**3. Results and Discussion**

Considering the TEM analysis in Figure 3a,b, it is possible to note that the specimen corner is not as sharp and smooth as one might expect. This results from the very high sputtering rates of Mg in conjunction with the broadening of the ion beam. Moreover, we note that the roughness is more pronounced along the upper sides, related to diffraction analysis spots one and four, respectively. From the indicated loading direction and the electron diffraction information in Figure 3c, it is evident that the sample is loaded along the intended 2110 direction. While there is slight indication of additional diffraction rings in this image, they are much more pronounced in Figure 3d and can be indexed as MgO. Thus, we consider that the bottom side of the tensile sample was polished last during FIB preparation. As such, there is a rather smooth edge and only a minimal amount of nanocrystalline MgO on the surface. Contrarily, on the upper side that was finished before, redeposition of sputtered Mg could take place, causing a rougher surface that is more prone to oxidation, thereby explaining the rougher appearance and more distinct MgO diffraction signal. Thus, we conclude that we can assure that the crystal orientation for our samples is uniform and consistent with expectations, but there is a nanocrystalline MgO layer that could affect the observability of surface features during in-situ SEM testing and might in the worst case act as a confining hard shell. Mg is known to form an oxide easily, and we observed such an MgO layer previously, in particular upon heat treatments of nanoscale Mg pillars [31]. However, for the given situation of few micrometre sized pillars and few nm thick oxide layer, we do not expect pronounced influences in terms of a confining layer.

We start with the deformation mode easiest to activate in Mg, basal slip. As evident for the 4-μm sized Mg 2112 micro-compression specimen shown in Figure 5, the flow curve in Figure 5a exhibits some minor and one major event during plastic deformation, which takes place at flow stresses in the range of 60–80 MPa. These events can be directly correlated to slip steps emerging on the sample surface during testing, as shown in the inset to Figure 5a. This is further supported by inclined post-mortem SEM images taken from the front and back, where one large and one smaller slip step are well discerned (Figure 5c,d). This localised slip behaviour was also reported earlier [12] and is in excellent agreement to common observations for dislocation slip based on a limited number of dislocation sources in other metals exhibiting a low Peierls barrier [23]. Given the sample crystallography and observed slip plane inclination, it is certain to ascribe this plastic deformation to basal slip [12]. A feature of note here is the oxide layer well displayed on the detail of an approximately 400 nm wide mayor slip step (Figure 5b). This MgO layer has a thickness of ~10 nm [31] and stretches conformal over the emerged slip step, which required roughly 1200 basal plane dislocations with 1120 direction to exit in order to form the slip step. The important implication is that this MgO layer does not break easily and thus has the tendency to cover faint surface steps. Thus, it cannot be determined with certainty whether the other smaller features along the stress–strain curve correspond to reactivation of dislocation sources that already operated and produced a multitude of dislocations resulting in observable slip steps, or the activation of new sources with resultant slip steps that might be not well discernible on the specimen surface yet due to this oxide layer. However, considering that it is considerably harder to nucleate dislocations from an interface than to mobilise pre-existing ones, it seems likely that some residual defects allowed for generation of a dislocation source (classically Frank–Read type, double cross-slip type or single armed source type) in the interior of the specimens.

**Figure 5.** Micro-compression test on a 4-μm Mg 2112 pillar. (**a**) Stress–strain behaviour showing some minor plastic events and one mayor stress drop. The inset depicts still images of the sample at points A and B of the experiment, as well as the crystal unit cell. (**b**) Detailed post mortem inspection of a large slip offset. (**c**,**d**) Front and backside view of the sample after testing, indicating a large and a smaller surface steps on the specimen surface.

Turning to the 4-μm Mg[0001]-oriented sample shown in Figure 6, we note that the stress–strain data in Figure 6a exhibit an initial linear elastic regime followed by a yield point at ~275 MPa, to be continued by a plastic deformation period exhibiting pronounced strain hardening. The loading portion of the curve exhibits a noticeable bend indicative of slight misalignment between sample and flat punch, while the deduced elastic modulus amounts to ~40 GPa, which is in reasonable accordance with calculated orientation dependent values [32] based on experimental elastic constants [33] and lattice spacing [34] as summarised in Table 2. Since local plastic deformation should correct for the local contact issues at the initial loading, the lower experimental value upon elastic unloading from a plastically deformed sample might result from a non-perfect accounting of parasitic compliance effects, which could be eliminated, for example, by measuring the deformation directly on the sample surface using digital image correlation [35]. Alternatively, this could originate from the reverse motion and straightening of bulged out dislocations upon unloading, similar to what is frequently referred to as a Bauschinger effect in bending geometries [36]. In that case in-situ TEM observations could help to clarify the origin, but this goes beyond the scope of this work. The images recorded during in-situ deformation as well as after loading (Figure 6b) display a distinct shortening of the sample, but only minimal traces of deformation on the surface, in fact the most pronounced notion is a certain sample barrelling. Loading along this crystal direction should suppress basal and prismatic slip, as well as - 1012 twinning. Still, macroscopic compression tests on Mg[0001] reported a certain amount of twinning to take place due to barrelling and

