In conclusion, we focused on the analysis of fundamental mechanical behavior of np-Au depending on the ligament size. the reasons why the in-depth study on the ligament-size effect is necessary were introduced in Chapter 2 and at the beginning of each Chapter.
Firstly, we investigated the structural evolution during ligament coarsening by 3D reconstruction model. 3D reconstruction was carried out by the repetition of serial cross-sectioning and taking SEM images automatically. It was revealed that the coarsening of np-Au is carried by surface diffusion dominantly and it yields the self-similar structural evolutions in terms of ligament-size distribution, surface-to-volume ratio, and connectivity. These results means that structural effect is negligible for the ligament-size effect.
And then, to figure out the fundamental mechanical properties of np-Au, we performed the uniaxial tensile and compressive tests on four np-Au samples without any external factors affecting the mechanical properties such as defects and grain boundaries. It was confirmed the tension-compression asymmetric behavior in np-Au regarding to yield strengths and ligament-size effect. Tensile yield strength was greater than compressive yield strength except for the largest ligament size sample, which showed similar yield strengths. For the ligament-size effect, tension showed a clear size-effect for all ligament sizes while compression revealed the bulk-like behavior beyond the dL of 402 nm. These asymmetric results could be attributed to different dominant deformation behavior of ligaments;
necking and failure by axial deformation in tension, but bending and shear deformation in compression.
With combining the typical Gibson-Ashby model, it was revealed that the applied resolved shear stress induced by bending and shear deformation are greater than those induced by axial deformation, leading to the lower compressive yield strength. In addition, the higher probability of dislocation retention in ligaments by stress distribution in compression resulted in the earlier bulk-like behavior at the smaller ligament size in compression.
In addition, we investigated the time-dependent deformation behavior of np-Au by performing the nanoindentation creep tests with four np-Au samples. The results indicated that the creep behavior in terms of total creep strain 𝜀total and QSS creep rate 𝜀̇𝑄𝑆𝑆was increased with increasing ligament size while the greatest creep behavior was shown for the smallest ligament size. After alumina coating on np-Au surface, the creep behavior was increased, but it was decreased only at the smallest ligament size. the dominant creep mechanism was dislocation mediated creep for all ligament sizes, but dominant dislocation mechanism was different each other stochastically; surface nucleated source for the smallest ligament size, but initial dislocation source for the other ligament sizes. The surface coating on np-Au caused the restraint of dislocation nucleation at the surface and dislocation escape to the surface, leading
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to the increase of initial dislocations in the coated ligaments at the beginning of creep. Under the initial dislocation source as dominant dislocation mechanism, the higher initial dislocations caused the more pronounced creep behavior. Meanwhile, under the surface nucleation as dominant dislocation mechanism, creep behavior was decreased after surface coating due to restrained surface nucleation, but it was much pronounced for the smallest ligament size than the other sizes, which could be attributed to the involvement of image force and/or surface energy.
I hope that this research makes it possible to more accurate analysis of mechanical properties for the nanoporous materials, and I believe that this research can be used as cornerstone of improving the mechanical properties of nanoporous materials.
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References
[1] L.J. Gibson, M.F. Ashby, Cellular solids: structure and properties, Cambridge Univ. Press, Cambridge, 2010.
[2] S.J. Yeo, M.J. Oh, P.J. Yoo, Structurally Controlled Cellular Architectures for High-Performance Ultra-Lightweight Materials, Adv Mater 31(34) (2019) e1803670.
[3] S. Araby, A. Qiu, R. Wang, Z. Zhao, C.-H. Wang, J. Ma, Aerogels based on carbon nanomaterials, Journal of Materials Science 51(20) (2016) 9157-9189.
[4] J. Banhart, Manufacture, characterisation and application of cellular metals and metal foams, Prog Mater Sci 46(6) (2001) 559-U3.
[5] T.A. Schaedler, A.J. Jacobsen, A. Torrents, A.E. Sorensen, J. Lian, J.R. Greer, L. Valdevit, W.B.
Carter, Ultralight Metallic Microlattices, Science 334(6058) (2011) 962-965.
[6] X.Y. Zheng, H. Lee, T.H. Weisgraber, M. Shusteff, J. DeOtte, E.B. Duoss, J.D. Kuntz, M.M. Biener, Q. Ge, J.A. Jackson, S.O. Kucheyev, N.X. Fang, C.M. Spadaccini, Ultralight, Ultrastiff Mechanical Metamaterials, Science 344(6190) (2014) 1373-1377.
