation line. (b) Stereographic representation corresponding to image (a). The sGB habit plane is reported in blue. The three Burgers vectors are also circled. Colors online.</figcaption></figure>

The second example is illustrated in **Figure 10**, which depicts a sGB with three independent dislocation populations. It distinctly exhibits different parts. Hexagonal parts are formed by the reaction of $d_1$ (blue) and $d_2$ (green) dislocations (*b* standing along <110> directions, oriented at 120° to each other), which produce $d_3$ (red) dislocations. This entire lattice is out of contrast with the diffraction vector [111] (*cf*. Figure 10(a)). It seems that some of these network hexagons are deformed by a third population of dislocations, $d_4$ (yellow), which react with the $d_1$ (blue) dislocations (*b* standing along <110> directions, oriented at 90° to each other) to form $d_5$ (purple) dislocations (*b* along <100>). Finally, a square network results from the interaction between $d_3$ (red) and $d_5$ (purple) dislocations (*b* oriented at 90° to each other). It is likely that this sGB, initially hexagonal, made of two independent populations of dislocations (*b* oriented at 120° to each other), is the result of the interactions with extrinsic dislocations visible on the left side of the images and/or with dislocations from a second sGB visible on the right side (*cf*. Figure 10(c)).
<figure><img src="image_15.png" /><figcaption>**Figure 10.** (a-c) BF TEM images showing a mixed sGB involving three independent dislocation populations under various diffraction conditions. In image (a), *d*₁, *d*₂ and *d*₃ are out of contrast. In image (b), *d*₁ is out of contrast and *d*₂ and *d*₃ have a double contrast. In images (c), *d*₂ is out of contrast. (d) Stereographic representation corresponding to image (b). The Burgers vectors *b*₁ to *b*₅ are circled with corresponding colors. Colors online.</figcaption></figure>

Thirdly, dislocations are sometimes observed near sGBs. As explained in Section 2 and in [22], we performed a 3D reconstruction of such a structure to study the possible interactions between dislocation lines and networks in more details (cf. **Supplementary Materials – Movie 1**).
Here, the studied sGB exhibits two distinct parts on each side of a manufacturing porosity (Figure 11(a)). These two parts are not characterized by the same networks but have dislocations in common. In the upper part (highlighted in orange in Figure 11(a)), the dislocation network consists of three independent populations of dislocations. The dislocations $d_2$ and $d_4$, indicated in green and red respectively (Burgers vectors along <110> directions, oriented at 90° to each other), react to form a Hirth junction with the $d_5$ (yellow) dislocations (Burgers vector along <100>, out of contrast in Figure 11(a)). A third population, $d_1$, indicated in blue (Burgers vector along another <110> direction), forms a square network with the $d_5$ (yellow) dislocations (Burgers vectors are orthogonal). In the lower part, the hexagonal network is made of two independent populations of dislocations. The dislocations $d_2$ and $d_1$, shown in green and blue respectively (Burgers vectors along <110> directions, oriented at 120° to each other), react to form the $d_3$ (purple) dislocations (out of contrast in Figure 11(a)).

Both parts of the sGB are viewed edge on for a sample tilt $\alpha$ between 16° and 10° (Figure 11 (c-d)). However, they do not exhibit the same trace. The trace of the upper part is very close to that of the (2200) plane (which contains the Burgers vectors of the dislocations forming the network in this part). The trace of the lower part corresponds to a high-index plane located between the (2200) and (111) planes (which contains the Burgers vectors of the dislocations involved in this second part) (Figure 11(b-c)).

