# Atomic force microscopy and transmission electron microscopy identification of deformation twinning in the Cr2AlC MAX phase

Salomé Parent, Anne Joulain, Hadi Bahsoun, Gilles Renou, Thierry Ouisse, Patrick Villechaise, Christophe Tromas

► To cite this version:

Salomé Parent, Anne Joulain, Hadi Bahsoun, Gilles Renou, Thierry Ouisse, et al. Atomic force microscopy and transmission electron microscopy identification of deformation twinning in the Cr2AlC MAX phase. Acta Materialia, 2024, 270, pp.119836. 10.1016/j.actamat.2024.119836. hal-04562546

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Submitted on 17 Apr 2025

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# Atomic Force Microscopy and Transmission Electron Microscopy identification of deformation twinning in the Cr₂AlC MAX phase

Salomé Parent¹, Anne Joulain¹, Hadi Basoun¹, Gilles Renou², Thierry Ouisse³, Patrick Villechaise¹, Christophe Tromas¹

¹ Intitut Pprime, UPR 3346 CNRS - UNIVERSITE de POITIERS – ENSMA, Département de Physique et Mécanique des Matériaux, 11 Bd Marie et Pierre Curie, Site du Futuroscope, TSA 41123, 86073 Poitiers CEDEX 9, France

² SIMaP-PM, 1130 Rue de la Piscine, Batiment ECOMARCH, BP75, 38402 St Martin d'Heres cedex, France

³ Univ. Grenoble Alpes, CNRS, Grenoble INP, LMGP, 38000 Grenoble, France

Corresponding author: christophe.tromas@univ-poitiers.fr +33 5 49 49 66 60

## ABSTRACT:

Elementary deformation mechanisms have been investigated in a single-crystalline Cr₂AlC MAX phase. Plastic deformation has been induced at room temperature by spherical nanoindentation, with a crystal orientation chosen to minimize basal slip and to promote local crystal reorientation. The combination of Atomic Force Microscopy surface observation, Transmission Electron Microscopy (TEM) characterization and Automated Crystal Orientation Mapping in a same region has provided a full 3D characterization of the deformation microstructure. Localized and isolated deformation twins have been identified below the indents. The whole microstructure consists in interactions between dislocations and {112̄4} twin variants. The TEM analysis also revealed activation of a 1/3 < 112̄0 > {1103} slip system never reported before in a MAX phase.

## KEYWORDS :

MAX phase, Nanoindentation, Nanomechanical testing, Twinning, Dislocation, Plasticity

## 1. INTRODUCTION

The ternary compounds known as MAX phases are a class of nano-lamellar ternary nitrides or carbides [1–4]. They name comes from their general formula M<sub>n+1</sub>AX<sub>n</sub>, where M is a transition metal, A is a A-group element, X is carbon or nitrogen, and n ranges from 1 to 3. Although these materials present
many interesting physical properties [5], their deformation mechanisms remain not well understood. MAX phases possess a hexagonal crystallographic structure, and like many hexagonal metals, their plastic behavior is mainly governed by basal slip with the classical $\frac{1}{3}\langle(11\bar{2}0)\rangle_{\{0001\}}$ slip systems [6–12]. In the last ten years, nanomechnical testing has often been used to investigate plasticity in MAX phases at small scale [13–19]. However, basal slip does not provide enough independent slip systems to account for any plastic deformation. Kink bands is a mechanism consisting in the formation of two dislocation walls of opposite Burgers vectors, in other words, two low angle tilt boundaries, that has been widely reported in MAX phases [20,21], as well as in hexagonal metals [22,23]. Kink bands result in local crystal reorientation and thus may help overcoming the lack of slip systems. Deformation twinning is another mechanism frequently observed in many hexagonal metals, which also allows for local crystal reorientation [24–28]. Recently, deformation twinning has been reported and characterized in the Ti₂AlN MAX phase after high temperature nanoindentation [29]. This was new since twinning had been ruled out in the early papers about MAX phases [20,30,31]. However, the question of the influence of the temperature in the twinning process was still open. Furthermore, a Berkovich indenter had been used at high load resulting in a complex deformation structure with many twin boundaries and secondary twinning. Finally, since the sample was a polycrystal, it was not easy to repeat the experiment in a similar crystal orientation and then to check the reproducibility of the deformation process.

The present study aims at going further in the understanding of the role played by twinning in the deformation process in MAX phases. For this purpose, nanoindentation test have been performed at room temperature with a spherical indenter. The plastic zone developed with this indenter shape is both less dense and more extended compared to that produced by a Berkovich indenter, which makes easier the identification of isolated defects. Furthermore, it is now possible to synthesize macroscopic single crystals of MAX phases [32,33]. We thus used Cr₂AlC single crystals oriented in such a way that the basal plane was edge on. This configuration is the less favorable for basal slip under the spherical indenter, so that other deformation mechanisms should be promoted. Furthermore, working with a single crystal offers the opportunity to check the reproducibility of the deformation processes, allowing to repeat a same indentation procedure in the same surface orientation.

In order to get a complete and accurate 3D characterization of the plastic zone generated around the indent, different techniques have been combined in the same area. Surface deformation around the spherical indents has been characterized by Atomic Force Microscopy (AFM), while the dislocation distribution in the volume has been revealed by Transmission Electron Microscopy (TEM) analysis in lamellas extracted in cross section through the same indents. The same individual defects have been thus characterized both through the traces they left at the surface and from their final position in the
volume. Then, crystallographic orientation maps have been built in the same TEM lamella thanks to
the ACOM-ASTAR technique [34] in order to identify the local crystallographic rotation in relation with
the defects. A particular attention has been paid to specific misorientation relationship allowing to
identify {1124} deformation twinning. Finally, a detailed analysis of a complex dislocation
configuration has revealed cross slip of basal dislocation through the activation of a 1/3 <1120>
{1103} slip system, never observed before in a MAX phase.

