Size-dependent transition of deformation behavior of Au nanowires

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1 Nano Research DOI /s z Nano Res 1 Size-dependent transition of deformation behavior of Au nanowires Na-Young Park 1,2, Ho-Seok Nam 1, Pil-Ryung Cha 1 ( ), and Seung-Cheol Lee 3 ( ) Nano Res., Just Accepted Manuscript DOI: /s z on September 3, 2014 Tsinghua University Press 2014 Just Accepted This is a Just Accepted manuscript, which has been examined by the peer-review process and has been accepted for publication. A Just Accepted manuscript is published online shortly after its acceptance, which is prior to technical editing and formatting and author proofing. Tsinghua University Press (TUP) provides Just Accepted as an optional and free service which allows authors to make their results available to the research community as soon as possible after acceptance. After a manuscript has been technically edited and formatted, it will be removed from the Just Accepted Web site and published as an ASAP article. Please note that technical editing may introduce minor changes to the manuscript text and/or graphics which may affect the content, and all legal disclaimers that apply to the journal pertain. In no event shall TUP be held responsible for errors or consequences arising from the use of any information contained in these Just Accepted manuscripts. To cite this manuscript please use its Digital Object Identifier (DOI ), which is identical for all formats of publication.

2 Template for Preparation of Manuscripts for Nano Research This template is to be used for preparing manuscripts for submission to Nano Research. Use of this template will save time in the review and production processes and will expedite publication. However, use of the template is not a requirement of submission. Do not modify the template in any way (delete spaces, modify font size/line height, etc.). If you need more detailed information about the preparation and submission of a manuscript to Nano Research, please see the latest version of the Instructions for Authors at TABLE OF CONTENTS (TOC) Authors are required to submit a graphic entry for the Table of Contents (TOC) in conjunction with the manuscript title. This graphic should capture the readers attention and give readers a visual impression of the essence of the paper. Labels, formulae, or numbers within the graphic must be legible at publication size. Tables or spectra are not acceptable. Color graphics are highly encouraged. The resolution of the figure should be at least 600 dpi. The size should be at least 50 mm 80 mm with a rectangular shape (ideally, the ratio of height to width should be less than 1 and larger than 5/8). One to two sentences should be written below the figure to summarize the paper. To create the TOC, please insert your image in the template box below. Fonts, size, and spaces should not be changed. Size-dependent transition of deformation behavior of Au nanowires Na-Young Park 1,2, Ho-Seok Nam 1, Pil-Ryung Cha 1,*, and Seung-Cheol Lee 3,* 1 School of Advanced Materials Engineering, Kookmin University, South Korea 2 Future Convergence Research Division, Korea Institute of Science and Technology (KIST), South Korea 3 Indo-Korea Science and Technology Center, Korea-Institute of Science and Technology (KIST), South Korea A new criterion for assessing the preferred deformation mode, slip or twin propagation, of nanowires as a function of diameter is presented. The simulation results demonstrate the size-dependent transition from superplastic deformation to rupture as nanowire diameter decreases. Provide the authors webside if possible. Author 1, webside 1 Author 2, webside 2