[7] J. Bauer, L.R. Meza, T.A. Schaedler, R. Schwaiger, X.Y. Zheng, L. Valdevit, Nanolattices: An Emerging Class of Mechanical Metamaterials, Advanced Materials 29(40) (2017).
[8] J. Bauer, S. Hengsbach, I. Tesari, R. Schwaiger, O. Kraft, High-strength cellular ceramic composites with 3D microarchitecture, Proc Natl Acad Sci U S A 111(7) (2014) 2453-8.
[9] J. Bauer, A. Schroer, R. Schwaiger, O. Kraft, Approaching theoretical strength in glassy carbon nanolattices, Nat Mater 15(4) (2016) 438-43.
[10] X. Wendy Gu, J.R. Greer, Ultra-strong architected Cu meso-lattices, Extreme Mechanics Letters 2 (2015) 7-14.
[11] X. Li, H. Gao, Mechanical metamaterials: Smaller and stronger, Nat Mater 15(4) (2016) 373-4.
[12] J. Bauer, A. Schroer, R. Schwaiger, O. Kraft, The Impact of Size and Loading Direction on the Strength of Architected Lattice Materials Advanced Engineering Materials 18(9) (2016) 1537- 1543.
[13] C.A. Volkert, E.T. Lilleodden, Size effects in the deformation of sub-micron Au columns, Philos Mag 86(33-35) (2006) 5567-5579.
[14] J.R. Greer, W.C. Oliver, W.D. Nix, Size dependence of mechanical properties of gold at the micron scale in the absence of strain gradients, Acta Mater 53(6) (2005) 1821-1830.
[15] J.R. Greer, J.T.M. De Hosson, Plasticity in small-sized metallic systems: Intrinsic versus extrinsic size effect, Prog Mater Sci 56(6) (2011) 654-724.
[16] J. Erlebacher, M.J. Aziz, A. Karma, N. Dimitrov, K. Sieradzki, Evolution of nanoporosity in dealloying, Nature 410(6827) (2001) 450-453.
102
[17] J. WeissmĂĽller, R.C. Newman, H.-J. Jin, A.M. Hodge, J.W. Kysar, Nanoporous Metals by Alloy Corrosion: Formation and Mechanical Properties, MRS Bull. 34(8) (2011) 577-586.
[18] J. Biener, A. Wittstock, L.A. Zepeda-Ruiz, M.M. Biener, V. Zielasek, D. Kramer, R.N. Viswanath, J. Weissmuller, M. Baumer, A.V. Hamza, Surface-chemistry-driven actuation in nanoporous gold, Nat. Mater. 8(1) (2009) 47-51.
[19] T. Fujita, P. Guan, K. McKenna, X. Lang, A. Hirata, L. Zhang, T. Tokunaga, S. Arai, Y. Yamamoto, N. Tanaka, Y. Ishikawa, N. Asao, Y. Yamamoto, J. Erlebacher, M. Chen, Atomic origins of the high catalytic activity of nanoporous gold, Nat. Mater. 11(9) (2012) 775-80.
[20] A. Wittstock, V. Zielasek, J. Biener, C.M. Friend, M. Baumer, Nanoporous Gold Catalysts for Selective Gas-Phase Oxidative Coupling of Methanol at Low Temperature, Science 327(5963) (2010) 319-322.
[21] J. Biener, A.M. Hodge, J.R. Hayes, C.A. Volkert, L.A. Zepeda-Ruiz, A.V. Hamza, F.F. Abraham, Size effects on the mechanical behavior of nanoporous Au, Nano Lett 6(10) (2006) 2379-2382.
[22] E. Detsi, E. De Jong, A. Zinchenko, Z. Vuković, I. Vuković, S. Punzhin, K. Loos, G. ten Brinke, H.A. De Raedt, P.R. Onck, J.T.M. De Hosson, On the specific surface area of nanoporous materials, Acta Mater. 59(20) (2011) 7488-7497.
[23] E. Detsi, M. van de Schootbrugge, S. Punzhin, P.R. Onck, J.T.M. De Hosson, On tuning the morphology of nanoporous gold, Scripta Mater. 64(4) (2011) 319-322.
