mechanical testing of cerium oxide nanoparticles in
atomic-scale Transmission Electron Microscopy (TEM)

R. Zhang, K. Masenelli-Varlot, T. Epicier, D. Stauffer, F. Chaput, L.

Joly-Pottuz

► To cite this version:

R. Zhang, K. Masenelli-Varlot, T. Epicier, D. Stauffer, F. Chaput, et al., mechanical testing of cerium oxide nanoparticles in atomic-scale Transmission Electron Microscopy (TEM). Materials Today Nano, 2025, 29, 10.1016/j.mtnano.2024.100564. hal-04927902

HAL Id: hal-04927902

https://hal.science/hal-04927902v1

Submitted on 20 Nov 2025

**HAL** is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>
*In Situ* Mechanical Testing of Cerium Oxide
Nanoparticles In Atomic-Scale Transmission Electron
Microscopy (TEM)

Rongrong Zhang<sup>a</sup>, Karine Masenelli-Varlot<sup>a,*</sup>, Thierry Epicier<sup>b</sup>, Douglas
Stauffer<sup>c</sup>, Frédéric Chaput<sup>d</sup>, Lucile Joly-Pottuz<sup>a</sup>

<sup>a</sup>INSA Lyon, Universite Claude Bernard Lyon 1, CNRS, MATEIS,
UMR5510, Villeurbanne, 69621, France

<sup>b</sup>Universite Claude Bernard Lyon 1, CNRS, IRCELYON,
UMR5256, Villeurbanne, 69621, France

<sup>c</sup>Bruker Nano Surfaces and Metrology, Hysitron Products, 9625 W 76th Street, Minneapolis, 55344, MN, USA

<sup>d</sup>ENS Lyon, CNRS UMR5182, Universite Claude Bernard Lyon 1, Laboratoire de Chimie, 46 allée d'Italie, Lyon, 69364, France

**Abstract**

*In situ* nanocompression tests in Electron Microscopy have proved to be an interesting tool for identifying the slip systems involved in plastic deformation. To go further in the investigation of the deformation mechanisms, we report here nanocompression experiments performed in a Cs-corrected Environmental Transmission Electron Microscope. The experiments were successfully performed on bixbyite-Ce₂O₃ nanocubes. Thanks to high resolution imaging, the different steps of the deformation mechanism - dislocation nucleation, dissociation and stacking fault formation - could be evidenced. The formation of stacking fault, unusual in face centered cubic structures, is discussed in light of the crystallographic structure and especially the location of oxygen vacancies.

Keywords: oxide, nanoparticle, in situ, transmission electron microscopy
(TEM), dislocation

PACS: 68.37.Og, 77.84.Bw, 62.20.fq

<footnote>*Corresponding author</footnote>
# 1. Introduction

Nanomaterials are nowadays widely used in our everyday life due to their unique characteristics, which may diverge considerably from their bulk counterparts. One of the most notable features of these materials is their high surface-to-volume ratio, which fundamentally alters their properties. In certain materials, a brittle-to-ductile transition can be observed when decreasing the specimen size [1, 2]. Large plasticity has also been observed at room temperature in ceramic materials, which are known to be brittle at bulk [3, 4, 5, 6, 7]. In monocrystalline nanoparticles, the yield stress may also increase with the sample size [8, 9]. Such behaviour has been attributed to the fact that the smaller size reduces the space available for pre-existing dislocations [10]. Moreover, there is strong tendency for dislocations to move to the surface due to image force, which reduces the probability of dislocation multiplication processes, as in bulk materials [11]. The requirement that dislocations be nucleated means that particle strength is larger than expected from space-limiting size effect, and can approach the theoretical yield strength of a material.

Cerium oxide (CeO$_x$) nanoparticles are used for various applications: catalysis, solid oxide fuel cells (SOFC) electrodes [12, 13], gas detection [14], and in the biomedical field to protect cells against damage (toxicants, radiation) [15]. In terms of its nanoscale mechanical properties and behavior, it is used as an abrasive in the process of chemical mechanical polishing (CMP) of semiconductor wafers [16]. Despite its widespread use in various technological domains, the deformation mechanisms in cerium oxide, especially when it is subjected to stresses at the nanometer scale, remain poorly understood. Moreover, the complexity of cerium oxide is enhanced by its ability to exist in different crystallographic phases: fluorite, bixbyite, hexagonal, mainly depending on the oxygen fraction $x$. CeO$_2$ has a fluorite structure. Its deformation mechanism may be the same as those of other oxides exhibiting a fluorite structure, with a primary slip system in the {100} planes [17] and a secondary slip system in the {110} planes [18]. When reduced into CeO$_x$ (with $1.5 \le x \le 2$), different structures should be considered. For Ce$_2$O$_3$, the hexagonal structure (space group 164) is the most stable. However, when reduced in a Transmission Electron Microscope (TEM) under the electron beam, a bixbyite (space group 206) is observed [19]. This transformation from fluorite CeO$_2$ to bixbyite Ce$_2$O$_3$ is due to the creation
of oxygen vacancies, as already reported by Silva *et al.* [20]. It has also been observed in the case of Y₂O₃ [21]. To the best of our knowledge, there is limited research concerning the slip systems in sesquioxides M₂O₃ in the bixbyite structure. Gaboriaud and Cadoz used TEM to analyze dislocations in Y₂O₃ samples previously deformed at high temperature [22]. They found deformation was mainly due to slip in {100} and {110} planes. However, they noticed that such planes did not contain the shortest Burgers vector, namely ½⟨111⟩. An ionic crystal model was then used by Gaboriaud and Boisson to calculate the energy of stacking faults in Y₂O₃ [23]. Stacking faults were found to be energetic and unlikely. A possible low-energy stacking fault could be described using ½⟨110⟩{100} slip system or by removing 4 successive {100} planes. The "layered atoms stacking concept" can also help determining the slip systems [24]. An overview of different anion-deficient fluorite-type oxides has recently been published by Gaboriaud [25]. In this paper, slip planes and Burgers vectors in M₂O₃ are discussed using the layered atom stacking and the shortest periodicity vector basic concepts. The experimental results are taken from with the literature on different bixbyite materials, among which Er₂O₃ compressed at high temperature, grounded Eu₂O₃ particles, and Y₂O₃ single crystals submitted to different deformation conditions. Very different slip systems are reported, not always in agreement with the shortest periodicity vector imposed by the oxygen sublattice, as determined from the layered atom stacking concept. Moreover, dislocation dissociation was observed several times. For instance in Eu₂O₃, the slip system ⟨110⟩{111} is reported, with dislocation dissociation into 1/12⟨112⟩ partials. On the contrary, the dissociation of a 1/4[110](001) dislocation in Y₂O₃ is not in agreement with theoretical calculations of the stacking fault energies computed in the {100} plane for a perfectly stoichiometric oxide. Further work is therefore required to better understand the deformation mechanism in bixbyite materials.