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4 Nano Research DOI (automatically inserted by the publisher) Research Article Size-dependent transition of deformation behavior of Au nanowires Na-Young Park 1,2, Ho-Seok Nam 1, Pil-Ryung Cha 1 ( ), and Seung-Cheol Lee 3 ( ) Received: day month year Revised: day month year Accepted: day month year (automatically inserted by the publisher) Tsinghua University Press and Springer-Verlag Berlin Heidelberg 2014 KEYWORDS Au nanowire, molecular dynamics, size-dependent transition, tensile deformation mechanism ABSTRACT Inspired by the controversy over tensile deformation modes of single-crystalline <110>/{111} Au nanowires, we investigated the dependency of the deformation mode on diameters of nanowires using the molecular dynamics technique. A new criterion for assessing the preferred deformation mode, slip or twin propagation, of nanowires as a function of nanowire diameter is presented. The results demonstrate the size-dependent transition, from superplastic deformation mediated by twin propagation to the rupture by localized slips in deformed region as the nanowire diameter decreases. Moreover, the criterion was successfully applied to explain the superplastic deformation of Cu nanowires. 1 Introduction With the recent development of nanotechnology, the structural and mechanical characteristics of nanowires due to their high surface-to-volume ratios have received considerable attention [1-8]. In particular, for the successful application of nanowires to nanoelectromechanical systems (NEMSs), it is essential to thoroughly understand their deformation mechanisms. Accordingly, such deformation mechanisms have been comprehensively studied with both delicate experiments and computer simulations including molecular dynamics (MD) simulations. As a result, it is well established, for example, that single-crystalline FCC <110>/{111} metal nanowires yield through the nucleation of a <112>/{111} partial dislocation at surface edges [9]. However, the deformation mechanism of nanowires after the yield point is rather controversial. After yielding, plastic deformation of Address correspondence to Pil-Ryung Cha, cprdream@kookmin.ac.kr; Seung-Cheol Lee, leesc@kist.re.kr

5 2 Nano Res. nanowires can occur through the activation and propagation of either full or partial dislocations. Based on previous interpretations taking into account the stacking fault energy Eisf and the Schmid factor, recent theoretical studies have explained the deformation characteristics of nanowires in terms of the generalized stacking fault energy (GSFE) curves and twinnability ( a ). The GSFE is the energy ratio Eisf/Eusf, where Eusf is the unstable stacking fault energy [10], and the twinnability is a function of the two energy ratios Eisf/Eusf and Eusf/Eutf, which takes into account the unstable twin fault energy Eutf as well [11]. However, although these models predict partial dislocation-mediated twin deformation for Au with a low Eisf, low Eisf/Eusf, and high a, recent MD simulations have reported that Au nanowires exhibit deformation due to slipping at room temperature [8, 12, 13]. The reasons for these contradictory predictions of the deformation mode of Au nanowires in theoretical models and simulation studies remain unclear. Interestingly, recent experiments have demonstrated the superplasticity of Au nanowires due to twin formation and propagation [14], which contradicts the MD simulations. In this work, we focus on this discrepancy between the theoretical model prediction, MD simulations, and experimental results. Here, we should note that the nanowires modeled in the MD simulations and experiments have different diameter ranges, primarily 4 nm in the MD simulations [8, 12, 13] and nm in the experiments [14]. In order to investigate the size dependence of the deformation mechanism, we conducted MD simulations of tensile deformation of single-crystalline Au nanowires, focusing in particular on the deformation behavior after the yield point. From these simulations, we found that large nanowires deform by twinning, which is consistent with experimental results, whereas small nanowires fail by full dislocation slip, as shown in previous MD simulations. Based on this observation, we suggest a new criterion for the deformation mode transition by estimating the nanowire diameter at which the flow stress involved in twin and the yield stress involved in slip cross over. This analysis predicts that a size-dependent transition will occur at Au nanowire diameters of approximately 7.6 nm. When the same model is applied to Cu nanowires, deformation by twin propagation is found to be favored for all sizes, as shown in previous reports [6, 8]. 2 Simulation detail Single-crystalline FCC <110>/{111} metal nanowires were constructed by cutting the bulk FCC structure in such a way that the nanowires had four {111} lateral facets with the z-axis parallel to the <110> directions [12]. In the notation <110>/{111} for the nanowires, <110> indicates the crystallographic direction of the nanowire axis and {111} indicates the lateral surfaces, as described in the literature [8, 12, 13]. The diameters of the nanowires were 4, 6, 10, 15, and 20 nm, which are defined as the longer lengths of the rhombic cross-sections. The aspect ratio of the nanowire diameter to the length was set to 9. The molecular dynamics simulations of nanowire deformation were performed using the LAMMPS code [15]. All simulations were performed at 300 K using the constant number, volume, and temperature (NVT) ensemble, where a constant temperature was maintained with a Nosé Hoover thermostat [16]. A periodic boundary condition was only imposed along a <110> crystallographic direction, i.e., the z-axis. The initial configurations were equilibrated at 300 K for 200 ps. After the relaxation, the nanowires underwent homogeneous tensile deformation by rescaling of the z-coordinates of all atoms, as described in the literature [17]. We applied a constant deformation rate of 10 8 /s. The atomic virial stress was calculated for every deformation step using the equilibrium atomic volume for the bulk lattice at a given temperature. To model the atomic interactions, we adopted the embedded-atom method (EAM) potential for Au originally developed by Voter and Chen [18, 19] and modified by Park [12] to improve the stacking fault energy in relation to the experimental value. In addition to the molecular dynamics simulations of the deformation behavior, a number of molecular