friction effects [37]. Turning to the present miniaturised compression test, we note only a slight discontinuity at a stress of ~275 MPa, but the absence of a flow plateau that could be indicative of a limited propagation of a - 1011 compression twin. This is not too surprising, as during compression twinning the twinned part would have to rotate significantly out of the loading axis (Figure 4), which is constrained by the laterally stiff sample setup and the friction between specimen and diamond flat punch [38]. However, a significant amount of work hardening is displayed, which favourably corresponds to the activation of pyramidal slip. As post mortem EBSD investigation further confirmed the absence of twinning, this discrete burst is explained by the avalanche-like activation of pyramidal slip on various planes, leading to the increased dislocation density and resultant work hardening in these microscale specimens. In general, it should be recognised that the formation and growth of a compression twin during compressive loading (see Figure 4) would yield a favourable configuration for subsequent basal slip, which is not observed and therefore further validates the assumption that the majority of deformation is carried by dislocation plasticity on pyramidal (π1 or π2) slip planes.

**Figure 6.** Micro-compression test on a 4-μm Mg[0001] specimen. (**a**) Stress-strain characteristic and (**b**) deformed specimen. Blue lines indicate original specimen geometry, while the inset indicates the unit cell and slip crystallography.

**Table 2.** Orientation dependent Young's moduli and Poisson's ratios for the cylindrically symmetrical Mg single crystal.


Relating this behaviour to the previously shown 2112 specimen, the strains at the first deviation from linear elasticity are similar, but the stress is about a factor of four higher in the [0001] specimen, which is expected in light of the different mechanisms (pyramidal slip versus basal slip). The fact that there are no pronounced slip bands is in accordance with the argument that deformation is mostly driven by pyramidal slip, as the higher number of available slip planes can lead to dislocation interaction and formation of kinks or jogs. Moreover, due to the large Burgers vector of <c+a> dislocations, they are dissociated into two partial dislocations. A recent study showed that those are intrinsically transformed to basal-dissociated immobile dislocation structures, which cannot contribute to plastic deformation, but serve as strong obstacles to the motion of all other dislocations inside the pillar [14], resulting in the strong strain hardening observed in the [0001] specimen. This is clearly different to the 2112 specimen, where the predominant deformation occurs on the

basal plane, having only two independent slip systems. Furthermore, the lack of "strainburst" type behavior in conjunction with the high strain hardening suggest no or only a minor occurrence of twinning, as previously shown macroscopically by Syed et al. [37].

To underline the previous point regarding difficult to activate deformation mechanisms and deformation constraints, we consider another miniaturised compression test on a Mg[1000] specimen with 2 μm width in Figure 7. Similar to the previous example, the stress-strain data shown in Figure 7a does not exhibit a distinct yield event, but a gradual elastic–plastic transition. At a stress of ~185 MPa a flow plateau is observed, corresponding to a distortion of the micro-compression sample evident in Figure 7c. After the distinct load-drop at a strain of 0.07, we observe the emergence of a distinct slip step at the position of the previous specimen distortion (Figure 7d), which grows during deformation at a constant flow stress of about 160 MPa. While the initial unloading slope appears quite similar to that upon initial loading, the unloading curve develops a remarkable bend back, indicative of a significant amount of reverse plasticity. Alternatively, this could be ascribed to geometric changes occurring during the experiment. We attribute the gradual elastic–plastic transition again to pyramidal slip activity, and the constant flow plateau to the activation of basal slip in the locally modified crystallography of the deformed specimen. Initially, this basal slip is confined by the surface oxide layer. Once this breaks at the distinct stress drop, the slip step becomes well discernible on the sample surface and grows with continuing deformation.

Coming back to the previously mentioned aspect of confinement effects on twinning, we conducted related micro-tensile tests on an Mg[0001] crystal orientation using a 4-μm tensile sample in Figure 8, as this would permit the formation of a tension twin. As reported earlier, the longer aspect ratio tensile geometry is more compliant and allows for lateral adjustments [38]. In Figure 8a, we observe an elastic–plastic transition followed by a rather constant flow stress in the range of 80 to 90 MPa. This corresponds well to the nucleation and growth of a tensile twin seen in in Figure 8d,e. The pronounced load drop at a strain of 0.08 relates to the nucleation of a second tensile twin on the left hand side of the tensile specimen, as also indicated in the in-situ image shown as Figure 8f. Taking the specimen back into the TEM after unloading, in Figure 8b we observe the distinct crystal orientation change at the twin front in the area indicated by a dashed rectangle in Figure 8f. Thus, this setup allows for the unhindered nucleation and propagation of tensile twins.

