When ‘smaller is stronger’ no longer holds

References

• Parthasarathy TA, Rao SI, Dimiduk DM, et al. Contribution to size effect of yield strength from the stochastics of dislocation source lengths in finite samples. Scr Mater. 2007;56:313–316. doi: 10.1016/j.scriptamat.2006.09.016
   Web of Science ®Google Scholar
• Greer JR, De Hosson JTM. Plasticity in small-sized metallic systems: intrinsic versus extrinsic size effect. Prog Mater Sci. 2011;56:654–724. doi: 10.1016/j.pmatsci.2011.01.005
   Web of Science ®Google Scholar
• Uchic MD, Shade PA, Dimiduk DM. Plasticity of micrometer-scale single crystals in compression. Annu Rev Mater Res. 2009;39:361–386. doi: 10.1146/annurev-matsci-082908-145422
   Web of Science ®Google Scholar
• Pande CS, Cooper KP. Nanomechanics of Hall–Petch relationship in nanocrystalline materials. Prog Mater Sci. 2009;54:689–706. doi: 10.1016/j.pmatsci.2009.03.008
   Web of Science ®Google Scholar
• Greer JR, Nix WD. Nanoscale gold pillars strengthened through dislocation starvation. Phys Rev B. 2006;73:245410. doi: 10.1103/PhysRevB.73.245410
   Web of Science ®Google Scholar
• Shan ZW, Mishra RK, Syed Asif SA, et al. Mechanical annealing and source-limited deformation in submicrometre-diameter Ni crystals. Nat Mater. 2008;7:115–119. doi: 10.1038/nmat2085
   PubMed Web of Science ®Google Scholar
• Wang Z-J, Li Q-J, Shan Z-W, et al. Sample size effects on the large strain bursts in submicron aluminum pillars. Appl Phys Lett. 2012;100:071906. doi: 10.1063/1.3681582
   Web of Science ®Google Scholar
• Richter G, Hillerich K, Gianola DS, et al. Ultrahigh strength single crystalline nanowhiskers grown by physical vapor deposition. Nano Lett. 2009;9:3048–3052. doi: 10.1021/nl9015107
   PubMed Web of Science ®Google Scholar
• Seo J-H, Yoo Y, Park N-Y, et al. Superplastic deformation of defect-free Au nanowires via coherent twin propagation. Nano Lett. 2011;11:3499–3502. doi: 10.1021/nl2022306
   PubMed Web of Science ®Google Scholar
• Chen LY, Richter G, Sullivan JP, et al. Lattice anharmonicity in defect-free Pd nanowhiskers. Phys Rev Lett. 2012;109:125503. doi: 10.1103/PhysRevLett.109.125503
   PubMed Web of Science ®Google Scholar
• Roos B, Kapelle B, Richter G, et al. Surface dislocation nucleation controlled deformation of Au nanowires. Appl Phys Lett. 2014;105:201908. doi: 10.1063/1.4902313
   Web of Science ®Google Scholar
• Zhu T, Li J, Samanta A, et al. Temperature and strain-rate dependence of surface dislocation nucleation. Phys Rev Lett. 2008;100:025502. doi: 10.1103/PhysRevLett.100.025502
   PubMed Web of Science ®Google Scholar
• Weinberger CR, Jennings AT, Kang K, et al. Atomistic simulations and continuum modeling of dislocation nucleation and strength in gold nanowires. J Mech Phys Solids. 2012;60:84–103. doi: 10.1016/j.jmps.2011.09.010
   Web of Science ®Google Scholar
• Li Q-J, Li J, Shan Z-W, et al. Strongly correlated breeding of high-speed dislocations. Acta Mater. 2016;119:229–241. doi: 10.1016/j.actamat.2016.07.053
   Web of Science ®Google Scholar
• Li Q-J, Li J, Shan Z-W, et al. Surface rebound of relativistic dislocations directly and efficiently initiates deformation twinning. Phys Rev Lett. 2016;117:165501. doi: 10.1103/PhysRevLett.117.165501
   PubMed Web of Science ®Google Scholar
• Li Q-J, Xu B, Hara S, et al. Sample-size-dependent surface dislocation nucleation in nanoscale crystals. Acta Mater. 2018;145:19–29. doi: 10.1016/j.actamat.2017.11.048
   Web of Science ®Google Scholar
• Hara S, Izumi S, Sakai S. Reaction pathway analysis for dislocation nucleation from a Ni surface step. J Appl Phys. 2009;106:093507. doi: 10.1063/1.3254178
   Web of Science ®Google Scholar
• Wang Z-J, Li Q-J, Cui Y-N, et al. Cyclic deformation leads to defect healing and strengthening of small-volume metal crystals. Proc Natl Acad Sci. 2015;112:13502–13507. doi: 10.1073/pnas.1518200112
   PubMed Web of Science ®Google Scholar
• Mousseau N, Béland LK, Brommer P, et al. The activation-relaxation technique: ART nouveau and kinetic ART. J At Mol Opt Phys. 2012;2012:925278.