## 2. MATERIALS AND METHODS

Cr₂Alc single crystal has been synthesised by high temperature solution growth [32]. The produced sample was a platelet of two cm² (cf. Fig 1a), oriented along the basal plane, with a thickness of 500µm. The platelet has been embedded edge on in a bakelite resin (cf. Fig 1b) to be ground with resin bonded diamond discs, and mechanically polished with diamond suspensions with grain size ranging from 6 µm down to 1 µm. A final chemo-mechanical polishing stage has been performed with colloidal silica to remove work hardened surface layer, in order to achieve a surface free of defect and with a RMS roughness better than 1 nm. The crystallographic orientation of the final surface has been

characterized by Electron Back Scattered Diffraction (EBSD). It appeared that the basal plane was
perfectly edge on and that the surface was at 3.3 degrees from a (1120) plane.

Nanoindentation tests have been performed at room temperature in force-controlled mode with an
Ultra Nano-Hardness Tester U-NHT from Anton Paar equipped with a spherical diamond tip with a
radius of curvature of 5.3 µm (Fig. 1c). Surface deformation around the indent has been characterized
by Atomic Force Microscopy (AFM) using a Dimension D3100 microscope from Bruker operated in
tapping mode. AFM images were processed with the software WSxM [35].

Transmission Electron Microscopy (TEM) thin foils have been extracted by Focused Ion Beam (FIB) with
a Helios NanoLab G3 CX from Thermo Fisher Scientific. The thin foils have been cut parallel to the basal
plane, at the centre of the indents and were about 10 µm long, 5 µm wide and 80 to 100 nm thick.

<figure><img src="image_2.png" /><figcaption>**Figure 1:** (a) Cr₂Alc single crystal, (b) schematic of the single crystal embedded with the basal plane edge on, (c) schematic of the basal plane orientation relative to the indented surface.</figcaption></figure>
Then the thin foils have been characterized by two TEM, a 3010 form JEOL and a TALOS F200S G2 from ThermoFisher Scientific. Local crystallographic orientation maps have been then obtained on the same thin foil with the ACOM-ASTAR technique using a 2100 TEM from JEOL. Crystallographic orientation data have been analysed with MTEX-MATLAB toolbox [36], Pycotem [37] and ATEX softwares [38]. Four similar indents have been characterized in the same manner (AFM, TEM and ACOM-ASTAR).

# 3. Results

## 3.1. NANOINDENTATION INDUCED DEFORMATION

Fig 2a and 2b present the nanoindentation curve and the AFM observation of a spherical nanoindentation performed at 9 mN. For such a low load, the residual depth of the indent is about 4 nm, and the surface deformation reveals only parallel steps along the [10̄10] direction, which are slip lines due to the activation of basal slip in adjacent planes. As shown on the cross section in the inset of Fig 2b, the height of these steps is lower than 1 nm, so that each of them correspond to the *gliding* of few dislocations. As schematically presented in Fig 1c, this slip lines distribution is expected since the shear in basal plane must be maximum in the planes tangent to the contact circle. Furthermore, the Hertz law, which corresponds to a purely elastic sphere-plane contact, has been plotted for comparison on the nanoindentation curve. It shows that the first deviation from an elastic contact appears at a penetration depth of about 20 nm (a *pop-in* can be distinguished on the loading curve), which corresponds to a contact

circle between the indenter and the surface of 0.65µm in diameter. In the same manner, even if some

<figure><img src="image_3.png" /><figcaption>Figure 2: Nanoindentation curves (a) and AFM image (b) of a 9 mN spherical indent. The green and blue circles indicate the contact circle at the first pop in and at maximum load. (c) and (d), same analysis for a 90 mN indent. In addition to basal slip lines, traces at 64° from the basal slip line are observed around 90 mN indents (blue arrows in (d) and (e)).</figcaption></figure>
plastic deformation has taken place, the contact diameter at maximum penetration depth has been estimated from the Hertz law to be 1.10 µm. These two contact circles have been represented in the AFM image in Fig. 2b and it can be observed that most of the slip lines are comprised within these two circles, confirming that basal slip has been activated in successive planes tangent to the contact circle all along the penetration of the indenter.

Fig. 2c and 2d present the case of a 90 mN load spherical indent with a residual depth of 170 nm. Many basal slip lines are still observed, but in this case the residual indent has a more pronounced spherical shape. Interestingly, several unexpected surface traces can be observed on both side of the indent (cf. blue arrows Fig. 2d). These traces are oriented at 64° from the basal slip traces. It must be mentioned that these traces have been systematically observed around the four indents performed in similar conditions. Fig 2e present an AFM 3D view of one of these traces at smaller scale. It can be seen that this defect is not a step, but a slope of few degrees with a width of about 50 nm. This defect will be called S defect in the following. It can also be observed that the direction of the basal slip traces changes inside the S defect (particularly clear in the upper part of Fig. 2e), showing that this defect corresponds probably to a local crystal rotation. All these reasons lead to consider that the S defect may be the surface trace of a deformation twin. To go further with this hypothesis, this defect will be now characterized in the volume.

A TEM lamella has been cut by focused ion beam parallel to the basal plane across the 90mN indent shown in Fig. 2d. Fig. 3 combines the AFM surface observation of the residual spherical indent and a TEM image, with an inset showing the position of the extracted lamella relative to the indent. The TEM image is a bright field image obtained with the sample only slightly disoriented from the [0001] zone axis in order to obtain a fine contrast of microstructural defects. In such conditions, the thin foil is tilted of only few degrees that allows correspondence between the AFM image of the surface and TEM image in volume. Defects on surface match perfectly with defects visible in the volume, on the TEM image.

