Nanoscale Crystal Plasticity: Rising to the Surface

A crystalline material such as gold undergoing a permanent change in shape when loaded mechanically is the result of crystal plasticity. The scientific inquiry for the ideal strength against plastic deformation in crystals has been a focal point for research for almost 90 years¹. Advances in this field have had many important technological implications for improving strength and failure resistance in structural materials, as well as in metal forming processes.

The primary mechanical properties affected by crystal plasticity are the elastic limit, the tensile ductility, which includes strain-hardening phenomena, and the hardness. Control over the size of microstructural features at different length scales, such as grains and precipitates, has had many successful results in augmenting strength in bulk crystalline solids. Remarkably, seminal experiments by Brenner in the 1950’s have also proved that the strength of micrometer-scale, defect-free crystalline filaments or whiskers deformed in tension could be at least one order of magnitude greater than that of their bulk counterparts via size reduction².

Today, this fundamental aspect is pertinent for miniaturized applications such as micro-electromechanical systems (MEMS), because creating robust crystalline films at sub-micrometer length scale is essential in order to ensure that such devices perform well over time. At the nanoscale, more exciting applications lie in interfacing low-dimensional materials like metallic nanostructures to biomolecules and cells for cancer therapy³. Metallic nanowires can be used to guide electromagnetic radiations or plasmons for sensing applications and on-chip optical data transfer⁴. They can also bind together to create complex solid structures by mechanical manipulation⁵. A precise understanding of metal plasticity at reduced length scale is of considerable importance for such applications.

The significance of size effects on mechanical properties at the nanoscale has long been recognized since the nanotechnology era started [6]. The idea that, for materials properties, the world of the nanoscale is not simply a scale-down version of the macroscale is now well-established. In particular, recent progress has shown that in addition to microstructure, surfaces play a key role in nanoscale crystal plasticity and its size dependence. In the following, I will use gold as an example to illustrate how surfaces dramatically impact on crystal plasticity and strength at the nanoscale. To this end, it must be remembered that pure gold is one of the softest metals with a maximum tensile strength of ~120 MPa.

Size vs. Dislocations

In 2004, Uchic et al.⁷ first revisited Brenner’s classic experiments by plastically deforming micropillars made from focused-ion beam (FIB) milling of metallic single-crystals. This approach has shown that cylindrical gold crystals of 245 nm in diameter exhibited a tensile strength of 360 MPa, that is, three times the strength of bulk gold⁸.

FIB-machined metallic nanostructures are known to possess preexisting line defects, called dislocations, due to the initial crystal microstructure and FIB-induced surface damage. As dislocations are the primary carriers of plasticity in metals, it therefore prevails to characterize the influence of dislocation densities on plastic flow stresses and the underlying dislocation processes in nanoscale crystals under deformation.

For that purpose, past computer simulations of dislocation dynamics have revealed a new size-dependent hardening mechanism mediated by free surfaces in submicrometer metallic pillars referred to as source-truncation hardening⁹. This process corresponds to the breaking of preexisting dislocation loops intersecting the free surface to form shorter single-arm sources, which are kept inactive until there is a sufficient rise in the applied stress. A second surface-mediated mechanism, hardening by dislocation starvation, was proposed when the rate of dislocation escape at free surfaces is found to exceed that for dislocation multiplication, to the extent that plastic deformation becomes source-limited¹⁰.

Size vs. Twin Boundaries

Gold nanowires grown by bottom-up approaches from wet chemical growth or physical deposition are typically less than 100 nm in diameter and defect-free crystals. In theory, this makes them ideal systems for approaching ultrahigh strengths. Because such small volumes cannot easily store dislocations, fracture is quasi-brittle and governed by localized crystal slip initiated from the free surface¹¹. Nevertheless, twinning occurs ubiquitously during nanoscale crystal growth and is found to improve crystal plasticity in gold nanowires.

Figure 1 schematically displays different types of twinned microstructures observed experimentally in gold nanowires from wet chemistry. Large-scale molecular dynamics simulations have revealed in the past that the addition of nanoscale twins to gold nanowires can act to either increase or decrease their resistance to slip in tension, depending on both sample diameter and number of twins per unit length^12,13.

Figure 1. Different types of twinned microstructures observed in gold nanowires grown by wet chemistry. (a) Defect-free circular nanowire. (b) Periodically-twinned circular nanowire with constant twin boundary spacing (TBS). (c) Periodically-twinned nanowire with zigzag surface morphology made of {111} facets and constant TBS.

Also, a sharp transition from quasi-brittle behavior to significant strain-hardening and ultrahigh plastic flow stresses was observed in periodically-twinned gold nanowires for a proper ratio of twin boundary spacing (TBS) to diameter^14,15. For instance, Figure 2 shows the atomic-level simulation snapshot for a periodically-twinned gold nanowire deformed in tension by ductile fracture. In this case, significant strain-hardening effects due to the blockage of crystal slip by preexisting twin boundaries took place. This caused the maximum tensile strength to rise to 3.2 GPa, that is more than 25 times larger than the bulk tensile strength.