   Google Scholar
• Marian J, Knap J. Breakdown of self-similar hardening behavior in Au nanopillar microplasticity. Int J Multiscale Comput Eng. 2007;5:287–294. doi: 10.1615/IntJMultCompEng.v5.i3-4.100
   Web of Science ®Google Scholar
• Gan Y, Chen JK. Molecular dynamics study of size, temperature and strain rate effects on mechanical properties of gold nanofilms. Appl Phys A. 2009;95:357–362. doi: 10.1007/s00339-008-4970-8
   Web of Science ®Google Scholar
• Ho DT, Kwon S-Y, Park HS, et al. Metal nanoplates: smaller is weaker due to failure by elastic instability. Phys Rev B. 2017;96:184103. doi: 10.1103/PhysRevB.96.184103
   Web of Science ®Google Scholar
• Lührs L, Zandersons B, Huber N, et al. Plastic poisson’s ratio of nanoporous metals: a macroscopic signature of tension–compression asymmetry at the nanoscale. Nano Lett. 2017;17:6258–6266. doi: 10.1021/acs.nanolett.7b02950
   PubMed Web of Science ®Google Scholar
• Tian L, Li J, Sun J, et al. Visualizing size-dependent deformation mechanism transition in Sn. Sci Rep. 2013;3:2113. doi: 10.1038/srep02113
   PubMed Web of Science ®Google Scholar
• Merkle AP, Marks LD. Liquid-like tribology of gold studied by in situ TEM. Wear. 2008;265:1864–1869. doi: 10.1016/j.wear.2008.04.032
   Web of Science ®Google Scholar
• Yue Y, Chen N, Li X, et al. Crystalline liquid and rubber-like behavior in Cu nanowires. Nano Lett. 2013;13:3812–3816. doi: 10.1021/nl401829e
   PubMed Web of Science ®Google Scholar
• Lu Y, Huang JY, Wang C, et al. Cold welding of ultrathin gold nanowires. Nat Nanotechnol. 2010;5:218–224. doi: 10.1038/nnano.2010.4
   PubMed Web of Science ®Google Scholar
• Sun J, He L, Lo Y-C, et al. Liquid-like pseudoelasticity of sub-10-nm crystalline silver particles. Nat Mater. 2014;13:1007–1012. doi: 10.1038/nmat4105
   PubMed Web of Science ®Google Scholar
• Zhong L, Sansoz F, He Y, et al. Slip-activated surface creep with room-temperature super-elongation in metallic nanocrystals. Nat Mater. 2017;16:439–445. doi: 10.1038/nmat4813
   PubMed Web of Science ®Google Scholar
• Castro T, Reifenberger R, Choi E, et al. Size-dependent melting temperature of individual nanometer-sized metallic clusters. Phys Rev B. 1990;42:8548–8556. doi: 10.1103/PhysRevB.42.8548
   PubMed Web of Science ®Google Scholar
• Chen LY, He M, Shin J, et al. Measuring surface dislocation nucleation in defect-scarce nanostructures. Nat Mater. 2015;14:707–713. doi: 10.1038/nmat4288
   PubMed Web of Science ®Google Scholar
• Li J. Diffusive origins. Nat Mater. 2015;14:656–657. doi: 10.1038/nmat4326
   PubMed Web of Science ®Google Scholar
• Joachim C, Gimzewski JK, Aviram A. Electronics using hybrid-molecular and mono-molecular devices. Nature. 2000;408:541–548. doi: 10.1038/35046000
   PubMed Web of Science ®Google Scholar
• Strachan DR, Johnston DE, Guiton BS, et al. Real-time TEM imaging of the formation of crystalline nanoscale gaps. Phys Rev Lett. 2008;100:56805. doi: 10.1103/PhysRevLett.100.056805
   Web of Science ®Google Scholar