6 Nano Res. 3 statics calculations were carried out separately using the conjugate gradient method in order to investigate the planar fault energies of the nanowires. 3 Results and discussion First, tensile deformation simulations of the nanowires were carried out using MD. Figure 1 presents the engineering stress-strain curves for nanowires with diameters of 4, 6, 10, 15, and 20 nm. The yield stress increased with decreasing size, following the smaller is stronger trend. The 4 nm nanowire exhibited a yield stress of 2.8 GPa, which is slightly lower than those found in other simulations ( GPa) [8, 20]. The different yield stress values may be attributed to the different interatomic potentials adopted in those simulations. Meanwhile, the 20 nm nanowire had a yield stress of 1.6 GPa, which is in good agreement with the experimental value of 1.5 GPa reported in a recent tensile test [14]. After the yield point, the stress decreased significantly and exhibited flow stress. As the diameter increased, the magnitude of the stress drop decreased. The yielding of the 4 nm nanowire produced a precipitous reduction in stress (by 1.4 GPa) at a strain (ε) of approximately 5.6 %, whereas the yielding of the 20 nm nanowire produced a gradual reduction (by 0.9 GPa) in a strain range of %. Note that all of the nanowires exhibited deformation by twinning after the yield point, although the size of the twinned region along the loading direction, meaning the sweeping distance of the twin boundary, depended on the size. Interestingly, a distinct deformation mode was found between 6 and 10 nm. Nanowires less than 6 nm in diameter failed by slip, as inferred from the inset in Fig. 1, whereas nanowires greater than 10 nm in diameter deformed by twinning throughout the whole nanowire. In order to clarify the two distinct deformation modes, we analyzed the atomic structures of the nanowires with diameters of 6 and 10 nm, as shown in Fig. 2. Atoms in the magnified section view are colored according to their local crystallographic structure using the Ackland method [21]: green, orange, sky blue, and dark blue stand for FCC, HCP, BCC, and unresolved structures, respectively. The surface view was visualized using the AtomEye program [22], and the atoms are colored according to their coordination number: magenta, gray, purple, and red stand for 9, 8, 7, and 6, respectively. Figure 2 (a) shows that the 6 nm nanowire begins to fail at around ε = 14 %. Surprisingly, necking is initiated by nucleation of a full dislocation in the twinned <100>/{100} region, as indicated by an arrow at ε = 14.0 %, and not by a trailing partial dislocation in the pristine <110>/{111} region. Although it is not shown in Fig. 2, this kind of secondary yielding also occurred in the 4 nm nanowires, as indicated at ε = 7.3 % in the strain-stress curves in Fig. 1. The progress from the initial twinning to the following secondary yielding is faster in the 4 nm nanowire than in the 6 nm nanowire. On the other hand, the 10, 15, and 20 nm nanowires experienced lattice reorientation from <110>/{111} to <100>/{100} through twin propagation along the loading direction. The secondary yielding was not observed at those sizes. This is consistent with the results of recent experiments demonstrating the plastic deformation of Au nanowires induced by coherent twin propagation [14]. Even though several dislocations were nucleated in the twinned region, as shown in Fig. 2(b), most dislocations did not develop into full dislocations that could lead to secondary yielding or necking. Instead, they disappeared or remained within the surface region during the deformation. As a first step in understanding the size dependence of the deformation mechanism of Au nanowires, we investigated the GSFE of the nanowires as a function of their diameters and compared it to the bulk counterpart. The GSFE of the Au bulk was calculated using the rigid box separation method, as implemented in previous studies [23]. Note that in previous theoretical model studies, the GSFE of the nanowires was calculated based on the equilibrium state of the bulk structure. However, since Au nanowires naturally contract relative to their bulk counterparts due to tensile surface stresses, the GSFE calculated using the bulk Nano Research