To understand the mechanical response of nanomaterials, researchers use a variety of *in situ* techniques that allow the observation and measurement of properties under specific conditions. Among these techniques, *in situ* Atomic Force Microscopy (AFM), *in situ* Scanning Electron Microscopy (SEM), and *in situ* Transmission Electron Microscopy (TEM) stand out for their ability to provide detailed insights into the behavior of materials at the nanoscale. *In situ* AFM is used to probe the surface properties and mechanical behavior of nanomaterials under various conditions. This technique can measure forces
with high sensitivity and map the topography of materials at the nanometer scale, providing valuable information on the mechanical properties such as elasticity, hardness, and adhesion [26, 27]. *In situ* SEM allows real-time observation of structural changes due to a wide variety of external stimuli, including stress, temperature, and environment. This technique can be particularly useful to study fracture mechanics, crack propagation, and surface evolution of materials under different environmental conditions [28]. An example of its application includes the heating of CeO₂ microspheres, where *in situ* SEM can monitor the changes in morphology and structure at elevated temperatures[29]. *In situ* TEM is a powerful method for examining nanomaterials, allowing for the direct observation of their internal structures and behaviors under different conditions, such as mechanical stress [30, 31]. Unlike SEM, TEM offers unmatched resolution, making it possible to study phenomena including dislocations, phase changes, and deformation mechanisms at the atomic scale [32, 33, 34, 35]. Compared with *in situ* SEM or *in situ* AFM, *in situ* TEM experiments remain very difficult and the studies generally present results on a few objects. Nevertheless, the advantage of this technique lies in its capability not only to visualize internal transformations in real-time but also to collect quantitative data (force, displacement), providing a detailed and holistic understanding of the material response to external stimuli.

This paper deals with the determination of the deformation mechanism in individual bixbyite-Ce₂O₃ nanoparticles. As it is known that fluorite-CeO₂ may reduce and transform into bixbyite under the electron beam, we report *in situ* compression tests in TEM to investigate whether reduction has an impact on the mechanical properties of the nanoparticles. The focus on atomic resolution imaging is crucial for two main reasons. Firstly, it is necessary to determine the crystallographic phase transformation (fluorite or bixbyite). Secondly, monitoring the evolution of defects within the nanoparticles, such as dislocation nucleation or dissociation, and stacking faults appearance, is vital for a deep understanding of the deformation mechanism.

## 2. Experimental design

### 2.1. *sample preparation*

CeO₂ nanocubes were synthesized using hydrothermal method [36, 37, 38]. Their cubic shape is convenient for *in situ* nanocompression testing, as
the compression axis is fixed and no rotation can occur during the test. In
this configuration, the (001) plane is parallel to the indenter and the sub-
strate surfaces, and the compression direction is [001], as shown in Figure 1.
The main drawback of this geometry is that it is not possible to use other
loading directions without a specific nanostructuration of the substrate. As
a consequence of such fixed loading direction, slip cannot occur in the {100}
planes cannot occur (Schmid factor equal to zero).

Sample preparation is a critical process aiming at minimizing artifacts in
such a small compression system. In this study, several key steps have been
identified.

* Substrate Preparation: The choice of the substrate is very important. It should ideally be flat and harder than the studied nanoparticles. It must also be sufficiently electrically conductive to avoid possible charging problems under electron irradiation. In the following, the substrate used was either a silicon wedge provided by Bruker/Hysitron, or a polished piece of sapphire.

* Nanocube deposition onto the substrate edge: ideally, the nanocubes should be dispersed onto the substrate, so that nanocubes could be tested individually. This step is crucial to accurately capture the behavior of particles under compression, and measure the corresponding force. In the present study, the nanocubes were deposited by solvent evaporation, or dry-deposited.

## 2.2. *in situ* mechanical tests

In situ TEM nanocompression experiments were then performed on a Bruker/Hysitron PI95 Picoindenter holder inserted in a Cs-corrected FEI Titan ETEM G2 80-300, operated at 300 kV and equipped with a Gatan OneView camera. A flat diamond punch was used. Compression tests were conducted in displacement control mode, with a constant loading rate ranging from 0.1 to 0.5 nm/s. Videos were acquired throughout the compression test, with a fixed acquisition rate of 25 frames per second (fps). This rapid image acquisition ensures a detailed and dynamic record of the sample's behavior at the nanoscale.

Under electron beam irradiation, CeO₂ can be reduced to Ce₂O₃ bixbyite structure [19]. In order to make sure that the tested nanocube were irradiated into bixbyite, the electron beam was highly condensed on the sample
<figure><img src="image_2.png" /><figcaption>Figure 1: Set-up used for *in situ* mechanical testing in Transmission Electron Microscopy. a) front end of a Bruker/Hysitron PI95 picoindenter. b) scheme showing one nanocube placed on the edge of a silicon wedge. The force and imaging directions used in the present study are indicated.</figcaption></figure>

prior to the compression experiments. High resolution imaging was carried out and the crystallographic phase was investigated by indexing the electron diffraction pattern. A previous study based on high resolution imaging, electron diffraction and electron energy-loss spectroscopy, showed that under these conditions, the composition of the nanocube was close to Ce₂O₃, its crystallographic phase being indeed bixbyite [19].

Several cycles were performed on individual nanocubes deposited onto a polished sapphire substrate to study the influence of the oxygen vacancies. In this case, the oxygen content and hence the crystallographic phase was tuned by adjusting the intensity of electron beam [19]. Using a high electron dose rate, the nanocube exhibited the bixbyite structure, whereas it kept the original fluorite structure under low electron dose rate. Before each compression test, the electron beam was blanked during a few minutes to let the nanocube return to the fluorite structure thank to the residual oxygen present in the microscope vacuum. Engineering stress/strain curves were plotted from the values of the force measured with the PI95 device. The real displacement of the tip was measured in the video using Digital Image Correlation (DIC), with sub-pixel resolution (1/100 pixel). The points on the stress-strain curves had to be correlated with the TEM images. Since the transducer provided eight times more data points than the number of frames
<figure><img src="image_3.png" /><figcaption>Figure 2: Characterization of Ce₂O₃ nanocube before compression. (a) Configuration of the cube. (b) Observed region during the tests (frame 1 of the movie). c) high resolution image obtained from the red square in Figure 2b, with the indexed diffractogram, characteristic of bixbyite (zone axis [110]).</figcaption></figure>

given by the camera, the number of points provided by the transducer was
reduced by averaging each eight consecutive force data points, resulting in
stress-strain curves with the correct number of points and reduced noise.