• Reed MA, Zhou C, Muller CJ, et al. Conductance of a molecular junction. Science. 1997;278:252–254. doi: 10.1126/science.278.5336.252
   Web of Science ®Google Scholar
• Strachan DR, Smith DE, Fischbein MD, et al. Clean electromigrated nanogaps imaged by transmission electron microscopy. Nano Lett. 2006;6:441–444. doi: 10.1021/nl052302a
   PubMed Web of Science ®Google Scholar
• Han W-Z, Huang L, Ogata S, et al. From “smaller is stronger” to “size-independent strength plateau”: towards measuring the ideal strength of iron. Adv Mater. 2015;27:3385–3390. doi: 10.1002/adma.201500377
   PubMed Web of Science ®Google Scholar
• Zuo L, Ngan AHW, Zheng GP. Size dependence of incipient dislocation plasticity in Ni3Al. Phys Rev Lett. 2005;94:95501. doi: 10.1103/PhysRevLett.94.095501
   PubMed Web of Science ®Google Scholar
• Zuo L, Ngan AHW. Molecular dynamics study on compressive yield strength in Ni3Al micro-pillars. Philos Mag Lett. 2006;86:355–365. doi: 10.1080/09500830600803890
   Web of Science ®Google Scholar
• Bei H, Gao YF, Shim S, et al. Strength differences arising from homogeneous versus heterogeneous dislocation nucleation. Phys Rev B. 2008;77:060103. doi: 10.1103/PhysRevB.77.060103
   Web of Science ®Google Scholar
• Johnson KL. Contact mechanics. Cambridge: Cambridge University Press; 1984.
   Google Scholar
• Valentini P, Gerberich WW, Dumitrică T. Phase-transition plasticity response in uniaxially compressed silicon nanospheres. Phys Rev Lett. 2007;99:175701. doi: 10.1103/PhysRevLett.99.175701
   PubMed Web of Science ®Google Scholar
• Zhu T, Li J, Van Vliet K, et al. Predictive modeling of nanoindentation-induced homogeneous dislocation nucleation in copper. J Mech Phys Solids. 2004;52:691–724. doi: 10.1016/j.jmps.2003.07.006
   Web of Science ®Google Scholar
• Ogata S, Li J, Hirosaki N, et al. Ideal shear strain of metals and ceramics. Phys Rev B. 2004;70:104104. doi: 10.1103/PhysRevB.70.104104
   Web of Science ®Google Scholar
• Lowry MB, Kiener D, LeBlanc MM, et al. Achieving the ideal strength in annealed molybdenum nanopillars. Acta Mater. 2010;58:5160–5167. doi: 10.1016/j.actamat.2010.05.052
   Web of Science ®Google Scholar
• Brenner SS. Tensile strength of whiskers. J Appl Phys. 1956;27:1484–1491. doi: 10.1063/1.1722294
   Web of Science ®Google Scholar
• Brenner SS. Growth and properties of “whiskers”: further research is needed to show why crystal filaments are many times as strong as large crystals. Science. 1958;128:569–575. doi: 10.1126/science.128.3324.569
   PubMed Web of Science ®Google Scholar
• Clatterbuck DM, Chrzan DC, Morris JW. The inherent tensile strength of iron. Philos Mag Lett. 2002;82:141–147. doi: 10.1080/095008302317262642
   Web of Science ®Google Scholar
• Gall K, Diao J, Dunn ML. The strength of gold nanowires. Nano Lett. 2004;4:2431–2436. doi: 10.1021/nl048456s
   Web of Science ®Google Scholar
• Bei H, Shim S, George EP, et al. Compressive strengths of molybdenum alloy micro-pillars prepared using a new technique. Scr Mater. 2007;57:397–400. doi: 10.1016/j.scriptamat.2007.05.010