7 4 Nano Res. structure is likely to be insufficient to explain the unique properties of the nanowires. Moreover, the typical rigid box separation method does not intrinsically reflect the size dependence of the deformation mechanism. New approach to the GSFE curve has been reported recently [20, 24]. Jiang et al. [24] have suggested a surface stacking fault energy (SSF) approach in which the relaxed nanowire structure are directly applied in the calculation, in contrast to the typical rigid box separation method. Jennings et al. [20] have shown the stress-dependent GSFE curves under the uniaxial loading condition. For uniaxial loading, they have measured all strain components under the uniaxial stress by experiments and applied to the GSFE calculations. Inspired by the latter approach, we calculated the GSFE curves under the compressive strains, which are caused by the surface stress and depend on the diameters of nanowires, using the rigid box separation method. The compressive strain corresponding to each diameter of nanowire was obtained from the energy minimum configuration of the nanowire following the literature [25]. Table 1 shows the amount of contraction calculated from the energy minimization, and the planar fault energies of nanowires obtained from the GSFE curves for diameters of 4, 6, 10, 15, and 20 nm and for the bulk counterpart. For ideal bulk Au, the amount of contraction would be zero owing to the absence of surfaces. However, the nanowires should be intrinsically strained with respect to the bulk counterpart owing to their surfaces. Nanowires of 4, 6, 10, 15, and 20 nm in diameter had total energy minima at strains of 2.18, 1.61, 1.00, 0.92, and 0.87 %, respectively. Moreover, it was found that these high amounts of contraction of the small nanowires directly changed the planar fault energies in the GSFE. As the size decreased, Eisf decreased, whereas Eusf increased. Consequently, Eisf/Eusf decreased and a increased. A lower Eisf/Eusf ratio means a higher energy barrier for the nucleation of a trailing partial dislocation, implying deformation by twinning [10]. A higher a with a small Eisf/Eusf and a large Eusf/Eutf also means a higher energy barrier for the nucleation of a trailing partial dislocation and a lower barrier for the nucleation of a twinning partial dislocation, indicating deformation by twinning as well [11]. Therefore, if our data for the GSFE and twinnability are interpreted in this way, the tendency to deform by twinning is expected to increase as the size decreases. However, in our MD simulations, small nanowires are deformed by slip, unlike the large nanowires that are deformed by twin, as seen in Fig. 1 and Fig. 2. Therefore, we found that the GSFE and twinnability failed to explain the size-dependent deformation behavior. The discrepancy between the prediction based on the GSFE and our MD results can be attributed to the fact that the twinning tendency parameters calculated from the GSFE are based on a pristine <110> structure, whereas the transition-to-failure mode seen in our simulations is initiated by the secondary yielding in the twinned <100> region. Therefore, an explanation of the mechanism of the secondary yielding shown in Fig. 2(a) is necessary. Since the initial yielding mechanisms were similar for all the sizes, i.e., partial dislocation-mediated plastic deformation leading to twinning, we focused on the plastic deformation behavior after the initial yield point. In the stress-strain curves and structural analysis, the plastic deformation of Au nanowires appears to have two mechanisms: either secondary yielding in the twinned <100>/{100} region (seen for 4 and 6 nm nanowires) or twin propagation (seen for 10, 15, and 20 nm nanowires). Here, we suggest a new criterion determining the deformation mechanism for a given Au nanowire size based on comparing the stress value required for secondary yielding with that required for twin propagation. The stress value required for secondary yielding can be determined from the yield stress of <100>/{100} nanowires, and that for twinning can be determined from the average flow stress during the twin deformation in the stress-strain curves. In order to obtain the yield stress of the twinned <100>/{100} region, tensile deformation simulations of <100>/{100} Au nanowires with

