Supplementary Information for
In Situ Observation of Dislocation Nucleation and Escape in a Submicron Al Single Crystal Sang Ho Oh*, Marc Legros, Daniel Kiener and Gerhard Dehm *To whom correspondence should be addressed. E-mail:
[email protected] (S.H.O) This PDF file includes: Materials and Methods Changes in dislocation source configuration with deformation Figs. S1, S2, S3, S4 and S5 References Other Supplementary Information for this manuscript includes the following: Supplementary Movie 1, 2, 3 and 4
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Materials and Methods 1. Preparation of single crystal Al films on polyimide The epitaxial Al film was deposited on a (001)-oriented NaCl single crystal substrate (30 × 30 mm2) at 300°C by magnetron sputtering. After the Al deposition an ~8 μm thick layer of polyimide was spin-coated on top of the Al film using conventional precursors (PI2611, HD Microsystems). Subsequently, the polyimide was cured for 1 h at 350° C in a glass oven under N2 atmosphere. After curing, the sample was immersed in deionized water to remove the NaCl substrate. The average film thickness of Al was measured to be 455 ± 25 nm in cross-sectional transmission electron microscopy (TEM) (S1). The Al film grew in a three dimensional island mode on the NaCl substrate with a cubeon-cube orientation relationship: Al(001)//NaCl(001) and Al[100]//NaCl[100] (Fig. S1). The average island size was measured to be ~5 μm. The selected area electron diffraction revealed the [001] zone axis pattern at zero tilt angle in plan-view TEM (the inset in Fig. S1(A)), demonstrating the single crystal structure of the Al film. The single crystal Al film contained a dislocation density of ~2 × 1013 m-2, which was introduced to relieve the thermal strain while the polyimide is cured. The thermal expansion coefficients of Al, polyimide, and NaCl are 23 × 10-6 K-1, 3 × 10-6 K-1, and 44 × 10-6 K-1, respectively. A typical microstructure and dislocation configuration are shown in Fig. S1(B). 2. Structuring the Al film into a tensile sample by FIB machining A piece of Al/polyimide stripe with ~3 mm length and less than ~2 mm width was cut along the directions and fixed on a rectangular Cu support using a conventional superglue. The Cu support is 3 mm wide, 6 mm long, about 0.1 mm thick and has 1 mm diameter holes at both ends to fix it with screws to the straining stage. The center of the support contains a 1 × 2 mm2 sized rectangular hole over which the Al/polyimide stripe was glued. The polyimide was coated with carbon to avoid charging during focused ion beam (FIB; Leo XB 1540) machining with a Ga+ ion beam. The FIB design started with shaping the side grooves for stress concentration (Fig. S2(A)). A Ga+ ion beam current of ≤10 nA at an accelerating voltage of 30 kV was used. In the middle of the side grooves a square of 100 × 100 µm2 in dimension was milled down to a remaining polyimide thickness of less than ∼3 µm in order to obtain an electron transparent area of constant thickness without perforation (Fig. S2(A)). The Ga+ ion milling time was calibrated for the applied parameters by cutting test structures in a polyimide reference sample. If the sample was not sufficiently milled, additional thinning was performed by Ar+ ion milling (Gatan Duomill) with liquid nitrogen cooling of the sample. A typical tensile testing sample is shown in Fig. S2(A) (S2). 2
The wire patterns were shaped within the electron transparent window. For patterning, rectangular-shaped holes (2 × 10 μm2) were milled from the Al film surface side to prevent buildup of removed materials on the Al surface with the opening of slits (Fig. S2(B)). The FIB milling was performed with the Ga+ ion beam current of ≤ 100 pA. As shown in Fig. S2(B), a pattern of five wires was shaped with widths of 3.0, 2.0, 0.5, 0.2 and 1.0 μm (from the top to bottom in Fig. S2(B)). The length was kept constant at 10 μm. Adjusting the two beam (the Ga+ ion beam for FIB milling and the electron beam for SEM imaging) coincidence setup, all milling operations for final structuring were defined solely in SEM view. This ensured no Ga exposure to the investigated material. 3. In situ TEM straining experiment Displacement-controlled tensile deformation was carried out using a single-tilt straining holder (Gatan) in a 200 kV TEM (Jeol, JEM-2010). Among the parallel patterns the 1 μm wide one was most effectively stretchable when the tensile testing sample was strained by the displacement control. The thinner wires, i.e. 0.2 and 0.5 μm wide ones, were bent after FIB patterning, so that they could not be stretched within the displacement range of the 1µm wire used for this study (Fig. S3(c)). The dislocation dynamics were observed in bright-field diffraction contrast and recorded on a CCD camera with 25 frames per second. 4. Measurement of strain rate The displacement of the strain holder was increased in a stepwise manner. In the beginning of straining (ε ≤ 40%) the strain could be estimated by measuring the side notch distance (e.g. Fig. S3A and B). The uncertainty in the measurement of notch distance on TEM images was ~40 nm. After the failure of polyimide, owing to the appearance of broken polyimide edges, the strain could be measured more precisely with an uncertainty of ~10 nm (Fig. S3C). The distance between the broken polyimide edges was measured at the three different locations as shown in Fig. S3C. The measured distances at the three locations are plotted as a function of time in Fig. S4A, which serves as the foundation for strain and strain rate calculations. The most consistent one is AA (taken from the broken edges on the left), then CC is comparable (taken at the center) and BB (taken at the right) which varies and depends strongly on the tilt. Taking the distance measurement AA (Fig. S4B), the strain rate was maintained constantly low just before the dislocation avalanche, which is in the range of 10-4 s-1. Then the strain rate jumps to 10-3 s-1 and, during the dislocation avalanche, it must have gone up to 2 × 10-2 s-1 before the formation of crack. The increase of strain rate by one order of magnitude from 10-4 s-1 to 10-3 s-1 resulted in a multiplication of the dislocation 3