   Web of Science ®Google Scholar
• Krenn CR, Roundy D, Morris JW, et al. Ideal strengths of bcc metals. Mater Sci Eng A. 2001;319–321:111–114. doi: 10.1016/S0921-5093(01)00998-4
   Web of Science ®Google Scholar
• Dimiduk DM, Uchic MD, Parthasarathy TA. Size-affected single-slip behavior of pure nickel microcrystals. Acta Mater. 2005;53:4065–4077. doi: 10.1016/j.actamat.2005.05.023
   Web of Science ®Google Scholar
• Gu XW, Loynachan CN, Wu Z, et al. Size-dependent deformation of nanocrystalline Pt nanopillars. Nano Lett. 2012;12:6385–6392. doi: 10.1021/nl3036993
   PubMed Web of Science ®Google Scholar
• Tucker GJ, Aitken ZH, Greer JR, et al. The mechanical behavior and deformation of bicrystalline nanowires. Model Simul Mater Sci Eng. 2013;21:015004. doi: 10.1088/0965-0393/21/1/015004
   Web of Science ®Google Scholar
• Ramachandramoorthy R, Gao W, Bernal R, et al. High strain rate tensile testing of silver nanowires: rate-dependent brittle-to-ductile transition. Nano Lett. 2016;16:255–263. doi: 10.1021/acs.nanolett.5b03630
   PubMed Web of Science ®Google Scholar
• Wu ZX, Zhang YW, Jhon MH, et al. Nanostructure and surface effects on yield in Cu nanowires. Acta Mater. 2013;61:1831–1842. doi: 10.1016/j.actamat.2012.11.053
   Web of Science ®Google Scholar
• Wang J, Sansoz F, Huang J, et al. Near-ideal theoretical strength in gold nanowires containing angstrom scale twins. Nat Commun. 2013;4:1742. doi: 10.1038/ncomms2768
   PubMed Web of Science ®Google Scholar
• Filleter T, Ryu S, Kang K, et al. Nucleation-controlled distributed plasticity in penta-twinned silver nanowires. Small. 2012;8:2986–2993. doi: 10.1002/smll.201200522
   PubMed Web of Science ®Google Scholar
• Jang D, Li X, Gao H, et al. Deformation mechanisms in nanotwinned metal nanopillars. Nat Nanotechnol. 2012;7:594–601. doi: 10.1038/nnano.2012.116
   PubMed Web of Science ®Google Scholar
• Qin Q, Yin S, Cheng G, et al. Recoverable plasticity in penta-twinned metallic nanowires governed by dislocation nucleation and retraction. Nat Commun. 2015;6:5983. doi: 10.1038/ncomms6983
   PubMed Web of Science ®Google Scholar
• Narayanan S, Cheng G, Zeng Z, et al. Strain hardening and size effect in five-fold twinned Ag nanowires. Nano Lett. 2015;15:4037–4044. doi: 10.1021/acs.nanolett.5b01015
   PubMed Web of Science ®Google Scholar
• Wang Z-J, Li Q-J, Li Y, et al. Sliding of coherent twin boundaries. Nat Commun. 2017;8:1108. doi: 10.1038/s41467-017-01234-8
   PubMed Web of Science ®Google Scholar
• Deng C, Sansoz F. Near-ideal strength in gold nanowires achieved through microstructural design. ACS Nano. 2009;3:3001–3008. doi: 10.1021/nn900668p
   PubMed Web of Science ®Google Scholar
• Jang D, Greer JR. Size-induced weakening and grain boundary-assisted deformation in 60 nm grained Ni nanopillars. Scr Mater. 2011;64:77–80. doi: 10.1016/j.scriptamat.2010.09.010
   Web of Science ®Google Scholar
• Wang L, Teng J, Liu P, et al. Grain rotation mediated by grain boundary dislocations in nanocrystalline platinum. Nat Commun. 2014;5:4402.