**Figure 7.** Micro-compression testing on a 2-μm Mg[0001] sample. (**a**) Stress-strain curve showing an extended elastic–plastic transition, followed by a distinct load drop and a flow plateau. Notably, the unloading portion exhibits a remarkable amount of reverse plasticity. (**b**–**d**) In-situ images in correlation to the flow curve, documenting the onset of plasticity by pyramidal slip, the nucleation of basal slip and the continuous growth of the related almost horizontal slip step.

**Figure 8.** Micro-tensile test of a 4-μm Mg[0001] sample. (**a**) Stress–strain curve and (**b**) post mortem TEM image showing the formed twin boundary indicated by an arrow. (**c**–**f**) In-situ SEM images as indicated in (**a**), corresponding to the yield point, initiation of the first tensile twin, propagation of the twin, and nucleation of a second twin, respectively. The area inspected by TEM in (**b**) is indicated in (**f**).

It is well known that Mg exhibits two distinctly different twins when compressed ( - 1011 contraction twin) or elongated (- 1012 tensile twin) along the [0001] axis. While the so called contraction twin is only rarely observed because of the higher activation threshold, tensile twinning is observed frequently and considered a major carrier of deformation in Mg. The slight twist in the tensile specimen might have worked as a catalyst for twin nucleation, but it is definitely the more favourable loading direction for tensile twinning. After first and second twinning events occur, the loading axis of the pillar is changed from [0001] to ~ 1010 because the crystal is reoriented by 86◦ upon twinning. Under 1010 tensile loading, the contraction twin would be crystallographically favoured, but the critical resolved shear stress for contraction twinning is much higher than 90 MPa. This makes activation of another twin within the twinned part very unlikely.

An interesting notion is that the threshold for twinning does not seem to be constant. Previously, we showed that the nucleation of deformation twins is not a purely stress driven process, but is triggered by dislocation bulges on the prismatic plane [39], which are dependent on the very local stress and strain state and can therefore not always be derived just from considering a global stress value.

To compare the tensile twinning observed in tension to the activation of the same mechanism in compression, the last example concerns a miniaturised compression test of a 2-μm wide specimen along the Mg 2110 direction. For this crystallographic orientation, due to the specific crystal rotation created by the twin, lateral confinement effects should be less pronounced and thus also allow twinning to take place during compression. In fact, this specific orientation was previously studied by our group in a combined in-situ SEM and in-situ TEM fashion and we will therefore be rather brief and only mention the

essential facts, while all details can be found elsewhere [39]. In Figure 9a, we again observe a clear elastic regime followed by a distinct burst and load drop at a stress of about 400 MPa, followed by an overshoot of the indenter due to a not sufficiently fast feedback control, thereby releasing the strain energy stored in the system. Distinct distortion of the specimen geometry, in fact a slight kink of the top part due to the twinning reorientation by 86◦, is seen in point B in the inset upon elastic reloading. Thus, we can assign this again to the nucleation and propagation of a tensile twin. After elastic reloading, we observe a constant stress plateau at ~200 MPa, where slip steps emerge as seen in the inset corresponding to point C along the stress–strain data. This corresponds to basal slip in the twinned part of the specimen, as reported earlier [39]. In Figure 9b an inclined post mortem SEM image shows the slip steps in more detail.

**Figure 9.** In-situ SEM micro-compression test of a 2-μm Mg 2110 sample. (**a**) Stress–strain data showing elastic limit, a distinct plastic event followed by reloading, a plateau stress, and final unloading. Corresponding still images from the in-situ video relating to points A–C indicated in the stress–strain curve are provided as insets. (**b**) Inclined post mortem image of the deformed specimen, showing a slight tilt of the twinned part, as well as slip steps within this sample portion.

It is noteworthy that for the smaller 2-μm specimen examined here, the flow stress for basal slip is in the range of 200 MPa, while we measured only about 70 MPa for the 4-μm sample in Figure 5. This is mostly due to the sample size effect, with additional contributions from different Schmid factors to be accounted for.

