Aesar, Item No ) in a tube furnace using CVD. Cu foil was inserted into a quartz tube

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1 Supporting Information 01. Large scale graphene (100 x 200 mm 2 ) was grown on a 25 µm thick Cu foil (Alfa Aesar, Item No ) in a tube furnace using CVD. Cu foil was inserted into a quartz tube and left in vacuum at pressure of <5x10-3 Torr and heated up to 1,000 o C for 1 hour. CH 4 gas (15 sccm) was then injected into the quartz tube for 20 minutes, and the system was cooled down to room temperature. All of processes were conducted under H 2 flow (10 sccm) in Ar (500 sccm) environment. CVD grown graphene on Cu foil was then spin-coated with PMMA support layer, and the Cu foil was etched by an aqueous solution of ammonium persulfate 1% in DI water. Released PMMA film with graphene was floated in the water and rinsed several times with distilled water, and the PMMA/graphene was scooped with a Cu-deposited polyimide substrate (width: 4 mm, length: 70 mm and thickness: 125 μm). Here, Cu layers of 100 nm in thickness were deposited using DC magnetron sputtering (SNTEK Inc. Co-sputtering system) at rate of 0.83Ås under a 50W and Ar pressure of 12 mtorr. The transferred sample was then heated to 80 o C for 5 minutes to dry out the water and then cleaned with acetone for 5 minutes to remove the PMMA. This process was repeated to fabricate the nanolayered Cu/Gr composite. Cross-sectional images of the samples were obtained by using focused ion beam (FIB, Quanta 3D FEG) milling. 1

2 Intensity (a.u.) Supporting Information 02. XRD (D/MAX-2500) results indicated strong (111) texture, as expected. The XRD results together with TEM (Tecnai F30 ST) cross-section images were used to determine the average grain sizes in Cu and Cu/Gr to be ~60 nm. (111) Cu (200) (220) (311) Cu/Gr PI Figure S1. XRD for Cu electrode and Cu/Gr composite indicating strong (111) texture in both specimens. 2

3 Supporting Information 03. Comparison of Cu/Gr to other interface engineered materials Incorporating high density of interfaces can greatly enhance the strength of the structural material. Cu/Gr is known to be ultra-high strength (1.4 GPa at =70 nm) 1, and was also demonstrated in this study to have the ability to block crack propagations that in turn results in enhanced resistance to fatigue-induced damage. Other types of interface engineered metals include nanocrystalline and nanotwinned Cu as well as the use of a secondary metal in the form of nanolayered composite. The strengths of these materials with similar governing length scale to the Cu/Gr with repeat layer spacing of 70 nm is summarized in Table S1 for comparison. Nanocrystalline Cu with the grain size of ~25 nm has strength of ~900 MPa, but the strength is reduced to ~500 MPa for grain size of ~60 nm. 2-4 Nanotwinned Cu with columnar grains with nanoscale twin spacing of 6.7 nm and average columnar grain size of 250 nm showed strength of ~350 MPa. 3, 5 Therefore, the strength of Cu/Gr exceeds the observable strengths in nanocrystalline and nanotwinned Cu. As for the Cu based nanolayered composites, the Cu/Ni multilayered sample has strength of ~1.0 GPa for repeat layer spacing of 100 nm 6 and Cu/Nb has strength of 1.2 GPa for repeat layer spacing of 86 nm. 7 It should be noted, however, that the Cu/Ni and Cu/Nb consists of 50% Cu and 50% Ni or Nb, whereas only a single atomic layer in thickness graphene (hence with minimal volume fraction effect) is used as an enforcement in Cu/Gr. Although there are no reports on Cu layered with another type of metal with thickness approaching the dimension of a single atomic layer, the strength is expected to reduce with reduction in the thickness of the secondary metal as the interface becomes easier for dislocations to be transmitted across. Given the effectiveness of graphene as a strength enhancer, there are also reports on polymer/gr composites such as polycarbonate/gr nanolayers with repeat layer spacing of 3

4 0.032~0.11 mm. This work has demonstrated that improved mechanical properties are achievable even with extremely low volume fraction of graphene inserted. 8 Table S1. Strengths of different interface engineered metals. 4

