Size dependence of strength of gold at the micron scale in the absence of strain gradients

In bulk form, the yield stress and strength of the material remain nearly constant regardless of the sample size because the sample dimensions are large compared to the length scale characterizing the material's microstructure. However, when the geometries of critical dimensions on a device approach the size of material's microstructure, size effects prevail, and bulk properties can no longer be used to predict mechanical behaviour. Pure metals and alloys, exhibit strong size effects at the sub-micron scale: smaller samples consistently yield at higher stresses. In many earlier experiments, size effects in indentation, torsion and bending were understood in terms of strain gradients that create geometrically-necessary dislocations leading to hardening. Even without strain gradients, strengths of thin films on substrates are found to scale inversely with film thickness. While these studies constitute important size effects on plasticity, they arise from constraining effects of surrounding layers. Another set of size effects has been observed for crystals that are initially dislocation-free, as pristine metal whiskers yielded at nearly theoretical strengths. In the earliest stages of nanoindentation, crystal volume being probed can be dislocation-free, requiring large indentation stresses to nucleate new dislocations. Molecular dynamics simulations agree that smaller is stronger. In spite of much progress there is still no unified theory for plastic deformation at the sub-micron scale. Our attention is focused on size effects arising in unconstrained geometries, in the absence of strong strain gradients, and with non-zero initial dislocation densities. Gold nanopillars ranging in diameter between 200 nm and several microns were fabricated using Focused Ion beam (FIB) machining with Ga+ ions and microlithography followed by electroplating. These small pillars were found to plastically deform in uniaxial compression at stresses as high as 800 MPa, a value ∼50 times higher than for bulk gold. We believe these high strengths are controlled by hardening by dislocation starvation, unique to very small crystals. In this mechanism, the mobile dislocations have a higher probability of annihilating at a nearby free surface than being pinned by other dislocations. When the starvation conditions are met, plasticity is accommodated by the nucleation and motion of new dislocations.