**3. Results and discussion**

A nanocube of size 52 nm, deposited onto a silicon wedge, was com-
pressed with a loading rate of 0.1 nm/s. Figure 2(a) presents the original
state of the cube (frame 1 from the movie in supporting information, where
the onset of compression is considered to occur at frame 101). In order to
achieve atomic resolution and induce the transformation of the cube into
bixbyite under irradiation, a quite condensed electron beam was used (see
Figure 2(b), in which the region of interest is indicated by a red square). Due
to this experimental configuration and due to the fact that the nanocube is
partially hidden by the substrate, it was not possible to observe the entire
cube. Therefore, quantitative data such as stress and strain are not pre-
sented and we report hereafter changes in microstructure that take place
during compression. Nevertheless, a high-resolution image captured before
compression revealed no visible defects, see Figure 2(c). The diffractogram
is characteristic of the bixbyite structure (space group Ia-3) with the zone
axis [110].

The [110] zone axis provides a clear view of the {111} planes, at the
atomic scale. From the literature, this orientation was expected to be the
<figure><img src="image_4.png" /><figcaption>Figure 3: *In situ* formation of a stacking fault in a 52 nm Ce₂O₃ nanocube. (a) After tip engagement, during loading (frame 167). There is no extended defect as in Figures 3b and 3c. (b) Upon loading (frame 181), a dislocation is created. The dislocation marker is just positioned indicatively as a guide for the eye. (c) A stacking fault is created through dissociation of the dislocation (frame 203).</figcaption></figure>

most appropriate one. Indeed, as the dislocations gliding in the {100} planes cannot be activated here, the planes {111} are expected to play a major role in the deformation [39]. Compression leads to the generation of multiple stacking faults along similar crystallographic directions. A representative stacking fault generation is illustrated in Figure 3. Before a stacking fault forms, a dislocation emerges.

By analysing the high-resolution images, the Burgers vector of the dislocation can be determined. Figure 4(a) shows the region of interest, where the perfect dislocation has started to extend as a stacking fault. The Burgers circuit confirms the closure failure. The vector needed to complete the circuit is found to be $\frac{1}{4}[\overline{12}]$, representing the projection of the dislocation's Burgers vector onto the (110) plane. The magnitude of this vector, measured in Figure 4(b), is 0.335 nm. Typically, in a metal with a known slip system, the Burgers vector of the dislocation can be directly determined by drawing such Burgers circuits. However, in Ce₂O₃, the priority among the slip systems in the {100}, {110}, and {111} planes has not been identified. Additionally, there are several vectors from different slip planes that are equivalent when projected onto the (110) plane. In the subsequent analysis, these possibilities will be considered to determine the actual Burgers vector of this dislocation.

In Figure 3(c), during compression, one side of the stacking fault ends at the surface. The vectors of the two partial dislocations are measured in the first frame where the stacking fault is visible, at 1.4 s, as shown in Figures 5
<figure><img src="image_5.png" /><figcaption>Figure 4: Measurement of the projected Burgers vector of a perfect dislocation seen on the frame acquired at 0.56 *s* (frame 183). (a) Burgers circuit (yellow) with the projected Burgers vector (red arrow), of direction [112]. The inset shows the diffractogram. (b) Measurement of the length of the projected Burgers vector from the intensity level profile. (c) Bixbyite unit cell, with the [101] direction corresponding to the true Burgers vector. Some cerium atoms aligned along this direction are colored in blue. Oxygen and the other cerium atoms are in red and green, respectively.</figcaption></figure>

and 6. By drawing Burgers circuits at each end of the stacking fault, the projected Burgers vectors can be determined. To complete both circuits, vectors parallel to [112] are needed for the initial perfect dislocation. The lengths of the bottom and top vectors are found to be 0.227 *nm* and 0.105 *nm*, respectively (see Figures 5(b) and 6(b)). Taking into account the cerium sublattice observed with the zone axis [110] (see Figures 5(c) and 6(c)), the projected Burgers vectors of the bottom and top partial dislocations correspond to the [112] and [211] directions, respectively.

Based on the experimental observations, the formation of stacking faults in bixbyite-Ce₂O₃ seems to be similar to that observed in face-centered cubic (fcc) metals. Indeed, stacking faults in fcc metals typically occur through the dissociation of ⟨110⟩{111} perfect dislocations, such as [40, 41, 42]. The similarities may originate from the fact that the sublattice of cerium atoms in Ce₂O₃ is a fcc lattice. However, the oxygen sublattice should also be considered to further determine the deformation mechanism in Ce₂O₃. Interestingly, the appearance of stacking faults in bixbyite-Y₂O₃ under electron irradiation was also proposed in the literature from weak-beam dark field observations [43], and in bixbyite-Eu₂O₃ under electron irradiation using high resolution imaging [44]. Stacking fault energies were also computed in Y₂O₃ and the results highlighted the low energy of the stacking faults
<figure><img src="image_6.png" /></figure>

Figure 5: Measurement of the projected Burgers vector of the partial dislocation at the bottom of the stacking fault created by the perfect dislocation shown in Figure 4 (frame 203, acquired at 1.4 s). (a) Burgers circuit (yellow) with the projected Burgers vector (red arrow), of direction [112]. (b) Measurement of the length of the projected Burgers vector from the intensity level profile. (c) Bixbyite unit cell, with the [112] direction corresponding to the true Burgers vector. Some cerium atoms aligned along this direction are colored in blue. Oxygen and the other cerium atoms are in red and green, respectively.