8 Nano Res. 5 different sizes were conducted. The stress-strain curves for the <100>/{100> nanowires are presented in Fig. S2. Since the twin formation was accompanied by a reduction in the cross-sectional area, from rhombic to square, the flow stress values needed to be adjusted for the reduced area and are listed in Table S1. The conversion was calculated as follows: σ = σ1 A1/A2, where σ1 is the flow stress at the rhombic cross-sectional area A1 and σ is the converted flow stress for the square cross-sectional area A2. Interestingly, we found that the yield stress and the average flow stress apparently have a linear relationship with the inverse of the nanowire diameter [see Fig. S3 of the Electronic Supplementary Material (ESM)], as previously reported in the literatures [27, 28]. Therefore, the yield stress of the <100>/{100} structure and the flow stress of the <110>/{111} structure are both modeled as linear functions of the inverse of the diameter (see Fig. S3 and S4 of the ESM). Figure 3 shows the <100>/{100} yield stress and the <110>/{111} flow stress as linear functions of the inverse of the diameter. The cross-sectional areas at given diameters are also presented in the upper x-scales of Fig. 3. Interestingly, the crossover between the two lines is clearly seen, which means a transition between the two deformation mechanisms. At small sizes, the <100>/{100} yield stress is lower than the <110>/{111} flow stress, indicating that small nanowires are likely to fail because of secondary yielding in the twinned region. On the other hand, at large sizes, the <110>/{111} flow stress is lower than the <100>/{100} yield stress, indicating that the large nanowires are likely to deform by twinning. Clearly, the transition occurs at a cross-sectional area of 9.72 nm 2, which is equivalent to 7.6 nm in diameter. This model explains the transition of deformation behavior observed between 6 and 10 nm in our MD simulation well. In order to validate our criterion, the same interpretation is applied to single-crystalline <110>/{111} Cu nanowires with diameters ranging from 3 to 15 nm. The stress-strain curves of the <110>/{111} and <100>/{100} Cu nanowires are given in Fig. S5 in the ESM. Cu nanowires are well known to deform by twinning, even at a small diameter of 3.39 nm [8]. Based on our interpretation, as shown in Fig. 4, Cu nanowires are predicted to deform through twin propagation in all ranges, because the <110>/{111} flow stress is lower than the <100>/{100} yield stress for all nanowire sizes. Even at 3 nm, the <110>/{111} flow stress was found to be much lower than the <100>/{100} yield stress, by 4 GPa. Our prediction of an increased tendency to deform by twinning for Cu nanowires agrees with the results of previous MD simulations [6, 8] and experiments [28]. 4 Conclusions In summary, our MD simulations of the tensile deformation of single-crystalline <110>/{111} Au nanowires showed that transition behavior occurs between 6 and 10 nm in diameter. Nanowires larger than 10 nm in diameter deform through coherent twin propagation along the loading direction, whereas those less than 6 nm fail by necking that is initiated by nucleation of a full dislocation in the twinned <100>/{100} region. This transition of the deformation mechanism was quantitatively assessed by comparing the relative contributions of the yield stress in the <100>/{100} structure, which causes failure due to necking, and the flow stress, which is required for twin boundary propagation, as a function of nanowire size. As a result, a size-dependent transition of the deformation mechanism was found at a diameter of 7.6 nm for Au nanowires. Our methodology was verified by applying to Cu nanowires, in which the twinning mechanism operates at all sizes. The results of the present study will be helpful in providing a fundamental understanding of the mechanical properties of nanowires, and they are expected to be useful in the application to functional nano-materials. Acknowledgements This research was supported by the Basic Science Research Program through NRF funded by the Ministry of Education (2012R1A1A ) and Nano Research