Dislocations are also present near this sGB. We have shown in our previous work [21] that they primarily have an edge character and the same Burgers vector as the $d_4$ (red) dislocations. It is notable that they are only present near the lower part, which does not contain dislocations with the same Burgers vector in its network. On the 3D reconstruction, some dislocation lines reach the sGB on the porosity and on the part outlined in black in Figure 11(a), which corresponds to $d_2$ (green) dislocations that are not in the same plane as the rest of the network. It is possible that the extrinsic dislocations that arrived on the network and piled up may have reacted with intrinsic dislocations of the upper part. They formed Hirth junctions, leading to a complexification of the initial network, as the configuration in this part is more favourable for Hirth junction formation than in the lower part, where dislocations still pile up.
<figure><img src="image_16.png" /><figcaption>Figure 11. (a, c, d) BF TEM images showing dislocations on a sGB involving three or two independent dislocation populations under different diffraction conditions. (b) Stereographic representation corresponding to image (c), where the sGB is seen edge on. The different Burgers vectors are circled. The traces of the upper and lower parts of the sGB are reported. Colors online.</figcaption></figure>

Other sGBs made of several different networks are shown in the **Supplementary Materials-3**.

**4. Discussion**

4.1. Types of sub-grain boundary in UO₂ polycrystals generated during high-temperature and constant strain rate compression tests

This article examines sGBs formed in UO₂ samples subjected to compression testing at 1550°C with a constant strain rate of 10⁻⁴ s⁻¹. A total of 26 sGBs were studied in detail, using conventional TEM, in the different thinned grains of the three samples strained up to 1.7, 8.1 and 22%. We identified different types of sGBs based on the level of deformation. The results are summarized in Table 3. At the lowest
strain level (1.7%), simple sGBs were predominantly observed, characterized by one or two independent dislocation populations arranged in parallel lines or hexagonal networks. As the strain level increased, five types of sGBs were identified. While complex sGBs involving three dislocation populations became more prevalent, sGBs made of a single dislocation population remained present even at the highest strain levels. Additionally, low misoriented sGBs were still observed at the highest strain value using EBSD. This suggests a continuous formation of new simple and weakly misoriented sGBs with increasing strain, as previously observed in [30]. Further study is needed to determine if any specific type of sGB is preferentially formed. However, based on the current results, no such preference appears under the deformation conditions studied. The majority of the studied sGBs exhibits a tilt or a mixed character.

Except for sGBs involving two non-parallel populations which interact to form hexagonal networks, the other observed sGBs are described in detail for the first time in UO₂. Indeed, in the literature, for TEM examinations, only detailed information about hexagonal networks involving Burgers vectors standing along <110> directions oriented at 120° to each other is available. For example, Dherbey *et al.* [12] observe hexagonal networks after compression creep tests between 10 and 80 MPa on polycrystals, for strains above 3.6% at 1465 °C. Alamo *et al.* [17] also highlight similar hexagonal networks after compression tests on a single crystal oriented to activate two slip systems, at 1000 and 1200 °C after strains of 7% and 5%, respectively. Both studies reported more complex structures (involving square network parts) but provided limited details.

<table><caption>Table 3. Types and number of sGBs formed after compression tests conducted at 1550 °C with a constant strain rate of 10⁻⁴ s⁻¹ up to strains of 1.7%, 8.1% and 22%.</caption><thead><tr><th>Strain level</th><th>1 population (tilt character)</th><th>2 parallel populations (tilt character)</th><th>2 populations, b at 120° forming a junction (mixed character)</th><th>2 populations, b at 90° forming a Hirth junction (mixed character)</th><th>3 populations (mixed character)</th><th>Total studied</th></tr></thead><tbody><tr><td>1.7%</td><td>1</td><td>-</td><td>1</td><td>-</td><td>-</td><td>2</td></tr><tr><td>8.1%</td><td>-</td><td>1</td><td>3</td><td>1</td><td>7</td><td>12</td></tr><tr><td>22%</td><td>2</td><td>2</td><td>2</td><td>3</td><td>3</td><td>12</td></tr></tbody></table>

## 4.2. Dislocation network formation mechanisms

The initial stages of deformation involve a relatively free motion of dislocations through glide and climb mechanisms. Gradually, these dislocations begin to interact within the original grains. As previously observed [21], some dislocations may pile up or become entangled near original GBs or manufacturing porosities, which act as barriers to dislocation motion. Consequently, the presence of porosities and initial GBs, where dislocations can be stopped, may facilitate the formation of tangled dislocation networks [11]. The dislocation density is expected to increase rapidly in these areas during pellet deformation. In certain configurations, dislocations may reorganize to form sGBs. These initial sGBs are presumed to be relatively simple, involving one or two dislocation populations (parallel lines, as shown in Figure 3, or hexagonal networks, as shown in Figure 5), as observed at the lowest strain value
(1.7%). As evidenced by the EBSD map at the lowest strain value (see Figure 1(a)), only a few, low-angle sGBs are initially generated.