<figure><img src="image_7.png" /></figure>

Figure 6: Measurement of the projected Burgers vector of the partial dislocation at the top of the stacking fault created by the perfect dislocation shown in Figure 4 (frame 203 acquired at 1.4 s). (a) Burgers circuit (yellow) with the projected Burgers vector (red arrow), of direction [112]. (b) Measurement of the length of the projected Burgers vector from the intensity level profile. (c) Bixbyite unit cell, with the [211] direction corresponding to the true Burgers vector. Some cerium atoms aligned along this direction are colored in blue. Oxygen and the other cerium atoms are in red and green, respectively.
<table><caption>Table 1: Shortest periodicity vectors and their magnitudes in Ce₂O₃</caption><thead><tr><th></th><th>Cerium cation (8b)</th><th>Magnitude of the vector (Å)</th><th>Oxygen anion (16c)</th><th>Magnitude of the vector (Å)</th></tr></thead><tbody><tr><td>(100)</td><td><sup>1</sup>/<sub>2</sub>[010]</td><td>5.71</td><td>[010]</td><td>11.41</td></tr><tr><td>(110)</td><td><sup>1</sup>/<sub>2</sub>[111]</td><td>rev9.88</td><td><sup>1</sup>/<sub>2</sub>[111]</td><td>9.88</td></tr><tr><td>(111)</td><td><sup>1</sup>/<sub>2</sub>[110]</td><td>8.07</td><td>[110]</td><td>16.14</td></tr></tbody></table>

$b = \frac{a}{2}\langle 110 \rangle\{100\}$ [39]. However, this cannot explain our observations since slip systems in the $\{100\}$ planes cannot be activated here.

In order to better understand the deformation mechanism in bixbyite-Ce₂O₃ under compression, the "layered atom stacking concept" is used [24]. According to this concept, glide occurs mainly in the atomic layer composed of a triangular atom network, also known as the Kagome lattice [45]. This lattice consists of equilateral triangles formed by joining one type of atoms, whether anions or cations. Due to the high atomic density and large layer spacing between these triangular atom networks, gliding is easy in these planes, similar to the densest planes in metals. The shortest periodicity vectors in the planes $\{100\}$, $\{110\}$ and $\{111\}$ are shown in Figure 7. The directions and lengths of the shortest periodicity vectors are summarized in Table 1.

The possible Burgers vectors of perfect dislocations are equal to one half the shortest periodicity vectors [24]. In order to narrow down the possible configurations, it is important to focus on the slip systems that can be activated when the loading direction is [001]. Specifically, the Schmid factors of $\langle 010 \rangle\{100\}$ and $\langle \bar{1}11 \rangle\{110\}$ are both theoretically zero. By excluding these slip systems, the $\langle 0\bar{1}1 \rangle\{111\}$ slip system is the only one to be considered here. Figure 8 illustrates the possible vectors belonging to the $\langle 011 \rangle\{111\}$ slip system with projection vectors on the (110) plane parallel to $[1\bar{1}2]$. The figure shows four possibilities: $[01\bar{1}](111)$, $[101](\bar{1}11)$, $[01\bar{1}](\bar{1}11)$, and $[101](11\bar{1})$. Among the four possible vectors, the length of the vector $\frac{1}{4}[101]$ is 0.4035 nm and its projection on the (110) plane is 0.349 nm. This value is very close to the value obtained from the TEM image shown in Figure 4. Therefore, it can be reasonably considered that the Burgers vector of this perfect dislocation is $\frac{1}{4}[101]$. By comparing this result with the shortest periodicity vectors in Table 1, it can be concluded that the Ce sublattice governs the slip system. Moreover, it is noteworthy that the angle between the Burgers vector and the dislocation line [110] is 60°, indicating that this is a mixed dislocation, as found in Eu₂O₃ [44].
<figure><img src="image_8.png" /><figcaption>Figure 7: Determination of the shortest periodicity vectors in Ce₂O₃ for the Ce and O sublattices, in 3 different planes: (100), (110) and (111). The vectors are indicated by arrows. In the Ce sublattice, Ce atoms are represented in green or blue, depending on the Wyckoff position (2d or 8b, respectively). In the O sublattice, the oxygen atoms giving the shortest periodicity vectors are represented in blue.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Figure 8: Models for the perfect dislocation observed in Figure 4. (a) Scheme of the dislocation vector. The red dotted line is the measured vector. The pink rectangle corresponds to the (110) observation plane. (b) List all possible slip systems whose projection vector onto the (110) plane is [112]. The black solid line is the Burgers vector and the orange surface is the slip plane.</figcaption></figure>
Based on the information provided in Figures 5 and 6, the projected Burgers vector of the upper partial is measured equal to 0.105 nm, while that of the lower partial is 0.227 nm. The lengths of the vectors $\frac{1}{4}[211]$ and $\frac{1}{4}[1\bar{1}2]$ projected onto the (110) plane are 0.36 nm and 0.67 nm, respectively. Comparing these distances with those measured in the TEM image, the Burgers vector of both partial dislocations can be determined as $\frac{1}{12}[211]$ for the upper partial and $\frac{1}{12}[1\bar{1}2]$ for the lower partial. Such determination gives the following dissociation scheme:

$$ \frac{1}{4}[101] \rightarrow \frac{1}{12}[1\bar{1}2] + \frac{1}{12}[211] $$

This dissociation scheme is in agreement with what was previously reported on the motion of dislocations near the surface in bixbyite-Eu₂O₃ under electron irradiation [44]. It also perfectly corresponds to what is known on metals:

$$ \frac{1}{2}[101] \rightarrow \frac{1}{6}[1\bar{1}2] + \frac{1}{6}[211] $$

taking into account the fact that the unit cell of bixbyite is a double fcc unit cell for cerium atoms (to account for the distribution of the oxygen vacancies).