9 6 Nano Res. ( ), and by Leading Foreign Research Institute Recruitment Program through NRF funded by MSIP (2013K1A4A ). This research was also supported by Nano Material Technology Development Program through the NRF funded by the Ministry of Education, Science and Technology ( ) and by the Convergence Agenda Program (CAP) of the Korea Research Council of Fundamental Science and Technology (KRCF). Electronic Supplementary Material: Supplementary material on the calculations of GSFE curves and on the assessment of a size-dependent transition is available in the online version of this article at References [1] Weinberger, C. R.; Cai, W. Atomistic Simulations and Continuum Modeling of Dislocation Nucleation and Strength in Gold Nanowires. J. Mater. Chem. 2012, 22, [2] Gall, K.; Diao, J.; Dunn, M. L. The Strength of Gold Nanowires. Nano Lett. 2004, 4, [3] Wu, B.; Heidelbert, A.; Boland, J. Mechanical Properties of Ultrahigh-Strength Gold Nanowires. J. Nat. Mater. 2005, 4, [4] Lu, Y.; Song, J.; Huang, J. Y.; Lou, J. Fracture of Sub-20nm Ultrathin Gold Nanowires. Nano Res. 2011, 4, [5] Diao, J.; Gall, K.; Dunn, M. L. Surface-Stress-Induced Phase Transformation in Metal Nanowires. Nat. Mater. 2003, 2, [6] Liang, W.; Zhou, M.; Ke, F. Shape Memory Effect in Cu Nanowires. Nano Lett. 2005, 5, [7] Park, H. S.; Gall, K.; Zimmerman, J. A. Shape Memory and Pseudoelasticity in Metal Nanowires. Phys. Rev. Lett. 2005, 95, [8] Liang, W.; Zhou, M. Atomistic Simulations Reveal Shape Memory of FCC Metal Nanowires. Phys. Rev. B 2006, 73, [9] Diao, J.; Gall, K.; Dunn, M. L. Yield Strength Asymmetry in Metal Nanowires. Nano Lett. 2004, 4, [10] Van Swygenhoven, H.; Derlet, P. M.; Frøseth, A. G. Stacking Fault Energies and Slip in Nanocrystalline Metals. Nat. Mater. 2004, 3, [11] Tadmor, E. B.; Hai, S. A Peierls Criterion for the Onset of Deformation Twinning at a Crack Tip. J. Mech. Phys. Solids 2003, 56, [12] Park, H. S.; Zimmerman, J. A. Modeling Inelasticity and Failure in Gold Nanowires. Phys. Rev. B 2005, 72, [13] Park, H. S.; Gall, K.; Zimmerman, J. A. Deformation of FCC Nanowires by Twinning and Slip. J. Mech. Phys. Solids 2006, 54, [14] Seo, J.-H.; Yoo, Y.; Park, N.-Y.; Yoon, S.-Y.; Lee, H.; Han, S.; Lee, S.-W.; Seong, T.-Y.; Lee, S.-C.; Lee, K.-B. et al. Superplastic Deformation of Defect-Free Au Nanowires via Coherent Twin Propagation. Nano Lett. 2011, 11, [15] Plimpton, S. Fast Parallel Algorithms for Short-Range Molecular Dynamics. J. Comput. Phys. 1995, 117, [16] Allen, M. P.; Tildsley, D. J. Computer Simulation of Liquids; Oxford University Press: New York, [17] Rabkin, E.; Nam, H. S.; Srolovitz, D. J. Atomistic Simulation of the Deformation of Gold Nanowires. Acta Mater. 2007, 5, [18] Voter, A. F.; Chen, S. P. Characterization of Defects in Materials. Mater. Res. Soc. Symp. Proc. Materials Research Society, Pittsburgh, Pennsylvania, 1987, 82, 175. [19] Voter, A. F. Embedded Atom Method Potentials for Seven FCC Metals: Ni, Pd, Pt, Cu, Ag, Au, and Al. Los Alamos Unclassified Technical Report No. LA-UR , [20] Jennings, A.T.; Weinberger, C. R.; Lee, S.-W.; Aitken, Z. H.; Meza, L; Greer, J. R. Modeling Dislocation Nucleation Strengths in Pristine Metallic Nanowires under Experimental Conditions. Acta Mater. 2013, 61, [21] Ackland, J. Applications of Local Crystal Structure Measures in Experiment and Simulation. Phys. Rev. B 2006, 73, [22] Li, J. AtomEye: An Efficient Atomistic Configuration Viewer. Modell. Simul. Mater. Sci. Eng. 2003, 11, [23] Zimmerman, J. A.; Gao, H.; Abraham, F. F. Generalized Stacking Fault Energies for Embedded Atom FCC Metals. Modell. Simul. Mater. Sci. Eng. 2000, 8, [24] Jiang, J.-W.; Leach, A. M.; Gall, K.; Park, H. S.; Rabczuk, T. A Surface Stacking Fault Energy Approach to Predicting Defect Nucleation in Surface-dominated Nanostructures. J. Mech. Phys. Solids 2013, 61, [25] Liang, H.; Upmanyu, M.; Huang, H. Size-dependent Elasticity of Nanowires: Nonlinear Effects. Phys. Rev. B 2005, 71, [26] Stobbs, W. M.; Sworn, C. H. The Weak Beam Technique as Applied to the Determination of the Stacking-Fault Energy of Copper. Phil. Mag. 1971, 24, [27] Zhang, W.; Wang, T.; Chen, X. Effect of Surface Stress on the Asymmetric Yield Strength of Nanowires. J. Appl. Phys. 2008, 103, [28] Yu, Q.; Shan, Z.-W.; Li, J.; Huang, X.; Xiao, L.; Sun, J.; Ma, E. Strong Crystal Size Effect on Deformation