<figure><img src="image_4.png" /><figcaption>Figure 3: Combination of AFM and TEM image of the 90 mN spherical indent shown fig 2d. The S defect is observed both at the surface and in the volume. A high density of basal plane dislocations is observed below de indent as well as thin horizontal bands in dark contrast ($H_0$ to $H_3$). On the left, an isolated dislocation structure (L) looks like a ladder.</figcaption></figure>
The first observation from the TEM image is the confined deformation structure. Just below the indent, a highly deformed area of 1.5µm depth and 3.5µm width is observed. The defect density is too high to analyse individual dislocations or other defect features. Below this area, a dislocation structure is in contrast down to 6 µm below the surface whereas the residual depth of the indent is only 170 nm. Most of the dislocations present long segments lying in the basal plane with some junctions. This area is delimited by curved dislocation segments. Thin horizontal bands, about 100 nm thick, are also visible in a dark contrast. They have been labelled H₀ to H₃ and will be analysed later in this paper. On the left, the crystal is free of defects except a long-isolated defect parallel to the [112̄0] direction. This defect, which looks like a ladder, will be labelled L defect, and will be described in detail in section 3.3. These characteristics are highly reproducible since they have been also observed in three other lamellas extracted from three similar indents.

Focusing on the area below the surface, a dark line parallel to the [1100] direction is visible. This defect matches exactly with the S defect observed at the surface. This is even more visible in Fig 4a and 4b, which is a comparison at the same scale of the AFM and TEM observations. Interestingly, one can notice in the AFM image that many tiny basal slip lines of few angstroms in height stop all along the same direction perpendicular to the basal plane trace. Since a slip line is the trace left at the surface by the propagation of dislocations, the end of a slip line reveals the final position of the emergence point of the dislocations. In this way, all these slip lines reveal a dislocation wall, that is basal dislocations lying in adjacent basal planes, one above the other, as schematically shown in Fig. 4a. At

the same position, a dark contrast in also observed in the TEM bright field in Fig 4b. In Fig. 4c, the sample has been tilted and the same area is observed in Weak Beam Dark Field with a diffraction vector $\vec{g} = 11\bar{2}0$. In this case, the dislocations composing this dislocation wall are easily resolved. Only few dislocations are observed since the dislocation wall is perpendicular to the TEM lamella which is less than 100 nm thick.

Thanks to the combination of AFM surface observation and TEM analysis, the S defect appears to be a thin planar defect intersecting the (112̄10) surface along a

<figure><img src="image_5.png" /></figure>

Figure 4: Observation of the S defect at the surface by AFM (a) and in cross section by TEM in bright field (b) and weak beam (c). A dislocation wall is also noticed edge on in the TEM image (b and c) and in the AFM image through the arrest points of the dislocation slip lines. The S defect lies in a (112̄4) plane as schematized in (d).
direction at 64° from the basal plane trace, and intersecting the basal plane along a [1100] direction. It can be concluded that the S defect is a thin band parallel to a (112̄4) plane which is the dense plane that satisfy these two geometrical conditions. This can be easily checked since the common direction between the indented (12̄10) surface and the (112̄4) plane is [404̄3]. The angle between this direction and the basal plane trace [101̄0] is effectively 62.7° for the lattice parameters of Cr₂AlC. This is schematically presented in fig 4d. At this point, it is thus established that the S defect is a thin planar defect induced during the nanoindentation test, which is parallel to a (112̄4) plane and produces a slope at the surface as well as a crystal reorientation. Cristal orientation mapping will thus be used to check whether this defect is a (112̄4) twin.

## 3.2. TWINS CHARACTERIZATION

Fig. 5a presents a misorientation map obtained by ACOM-ASTAR with a step size of 15 nm on the same TEM lamella as in Fig 3. The misorientation angles are relative to the less deformed region in the lower left corner of the map. The S defect as well as the H₀-H₃ bands identified in Fig 3, show a high misorientation contrast (the H₀ defect, which is thinner, is only hardly visible at this resolution). Since

S defect is suspected to be a {112̄4} twin, the method proposed by Wright and Larsen [39] and Mason et al [40], and applied in many deformation twins studies [41,42] will be used to check this hypothesis through the crystallographic orientation information. First, the expected misorientation angle for a {112̄4} twin in Cr₂AlC, which can be seen as a geometrical reflection of the parent crystal across the twin plane, is 48.2° (see Fig 5b). Fig. 5c present a second misorientation map with a higher resolution (5 nm step size) focused on the S defect, with an inset showing the plot of the misorientation from initial point across the S defect. It appears that the S defect is a thin band with a relative misorientation of 45°, which is in good agreement with the expected 48.2°.

<figure><img src="image_6.png" /></figure>

Figure 5: (a) and (c) Misorientation map relative to the non-deformed matrix (angular scale 0°-60°). (b) reflection twin for a hexagonal crystal with c/a=4.48. The misorientation angle between the parent and the twin is 48.2°. (d) {112̄4} pole figure of the region shown in (c). The circle in the pole figure highlights the overlapping of a pole from the matrix and the S defect, and the red solid line indicates the direction of boundary between the matrix and the S defect transferred to the pole figure.
Interestingly, this map also reveals the dislocation wall already identified in Fig. 4, with a misorientation angle of 1.5°. The second criterion to be checked, is the presence of a common normal to the twinning plane in the parent crystal and in the S defect. For this purpose, the {112̄4} pole figure has been plotted in Fig. 5d both for the S defect and for the rest of the area shown in Fig. 5c. It can be observed that the (112̄4) pole of the parent crystal overlaps the (2̄114) pole of the S defect demonstrating that these two regions share a common {112̄4} plane. Finally, the last criterion to check is the orientation of the trace of the potential twin boundary. The trace of the boundary of the S defect has been transferred in brown line on the pole figure in Fig. 5d. The normal to this trace, which has been plotted in dotted line, goes through the overlapping poles, showing that the trace of the S boundary correspond to the trace of a (112̄4) in the parent crystal. Finally, these three criteria (misorientation angle, common {112̄4} plane and boundary of the S defect parallel to a (112̄4) plane trace) confirm that the S defect is a (112̄4) deformation twin.