Given the large values of the shortest periodicity vectors, dislocation dissociation is not surprising. Indeed large Burgers vectors equates to a high energy density of the dislocation core [43]. The Ce₂O₃ bixbyite structure is obtained by oxygen vacancies formation in the CeO₂ structure. It can be considered as a super cubic cell with a lattice parameter roughly twice that of the fcc CeO₂ structure. The dissociation of the [101] dislocation can hence be compared to what happens in a fcc structure. {222} planes are complex in the bixbyite structure since they are composed of 6 planes of oxygen and 3 planes of cations, all of them being corrugated [25]. Figure 9 shows the arrangement of the oxygen ions in the (222) plane of Ce₂O₃. As explained for the determination of the Kagome lattice, there are many vacancies in this plane, and these oxygen vacancies present a "Y" pattern [24, 25]. This Y pattern can explain the dissociation of [101] into two partials is shown in Figure 9 with the movement of oxygen atoms along the direction [1\bar{1}2] or [221]. The dissociation of the dislocation can hence be explained by the oxygen vacancies and also by considering the Ce cations are all equivalents even if they are not on the same wyckoff sites, as schematically represented by Gaboriaud et al. [25] from results obtained by Ning et al. [44].
<figure><img src="image_10.png" /><figcaption>Figure 9: Oxygen {222} plane containing vacancies forming a Y pattern. The Burgers vectors of the perfect and partial dislocations are indicated by blue and black arrows, respectively. Atom movements are facilitated at the vicinity of the Y patterns thanks to dislocation dissociation.</figcaption></figure>
In order to confirm that oxygen vacancies are at the origin of dislocation dissociation and stacking fault formation in bixbyite-Ce₂O₃, we study hereafter how the "oxygen-deficient" state affects the mechanical behavior of an individual nanocube. Figure 10 shows the strain-stress curves and microstructural changes in an individual nanocube during four successive compression tests. The zone axis is [110], whereas the compression axis is [100]. In these consecutive tests, quantitative values of the slopes are not given as the uncertainty on Young's modulus greatly depends on the contact geometry and accuracy. The elastic properties of fluorite and bixbyite cerium oxide nanocubes are discussed elsewhere in light of DFT + U calculations [19]. The yield stresses correspond to the first important change in the slope of the curve. The amount of plastic deformation is measured directly from the curves. It is 11.0 % for the first test, then 9.3 and 5.5 % are added at the end of the 2nd and 3rd tests. Thus, at the end of the 2nd test, total plastic deformation is 20.3 % (25.8 % at the end of the 3rd test). For the 4th test, considering that the first 4.8 % of engineering strain corresponds to a reorientation of the nanocube, the strain rate is measured equal to 23.2 % (total plastic strain 49 %).

For the first and third tests, the cube exhibits a bixbyite structure, with oxygen vacancies forming the Y-pattern described before. Interestingly, stacking faults appear during compression. On the contrary, the second and fourth tests are performed on fluorite, which does not contain any oxygen vacancy. No stacking fault can be observed. A detailed study of the contrasts occurring in fluorite at low electron dose reveals that deformation occurs mainly through the glide of perfect screw dislocations from the ⟨110⟩{111} slip system [46]. The yield stress increases from the first to the last compression test, which could be due to the fact there is an accumulation of defects causing the nanocube to harden [47]. However, a significant decrease of the yield stress is observed between the second and third test, which can be correlated with the formation of stacking faults. It can hence be concluded that the presence of oxygen vacancies are the cause of dislocation dissociation and stacking fault formation, and consequently reduce the yield stress.

Such experiment sheds new light on the appearance of the stacking faults. Indeed, the stacking faults disappear when the beam is blanked. Phase transformation from fluorite to bixbyite is known to occur at high electron dose rate. Moreover, it is reversible as the sample can easily be oxidized again thanks to residual oxygen present in the microscope column [48]. The disappearance of stacking faults can therefore be attributed to the reducing
<figure><img src="image_11.png" /><figcaption>Figure 10: stress-strain curves and images before/after four successive compression tests on the same individual nanocube, observed with the zone axis [110]. Under a high electron dose rate, the nanocube exhibits the bixbyite structure, whereas the fluorite structure is preserved with a low electron dose rate. The beam is blanked between the tests, so that the nanocube can return into the fluorite structure before each test thanks to the residual oxygen present in the vacuum. Stacking faults are found to occur only in bixbyite.</figcaption></figure>
effect of the electron beam and is further evidence of the key role played by
oxygen vacancies. Moreover, one specific type of mechanism can account to
the formation and the disappearance of the stacking faults: crystallographic
shear. Crystallographic shear is known to occur in metal oxides composed of
MeO₆ octahedrons, rutile TiO₂ being the most famous example [49]. In such
materials, extended defects - so-called Wadsley defects - are created through
ordering on anion vacancies, leading to the removal of whole anion planes.
The formation of Wadsley defects has also been observed *in situ* in TiO₂ un-
der electrical bias [50]. Bixbyite is actually not composed of MeO₆ octahedra.
It should rather be schematically represented as a metal ion surrounded by
a cube of oxygen atoms, with two missing oxygen atoms, located either on a
diagonal of the cube, or on a diagonal of a face [39]. However, a pre-condition
for the growth of a Wadsley defect is its direct contact with the free surface.
Indeed, in that configuration, the dislocation loop surrounding the Wadsley
defect is in contact with the surface and promotes the diffusion of oxygen
towards the external surface [49]. Although the dissociation scheme is dif-
ferent, such structures have been observed in bixbyite Y₂O₃ under electron
irradiation, using weak-beam dark field imaging. The authors explained the
observations by pipe diffusion of oxygen through the dislocation core. They
however did not identify the chemical composition of the extended defects
[43]. In nano-objects, dislocations are generally found to nucleate at the sur-
face [51, 52] so the perfect dislocations could indeed act as pipes for oxygen
diffusion, which would facilitate the formation of Wadsley defects. Actually,
pipe diffusion may not even be required as the small size of the sample is
known to promote the re-insertion of oxygen [48], which indicates that oxy-
gen diffusion is very easy in bixbyite-Ce₂O₃. On the contrary, the absence of
oxygen vacancies seems to hinder oxygen diffusion and hence the formation
of Wadsley defects. From that point of view, even though the cerium atoms
are not surrounded by 6 oxygen ones in bixbyite, oxygen diffusion and sub-
sequent vacancy ordering can fully explain the formation of Wadsley defects
upon loading, their disappearance during beam blanking and their absence
in vacancy-free fluorite.

**4. Conclusions**

In this work, we used advanced high resolution transmission electron mi-
croscopy combined with *in situ* mechanical testing to investigate the deforma-
tion mechanism of individual Ce₂O₃ nanocubes with the bixbyite structure.
The nanocubes were found to be initially defect-free. In a 52 *nm* nanocube observed with the zone axis [110] and compressed along the [100] direction, a perfect 1/4[101] 60°-mixed dislocation was indexed close to the nanocube free surface. The magnitude of the Burgers vector suggests that the cerium sublattice - and not the oxygen one - is involved into the formation of this dislocation.