Figure 2. Atomic-level computer simulation of plastic deformation and ductile fracture in a periodically-twinned gold nanowire under pure tension.

Size vs. Surface Morphology

Macroscopically, it is largely admitted that surface defects act to decrease the stress required for dislocation nucleation and thus the elastic limit. Recent atomistic simulations, however, have just predicted an opposite trend in gold nanowires. Specifically, it was found that the tensile strength of gold nanowires with complex zigzag morphologies consisting of {111} surface facets, similar to that shown in Figure 1c, can be more than 45 times larger than that of bulk gold, which corresponds to near-ideal stress levels (5.5 GPa)¹⁶.

Furthermore, other simulations have shown a dramatic decrease in strain-rate sensitivity at different temperatures in these periodically-twinned zigzag Au nanowires in comparison to defect-free Au nanowires with circular cross-section¹⁷. This behavior is markedly different from that generally observed in bulk face-centered cubic metals like gold where introduction of nanoscale twins significantly increases yield stress sensitivity to strain-rate. Surface faceting in twinned Au nanowires gives rise to a novel yielding process associated with the nucleation and propagation of full dislocations along {001}<110> slip systems, instead of the common {111}<112> partial slip observed in face-centered cubic metals. In summary, these simulations suggest that special defects such as twins and surface facets can be utilized to approach the ideal strength of gold in nanowires.

Acknowledgment

Support from the U.S. National Science Foundation (grant DMR-0747658) and the computer resources of the Vermont Advanced Computing Center are gratefully acknowledged.

References

1. Frenkel, J., Zur Theorie der Elastizitätsgrenze und der Festigkeit kristallinischer Körper. Zeitschrift für Physik, 1926. 37: p. 572-609.
2. Brenner, S.S., Growth and Properties of "Whiskers". Science, 1958. 128(3324): p. 569-575.
3. Gao, J. and B. Xu, Applications of nanomaterials inside cells. Nano Today, 2009. 4(1): p. 37-51.
4. Lal, S., S. Link, and N.J. Halas, Nano-optics from sensing to waveguiding. Nature Photonics, 2007. 1(11): p. 641-648.
5. Lu, Y., et al., Cold welding of ultrathin gold nanowires. Nature Nanotechnology, 2010. 5(3): p. 218-224.
6. Ratner, M. and D. Ratner, Nanotechnology: A gentle introduction to the next big idea. 2002: Prentice Hall. 208.
7. Uchic, M.D., et al., Sample dimensions influence strength and crystal plasticity. Science, 2004. 305(5686): p. 986-989.
8. Kim, J.Y. and J.R. Greer, Tensile and compressive behavior of gold and molybdenum single crystals at the nano-scale. Acta Materialia, 2009. 57(17): p. 5245-5253.
9. Parthasarathy, T.A., et al., Contribution to size effect of yield strength from the stochastics of dislocation source lengths in finite samples. Scripta Materialia, 2007. 56(4): p. 313-316.
10. Greer, J.R. and W.D. Nix, Nanoscale gold pillars strengthened through dislocation starvation. Physical Review B, 2006. 73(24): p. 245410.
11. Richter, G., et al., Ultrahigh Strength Single Crystalline Nanowhiskers Grown by Physical Vapor Deposition. Nano Letters, 2009. 9(8): p. 3048-3052.
12. Deng, C. and F. Sansoz, Size-dependent yield stress in twinned gold nanowires mediated by site-specific surface dislocation emission. Applied Physics Letters, 2009. 95(9): p. 091914.
13. Deng, C. and F. Sansoz, Repulsive force of twin boundary on curved dislocations and its role on the yielding of twinned nanowires. Scripta Materialia, 2010. 63(1): p. 50-53.
14. Deng, C. and F. Sansoz, Fundamental differences in the plasticity of periodically twinned nanowires in Au, Ag, Al, Cu, Pb and Ni. Acta Materialia, 2009. 57(20): p. 6090-6101.
15. Deng, C. and F. Sansoz, Enabling Ultrahigh Plastic Flow and Work Hardening in Twinned Gold Nanowires. Nano Letters, 2009. 9(4): p. 1517-1522.
16. Deng, C. and F. Sansoz, Near-Ideal Strength in Gold Nanowires Achieved through Microstructural Design. ACS Nano, 2009. 3(10): p. 3001-3008.
17. Deng, C. and F. Sansoz, Effects of twin and surface facet on strain-rate sensitivity of gold nanowires at different temperatures. Physical Review B, 2010. 81(15): p. 155430.