[24] Y. Ding, Y.J. Kim, J. Erlebacher, Nanoporous Gold Leaf: ?Ancient Technology?/Advanced Material, Adv. Mater. 16(21) (2004) 1897-1900.
[25] A.J. Forty, P. Durkin, A Micro-Morphological Study of the Dissolution of Silver-Gold Alloys in Nitric-Acid, Philos Mag A 42(3) (1980) 295-318.
[26] A.M. Hodge, J. Biener, J.R. Hayes, P.M. Bythrow, C.A. Volkert, A.V. Hamza, Scaling equation for yield strength of nanoporous open-cell foams, Acta Mater. 55(4) (2007) 1343-1349.
[27] F. Kertis, J. Snyder, L. Govada, S. Khurshid, N. Chayen, J. Erlebacher, Structure/Processing Relationships in the Fabrication of Nanoporous Gold, JOM 62(6) (2010) 50-56.
[28] C.A. Volkert, E.T. Lilleodden, D. Kramer, J. WeissmĂĽller, Approaching the theoretical strength in nanoporous Au, Appl. Phys. Lett. 89(6) (2006).
[29] H. Jeon, N.R. Kang, E.J. Gwak, J.I. Jang, H.N. Han, J.Y. Hwang, S. Lee, J.Y. Kim, Self-similarity in the structure of coarsened nanoporous gold, Scripta Mater 137 (2017) 46-49.
[30] H. Jeon, S. Lee, J.Y. Kim, Tension-compression asymmetry in plasticity of nanoporous gold, Acta Mater 199 (2020) 340-351.
[31] H. Jeon, J.H. Woo, E. Song, J.Y. Kim, Manuscript submitted for publication.
[32] A.J. Forty, Corrosion Micro-Morphology of Noble-Metal Alloys and Depletion Gilding, Nature 282(5739) (1979) 597-598.
103
[33] R. Morrish, A.J. Muscat, Dealloying Multiphase AgCu Thin Films in Supercritical CO2, The Journal of Physical Chemistry C 117(23) (2013) 12071-12077.
[34] E. Rouya, M.L. Reed, R.G. Kelly, H. Bart-Smith, M.R. Begley, G. Zangari, Synthesis of Nanoporous Gold Structures via Dealloying of Electroplated Au-Ni Alloy Films, ECS Transactions 6(41) (2007).
[35] J. Snyder, P. Asanithi, A.B. Dalton, J. Erlebacher, Stabilized Nanoporous Metals by Dealloying Ternary Alloy Precursors, Advanced Materials 20(24) (2008) 4883-4886.
[36] R.C. Newman, S.G. Corcoran, J. Erlebacher, M.J. Aziz, K. Sieradzki, Alloy corrosion, Mrs Bull 24(7) (1999) 24-28.
[37] H.W. Pickering, Characteristic Features of Alloy Polarization Curves, Corros Sci 23(10) (1983) 1107-&.
[38] D.M. Artymowicz, J. Erlebacher, R.C. Newman, Relationship between the parting limit for de- alloying and a particular geometric high-density site percolation threshold, Philos Mag 89(21) (2009) 1663-1693.
[39] S. Xiao, F. Xiao, Y. Hu, S. Yuan, S. Wang, L. Qian, Y. Liu, Hierarchical nanoporous gold-platinum with heterogeneous interfaces for methanol electrooxidation, Sci Rep 4 (2014) 4370.
[40] Y. Ding, M.W. Chen, Nanoporous Metals for Catalytic and Optical Applications, Mrs Bull 34(8) (2009) 569-576.
[41] C. Zhu, Z. Qi, V.A. Beck, M. Luneau, J. Lattimer, W. Chen, M.A. Worsley, J.C. Ye, E.B. Duoss, C.M. Spadaccini, C.M. Friend, J. Biener, Toward digitally controlled catalyst architectures:
Hierarchical nanoporous gold via 3D printing, Sci Adv 4(8) (2018).
[42] R. Li, K. Sieradzki, Ductile-brittle transition in random porous Au, Phys Rev Lett 68(8) (1992) 1168-1171.
[43] J. Biener, A.M. Hodge, A.V. Hamza, Microscopic failure behavior of nanoporous gold, Applied Physics Letters 87(12) (2005).