The vicinity of oxygen vacancies in the {111} planes facilitates its dis-
sociation into two partials with Burgers vectors 1/12⟨112⟩, according to the
following dissociation scheme: 1/4[101] → 1/12[112] + 1/12[211]. The dissocia-
tion into two partials is accompagnied with the formation of a stacking fault.
By submitting an individual nanocube to successive compression cycles with
different irradiation conditions, we could test the same nanocube with two
different crystallographic phases: the initial one, fluorite, with no oxygen
vacancies on one side, and the irradiated one, bixbyite, with oxygen vacan-
cies in the {111} planes on the other side. Extended defects were found to
be formed in bixbyite but not in fluorite. Moreover, when they could be
healed after unloading by blanking the electron beam, a condition known to
re-oxidize the sample, which returns to the fluorite phase. Although Ce₂O₃
does not contain the MeO₆ octahedra that re-arrange by crystallographic
shear in metal oxide, the mechanism of Wadsley defect formation, involving
oxygen diffusion and vacancy ordering, can fully explain our observations.
The absence of oxygen vacancies hinders oxygen diffusion in fluorite, which
leads to a higher yield stress. This suggests that the main diffusion pipes in
bixbyite are actually not the dislocation cores, but the {111} planes contain-
ing the oxygen vacancies.

Lastly, this study highlights the capabilities of *in situ* mechanical testing
in advanced transmission electron microscopy. The stability of up-to-date
systems enables the acquisition of high resolution images all along the tests
on individual nanoparticles of size a few tens of nanometers. In combina-
tion with crystallographic considerations, such as the layered atom stacking
concept, very precise pieces of information regarding the deformation mech-
anism can be obtained. This is crucial for the design of nanomaterials with
optimized mechanical properties.

**5. Declaration of competing interests**

The authors declare no financial interests/personal relationships which
may be considered as potential competing interests.
## 6. Data availability

Data will be made available on request.

## 7. Acknowledgements

This work was funded by the Labex IMust (project NANODEF), the French National Research Agence ANR (Project ANR-18-CE42-0009). The authors acknowledge the Consortium Lyon Saint-Etienne de Microscopie (CLYM) for the access to the microscope. KMV and LJP acknowledges P. Cordier for fruitful discussion.

## 8. Supporting information

The raw video is available online at:
https://www.youtube.com/watch?v=Taa5_xLTzKM

A zoomed-in view of the raw video at the location of the zone of interest shown in figure 3 is given as supporting information.

## References

[1] J. Glucklich, L. J. Cohen, Size as a factor in the brittle-ductile transition and the strength of some materials, International Journal of Fracture Mechanics 3 (1967) 278-289. URL: https://doi.org/10.1007/BF00182893. doi:10.1007/BF00182893.

[2] W. Gerberich, J. Michler, W. Mook, R. Ghisleni, F. Östlund, D. Stauffer, R. Ballarini, Scale effects for strength, ductility, and toughness in “brittle” materials, Journal of Materials Research 24 (2009) 898-906. doi:10.1557/jmr.2009.0143.

[3] E. Calvié, J. Réthoré, L. Joly-Pottuz, S. Meille, J. Chevalier, V. Garnier, Y. Jorand, C. Esnouf, T. Epicier, J. Quirk, et al., Mechanical behavior law of ceramic nanoparticles from transmission electron microscopy in situ nano-compression tests, Materials Letters 119 (2014) 107-110.

[4] I. Issa, J. Amodeo, J. Réthoré, L. Joly-Pottuz, C. Esnouf, J. Morthomas, M. Perez, J. Chevalier, K. Masenelli-Varlot, In situ investigation of MgO nanocube deformation at room temperature, Acta Materialia 86 (2015) 295-304.
[5] J. Luo, J. Wang, E. Bitzek, J. Y. Huang, H. Zheng, L. Tong, Q. Yang, J. Li, S. X. Mao, Size-dependent brittle-to-ductile transition in silica glass nanofibers, Nano letters 16 (2016) 105–113.

[6] I. Issa, L. Joly-Pottuz, J. Réthoré, C. Esnouf, T. Douillard, V. Garnier, J. Chevalier, S. Le Floch, D. Machon, K. Masenelli-Varlot, Room temperature plasticity and phase transformation of nanometer-sized transition alumina nanoparticles under pressure, Acta Materialia 150 (2018) 308–316.

[7] J. Li, J. Cho, J. Ding, H. Charalambous, S. Xue, H. Wang, X. L. Phuah, J. Jian, X. Wang, C. Ophus, et al., Nanoscale stacking fault-assisted room temperature plasticity in flash-sintered TiO₂, Science advances 5 (2019) eaaw5519.

[8] A. J. Wagner, E. D. Hintsala, P. Kumar, W. W. Gerberich, K. A. Mkhoyan, Mechanisms of plasticity in near-theoretical strength sub-100nm Si nanocubes, Acta Materialia 100 (2015) 256–265. URL: https://www.sciencedirect.com/science/article/pii/S1359645415006060. doi:https://doi.org/10.1016/j.actamat.2015.08.029.

[9] I. Issa, L. Joly-Pottuz, J. Amodeo, D. J. Dunstan, C. Esnouf, J. Réthoré, V. Garnier, J. Chevalier, K. Masenelli-Varlot, From dislocation nucleation to dislocation multiplication in ceramic nanoparticle, Materials Research Letters 9 (2021) 278–283.

[10] D. Dunstan, A. Bushby, The scaling exponent in the size effect of small scale plastic deformation, International Journal of Plasticity 40 (2013) 152–162. URL: https://www.sciencedirect.com/science/article/pii/S0749641912001180. doi:https://doi.org/10.1016/j.ijplas.2012.08.002.

[11] J. R. Greer, W. C. Oliver, W. D. Nix, Size dependence of mechanical properties of gold at the micron scale in the absence of strain gradients, Acta Materialia 53 (2005) 1821–1830. URL: https://www.sciencedirect.com/science/article/pii/S1359645404007670. doi:https://doi.org/10.1016/j.actamat.2004.12.031.

[12] L. Li, B. Zhu, J. Zhang, C. Yan, Y. Wu, Electrical properties of nanocube CeO₂ in advanced solid oxide fuel cells, International Journal of Hydrogen Energy 43 (2018) 12909–12916. URL:
https://www.sciencedirect.com/science/article/pii/S0360319918316653.
doi:https://doi.org/10.1016/j.ijhydene.2018.05.120, china-Europe Fo-
rum for Advanced Fuel Cell and New Energy.

[13] M. S. Arshad, C. Billing, D. G. Billing, W. Guan, Phase-assisted tailored conductivity of doped ceria electrolytes to boost SOFC performance, ACS Applied Materials & Interfaces 15 (2023) 39396-39407.