5 Supporting Information 04. TEM (Grand ARM-300F, JEOL) analysis of Cu/Gr with 100 nm repeat layer spacing that is subjected to fatigue bending showed crack-like features that run along columnar grain boundaries of Cu layer. In the as-synthesized condition before bending fatigue testing, the columnar grain of the Cu (with average grain size of ~60nm) showed some growth twins as shown in Figure 2e, f. The TEM image of the Cu/Gr subjected to bending fatigue (Figure S2) also showed retention of the twinned microstructure within some grains. Since it would be difficult for crack to propagate through the interior of such twinned grains, the crack initiation and propagation will therefore occur preferential along the grain boundaries. twins 50nm crack Figure S2. TEM image of Cu/Gr nanolayers after bending fatigue testing at 1.6% strain to 1,000,000 cycles that indicate crack formation along the Cu grain boundaries. 5

6 Supporting Information 05. In this study, we performed MD simulation to verify the influence of graphene layer on crack propagation behavior of Cu electrode and Cu/Gr composite. In the MD simulation, we used embedded-atom method (EAM) potential 9 to consider the copper-copper interaction in copper block and airebo potential 10 with different potential parameter rc min cc = 2.0 Å to capture the carbon-carbon interaction in graphene sheet. In addition, we used Lennard-Jones (LJ) potential 1 to consider the interaction between copper and carbon atom at the Cu/Gr interface. DFT calculations indicated van der Waals interaction between the Cu and graphene interface, 1, 11, 12 and the well depth and equilibrium distance parameters of LJ potential were optimized to reproduce the DFT calculations. 1 The lattice constants of copper and graphene were Å and Å, respectively (see Figure S3). In order to model the initial Cu electrode and Cu/Gr composite, we constructed Cu block and Cu/Gr sandwich structure. To construct the Cu/Gr sandwich structure, we put the crystallographic orientation as X = [11 0] Cu [100] Gr, Y = [112 ] Cu [010] Gr and Z = [111] Cu [001] Gr. The subscript Cu and Gr represent the copper and graphene, respectively. Using the lattice constant and orientation of copper block and graphene sheet, we generated the two copper blocks and graphene sheet with small misfit strain in x and y-direction (ε xx = and ε yy = ) separately. The dimensions of copper block were L x = Å, L y = Å and L z = Å and graphene sheet were L x = Å and L y = Å. Then, we applied biaxial strain to graphene sheet in x and y-direction to satisfy the geometric compatibility between copper blocks and graphene sheet. Once we get the copper blocks and strained graphene sheet, we assembled the two copper blocks and strained graphene sheet into a Cu/Gr sandwich structure. We also constructed the Cu block with given crystallographic orientations. The dimensions of Cu block were L x = Å, L y = Å and L z =

7 Å. After construction of Cu block and Cu/Gr sandwich structure, the vertical crack was introduced at the free surface in negative z-direction. The dimensions of crack were l y 6 Å and l z 18 Å. The final dimensions of Cu block and Cu/Gr sandwich structure are shown in Figure S4. In the atomic simulation, the z-axis was perpendicular to the Cu/Gr interface and the periodic boundary condition was applied to x and y-direction. So as to find the initial atomic configuration of Cu block and Cu/Gr sandwich structure, we performed energy minimization procedure at 0 K using conjugate gradient method and then applied thermal equilibration procedure for 30 ps at 1 K using the Nosé-Hoover isothermal-isobaric (NPT) ensemble. After equilibration procedure, the uniaxial tension strain (ε =10 8 /s) was applied in y-direction using the Nosé-Hoover canonical (NVT) ensemble at 1 K. In the uniaxial tension test, we applied the fixed boundary condition on the free surface of the both Cu block and Cu/Gr sandwich structure in positive z-direction. In order to analyze the deformation mechanisms of Cu block and Cu/Gr sandwich structure, we computed the atomic shear strain for each strain level. 7

8 Figure S3. Unit cell structures of (a) copper and (b) graphene. Red and black sphere represent the copper and carbon atom, respectively. Figure S4. Dimensions of Cu block and Cu/Gr sandwich structure. The dimension of Cu block and Cu/Gr sandwich structure in out of plane direction (x-direction) is L x = Å. 8

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