To depict all discussed specimens in a comparative framework, the different critical resolved shear stresses (CRSS) were calculated, based on the Schmid factors summarised in Table 1, and are shown with respect to the different observed deformation mechanisms in Figure 10. There, the full symbols correspond to the first evident deviation from linear elastic loading as an indication for the beginning of the respective yield phenomena, while the open symbols correspond to the subsequent evident features of deformation: load drop corresponding to the large slip step for the 2112 specimen, load drop corresponding to the second evident twin formation for the [0001] tension specimen, and basal slip plateau following twinning for the 2110 specimen, respectively. The initial pyramidal slip CRSS occurring in the [0001] compression specimen was calculated for both, π1 and π2 slip, as the exact configuration is not known. However, based on the fact that π1 slip results in a lower CRSS, it can be assumed that it is easier to activate and therefore the majority contribution to plasticity in this specimen. This would also be in agreement with current observations by Xie et al. [40].

**Figure 10.** Critical resolved shear stresses (CRSS) of the previously detailed samples with regard to deformation mechanisms. The filled symbols represent initial deviation of the elastic load-displacement regime, while the open symbols depict evident deformation features, such as large load drops, which correspond to the respective mechanisms. For the Mg[0001] compression specimen, CRSS was calculated for both pyramidal planes (π1, π2) for comparison.

Comparing now the CRSS for tensile twinning in tension and compression as provided in Figure 10, it is evident that the necessary nucleation stress is considerably higher (~250%) for the 2-μm compression configuration than for the 4-μm tensile configuration. This could be partially attributed to the smaller geometric dimensions but seems unlikely to be a satisfying single cause explanation for this pronounced difference. Considering, however, not resolved stress but strain one could argue that the tensile strain along the [0001] direction is *<sup>ε</sup>tensile* <sup>=</sup> *<sup>σ</sup> <sup>E</sup>*<0001<sup>&</sup>gt; <sup>=</sup> 0.00173 in the tensile specimen, while it is *<sup>ε</sup>compression* <sup>=</sup> *<sup>σ</sup> <sup>E</sup>*<1120<sup>&</sup>gt; *<sup>ν</sup>*<1120<sup>&</sup>gt; <sup>=</sup> 0.00298 for the compression specimen, which is only an increase of ~60% for a sample size reduction by a factor of 2. Furthermore, this train of thought suggests that tensile twinning in Mg is rather a strain driven than a stress driven process.

In comparison with literature values concerning CRSS as summarised by Zhang and Joshi [30], our values are a factor 5–10 higher for basal slip and tensile twinning, and about a factor 2–3 higher for pyramidal slip. This could, even though not desired in the first place, again be related to be resultant of the small size of the samples. However, specifically in basal slip configuration with typical CRSS values in the single digit MPa range, it could also be a result of the high lateral stiffness in compression testing which causes a constrained deformation field [41], or additional pile-up contributions from FIB damage [42,43] or the thin MgO layer [31].

As evident from the previously shown experiments, the remarkable difference between easy and hard deformation modes in anisotropic materials such as Mg renders it rather challenging to probe specific mechanisms individually. However, as shown in the examples given above, it is well feasible, in particular when complemented by in-situ observations or respective post characterisation. In contrast, for a bulk experiment on a polycrystalline sample such differentiations would not be possible, as local stresses would always cause the unwanted activation of easy deformation mechanisms such as basal slip, either long before the actual hard mode is activated, or right after the crystal lattice was changed to a favourable orientation by local lattice distortions or twinning.

In terms of detailed insights and concrete dislocation or twinning mechanisms, a combined in-situ SEM/TEM study might be preferred, as the larger SEM experiments deliver bulk quantities if conducted on large enough specimens [28,44], while the TEM observations identify specific dislocation character or twinning relationships [39]. It should, however, be kept in mind that the different mechanisms could exhibit various strength scaling characteristics [10,18]. As such, for small enough specimens a transition between plastic mechanisms could occur [44] and mislead the data interpretation. Even changes in dislocation dynamics due to the high stresses in such highly confined nanoscale volumes are conceivable [45]. Therefore, such an undertaking ideally encompasses a complete size-dependent assessment.

From the more general application perspective, in our present work we turned to extraction of differently oriented lamellas from a bulk piece of single crystalline material. For experimental polycrystalline materials or alloys, this can easily be further reduced with respect to required material, say down to a specific single grain. Therefore, the extraction of lift-out lamellas from the grain of interest under specific orientations with respect to the surface normal, or from different grains with suited orientations, in a pick and place operation using a micromanipulator would be a feasible way [46]. As this most certainly requires larger amounts of surrounding material to be removed, modern developments such as Xe-FIBs or femtosecond laser machining [47,48] might prove helpful. Alternatively, different sample holders could be 3D printed to tilt the grain to the different selected orientations [7]. The only challenge remaining in that case is to FIB machine the sample top surface perpendicular with respect to the loading axis of the specimen situated within the tilted sample surface, as this requires a 90◦ tilting of the mounted sample.