The same kind of analysis has been performed on the defects H₁-H₃. Fig. 6 presents a misorientation map centred on these three defects and obtained with a step size of 8 nm. Here again, the cross section in the misorientation map shows that defects H₁, H₂ and H₃ present a misorientation of *respectively* 46°, 47° and 46° relative to the parent crystal, which is very close to the 48.2° expected value. The {112̄4} pole figures have been plotted for these three defects and for the parent crystal. The overlapping poles, as well as the boundaries traces, show that H₁ and H₃ are both (1̄21̄4) twins (the indices being relative to the parent crystal), whereas the H₂ defect is a (1̄21̄4) twin.

Other highly misoriented domains are visible in Fig. 5a between the H₀ defect

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

**Figure 6:** (a) Misorientation map relative to the non-deformed matrix (angular scale 0°-60°). (b) Misorientation profile (from the initial point) across the H₃, H₂ and H₁ defects: *they respectively present a 46°, 47° and 46° misorientation relative to the matrix.* (c), (d) and (e), superpositions of the {112̄4} pole figures of parent crystal (matrix) and respectively the H₁, H₂ and H₃ defects. The circles in the pole figure highlight the overlapping of a pole from the matrix and the H defects, and the solid lines indicates the direction of boundary between the matrix and the different H defects transferred to the pole figure.
and the indented surface. However, due to their very low thickness, and the small number of corresponding indexed pixels, the analysis was not pursued in these defects.

For the sake of clarity, the analysis of the misorientation relationship of all the defects described above has been carried out with respect to the undeformed perfect crystal, so that the reference for misorientation angles has been chosen far from the ident and the deformation microstructure. Under these conditions, there is a small contribution from the dislocation structure in the measurement of misorientation angles that can explain the slight deviation from the theoretical twinning angle, or an imperfect pole overlap between the twin and the parent crystal poles. This is particularly true for the S defect which is close to the residual indent and surrounded by dislocation walls.

### 3.3. DISLOCATION STRUCTURE ANALYSIS: L DEFECT

The H twins, individually characterized above, are strongly related to the dislocation structure. Actually, the whole configuration is confined in a spherical region delimited by basal dislocation walls (cf. Fig. 7), these dislocations being pinned at the extremities of the H twin bands. This demonstrates the strong interaction between the dislocations and the twins.

Apart from the confined deformed structure containing twinned areas and dislocations lying in the basal plane, the long-isolated L defect extends in the defect free crystal parallel to the [112̄0] direction.

Wada *et al.* [21] observed by TEM a similar defect in Ti₂AlC MAX phase deformed by nano-indentation. As in our case, the Ti₂AlC phase was indented on a {112̄0} surface and the TEM lamella cut parallel to the basal plane. The authors proposed from a rough estimation the out of basal slip system {12̄11}{12̄16}. However, they did not perform any detailed dislocation analysis by extinction method. In the following we present a full dislocation characterisation, firstly, the Burgers vectors being determined by $\vec{g} \cdot \vec{b}$ two beams method and secondly the slip plane being determined by appropriate sample orientation.

<figure><img src="image_8.png" /><figcaption>**Figure 7:** TEM image (bright field obtained with $\vec{g}_5 = \vec{1}10\overline{3}$) showing the interaction between basal dislocations and the H₁, H₂ and H₃ twin boundaries. The L dislocation configuration, introduced in Fig. 3, is also visible.</figcaption></figure>
Figure 8a presents a zoom of figure 3 focused on the L defect. Individual dislocations segments are visible and it may be observed that the L defect is constituted of interactions between long and short dislocations segments. Long segments correspond to dislocations lying in the basal plane, they are labelled D1, D2, D3, D4 and D5 when short segments are out of the basal plane, they are labelled R. Figure 8b presents a weak beam image obtained with the diffraction vector $-\vec{g}_1 = 11\bar{2}0$. In these diffraction conditions, the dislocations with classical Burgers vectors observed in MAX phases ($\vec{b} = \frac{1}{3} < 11\bar{2}0 >$) are in contrast. A systematic study of the dislocation configuration has been performed by imaging it with different $g$ vectors in weak beam conditions. The used $g$ vectors are $-\vec{g}_1 = 11\bar{2}0$; $\vec{g}_1 = \bar{1}\bar{1}20$; $\vec{g}_2 = \bar{1}2\bar{1}0$; $-\vec{g}_2 = 1\bar{2}10$; $\vec{g}_3 = \bar{2}110$; $-\vec{g}_3 = 2\bar{1}\bar{1}0$; $\vec{g}_4 = \bar{1}103$; $\vec{g}_5 = \bar{1}10\bar{3}$; $\vec{g}_6 = 01\bar{1}3$; $\vec{g}_7 = 01\bar{1}\bar{3}$.

As an example, figures 8c and 8d show contrasts obtained respectively with $\vec{g}_5 = \bar{1}10\bar{3}$ and with $\vec{g}_6 = 01\bar{1}3$. We observe that short R segments are all out of contrast in figure 8c and in contrast in figure 8d. On the contrary, all long segments D are in contrast in figure 8c, when some (D₁, D₂, D₃ and D₄) are out of contrast in figure 8d, all long segments are in contrast in figure 8c. Analysis of the dislocations segments contrasts are presented in Table 1. This contrasts analysis allows to conclude that the

<figure><img src="image_9.png" /><figcaption>Figure 8: TEM images in bright field (a) and (c)) and weak beam dark field ((b) and (d)) showing the dislocation configuration of the L defect for different diffraction conditions.</figcaption></figure>
Burgers vectors of the different dislocations are all $\vec{b} = \frac{1}{3} < 11\bar{2}0 >$ type: the short R segments correspond to $\vec{b}_1 = \frac{1}{3}[11\bar{2}0]$, dislocations D₁, D₂, D₃ and D₄ correspond to $\vec{b}_2 = \frac{1}{3}[\bar{2}110]$ and dislocation D₅ corresponds to $\vec{b}_3 = \frac{1}{3}[1\bar{2}10]$.

