*3.2. Slip Analysis by SEM*

After the in-situ compression test, the slip lines were firstly analyzed by SEM. Figures 3a and 4a show the observed slip lines in SEM for Ni and *α*-Brass, respectively. For Ni, the slip lines were very weak on the upper surface and there were only two obvious parallel slip lines for each crystal. Based on the direction of slip lines on the upper surface, the active slip planes were identified as B planes for each crystal as shown in Figure 3. Moreover, the active incoming slip system in the crystal II was identified to be B4 as shown in Figure 3 since it corresponds to the slip system with the highest Schmid factor or the highest RSS given by incompatibility stress formula [37] (see Table 1). Slip system B4 was then considered in the discrete dislocation pile-up simulations (see Section 4). However, for *α*-Brass, there were two obvious slip lines intersecting the upper surface for crystal I and two obvious slip lines intersecting the side surface for crystal II. Therefore, multiple active slip systems were present in both grains for the *α*-Brass sample. Based on the analysis of the slip line directions, the active slip planes were determined as A and C for crystal I and B and D for crystal II as shown in Figure 4. Moreover, from the analysis of Schmid factor or incompatibility stresses as described in Table 2, the active incoming slip systems were identified as A6 and C5 for crystal I. Slip system A6 was then considered in the discrete dislocation pile-up simulations due the specific direction of the studied pile-up (see Figure 6).

**Figure 3.** (**a**) crystallographic analysis of slip lines from SEM picture for the Ni sample; (**b**) theoretical analysis of slip systems based on microstructural data (see Table 1).

**Figure 4.** (**a**) crystallographic analysis of slip lines from SEM picture for the *α*-Brass sample; (**b**) theoretical analysis of slip systems based on microstructural data (see Table 2).

## *3.3. Slip Analysis by Ex-Situ AFM*

AFM measurements were performed on the upper surface by Dimension FastScan with ScanAsyst (Bruker, (Billerica, Mass., USA)) with tapping mode, so that the 3D topography of slip lines can be obtained and used to analyze dislocation distributions. It should be pointed out that these AFM measurements were carried out post-mortem after unloading (ex-situ measurements). The step size of scan was 30 nm with a scan rate of 1 Hz. The results were analyzed by NanoScope Analysis (v180r2sr3, Bruker, Billerica, Mass., USA). They were first of all flattened by polynomial fit of the second order, and then they were treated by a median filter with 9 × 9 matrix operation. Figures 5a and 6a show the 3D topography of the upper surface of Ni and *α*-Brass samples, respectively. The slip steps correspond to the slip lines presented in the SEM picture (Figure 3a for Ni and 4a for *α*-Brass). For the Ni sample, a slip step with classic features of dislocation pile-up was selected for analysis. The heights of the top line and the bottom line of this step were measured along the slip direction from GB which are marked as red and black lines, respectively, in Figure 5a. The measured data are presented in Figure 5c with the corresponding name "Top line" and "Bottom line". Then, they were fitted by the polynomial method which are marked as "Fit *h*Top" and "Fit *h*Bottom" in Figure 5c. The relative height of this slip step Δ*h* was calculated as the difference of the fitted heights between these two lines as shown in Figure 5c with the blue line. It was found that the height difference between the two lines at GB, <sup>Δ</sup>*h*GB ≈ 0.86 nm, was not zero, which is due to a weak slip transmission and/or dislocation absorption as observed in Figure 5a. The slip step height increased from GB along the slip direction and reached its maximum value Δ*h* ≈ 9.06 nm at about *d* ≈ 3.28 μm.

A similar analysis was performed in the crystal I of the *α*-Brass sample as shown in Figure 6. The observed pile-up had a typical dislocation configuration corresponding to slip on system A6. The slip transmission and/or dislocation absorption were even more intense compared to the Ni sample as <sup>Δ</sup>*h*GB ≈ 4.29 nm, but the propagation of dislocations in the adjoining grain had a shorter distance. The maximum of slip step height was Δ*h* ≈ 10.03 nm at about *d* ≈ 2.44 μm. There was an obvious peak valley in the middle part of the curve of slip step height, which might be caused by the intersection with another non coplanar slip line.

**Figure 5.** (**a**) ex-situ AFM topographic measurement for the Ni sample. The transmission phenomenon and/or dislocation absorption at GB are surrounded by the frame with red dashed lines. The green line indicates the direction of slip transmission. By comparison of this direction with the schematic presentation of the four slip planes in the crystal I (**b**) and by analysis of the transmission factors in Table 1 (B5 has the largest transmission factor), it can be assumed that the transmission phenomenon occurs in the B slip plane; (**c**) the result of slip step height measurement: red and black solid lines indicate the measured height of the top line and the bottom line of the step, respectively. The dash lines with corresponding color indicate the fitted results by the polynomial method with the correlation coefficient *R*<sup>2</sup> = 0.8176 for the top line and *R*<sup>2</sup> = 0.9898 for the bottom line. The blue line indicates the relative height of the slip step calculated as the difference of the fitted heights.

**Figure 6.** (**a**) ex-situ AFM topographic measurement for the *α*-Brass sample. The transmission phenomenon and/or dislocation absorption at GB are surrounded by the frame with red dashed lines. The green line indicates the direction of slip transmission. By comparison of this direction with the schematic presentation of the four slip planes in the crystal II (**b**), it can be assumed that the transmission phenomenon occurs in the A slip plane; (**c**) the result of slip step height measurement: red and black solid lines indicate the measured height of the top line and the bottom line of the step, respectively. The dash lines with corresponding color indicate the fitted results by the polynomial method with the correlation coefficient *R*<sup>2</sup> = 0.9982 for the top line and *R*<sup>2</sup> = 0.9973 for the bottom line. The blue line indicates the relative height of the slip step calculated as the difference of the fitted heights.