[44] T.J. Balk, C. Eberl, Y. Sun, K.J. Hemker, D.S. Gianola, Tensile and Compressive Microspecimen Testing of Bulk Nanoporous Gold, JOM 61(12) (2009) 26-31.
[45] E.J. Gwak, J.Y. Kim, Weakened Flexural Strength of Nanocrystalline Nanoporous Gold by Grain Refinement, Nano Lett 16(4) (2016) 2497-502.
[46] R.P. Eliott, F.A. Shunk, The Ag-Au (Silver-Gold) system, Bulletin of Alloy Phase Diagrams (1980).
[47] I. McCue, E. Benn, B. Gaskey, J. Erlebacher, Dealloying and Dealloyed Materials, Annual Review of Materials Research 46(1) (2016) 263-286.
[48] L.H. Qian, M.W. Chen, Ultrafine nanoporous gold by low-temperature dealloying and kinetics of nanopore formation, Applied Physics Letters 91(8) (2007).
104
[49] E.-J. Gwak, N.-R. Kang, U.B. Baek, H.M. Lee, S.H. Nahm, J.-Y. Kim, Microstructure evolution in nanoporous gold thin films made from sputter-deposited precursors, Scripta Mater 69(10) (2013) 720-723.
[50] S. Parida, D. Kramer, C.A. Volkert, H. Rosner, J. Erlebacher, J. Weissmuller, Volume change during the formation of nanoporous gold by dealloying, Phys Rev Lett 97(3) (2006) 035504.
[51] E. Seker, M. Reed, M. Begley, A thermal treatment approach to reduce microscale void formation in blanket nanoporous gold films, Scripta Mater 60(6) (2009) 435-438.
[52] Y. Sun, T.J. Balk, A multi-step dealloying method to produce nanoporous gold with no volume change and minimal cracking, Scripta Mater 58(9) (2008) 727-730.
[53] O. Okman, D. Lee, J.W. Kysar, Fabrication of crack-free nanoporous gold blanket thin films by potentiostatic dealloying, Scripta Mater 63(10) (2010) 1005-1008.
[54] O. Okman, J.W. Kysar, Fabrication of crack-free blanket nanoporous gold thin films by galvanostatic dealloying, Journal of Alloys and Compounds 509(22) (2011) 6374-6381.
[55] O. Okman, J.W. Kysar, Chapter 5. Microfabrication of Nanoporous Gold, Nanoporous Gold2012, pp. 69-96.
[56] J. Erlebacher, R.C. Newman, K. Sieradzki, Chapter 2. Fundamental Physics and Chemistry of Nanoporosity Evolution During Dealloying, Nanoporous Gold2012, pp. 11-29.
[57] N.J. Briot, T.J. Balk, Developing scaling relations for the yield strength of nanoporous gold, Philos.
Mag. 95(27) (2015) 2955-2973.
[58] L.-Z. Liu, X.-L. Ye, H.-J. Jin, Interpreting anomalous low-strength and low-stiffness of nanoporous gold: Quantification of network connectivity, Acta Mater 118 (2016) 77-87.
[59] L.-Z. Liu, H.-J. Jin, Scaling equation for the elastic modulus of nanoporous gold with “fixed”
network connectivity, Applied Physics Letters 110(21) (2017).
[60] N. Beets, D. Farkas, S. Corcoran, Deformation mechanisms and scaling relations in the mechanical response of nano-porous Au, Acta Mater. 165 (2019) 626-637.
[61] C. Soyarslan, S. Bargmann, M. Pradas, J. WeissmĂĽller, 3D stochastic bicontinuous microstructures:
Generation, topology and elasticity, Acta Mater 149 (2018) 326-340.
[62] X.-Y. Sun, G.-K. Xu, X. Li, X.-Q. Feng, H. Gao, Mechanical properties and scaling laws of nanoporous gold, Journal of Applied Physics 113(2) (2013).
[63] R. Liu, A. Antoniou, A relationship between the geometrical structure of a nanoporous metal foam and its modulus, Acta Mater 61(7) (2013) 2390-2402.
[64] N. Huber, R.N. Viswanath, N. Mameka, J. Markmann, J. WeiĂźmĂĽller, Scaling laws of nanoporous metals under uniaxial compression, Acta Mater. 67 (2014) 252-265.
[65] A.M. Hodge, T. John Balk, Chapter 4. Mechanical Properties of Nanoporous Gold, Nanoporous Gold2012, pp. 51-68.