<table><caption>Table 1: Contrasts of dislocations under different diffraction conditions. Symbol ✓: in contrast, χ: out of contrast.</caption><thead><tr><th></th><th>hkil</th><th>D1</th><th>D2</th><th>D3</th><th>D4</th><th>D5</th><th>R</th></tr></thead><tbody><tr><td>$\vec{g}_1$</td><td>$\bar{1}\bar{1}20$</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>$-\vec{g}_1$</td><td>$11\bar{2}0$</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>$\vec{g}_2$</td><td>$\bar{1}2\bar{1}0$</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>$-\vec{g}_2$</td><td>$1\bar{2}10$</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>$\vec{g}_3$</td><td>$\bar{2}110$</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>$-\vec{g}_3$</td><td>$2\bar{1}\bar{1}0$</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>$\vec{g}_4$</td><td>$\bar{1}103$</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>χ</td></tr><tr><td>$\vec{g}_5$</td><td>$\bar{1}10\bar{3}$</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>χ</td></tr><tr><td>$\vec{g}_6$</td><td>$01\bar{1}3$</td><td>χ</td><td>χ</td><td>χ</td><td>χ</td><td>✓</td><td>✓</td></tr><tr><td>$\vec{g}_7$</td><td>$01\bar{1}\bar{3}$</td><td>χ</td><td>χ</td><td>χ</td><td>χ</td><td>✓</td><td>✓</td></tr></tbody></table>

In order to determine the slip plane of the short segments, the sample has been tilted in such a way that the plane containing the defects is edge-on in the lamella. Figure 9a presents a bright field image obtained in multi beams condition, exactly in the diffraction condition presented in figure 9b. In such condition, the defect plane is edge on, and is identified as the (1103) pyramidal plane. As shown in figure 9c, the $\frac{1}{3}[11\bar{2}0]$ Burger vector belongs to the (1103) plane and to the (0001) plane: R dislocations are due to activation of the $\frac{1}{3}[11\bar{2}0](1103)$ slip system by cross slip from basal to pyramidal plane.

In figure 8b, we observe that the shorts R segments are actually constituted of “two parts” slightly “shifted” one from the other. Moreover, in figure 8c, these R

<figure><img src="image_10.png" /><figcaption>Figure 9: (a) TEM bright field image of the L defect observed edge on in multi beam conditions, The diffraction conditions are shown in (b). The L defect lies in a (1103) pyramidal plane, schematically represented in (c).</figcaption></figure>
dislocations are out of contrast and we may observe a "zig-zag" contrast of the D₁ segment. Such contrasts arise from the interaction between R dislocations and D₁ dislocation: the reaction results then in a "junction" segment with $\vec{b}_3 = \vec{b}_1 + \vec{b}_2$. Burgers vector and is always in contrast with the used g vector that is consistent with our observations.

Finally, the complete dislocation configuration is presented in figure 10: all observed dislocations have a Burgers vectors of $\frac{1}{3} < 11\bar{2}0 >$ type. The long D dislocations correspond to the $\frac{1}{3} < 11\bar{2}0 > \{0001\}$ slip systems and the R dislocations correspond to the

$\frac{1}{3}[11\bar{2}0](\bar{1}103)$ slip system. The configuration results from a junction of $\vec{b}_1 + \vec{b}_2 = \vec{b}_3$ type.

<figure><img src="image_11.png" /><figcaption>Figure 10: Schematic of the dislocation interactions involved in the L defect.</figcaption></figure>

## 4. DISCUSSION

This is the first time that deformation twinning is identified and reported at room temperature in a MAX phase. Revealing a twinning relationship through a crystallographic misorientation is relatively easy when the expected twinning plane is known. The twinning misorientation angle, as well as the twin boundary direction can be simply checked through the orientation maps. However, in the case of MAX phases, where twinning has always been ruled out, no specific twinning system was expected. In the present study, the combination of AFM surface observation and TEM cross section analysis has provided a complete 3D characterization of the S defect, suggesting a planar defect parallel to a $(11\bar{2}4)$ plane. This has been the starting point for the search for $\{11\bar{2}4\}$ twinning for the S defect, as well as for the H bands. The three other similar indents characterized in the same manner (AFM, TEM and ACOM-ASTAR) as the one reported here showed exactly the same twins with the same arrangement, demonstrating that the deformation twins are highly reproducible.

This result should be compared to the recent paper of Tomas et al. [29], where $\{11\bar{2}2\}$ deformation twinning had been observed below a nanoindentation imprint in the MAX phase Ti₂AlN. However, in this case, the nanoindentation had been performed at 800°C so that the influence of the high temperature on this deformation mode was still under question. From a temperature point of view, as twinning is expected to be favoured at lower temperatures, it is not surprising to observe it at room temperature. Furthermore, in the case of Ti₂AlN, Berkovich indent had been performed at high load.
The deformation structure was complex with many twin-twin interfaces, making their complete characterization difficult. In the present study, working with a single crystal enabled us to choose the sample orientation, and repeat the same experiment under strictly similar conditions. With the basal plane edge on, and using a spherical indenter, basal slip was not favoured in the middle of the indented area. Furthermore, due to the smooth shape of the spherical indenter, compared to the Berkovich one, the deformation structures were less dense, and the different identified twins were all isolated, showing simple twin-parent boundaries, which made their identification easier.

Fig. 11 summarizes in a schematic representation the three {112̄4} twin variants identified around the indent:

* (112̄4) variant for the S defect

* (1̄21̄4) variant for the H1 and H3 defects

* (1̄21̄4) variant for the H2 defects

It must be noticed that the (1̄21̄4) variants (H₁ and H₃) and the (1̄21̄4) variant (H₂) all intersect the basal plane along a same [101̄0] direction, which explains why the dark bands observed in TEM are parallel, but correspond to twins not inclined in the same direction relative to the basal plane (cf. Fig. 11). However, for symmetry reasons, both are equiprobable below the indent. It is worth noting that the sample orientation (basal plane edge on) and the position of the extracted thin foil (in the mediator plane of the indent) are unfavorable to basal slip, which is the main deformation mechanism reported in MAX phases. Alternative deformation mechanisms were thus expected.