density by a factor of 2 as imaged a few seconds later. Changes in dislocation source configuration with deformation We observed that the average source size tends to decrease with deformation as large sources are easily unpinned and/or cut by the interaction with other dislocations while newly developed single-armed sources become smaller (Fig. S5). For instance, the single-ended sources with sizes larger than 100 nm observed at beginning (Fig. S5A) were rarely observed at later straining stage. This tendency results from the weakness of large sources at a high stress level. The small sources activated in later stage of straining are located predominantly at the top and bottom corners of Al crystal (Fig. S5B) and emit dislocations towards the diagonal directions. The source sizes in Fig. S5A and B correspond to 135 ± 15 nm and 52 ± 15 nm, respectively. Supplementary Movies Movie 1: This TEM movie shows the dynamic motion of a prismatic type dislocation loop. The loop in the middle expands under the applied tensile stress and then transform to a perfect dislocation. This movie runs with 1/5 speed compared to real time (i.e. five frames per second). Movie 2: This TEM movie shows in real time the single-armed dislocation sources spiraling and emitting dislocations on parallel (111) planes under the applied tensile stress. The frame images of this movie are presented in Fig. 3 with a schematic illustration. Movie 3: This TEM movie shows the emission of a long dislocation from a relatively small dislocation source. This type of dislocation emission prevailed at the later stage of plastic flow. On the first loading step (seen as an image drift in the movie), a dislocation is emitted from a single-pinned source located at the lower left corner of the Al crystal. On the second loading step (the second image drift), the advancing dislocation segment escapes through the nearby surface while the retailing segment undergoes cross-slip before escaping. The frame images of this movie are presented in Fig. 4. Movie 4: A dislocation avalanche is induced in the Al wire by a sudden increase in the strain rate accompanied by opening a crack at the side groove. The dislocation density increases abruptly by a factor of 2, compared to the deformation carried out at a normal strain rate (i.e. 10-3-10-2 s-1). 4
References S1.
P. A. Gruber, C. Solenthaler, E. Arzt, R. Spolenak, Acta Mater. 56, 1876 (2008).
S2.
S. H. Oh, M. Legros, D. Kiener, P. Gruber, G. Dehm, Acta Mater. 55, 5558 (2007).
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Fig. S1. Plan-view TEM images showing (A) the island structure and (B) the dislocation configuration in the single crystal Al film on polyimide. The inset in (A) is a selected area diffraction pattern of the (001) oriented Al film.
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Fig. S2. (A) SEM image showing the side grooves and the electron transparent window made in the tensile testing sample by FIB. (B) SEM image of the parallel wires shaped within the electron transparent window by FIB. The wire lengths were fixed to 10 μm. The widths of the wires were 3.0, 2.0, 0.5, 0.2 and 1.0 μm (from top to bottom). (C) TEM image of the wire array before straining. The side notch made in the 1 μm wide pattern is indicated by an arrow.
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Fig. S3. TEM images of the side notched region in the 1 μm wide wire (A) before and (B) after tensile deformation. The local axial strain is estimated by measuring the notch length change with displacement, as denoted by the length, Lo and L. The calculated strain in (B) is ~40%. After the failure of polyimide, the distance between the broken polyimide edges was used to measure the strain as indicated in (C). The distance was measured at the three different locations, i. e. AA at the left side, CC at the center and BB at the right side of the polyimide edges. The distance changes with deformation time are plotted in Fig. S4A.
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Fig. S4. Plots of the distance between the broken polyimide edges as a function of time. (A) AA, BB and CC correspond to different locations where the distance has been measured (see Fig. S3C). The most consistent one is AA (taken from the broken edges on the left), then CC is comparable (taken at the center) and BB (taken at the right) which varies and depends strongly on the tilt. (B) In the distance measurement AA, the strain rate is determined to be constant at 10-4 s-1 just before the dislocation avalanche. Then the strain rate jumps to 10-3 s-1 and, during the dislocation avalanche, it rises up to 2 × 10-2 s-1 before the formation of crack.
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Fig. S5. An example of dislocation sources observed at different strain stages. Single-ended sources with the sizes of (A) 135 ± 15 nm at ε ≈ 80% and (B) of 52 ± 15 nm at ε ≈ 140%.
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