While the formation of tilt sGB with parallel lines necessitates climb, the formation of hexagonal networks appears to be more complex to understand. According to literature data, the hexagonal network is believed to result from the interaction of two screw dislocation populations from two different {100} or {110} slip planes in a {111} plane, implying the cross slip of the screw dislocations from {100} or {110} to {111} [17]. At 1550 °C, dislocations are believed to glide in a viscous manner (athermal regime) in the ½<110> {001} slip system and in a more thermally-activated fashion in ½<110> {110} [37][38][39][40]. Slip in ½<110> {111} is also possible since dislocations may cross slip rather easily from {100} or possibly from {110} to {111} [41][42], as also confirmed recently by molecular dynamics (MD) simulations [43]. However, in a previous work, we studied isolated dislocation lines (not involved in networks) in the same samples [21]. Using conventional tilt experiments, we highlighted dislocation motion by glide (sometimes involving cross slip) and by a mixed climb mechanism [23][34]. During this process, the dislocation moves in mixed climb planes close to, but clearly distinct from, slip and climb planes by a combination of glide and climb events. We can thus state that mobile dislocations can sometimes leave their original slip plane by climb, which is a way to spread the deformation in the crystal, not only on crystallographic slip planes. This enables dislocations to move more freely and with fewer crystallographic stresses at this temperature. As discussed in Sections 3.2.3 and 3.2.4, by comparing experimental and DD results, more complex mechanisms than slip and cross slip are supposed to be involved in the formation of the studied sGBs, since the final microstructure exhibits sGBs that are planar by portion and lying on non-crystallographic planes. Climb and mixed climb seem to play an important role in the formation of the observed networks.

With increasing strain (8.1% and 22%), TEM revealed more complex sGBs involving up to three dislocation populations (cf. Figure 8). EBSD results further showed an increase in the number of sGBs and their misorientation angles (cf. Figure 1(b) and (c)). As strain increases, isolated dislocations can also begin to interact with the increasing number of the sGBs. The behavior of a dislocation approaching a GB depends on the applied stress, temperature, and GB geometry. Depending on these parameters, the dislocation may be stored near the GB, absorbed into it, or pass through it. Generally, dislocation entry into a GB requires high stresses, driving the GB into a non-equilibrium state. The accumulation of several extrinsic dislocations then leads to an accumulation of stresses in the boundary which can block the entry of new dislocations and therefore the deformation of the sample. If the temperature is high enough, the stresses associated with the first dislocations entering a GB can relax, allowing it to absorb other dislocations. At moderate temperatures (T < 0.4T_m, where T_m is the melting temperature), GBs primarily act as dislocation barriers, causing dislocations to pile up. At higher temperatures, dislocations can be incorporated into GBs via several processes. They can react with intrinsic dislocations to form junctions. This process is very favourable only for low misoriented GBs. Alternatively, dislocations can decompose into sessile and glissile components, with the glissile products slipping to boundary ends and sessile products climbing and rearranging with intrinsic dislocations. These processes of stress relaxation lead the GB to a new state of equilibrium (new network, habit plane, misorientation...). As evidenced in Section 3.3, extrinsic dislocations can integrate into networks, increasing their complexity (involving more dislocation populations). Mansour et al. [20] also observe a sGB with a hexagonal network region and a parallel dislocation line region in a polycrystal after compression creep at 50 MPa and 1500 °C up to 8% strain. A transition zone between
these two regions, where hexagonal dislocation cells deform into parallel lines, is also noted. This
suggests a mechanism for the formation of complex sGBs through interactions between extrinsic
dislocations and sGBs. Such organized and complex networks, lying in multiple non-crystallographic
planes, are thought to result from dislocation climb out of their slip planes, facilitating local
rearrangement of extrinsic and intrinsic dislocations. Climb enables dislocations to move more freely,
promoting reorganization in planes other than pure slip planes. This mechanism is consistent with the
mechanical test temperature (0.54T_m), which allows fast diffusion processes [45], the mixed climb
dislocation motion observed in these samples [21], and the dislocation dynamics (DD) results. This
reorganization is often referred to as "dynamic recovery" or "polygonization" [46][47].