105
[66] N. Badwe, X. Chen, K. Sieradzki, Mechanical properties of nanoporous gold in tension, Acta Mater 129 (2017) 251-258.
[67] M.D. Uchic, D.M. Dimiduk, J.N. Florando, W.D. Nix, Sample dimensions influence strength and crystal plasticity, Science 305(5686) (2004) 986-989.
[68] J.-Y. Kim, J.R. Greer, Tensile and compressive behavior of gold and molybdenum single crystals at the nano-scale, Acta Mater 57(17) (2009) 5245-5253.
[69] H.-J. Jin, L. Kurmanaeva, J. Schmauch, H. Rösner, Y. Ivanisenko, J. Weissmüller, Deforming nanoporous metal: Role of lattice coherency, Acta Mater 57(9) (2009) 2665-2672.
[70] N. Mameka, K. Wang, J. Markmann, E.T. Lilleodden, J. Weissmüller, Nanoporous Gold—Testing Macro-scale Samples to Probe Small-scale Mechanical Behavior, Materials Research Letters 4(1) (2015) 27-36.
[71] S.S.R. Saane, K.R. Mangipudi, K.U. Loos, J.T.M. De Hosson, P.R. Onck, Multiscale modeling of charge-induced deformation of nanoporous gold structures, Journal of the Mechanics and Physics of Solids 66 (2014) 1-15.
[72] H. Rösner, S. Parida, D. Kramer, C.A. Volkert, J. Weissmüller, Reconstructing a Nanoporous Metal in Three Dimensions: An Electron Tomography Study of Dealloyed Gold Leaf, Advanced Engineering Materials 9(7) (2007) 535-541.
[73] T. Fujita, L.-H. Qian, K. Inoke, J. Erlebacher, M.-W. Chen, Three-dimensional morphology of nanoporous gold, Applied Physics Letters 92(25) (2008).
[74] Y.-c.K. Chen, Y.S. Chu, J. Yi, I. McNulty, Q. Shen, P.W. Voorhees, D.C. Dunand, Morphological and topological analysis of coarsened nanoporous gold by x-ray nanotomography, Applied Physics Letters 96(4) (2010).
[75] Y.-c.K. Chen-Wiegart, S. Wang, Y.S. Chu, W. Liu, I. McNulty, P.W. Voorhees, D.C. Dunand, Structural evolution of nanoporous gold during thermal coarsening, Acta Mater 60(12) (2012) 4972-4981.
[76] K.R. Mangipudi, V. Radisch, L. Holzer, C.A. Volkert, A FIB-nanotomography method for accurate 3D reconstruction of open nanoporous structures, Ultramicroscopy 163 (2016) 38-47.
[77] K. Hu, M. Ziehmer, K. Wang, E.T. Lilleodden, Nanoporous gold: 3D structural analyses of representative volumes and their implications on scaling relations of mechanical behaviour, Philos Mag 96(32-34) (2016) 3322-3335.
[78] M. Ziehmer, K. Hu, K. Wang, E.T. Lilleodden, A principle curvatures analysis of the isothermal evolution of nanoporous gold: Quantifying the characteristic length-scales, Acta Mater 120 (2016) 24-31.
[79] J. Erlebacher, Mechanism of coarsening and bubble formation in high-genus nanoporous metals, Phys Rev Lett 106(22) (2011) 225504.
106
[80] K. Kolluri, M.J. Demkowicz, Coarsening by network restructuring in model nanoporous gold, Acta Mater 59(20) (2011) 7645-7653.
[81] O. Zinchenko, H.A. De Raedt, E. Detsi, P.R. Onck, J.T.M. De Hosson, Nanoporous gold formation by dealloying: A Metropolis Monte Carlo study, Computer Physics Communications 184(6) (2013) 1562-1569.
[82] T. Hilderband, P. Ruegesgger, A new method for the model-independent assessment of thickness in three-dimensional images, Journal of Microscopy 185 (1997) 67-75.
[83] M. Doube, M.M. Klosowski, I. Arganda-Carreras, F.P. Cordelieres, R.P. Dougherty, J.S. Jackson, B. Schmid, J.R. Hutchinson, S.J. Shefelbine, BoneJ: Free and extensible bone image analysis in ImageJ, Bone 47(6) (2010) 1076-9.