[14] D. Baier, T. Priamushko, C. Weinberger, F. Kleitz, M. Tiemann, Selec-
tive discrimination between CO and H₂ with copper-ceria-resistive gas
sensors, ACS sensors 8 (2023) 1616-1623.

[15] I. Trenque, G. C. Magnano, M. A. Bolzinger, L. Roiban, F. Chaput, I. Pitault, S. Briançon, T. Devers, K. Masenelli-Varlot, M. Bugnet, D. Amans, Shape-selective synthesis of nanoceria for degradation of paraoxon as a chemical warfare simulant, Phys. Chem. Chem. Phys. 21 (2019) 5455-5465. URL: http://dx.doi.org/10.1039/C9CP00179D. doi:10.1039/C9CP00179D.

[16] X. Feng, D. C. Sayle, Z. L. Wang, M. S. Paras, B. Santora, A. C. Sutorik, T. X. Sayle, Y. Yang, Y. Ding, X. Wang, et al., Converting ceria polyhedral nanoparticles into single-crystal nanospheres, Science 312 (2006) 1504-1508.

[17] A. G. Evans, P. L. Pratt, Dislocations in the fluorite struc-
ture, The Philosophical Magazine: A Journal of Theo-
retical Experimental and Applied Physics 20 (1969) 1213-
1237. URL: https://doi.org/10.1080/14786436908228207.
doi:10.1080/14786436908228207. arXiv:https://doi.org/10.1080/14786436908228207.

[18] W. M. Sherry, J. B. V. Sande, TEM investigation of the plastic de-
formation behaviour of calcium fluoride, Philosophical Magazine A 40
(1979) 77-95. URL: https://doi.org/10.1080/01418617908234834.
doi:10.1080/01418617908234834. arXiv:https://doi.org/10.1080/01418617908234834.

[19] L. Joly-Pottuz, R. Zhang, T. Albaret, T. Epicier, I. Jenei, M. Co-
bian, D. Stauffer, M.-V. Karine, CeOₓ elastic properties: An in
situ nanocompression study in environmental transmission electron mi-
croscopy (etem), JOM 76 (2024) 2326-2335.
[20] J. L. F. Da Silva, Stability of the Ce₂O₃ phases: A DFT+U investigation, Phys. Rev. B 76 (2007) 193108. URL: https://link.aps.org/doi/10.1103/PhysRevB.76.193108. doi:10.1103/PhysRevB.76.193108.

[21] J. Mouzon, Synthesis of Yb:Y₂O₃ nanoparticles and fabrication of transparent polycrystalline yttria ceramics, 2005. Godkänd; 2005; 20061221 (haneit).

[22] R. J. Gaboriaud, J. Cadoz, Etude par microscopie électronique à haute tension de la configuration des dislocations, dans l'oxyde d'yttrium (y2o3) monocristallin déformé plastiquement, physica status solidi (a) 52 (1979) 95-101. URL: https://onlinelibrary.wiley.com/doi/abs/10.1002/pssa.2210520110. doi:https://doi.org/10.1002/pssa.2210520110.
arXiv:https://onlinelibrary.wiley.com/doi/pdf/10.1002/pssa.2210520110.

[23] R. J. Gaboriaud, M. Boisson, Dislocation studies.dissociation of the dislocation and plasticity of the yttrium sesquioxyde : Y2o3, J. Phys. Colloques 41 (1980) C6-171-C6-174. URL: https://doi.org/10.1051/jphyscol:1980644. doi:10.1051/jphyscol:1980644.

[24] K. Sikafus, R. Grimes, S. Corish, A. Cleave, M. Tang, C. Stanek, B. Uberuaga, J. Valdez, Layered atom arrangements in complex materials, Technical Report, Los Alamos National Lab.(LANL), Los Alamos, NM (United States), 2005.

[25] R. Gaboriaud, OverviewADFO. dislocations in anion-deficient fluorite-type oxides under harsh environment: Re2o3, pyrochlores, -phase., 2024. doi:10.13140/RG.2.2.28895.64167.

[26] Y. He, X. Ren, Y. Xu, M. H. Engelhard, X. Li, J. Xiao, J. Liu, J.-G. Zhang, W. Xu, C. Wang, Origin of lithium whisker formation and growth under stress, Nature Nanotechnology 14 (2019) 1042-1047. URL: https://doi.org/10.1038/s41565-019-0558-z. doi:10.1038/s41565-019-0558-z.

[27] Q. Liu, L. Zhang, H. Sun, L. Geng, Y. Li, Y. Tang, P. Jia, Z. Wang, Q. Dai, T. Shen, Y. Tang, T. Zhu, J. Huang,
In situ observation of sodium dendrite growth and concurrent mechanical property measurements using an environmental transmission electron microscopy-atomic force microscopy (etem-afm) platform, ACS Energy Letters 5 (2020) 2546–2559. URL: https://doi.org/10.1021/acsenergyylett.0c01214.

doi:10.1021/acsenergyylett.0c01214. arXiv:https://doi.org/10.1021/acsenergyylett.0c01214.

[28] J. Qu, X. Liu, Recent advances on sem-based in situ multiphysical characterization of nanomaterials, Scanning (2021).

doi:https://doi.org/10.1155/2021/4426254.

[29] G. Nkou Bouala, N. Clavier, J. Léchelle, A. Mesbah, N. Dacheux, R. Podor, In situ HT-ESEM study of crystallites growth within CeO₂ microspheres, Ceramics International 41 (2015) 14703–14711. URL:

https://www.sciencedirect.com/science/article/pii/S0272884215015060.

doi:https://doi.org/10.1016/j.ceramint.2015.07.194.

[30] D.-G. Xie, R.-R. Zhang, Z.-Y. Nie, J. Li, E. Ma, J. Li, Z.-W. Shan, Deformation mechanism maps for sub-micron sized aluminum, Acta Materialia 188 (2020) 570–578.

[31] S. Lee, A. Vaid, J. Im, B. Kim, A. Prakash, J. Guénolé, D. Kiener, E. Bitzek, S. H. Oh, In-situ observation of the initiation of plasticity by nucleation of prismatic dislocation loops, Nature communications 11 (2020) 2367.