   PubMed Web of Science ®Google Scholar
• Giga A, Kimoto Y, Takigawa Y, et al. Demonstration of an inverse Hall–Petch relationship in electrodeposited nanocrystalline Ni–W alloys through tensile testing. Scr Mater. 2006;55:143–146. doi: 10.1016/j.scriptamat.2006.03.047
   Web of Science ®Google Scholar
• Quek SS, Chooi ZH, Wu Z, et al. The inverse hall–petch relation in nanocrystalline metals: a discrete dislocation dynamics analysis. J Mech Phys Solids. 2016;88:252–266. doi: 10.1016/j.jmps.2015.12.012
   Web of Science ®Google Scholar
• Shen TD, Schwarz RB, Feng S, et al. Effect of solute segregation on the strength of nanocrystalline alloys: inverse Hall–Petch relation. Acta Mater. 2007;55:5007–5013. doi: 10.1016/j.actamat.2007.05.018
   Web of Science ®Google Scholar
• Carlton CE, Ferreira PJ. What is behind the inverse Hall–Petch effect in nanocrystalline materials? Acta Mater. 2007;55:3749–3756. doi: 10.1016/j.actamat.2007.02.021
   Web of Science ®Google Scholar
• Hahn EN, Meyers MA. Grain-size dependent mechanical behavior of nanocrystalline metals. Mater Sci Eng A. 2015;646:101–134. doi: 10.1016/j.msea.2015.07.075
   Web of Science ®Google Scholar
• Argon AS, Yip S. The strongest size. Philos Mag Lett. 2006;86:713–720. doi: 10.1080/09500830600986091
   Web of Science ®Google Scholar
• Schiøtz J, Tolla FDD, Jacobsen KW. Softening of nanocrystalline metals at very small grain sizes. Nature. 1998;391:561–563. doi: 10.1038/35328
   Web of Science ®Google Scholar
• Schiøtz J, Jacobsen KW. A maximum in the strength of nanocrystalline copper. Science. 2003;301:1357–1359. doi: 10.1126/science.1086636
   PubMed Web of Science ®Google Scholar
• Padmanabhan KA, Dinda GP, Hahn H, et al. Inverse Hall–Petch effect and grain boundary sliding controlled flow in nanocrystalline materials. Mater Sci Eng A. 2007;452–453:462–468. doi: 10.1016/j.msea.2006.10.084
   Web of Science ®Google Scholar
• Tang Y, Bringa EM, Meyers MA. Inverse Hall–Petch relationship in nanocrystalline tantalum. Mater Sci Eng A. 2013;580:414–426. doi: 10.1016/j.msea.2013.05.024
   Web of Science ®Google Scholar
• Zhu YT, Langdon TG. Influence of grain size on deformation mechanisms: an extension to nanocrystalline materials. Mater Sci Eng A. 2005;409:234–242. doi: 10.1016/j.msea.2005.05.111
   Web of Science ®Google Scholar