[84] A. Odgaard, H.J.G. Gundersen, Quantification of connectivity in cancellous bone, with special emphasis on 3-D reconstructions, Bone 14 (1993) 173-182.
[85] K. Michielsen, H. De Raedt, J.T.M. De Hosson, Aspects of mathematical morphology, Adv Imag Elect Phys 125 (2002) 119-194.
[86] M. Drechsler, J.J. Metois, J.C. Heyraud, Surface self-diffusion studied by microscopic measurements of crystallite profile evolutions, Surface Science 108(3) (1981) 549-560.
[87] H. Gobel, P.v. Blanckenhagen, A study of surface diffusion on gold with an atomic force microscope, Surface Science (1995) 885-890.
[88] I. Beszeda, I.A. SzabĂł, E.G. Gontier-Moya, Morphological evolution of thin gold films studied by Auger electron spectroscopy in beading conditions, Applied Physics A 78(7) (2004) 1079-1084.
[89] E.A. Brandes, G.B. Brook, C.J. Smithells, Smithells metals reference book. 7th ed., Butterworth- Heinemann, Oxford, Boston, 1998.
[90] J. Biener, A.M. Hodge, A.V. Hamza, L.M. Hsiung, J.H. Satcher, Nanoporous Au: A high yield strength material, Journal of Applied Physics 97(2) (2005).
[91] A.M. Hodge, J.R. Hayes, J.A. Caro, J. Biener, A.V. Hamza, Characterization and Mechanical Behavior of Nanoporous Gold, Advanced Engineering Materials 8(9) (2006) 853-857.
[92] M. Hakamada, M. Mabuchi, Mechanical strength of nanoporous gold fabricated by dealloying, Scripta Mater 56(11) (2007) 1003-1006.
[93] R. Dou, B. Derby, Deformation mechanisms in gold nanowires and nanoporous gold, Philos Mag 91(7-9) (2011) 1070-1083.
[94] Y.-C. Kim, E.-J. Gwak, S.-m. Ahn, J.-i. Jang, H.N. Han, J.-Y. Kim, Indentation size effect in nanoporous gold, Acta Mater 138 (2017) 52-60.
[95] D. Lee, X. Wei, M. Zhao, X. Chen, S.C. Jun, J. Hone, J.W. Kysar, Plastic deformation in nanoscale gold single crystals and open-celled nanoporous gold, Modelling and Simulation in Materials Science and Engineering 15(1) (2007) S181-S192.
107
[96] S. Sun, X. Chen, N. Badwe, K. Sieradzki, Potential-dependent dynamic fracture of nanoporous gold, Nat Mater 14(9) (2015) 894-8.
[97] R. Xia, C. Xu, W. Wu, X. Li, X.-Q. Feng, Y. Ding, Microtensile tests of mechanical properties of nanoporous Au thin films, Journal of Materials Science 44(17) (2009) 4728-4733.
[98] N.J. Briot, T. Kennerknecht, C. Eberl, T.J. Balk, Mechanical properties of bulk single crystalline nanoporous gold investigated by millimetre-scale tension and compression testing, Philos Mag 94(8) (2014) 847-866.
[99] E.-J. Gwak, H. Jeon, E. Song, N.-R. Kang, J.-Y. Kim, Twinned nanoporous gold with enhanced tensile strength, Acta Mater 155 (2018) 253-261.
[100] M. BĂĽrckert, N.J. Briot, T.J. Balk, Uniaxial compression testing of bulk nanoporous gold, Philos Mag 97(15) (2017) 1157-1178.
[101] A. Gouldstone, H.J. Koh, K.Y. Zeng, A.E. Giannakopoulos, S. Suresh, Discrete and continuous deformation during nanoindentation of thin films, Acta Mater. 48(9) (2000) 2277-2295.
[102] S.-H. Kim, Y.-C. Kim, S. Lee, J.-Y. Kim, Evaluation of tensile stress-strain curve of electroplated copper film by characterizing indentation size effect with a single nanoindentation, Met. Mater.
Int. 23(1) (2017) 76-81.
[103] J. Chen, L. Lu, K. Lu, Hardness and strain rate sensitivity of nanocrystalline Cu, Scripta Mater.
54(11) (2006) 1913-1918.