[32] B. Miao, S. Kondo, E. Tochigi, J. Wei, B. Feng, N. Shibata, Y. Ikuhara, The core structure of 60° mixed basal dislocation in alumina (α-AL₂O₃) introduced by in situ TEM nanoindentation, Scripta Materialia 163 (2019) 157–162. URL:

https://www.sciencedirect.com/science/article/pii/S1359646219300260.

doi:https://doi.org/10.1016/j.scriptamat.2019.01.011.

[33] E. Tochigi, B. Miao, S. Kondo, N. Shibata, Y. Ikuhara, TEM Characterization of Lattice Defects Associated with Deformation and Fracture in α-Al₂O₃, Springer Nature Singapore, Singapore, 2022, pp. 133–156. URL:

https://doi.org/10.1007/978-981-16-7715-17.doi : 10.1007/978-981-16-7715-17.X. Wang, S. Zheng, C. Deng, C. R.Weinberger, G. Wang, S. X.Mao, I. scaleobservationof5-foldtwininformationinnanoscalecrystalundermechanicalloading, Nanoscale 5, 1522–1532.
[34] D. Pang, W. Li, N. Zhang, H. He, S. Mao, Y. Chen, L. Cao, C. Li, A. Li, X. Han, Direct observation of oxygen vacancy formation and migration over ceria surface by in situ environmental transmission electron microscopy, Journal of Rare Earths 42 (2024) 676-682.

[36] Z. Wu, M. Li, J. Howe, H. M. I. Meyer, S. H. Overbury, Probing defect sites on CeO₂ nanocrystals with well-defined surface planes by raman spectroscopy and O₂ adsorption, Langmuir 26 (2010) 16595-16606.
URL: https://doi.org/10.1021/la101723w. doi:10.1021/la101723w.
arXiv:https://doi.org/10.1021/la101723w, PMID: 20617854.

[37] Z.-A. Qiao, Z. Wu, S. Dai, Shape-controlled ceria-based nanostructures for catalysis applications, ChemSusChem 6 (2013) 1821-1833.
URL: https://chemistry-europe.onlinelibrary.wiley.com/doi/abs/10.1002/cssc.201300428.
doi:https://doi.org/10.1002/cssc.201300428.

arXiv:https://chemistry-europe.onlinelibrary.wiley.com/doi/pdf/10.1002/cssc.201300428.

[38] I. Trenque, G. C. Magnano, M. A. Bolzinger, L. Roiban, F. Chaput, I. Pitault, S. Briançon, T. Devers, K. Masenelli-Varlot, M. Bugnet, et al., Shape-selective synthesis of nanoceria for degradation of paraoxon as a chemical warfare simulant, Physical Chemistry Chemical Physics 21 (2019) 5455-5465.

[39] Boisson, M., Gaboriaud, R.J., Calculs d'énergie de faute d'empilement dans le sesquioxyde d'yttrium (Y₂O₃), J. Physique Lett. 38 (1977) 177-181.
URL: https://doi.org/10.1051/jphyslet:01977003808017700.

doi:10.1051/jphyslet:01977003808017700.

[40] J. Venables, Deformation twinning in face-centred cubic metals, Philosophical magazine 6 (1961) 379-396.

[41] K. Lagerlöf, J. Castaing, P. Pirouz, A. Heuer, Nucleation and growth of deformation twins: a perspective based on the double-cross-slip mechanism of deformation twinning, Philosophical Magazine A 82 (2002) 2841-2854.

[42] J. Huang, Y. Wu, H. Ye, Deformation structures in ball milled copper, Acta materialia 44 (1996) 1211-1221.
[43] R. J. Gaboriaud, Dislocation core and pipe diffusion in Y₂O₃, Journal of Physics D: Applied Physics 42 (2009) 135410. URL: https://dx.doi.org/10.1088/0022-3727/42/13/135410. doi:10.1088/0022-3727/42/13/135410.

[44] X. Ning, H. Ye, In situ observations of dislocation motion and relevant surface phenomena in eu2o3, Philosophical Magazine A 62 (1990) 431–446.

[45] M. Mekata, Kagome: The story of the basketweave lattice, Physics Today 56 (2003) 12–13.

[46] R. Zhang, L. Joly-Pottuz, F. Chaput, D. Dunstan, K. Masenelli-Varlot, to be published (2025).

[47] D. D. Stauffer, A. Beaber, A. Wagner, O. Ugurlu, J. Nowak, K. Andre Mkhoyan, S. Girshick, W. Gerberich, Strain-hardening in submicron silicon pillars and spheres, Acta Materialia 60 (2012) 2471–2478. URL: https://www.sciencedirect.com/science/article/pii/S1359645411007506. doi:https://doi.org/10.1016/j.actamat.2011.10.045.

[48] A. C. Johnston-Peck, J. S. DuChene, A. D. Roberts, W. D. Wei, A. A. Herzing, Dose-rate-dependent damage of cerium dioxide in the scanning transmission electron microscope, Ultramicroscopy 170 (2016) 1–9. URL: https://www.sciencedirect.com/science/article/pii/S0304399116300936. doi:https://doi.org/10.1016/j.ultramic.2016.07.002.

[49] S. Mrowec, On the defect structure in nonstoichiometric metal oxides, Ceramurgia International 4 (1978) 47–58. URL: https://www.sciencedirect.com/science/article/pii/0390551978901199. doi:https://doi.org/10.1016/0390-5519(78)90119-9.

[50] R. J. Kamaladasa, A. A. Sharma, Y.-T. Lai, W. Chen, P. A. Salvador, J. A. Bain, M. Skowronski, Y. N. Picard, In Situ TEM Imaging of Defect Dynamics under Electrical Bias in Resistive Switching Rutile-TiO₂, Microscopy and Microanalysis 21 (2014) 140–153. URL: https://doi.org/10.1017/S1431927614013555. doi:10.1017/S1431927614013555. arXiv:https://academic.oup.com/mam/article-pdf/21/
[51] D. Mordehai, O. David, R. Kositski, Nucleation-controlled plasticity of metallic nanowires and nanoparticles, Advanced Materials 30 (2018) 1706710. URL: https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201706710. doi:https://doi.org/10.1002/adma.201706710. arXiv:https://onlinelibrary.wiley.com/doi/pdf/10.1002/adma.201706710.

[52] J. Amodeo, E. Maras, D. Rodney, Site dependence of surface dislocation nucleation in ceramic nanoparticles, npj Computational Materials 7 (2021). URL: https://doi.org/10.1038/s41524-021-00530-8. doi:10.1038/s41524-021-00530-8. arXiv:https://doi.org/10.1038/s41524-021-00530-8.