4.3. Dislocation network and their role in plasticity

According to Dherbey et al. [12], compression creep tests conducted on polycrystals at 1465 °C within the stress range of 10 to 80 MPa would induce GB sliding. This sliding is accompanied by dislocation insertions and extractions, suggesting dislocation climb and/or cross-slip. GB cracking related to sliding at the grain interfaces is observed after creep tests. However, in literature, many GB-related plasticity mechanisms are related to sliding [48] while this GB mechanism (e.g. the relative motion of two adjacent grains on a common boundary without deformation of the grains) in polycrystals is difficult [49][50] and less common than others, such as shear migration coupling or rotation for instance [51][52][53]. According to Salvo et al. [13] GBs are not cracked despite the high strain level (22%) at the end of their tests (the studied samples come from [13]). The authors attributed this discrepancy to the significantly higher density of the samples tested by Dherbey and co-auteurs. Salvo et al. also note a significant evolution of porosity at the pellet center during compression tests. The absence of GB fragmentation in these tests could be attributed to stress accommodation via pore compression and grain plasticity. In light of the current results, subsequent deformation in UO₂ may also involve sGB motion, as supported by [12], but not through sliding (sGBs do not lie in slip planes, which precludes real sliding in such interfaces) and in relation to porosity, which generates a pinning effect, as proposed in [18]. It is noteworthy that the majority of the studied sGBs are often connected to numerous manufacturing porosities.

**5. Conclusions**

The elementary mechanisms of deformation at GBs are governed by their geometry and chemistry, significantly influencing the mechanical properties of polycrystalline samples. Consequently, transmission electron microscopy (TEM) and electron backscatter diffraction (EBSD) characterizations are performed on polycrystalline UO₂ pellets subjected to uniaxial compression tests at a constant strain rate at 1550 °C. The aim is to investigate the characteristics of sGBs induced by these tests. Three samples, strained to final values of 1.7%, 8.1%, and 22%, are examined.

Various sGBs are observed in the samples, ranging from one parallel dislocation group (symmetrical tilt sGBs) to three independent dislocation populations (mixed sGBs). Some sGBs exhibited Hirth junctions, with Burgers vectors aligned along the <100> direction. No preferential formation of one sGB type is observed with increasing strain. As previously reported in the literature using EBSD, both the linear fraction and misorientation of sGBs increased with strain level. The presence of low misoriented sGBs at the highest strain level suggests their continuous creation and the progressive misorientation of older sGBs as they densify by incorporating more dislocations. Evidence of interactions between extrinsic dislocations and sGBs, leading to sGB complexification, is found in all
samples. The high complexity of sGBs in these UO₂ samples indicates their active role in deformation, accommodating numerous extrinsic dislocations. sGBs are planar by portion and lie on non-crystallographic planes, suggesting relatively high dislocation mobility during their formation processes (via climb, mixed climb, and glide in multiple planes). This is consistent with dislocation dynamics (DD) results and literature data at this temperature. Conversely, it seems not possible for these sGBs to contribute to deformation through sliding.

This study on sGB characteristics contributes significantly to the modelling of high-temperature viscoplastic behavior of UO₂ fuel at the nanoscale. It provides insights into complex dislocation interactions that remain the principal vector of deformation in this range of temperature and strain rate, and may help to understand phenomena observed in irradiated fuel, such as sub-grain formation near central regions in fuels irradiated at high burn-up.

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