[104] L. Lu, R. Schwaiger, Z.W. Shan, M. Dao, K. Lu, S. Suresh, Nano-sized twins induce high rate sensitivity of flow stress in pure copper, Acta Mater. 53(7) (2005) 2169-2179.
[105] Y.P. Cao, J. Lu, A new method to extract the plastic properties of metal materials from an instrumented spherical indentation loading curve, Acta Mater. 52(13) (2004) 4023-4032.
[106] H. Kashani, M. Chen, Flaw-free nanoporous Ni for tensile properties, Acta Mater 166 (2019) 402- 412.
[107] N.A. Senior, R.C. Newman, Synthesis of tough nanoporous metals by controlled electrolytic dealloying, Nanotechnol. 17(9) (2006) 2311-2316.
[108] B.-N.D. NgĂ´, A. Stukowski, N. Mameka, J. Markmann, K. Albe, J. WeissmĂĽller, Anomalous compliance and early yielding of nanoporous gold, Acta Mater. 93 (2015) 144-155.
[109] L.J. Gibson, M.F. Ashby, The Mechanics of 3-Dimensional Cellular Materials, P Roy Soc Lond a Mat 382(1782) (1982) 43-&.
[110] D. Farkas, A. Caro, E. Bringa, D. Crowson, Mechanical response of nanoporous gold, Acta Mater.
61(9) (2013) 3249-3256.
[111] H.J. Jin, J. Weissmuller, A Material with Electrically Tunable Strength and Flow Stress, Science 332(6034) (2011) 1179-1182.
[112] N. Mameka, J. Markmann, J. Weissmuller, On the impact of capillarity for strength at the
108 nanoscale, Nat. Commun. 8(1) (2017) 1976.
[113] L. Luhrs, B. Zandersons, N. Huber, J. Weissmuller, Plastic Poisson's Ratio of Nanoporous Metals:
A Macroscopic Signature of Tension-Compression Asymmetry at the Nanoscale, Nano Lett 17(10) (2017) 6258-6266.
[114] C.J. Ruestes, D. Farkas, A. Caro, E.M. Bringa, Hardening under compression in Au foams, Acta Mater. 108 (2016) 1-7.
[115] Y. Li, B.-N. Dinh NgĂ´, J. Markmann, J. WeissmĂĽller, Topology evolution during coarsening of nanoscale metal network structures, Phys. Rev. Mater. 3(7) (2019).
[116] I.N. Sneddon, The relation between load and penetration in the axisymmetric boussinesq problem for a punch of arbitrary profile, Int. J. Eng. Sci. 3(1) (1965) 47-57.
[117] T.H. Courtney, Mechanical behavior of materials, Waveland Press, Long Grove, Ill., 2005.
[118] D. Holec, F.D. Fischer, D. Vollath, Structure and surface energy of Au-55 nanoparticles: An ab initio lestudy, Comp Mater Sci 134 (2017) 137-144.
[119] Y.-N. Wen, J.-M. Zhang, Surface energy calculation of the fcc metals by using the MAEAM, Solid State Commun. 144(3-4) (2007) 163-167.
[120] W. Haiss, Surface stress of clean and adsorbate-covered solids, Rep Prog Phys 64(5) (2001) 591- 648.
[121] F.H. Buttner, H. Udin, J. Wulff, Surface Tension of Solid Gold, JOM 3(12) (1951) 1209-1211.
[122] J. Jiao, N. Huber, Deformation mechanisms in nanoporous metals: Effect of ligament shape and disorder, Comp Mater Sci 127 (2017) 194-203.
[123] D. Kiener, C. Motz, T. Schöberl, M. Jenko, G. Dehm, Determination of Mechanical Properties of Copper at the Micron Scale, Adv. Eng. Mater. 8(11) (2006) 1119-1125.
[124] C. Motz, T. Schöberl, R. Pippan, Mechanical properties of micro-sized copper bending beams machined by the focused ion beam technique, Acta Mater. 53(15) (2005) 4269-4279.
[125] B. Roos, B. Kapelle, G. Richter, C.A. Volkert, Surface dislocation nucleation controlled deformation of Au nanowires, Appl. Phys. Lett. 105(20) (2014).
[126] J.H. Hollomon, Tensile Deformation, T Am I Min Met Eng 162 (1945) 268-290.
[127] N.-R. Kang, E.-J. Gwak, H. Jeon, E. Song, J.-Y. Kim, Microstructural effect on time-dependent plasticity of nanoporous gold, International Journal of Plasticity 109 (2018) 108-120.