<figure><img src="image_12.png" /><figcaption>Figure 11: Schematic representation of the different {112̄4} twin variants identified below and around the indent.</figcaption></figure>

Concerning the dislocation structure, we have reported here an original arrangement, described as ladder-like defect (L). The complete analysis revealed that this structure involved the activation of a 1/3 < 112̄0 > {1̄103} slip system. Pyramidal slip in MAX phases has been already reported by Guitton et al. [43] in Ti₂AlN, but only after high temperature deformation, and without a complete
characterization of the pyramidal plane involved. The $\frac{1}{3} < 11\bar{2}0 > \{\bar{1}103\}$ slip system is reported here for the first time in MAX phases, with a full TEM characterization. It probably corresponds to cross slip of classical $\frac{1}{3} < 11\bar{2}0 >$ basal dislocations to a $\{\bar{1}103\}$ pyramidal plane. The activation of a $\frac{1}{3} < 11\bar{2}0 > \{\bar{1}103\}$ secondary slip system was unexpected, in particular in a defect free region of the crystal far from the indent axis, where the stress field is not very high. It is however highly reproducible and it has been observed in the four TEM lamellas studied. It must be noticed that this ladder defect initiates from the extremity of the twin band $H_0$ (cf. Fig. 3). Twin boundaries must play a role in the activation of this pyramidal slip. One possibility would be related to a specific twin-parent crystallographic orientation, so that basal slip within the twins would evolve into pyramidal slip after crossing the twin boundary. Another possibility would be related to recent considerations on basal plane dislocation core in MAX phases [44]. The authors suggest that specific core structures, associated with different dislocation configurations would induce non Schmid behaviour [19,44]. In any case, even if this $\{\bar{1}103\}$ slip plane was unexpected, it is the densest plane among the $\{\bar{1}10n\}$ family, and thus the more favourable for dislocation slip [45]. The ladder-like defect (L) also influences the basal dislocation configuration. As previously shown in Fig. 3, the whole dislocation structure below the indent is bounded by dislocation walls pinned at the extremities of the H twins. This configuration suggests that basal dislocation loops generated below the indent are confined between the H twin bands: when these dislocations grow under the indenter stress field, their extension along the indentation axis is impeded by the H twin boundaries, where they may be absorbed. In the lateral directions, the loops extend until reaching the end of the H twin bands, where they remain pinned, probably because of the local atomic disorder at the end of the twin boundary. These dislocations present a slight curvature, related to the residual stress field below the indent. The ladder-like defect L is the only case where the basal dislocations extend beyond the twin band extremities: the dislocations D (cf. Fig. 8c) are driven along the ladder-like defect trough their interaction with the dislocation pile-up reported before in the (1103) slip plane.

The major result of this study is that deformation twinning is possible in MAX phases at room temperature. It must now be considered when analysing deformation mechanisms in these materials since it allows local crystal reorientation making therefore possible the activation of basal slip when the initial orientation is not favourable. Furthermore, since we observed deformation twins far from the contact area, at a depth higher than 35 times the indentation depth, it demonstrates that twinning does not necessarily require high stress to be activated. In the literature, local crystal reorientation in MAX phases is often ascribed to kink bands [22,30,46-48]. However, although local reorientation is often reported, the nature of the rotation is never fully characterized, so that deformation twins may have sometimes been misinterpreted as kink bands. Actually, deformation structures showing both
twins and kink bands have been reported in different hexagonal materials where their complementary
role has been underlined [49,50]. Our results show that deformation twinning and kink bands must be
both considered in the deformation processes of MAX phases.

**5. CONCLUSION**

This article report, for the first time, {1124} deformation twins in a Cr₂AlC single crystal. This result was made possible by an original experimental approach: the combination of AFM surface observation and TEM cross section analysis provided a complete 3D characterization of planar defect parallel to a {1124} plane. This result served has input data for local misorientation analysis to identify {1124} twinning. These twins are significant since they are systematically observed and can explain how plastic deformation can initiate in a MAX phase when the basal slip is not in a geometrically favorable configuration. Furthermore, original dislocation structure has been observed, with the activation of a 1/3 < 1120 > {1103} slip system; never reported before in a MAX phase. Finally, the whole deformation microstructure below the indent results from an intimate combination between basal slip and deformation twinning. The interactions between basal dislocations and twin boundary may be the reason for the activation of this unexpected pyramidal slip. Further experiments, in particular micropillar compression tests, would provide similar configuration in a simpler stress field, likely to promote the characterisation an understanding of these interactions between dislocations and twins.

**ACKNOWLEDGMENTS**

Institut Pprime gratefully acknowledges "Contrat de Plan Etat - Région Nouvelle-Aquitaine" (CPER) as well as the "Fonds Européen de Développement Régional" (FEDER) [reference n°2017-3528710 (MAMMOUTh) and n°2018-3868210 (BACASMET)] for their financial support to the reported work. This work pertains to the French Government programs "Investissements d'Avenir" LABEX INTERACTIFS [reference ANR-11-LABX-0017-01] and EUR INTREE [reference ANR-18-EURE-0010].

**REFERENCES**

[1] W. Jeitschko, H. Holleck, H. Nowotny, F. Benesovsky, Die Verbindungen RuGa und RuGa₂, Monatshefte Fur Chemie 94 (1963) 838–840.

[2] V.H. Nowotny, Strukturchemie einiger Verbindungen der Übergangsmetalle mit den elementen C, Si, Ge, Sn, Progress in Solid State Chemistry 5 (1971) 27–70.

[3] M.W. Barsoum, T. El-Raghy, Synthesis and characterization of a remarkable ceramic: Ti₃SiC₂, Journal of the American Ceramic Society 79 (1996) 1953–1956.
[4] M.W. Barsoum, $M_{n+1}AX_n$ phases: a new class of solids thermodynamically stable nanolaminates, *Progress in Solid State Chemistry* 28 (2000) 201–281.

[5] M.W. Barsoum, T. El-Raghy, *The MAX Phases: Unique New Carbide and Nitride Materials: Ternary ceramics turn out to be surprisingly soft and machinable, yet also heat-tolerant, strong and lightweight*, American Scientist 89 (2001) 334–343.