10 Nano Res. 7 FIGURES. Twinning. Nature 2010, 463, Figure 3 Yield stress of <100>/{100} Au nanowires and flow stress during twin propagation of <110>/{111} Au nanowires as a function of the inverse of the diameter. Figure 1 (color online). Stress-strain curves of single-crystalline <110>/{111} Au nanowires during tensile loading. The inset shows the failure of a 4 nm nanowire. Figure 2 (color online) Magnified cross-sectional views and full surface views of (a) 6 nm nanowire at 12.5%, 14%, and 17.7% strain and (b) 10 nm nanowire at 7% and 20% strain. Atoms in the magnified view were colored according to the local crystallographic structure determined using the Ackland method [21]: green, orange, sky blue, and dark blue stand for FCC, HCP, BCC, and unresolved structures, respectively. Atoms in the surface view were colored according to their coordination number: magenta, gray, purple, and red stand for 9, 8, 7, and 6, respectively. Figure 4 Yield stress of <100>/{100} Cu nanowires and flow stress during twin propagation of <110>/{111} Cu nanowires as a function of the inverse of the diameter. Atomic structures for the twin deformation of Cu nanowires are also given. Nano Research

11 8 Nano Res. TABLES. Table 1 Predicted lattice contraction (d) and planar fault energies Eisf, Eusf, and Eutf for different nanowire sizes and bulk Au. Eisf/Eusf and τa are also calculated. Low Eisf/Eusf and high τa indicate a high tendency to deform by twinning. Size [nm] d [%] Eisf [mj/m 2 ] Eusf [mj/m 2 ] Eutf [mj/m 2 ] Eisf/Eusf τa Bulk Bulk Theory 31 [8] 101 [8] 122 [8] 0.31 [8] [8] Bulk Exp 30 [26]

