Dislocation behaviour

Figure 3-10 shows TEM images for the deformed [101]-oriented 800 nm-diameter sample. As illustrated in Figure 3-10a, the TEM sample was taken along the cross section of the pillar. Figure 3-10b shows that most of the deformation occurs at the top of the pillar and the strained parts are parallel to each other along the slip direction. From the enlarged view (Figure 3-10d), most of the dislocations are distributed in the centre, with the area near the sample’s surface being dislocation -free. But the inverse fast Fourier transform image (Figure 3-10f) shows that there are lattice distortions, meaning that the dislocation existed before deformation and escaped from the surface during deformation. The dislocation in Figure 3-10g can be seen on the slip plane, and close to the surface. This may be due to two reasons: (a) the cross slip locked the dislocation (Figure 3-10c), (b) the dislocation was annihilated

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during compression. As reported previously [136, 137], the FIB milling could damage the surface of the sample, leading to an amorphous layer or dislocation strengthening on the surface. As shown in Figure 3-10c, the damaged layer is only ~9.6 nm with a fine current (48 pA) during the FIB milling.

Figure 3-11 shows dark-field TEM images for the [111]-oriented 800 nm-diameter sample. The bright areas in Figure 3-11b are the main deformed parts of the pillar. The enlarged view of the area (Figure 3-11c-d), shows the dislocation lines in the deformed sample. Comparing the TEM results for both orientations, it seems that the [111]-oriented sample has greater dislocation density than the [101]-orientation sample. The method described in Ref. [138] was used to measure the dislocation density in the deformed pillar. The calculated dislocation density for the [101]- and [111]-oriented 800 nm-diameter samples was 3×1014 _{and 5.32×10}14 m-2, respectively. The lower dislocation density in the [101]-orientated pillar was possibly due to more slip events occurring during compression. More details are discussed in Section 3.3.4.

Figure 3-10 (a) Indication of TEM sample machined by FIB, (b) overview of the strained area (dark line), (c) Ga+ damaged zone, (d)-(g) dislocation and lattice distortion in the deformed pillar.

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Figure 3-11 (a) Indication of the TEM sample machined by FIB, (b) overview of the strained area (bright areas), (c)-(d) dislocations in the deformed area as indicated in (b) by red circles.

3.3.4 Molecular dynamic simulation

The stress-strain curves for the orientations [111] and [101] are shown in Figure 3-12a. As in the experimental results, the [111]-oriented nanopillar shows greater yield strength than that of the [101]-oriented pillar. However, after yielding, the flow stress of the [101]-oriented nanopillar fluctuates over a wide range (0.12 GPa to 2 GPa), whereas the flow stress of the [111]-oriented nanopillar is much less variable. The fluctuation of the flow stress after yielding is due to the dislocation behaviour [139]. The dislocation density for both orientations during compression is shown in Figure 3-12b. In the plastic strain, the dislocation density in the [111]-oriented pillar is higher than that of the [101]-oriented pillar, a finding which is consistent with the experimental results (Figure 3-10 and Figure 3-11).

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The detailed microstructure of the pillar under compression was studied from snapshots. Figure 3-12c presents the snapshots for the [101]-oriented sample. From those snapshots, most of dislocations move along the stacking fault and then annihilate from the surface. With the formation of cross slip (Figure 3-12c), some dislocations are locked in the crossed area while no dislocations exist on the slip plane, indicating that dislocations escape from the surface during the slip. For the [111]-oriented sample (Figure 3-12d), the stacking faults are distributed on the {111} planes bounded with perfect and partial dislocations. As shown in Figure 3-12d, dislocations entangle with each other, making it difficult for them to escape from the surface. As a result, the dislocation density increases. Further, since there are too many slip directions and planes in the [111] sample (Figure 3-12d), the annihilation of the dislocation is multi-directional, resulting in a wavy surface.

Figure 3-12 MD simulation results, (a) stress-strain curves for orientations [101] and [111], (b) dislocation density during compression, (c) snapshot of microstructure evolution in the [101]-oriented sample under compression, (d) snapshot of microstructure evolution in the [111]-oriented sample under compression.

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3.4. Discussion

3.4.1 Orientation effect

As shown in Figure 3-9c, the yield stress of the micron/submicron pillar in the FZ is orientation-dependent, with the [111] orientation having the highest yielding stress. The TEM images from the bulk show that the size and space of the phase in the FZ are quite large, so it is unlikely to include the phase in the pillar, as demonstrated in Figure 3-10b. Thus, it is reasonable to consider the pillar made from the FZ as a kind of FCC solid-solution material, of which the slip system(s) would be the one(s) having the highest Schmid factor among the {111} <110> slip systems. From the EBSD test, the Schmid’s factors of orientation [101], [111] and [-301] are 0.44, 0.32 and 0.5, respectively. Thus, the [111] pillar shows the highest stress when subjected to uniaxial loading.

The finding about the orientation effect on the strength at micro/submicro scales is consistent with that from Hagen et al. [140]. They reported that the strength of α-Fe with orientation [011] was greater than that of [010]. But the present finding differs from the report of Frick et al. [141], that a single crystalline Ni in orientation [111] with fewer slip systems had lower critical resolved shear stress (CRSS) than that with orientation of [269] with more slip systems. They attributed this interesting phenomenon to the possibility that there might have been more available slip planes for the [111] Ni at micro/submicro scales, which is contrary to Schmid’s law. It has also been reported that the orientation has no effect on the CRSS at micro/ submicro scales, such as Nb [142]. These studies demonstrate that Schmid’s law could break down at nanoscale [143]. At micro/ submicro scales, the yielding strength is determined by the activated dislocation source. In other words, the slip system with lower Schmid factors could be involved in the deformation.