[6] A. Guitton, A. Joulain, L. Thilly, C. Tromas, Dislocation analysis of $Ti_2AlN$ deformed at room temperature under confining pressure, *Phil. Mag.* 92 (2012) 4536–4546.

[7] L. Farber, I. Levin, M.W. Barsoum, *HRTEM study of a low angle boundary in plastically deformed $Ti_3SiC_2$, Phil Mag Lett 79 (1999) 163.

[8] B.J. Kooi, R.J. Poppen, N.J.M. Carvalho, J.T.M. De Hosson, M.W. Barsoum, $Ti_3SiC_2$: A damage tolerant ceramic studied with nano-indentations and transmission electron microscopy, *Acta Materialia* 51 (2003) 2859–2872.

[9] M.W. Barsoum, M. Radovic, *Elastic and Mechanical Properties of the MAX Phases*, Annu. Rev. Mater. Res. 41 (2011) 195–227. https://doi.org/10.1146/annurev-matsci-062910-100448.

[10] A. Joulain, L. Thilly, J. Rabier, Revisiting the defect structure of MAX phases: The case of $Ti_4AlN_3$, *Philosophical Magazine* 88 (2008) 1307–1320.

[11] E. Drouelle, A. Joulain, J. Cormier, V. Gauthier-Brunet, P. Villechaise, S. Dubois, P. Sallot, Deformation mechanisms during high temperature tensile creep of $Ti_3AlC_2$ MAX phase, *Journal of Alloys and Compounds* 693 (2017) 622–622–630. https://doi.org/10.1016/j.jallcom.2016.09.194.

[12] X.H. Wang, Y.C. Zhou, Microstructure and properties of $Ti_3AlC_2$ prepared by the solid–liquid reaction synthesis and simultaneous in-situ hot pressing process, *Acta Materialia* 50 (2002) 3143–3151. https://doi.org/10.1016/S1359-6454(02)00117-9.

[13] C. Tromas, P. Villechaise, V. Gauthier-Brunet, S. Dubois, Slip line analysis around nanoindentation imprints in $Ti_3SnC_2$: a new insight into plasticity of MAX-phase materials, *Philosophical Magazine* 91 (2011) 1265–1275. https://doi.org/10.1080/14786435.2010.494584.

[14] Z. Zhan, Y. Chen, M. Radovic, A. Srivastava, *Non-classical crystallographic slip in a ternary carbide – $Ti_2AlC$, Materials Research Letters 8 (2020) 275–281. https://doi.org/10.1080/21663831.2020.1748733.

[15] O. Gavalda-Diaz, J. Lyons, S. Wang, M. Emmanuel, K. Marquardt, E. Saiz, F. Giuliani, *Basal Plane Delamination Energy Measurement in a $Ti_3SiC_2$ MAX Phase*, JOM 73 (2021) 1582–1588. https://doi.org/10.1007/s11837-021-04635-9.

[16] J.T. Pürstl, T.E.J. Edwards, F.D. León-Cázares, R.P. Thompson, N.M. Della Ventura, N.G. Jones, W.J. Clegg, The effect of orientation on the deformation behavior of $Cr_2AlC$, *Acta Materialia* 257 (2023) 119136. https://doi.org/10.1016/j.actamat.2023.119136.

[17] C. Brüsewitz, I. Knorr, H. Hofsäss, M.W. Barsoum, C.A. Volkert, Single crystal pillar microcompression tests of the MAX phases $Ti_2InC$ and $Ti_4AlN_3$, *Scripta Materialia* 69 (2013) 303–306. https://doi.org/10.1016/j.scriptamat.2013.05.002.

[18] M. Higashi, S. Momono, K. Kishida, N.L. Okamoto, H. Inui, Anisotropic plastic deformation of single crystals of the MAX phase compound $Ti_3SiC_2$ investigated by micropillar compression, *Acta Materialia* 161 (2018) 161–170. https://doi.org/10.1016/j.actamat.2018.09.024.

[19] Z. Zhan, M. Radovic, A. Srivastava, *On the non-classical crystallographic slip in $Ti_{n+1}AlC_n$ MAX phases*, *Scripta Materialia* 194 (2021) 113698. https://doi.org/10.1016/j.scriptamat.2020.113698.

[20] M.W. Barsoum, L. Farber, T. El-Raghy, *Dislocations, kink bands, and room-temperature plasticity of $Ti_3SiC_2$, Metallurgical and Materials Transactions A: Physical Metallurgy and Materials Science* 30 (1999) 1727–1738.

[21] Y. Wada, N. Sekido, T. Ohmura, K. Yoshimi, Deformation Microstructure Developed by Nanoindentation of a MAX Phase $Ti_2AlC$, *Mater. Trans.* 59 (2018) 771–778. https://doi.org/10.2320/matertrans.MBW201703.

[22] E. Orowan, *Nature, A Type of Plastic Deformation New in Metals* 149 (1942) 463.

[23] J.B. Hess, C.S. Barrett, *Structure and nature of kink bands in zinc*, Trans. AIME 185 (1949) 599–606.
[24] A. Serra, D.J. Bacon, Computer simulation of screw dislocation interactions with twin boundaries in H.C.P. metals, Acta Metallurgica et Materialia 43 (1995) 4465-4481.
https://doi.org/10.1016/0956-7151(95)00128-I.

[25] J.W. Christian, Deformation Twinning, in: The Theory of Transformations in Metals and Alloys, Elsevier, 2002: pp. 859-960.
https://doi.org/10.1016/B978-008044019-4/50025-8.

[26] A. Kelly, K.M. Knowles, Crystallography and crystal defects, Third edition, Wiley, Hoboken, NJ, 2020.

[27] P.G. Partridge, The crystallography and deformation modes of hexagonal close-packed metals, Metal. Rev. 12 (1967) 169-194.
https://doi.org/10.1179/mtlr.1967.12.1.169.