12 Nano Res. Electronic Supplementary Material Size-dependent transition of deformation behavior of Au nanowires Na-Young Park 1,2, Ho-Seok Nam 1, Pil-Ryung Cha 1 ( ), and Seung-Cheol Lee 3 ( ) Supporting information to DOI /s12274-****-****-* 1. Calculation of GSFE curves under compressive strain Based on the molecular statics calculations carried out using the conjugate gradient method, we investigated the contraction of Au nanowires due to the tensile surface stresses as a function of the diameter. We applied strain in the range of -5.0 % to 1.0 % along the z-axis, as described in the literature [S1]. Figure S1 (a) shows that the nanowires are intrinsically strained. The strains at which the strain energies are at a minimum are -3.78, -2.18, -1.61, and % for nanowires with diameters of 2.4, 4, 6, and 10 nm, respectively. Then, the GSFE curves for Au nanowires were calculated under the equilibrium compressive strains obtained from Figure S1 (a). From the GSFE curves for the Au nanowires as shown in Figure S1 (b), we found that Eusf and Eutf increase as the size decreases. The twinnability τa is calculated as follows: 8 E a E isf usf E E usf utf Twin deformation is favored when the ratio of Eisf/Eusf is small and Eusf/Eutf is large, since a small value of Eisf/Eusf indicates a higher barrier for the nucleation of a trailing partial and a large value of Eusf/Eutf indicates a lower barrier for the nucleation of a twinning partial. Our results showed higher twinnability at smaller sizes with the lower Eisf/Eusf value of 0.25 and higher Eusf/Eutf value of 0.89, as compared with the bulk values of 0.3 and 0.85, respectively. 2. Assessment of a size-dependent transition of the deformation mechanism Figure S2 shows the engineering stress-strain curves for (a) <110>/{111} Au nanowires with diameters of 4, 6, 10, 15, and 20 nm and (b) <100>/{100} Au nanowires with diameters of 3.6, 6, 10, 15, and 20 nm. The flow stress values for <110>/{111} Au nanowires and the yield stress values for <100>/{100} Au nanowires with respect to the size are listed in Table S1. We note that the flow stresses were averaged with the stress values at the stress Nano Research Address correspondence to Pil-Ryung Cha, cprdream@kookmin.ac.kr; Seung-Cheol Lee, leesc@kist.re.kr

13 Nano Res. plateau associated with the twin deformation in the strain ranges of % for 4 nm, % for 6 nm, and % for 10, 15, and 20 nm nanowires. Interestingly, we found that the yield stress and the average flow stress apparently have a linear relationship with the inverse of the nanowire diameter. Therefore, the yield stress of the <100>/{100} structure and the flow stress of the <110>/{111} structure are modeled as linear functions of the inverse of the diameter. In Fig. S4, the flow stress of <110>/{111} Au nanowires was modified from the red dotted line to the red solid line by performing the conversion described in the main text. References [S1] Liang, H.; Upmanyu, M. Phys. Rev. B 2006, 71, Table S1 Average flow stress of <110>/{111} nanowires and yield stress of <100>/{100} nanowires with respect to the size. D is diameter and A1 and A2 are the cross-sectional area of a <110>/{111} nanowire and that when the nanowire shrinks to a <100>/{100} structure by twinning. <110>/{111} Nanowires <100>/{100} Nanowires D (nm) 1/D (nm -1 ) Flow stress, σ1 (GPa) A1 (nm) A2 (nm) Converted flow stress, σ2 (GPa) D (nm) 1/D (nm -1 ) Yield stress (GPa)

14 Nano Res. Figure S1 (a) Strain energy per atom as a function of compressive strain and (b) GSFE curves of Au nanowires under the equilibrium compressive strain. (a) (b) Figure S2 Stress-strain curves for (a) <110>/{111} and (b) <100>/{100} Au nanowires. (a) (b) Nano Research

15 Nano Res. Figure S3 (a) Yield stress and (b) flow stress average as a function of 1/D for Au nanowires. (a) (b) Figure S4 Yield stress of <100>/{100} Au nanowires and flow stress during twin propagation of <100>/{111} Au nanowires as a function of inverse of the diameter.

16 Nano Res. Figure S5 Stress-strain curves for (a) <110>/{111} and (b) <100>/{100} Cu nanowires. (a) (b) Nano Research