[128] X.-L. Ye, H.-J. Jin, Electrochemical control of creep in nanoporous gold, Applied Physics Letters 103(20) (2013).
[129] B.N. Lucas, W.C. Oliver, Indentation power-law creep of high-purity indium, Metall Mater Trans A 30(3) (1999) 601-610.
[130] I.-C. Choi, B.-G. Yoo, Y.-J. Kim, J.-i. Jang, Indentation creep revisited, Journal of Materials Research 27(1) (2011) 3-11.
109
[131] D.-H. Lee, M.-Y. Seok, Y. Zhao, I.-C. Choi, J. He, Z. Lu, J.-Y. Suh, U. Ramamurty, M. Kawasaki, T.G. Langdon, J.-i. Jang, Spherical nanoindentation creep behavior of nanocrystalline and coarse- grained CoCrFeMnNi high-entropy alloys, Acta Mater 109 (2016) 314-322.
[132] N.R. Kang, Y.C. Kim, H. Jeon, S.K. Kim, J.I. Jang, H.N. Han, J.Y. Kim, Wall-thickness-dependent strength of nanotubular ZnO, Sci Rep 7(1) (2017) 4327.
[133] I.-C. Choi, B.-G. Yoo, Y.-J. Kim, M.-Y. Seok, Y. Wang, J.-i. Jang, Estimating the stress exponent of nanocrystalline nickel: Sharp vs. spherical indentation, Scripta Mater 65(4) (2011) 300-303.
[134] D.C. Lin, D.I. Shreiber, E.K. Dimitriadis, F. Horkay, Spherical indentation of soft matter beyond the Hertzian regime: numerical and experimental validation of hyperelastic models, Biomech Model Mechanobiol 8(5) (2009) 345-58.
[135] G.E. Dieter, Mechanical Metallurgy 3rd edition, McGraw-Hill, New York, 1986.
[136] P. Yavari, T.G. Langdon, An Examination of the Breakdown in Creep by Viscous Glide in Solid- Solution Alloys at High Stress Levels, Acta Metall Mater 30(12) (1982) 2181-2196.
[137] T. Zhu, J. Li, A. Samanta, H.G. Kim, S. Suresh, Interfacial plasticity governs strain rate sensitivity and ductility in nanostructured metals, P Natl Acad Sci USA 104(9) (2007) 3031-3036.
[138] I.-C. Choi, Y.-J. Kim, M.-Y. Seok, B.-G. Yoo, J.-Y. Kim, Y. Wang, J.-i. Jang, Nanoscale room temperature creep of nanocrystalline nickel pillars at low stresses, International Journal of Plasticity 41 (2013) 53-64.
[139] H.J. Frost, M.F. Ashby, Deformation mechanism maps: the plasticity and creep of metals and ceramics., Pergamon Press, Oxford, 1982.
[140] H. Conrad, Plastic deformation kinetics in nanocrystalline FCC metals based on the pile-up of dislocations, Nanotechnology 18(32) (2007).
[141] A.T. Jennings, C. Gross, F. Greer, Z.H. Aitken, S.W. Lee, C.R. Weinberger, J.R. Greer, Higher compressive strengths and the Bauschinger effect in conformally passivated copper nanopillars, Acta Mater 60(8) (2012) 3444-3455.
[142] S.-W. Lee, A.T. Jennings, J.R. Greer, Emergence of enhanced strengths and Bauschinger effect in conformally passivated copper nanopillars as revealed by dislocation dynamics, Acta Mater 61(6) (2013) 1872-1885.
[143] Y.-n. Cui, Z.-l. Liu, Z. Zhuang, Theoretical and numerical investigations on confined plasticity in micropillars, Journal of the Mechanics and Physics of Solids 76 (2015) 127-143.
[144] K.S. Ng, A.H.W. Ngan, Effects of trapping dislocations within small crystals on their deformation behavior, Acta Mater 57(16) (2009) 4902-4910.
[145] R. Gu, A.H.W. Ngan, Effects of pre-straining and coating on plastic deformation of aluminum micropillars, Acta Mater 60(17) (2012) 6102-6111.
[146] G.K. Williamson, R.E. Smallman, Dislocation Densities in Some Annealed and Cold-Worked