[28] J.W. Christian, S. Mahajan, Deformation twinning, Prog. Mat. Sci. 39 (1995) 1-157.

[29] C. Tromas, S. Parent, W. Sylvain, L. Thilly, G. Renou, C. Zehnder, S. Schröders, S. Korte-Kerzel, A. Joulain, Nanoindentation-induced deformation twinning in MAX phase Ti₂AlN, Acta Materialia 227 (2022) 117665.
https://doi.org/10.1016/j.actamat.2022.117665.

[30] M.W. Barsoum, T. El-Raghy, Room-temperature, ductile carbides, Metallurgical and Materials Transactions A: Physical Metallurgy and Materials Science 30 (1999) 363-369.

[31] T. El-Raghy, M.W. Barsoum, A. Zavaliangos, S.R. Kalidindi, Processing and mechanical properties of Ti₃SiC₂: II, Effect of grain size and deformation temperature, Journal of the American Ceramic Society 82 (1999) 2855-2860.

[32] T. Ouisse, E. Sarigiannidou, O. Chaix-Pluchery, H. Roussel, B. Doisneau, D. Chaussende, High temperature solution growth and characterization of Cr₂AlC single crystals, Journal of Crystal Growth 384 (2013) 88-95.
https://doi.org/10.1016/j.jcrysgro.2013.09.021.

[33] H.J. Rathod, T. Ouisse, M. Radovic, A. Srivastava, Room temperature crack-healing in an atomically layered ternary carbide, Sci. Adv. 7 (2021) eabg2549.
https://doi.org/10.1126/sciadv.abg2549.

[34] E.F. Rauch, M. Véron, Automated crystal orientation and phase mapping in TEM, Materials Characterization 98 (2014) 1-9.
https://doi.org/10.1016/j.matchar.2014.08.010.

[35] I. Horcas, R. Fernandez, J.M. Gomez-Rodriguez, J. Colchero, J. Gomez-Herrero, A.M. Baro, WSXM: A software for scanning probe microscopy and a tool for nanotechnology, Review of Scientific Instruments 78 (2007) 013705.

[36] R. Krakow, R.J. Bennett, D.N. Johnstone, Z. Vukmanovic, W. Solano-Alvarez, S.J. Lainé, J.F. Einsle, P.A. Midgley, C.M.F. Rae, R. Hielscher, On three-dimensional misorientation spaces, Proc. R. Soc. A. 473 (2017) 20170274.
https://doi.org/10.1098/rspa.2017.0274.

[37] F. Mompiou, R. Xie, *pycotem*: An open source toolbox for online crystal defect characterization from TEM imaging and diffraction, Journal of Microscopy (2020) jmi.12982.
https://doi.org/10.1111/jmi.12982.

[38] B. Beausir, J.-J. Fundenberger, Analysis Tools for Electron and X-ray diffraction, ATEX - software, (n.d.). www.atex-software.eu.

[39] S.I. Wright, R.J. Larsen, Extracting twins from orientation imaging microscopy scan data, J Microsc 205 (2002) 245-252.
https://doi.org/10.1046/j.1365-2818.2002.00992.x.

[40] T.A. Mason, J.F. Bingert, G.C. Kaschner, S.I. Wright, R.J. Larsen, Advances in deformation twin characterization using electron backscattered diffraction data, Metall and Mat Trans A 33 (2002) 949-954.
https://doi.org/10.1007/s11661-002-0164-8.

[41] S. Xu, M. Gong, Y. Jiang, C. Schuman, J.-S. Lecomte, J. Wang, Secondary twin variant selection in four types of double twins in titanium, Acta Materialia 152 (2018) 58-76.
https://doi.org/10.1016/j.actamat.2018.03.068.

[42] N.M. Della Ventura, A. Sharma, C. Cayron, S. Kalácska, T.E.J. Edwards, C. Peruzzi, M. Jain, J.T. Pürstl, R.E. Logé, J. Michler, X. Maeder, Response of magnesium microcrystals to c-axis compression and contraction loadings at low and high strain rates, Acta Materialia 248 (2023) 118762.
https://doi.org/10.1016/j.actamat.2023.118762.

[43] A. Guitton, A. Joulain, L. Thilly, C. Tromas, Evidence of dislocation cross-slip in MAX phase deformed at high temperature, Scientific Reports 4 (2014).
https://doi.org/10.1038/srep06358.
[44] G. Plummer, M.W. Barsoum, C.R. Weinberger, G.J. Tucker, Basal dislocations in MAX phases: Core structure and mobility, *Materialia* 21 (2022) 101310.
https://doi.org/10.1016/j.mtla.2021.101310.

[45] W. Szewc, L. Pizzagalli, S. Brochard, E. Clouet, Onset of plasticity in zirconium in relation with hydrides precipitation, *Acta Materialia* 114 (2016) 126–135.
https://doi.org/10.1016/j.actamat.2016.05.025.

[46] M.W. Barsoum, T. Zhen, S.R. Kalidindi, M. Radovic, A. Murugaiah, Fully reversible, dislocation-based compressive deformation of Ti 3SiC2 to 1 GPa, *Nature Materials* 2 (2003) 107–111.

[47] N.G. Jones, C. Humphrey, L.D. Connor, O. Wilhelmsson, L. Hultman, H.J. Stone, F. Giuliani, W.J. Clegg, On the relevance of kinking to reversible hysteresis in MAX phases, *Acta Materialia* 69 (2014) 149–161.
https://doi.org/10.1016/j.actamat.2014.01.045.

[48] F.C. Frank, A.N. Stroh, On the theory of kinking, *Proceedings of the Physical Society. Section B* 65 (1952) 811–821.

[49] R.E. Reed-Hill, W.H. Hartt, W.A. Slippy, Double accommodation kinking and growth of {1121} twins in zirconium, *Trans. of Met. Soc.* 242 (1968) 2211–2215.

[50] J.W. Christian, The theory of transformations in metals and alloys. Pt. 2: ..., 3. ed, *Pergamon, Amsterdam, 2002*.