Figure 1

Nanopillar compression tests. (a),(b) SEM images of a 868-nm-diameter Nb pillar at 52” tilt, before and after compression, respectively. (b) Pillar after final catastrophic slip event; slip data at the largest strains are excluded from the analysis. (c) Characteristic stress-strain curves (each contains thousands of points) for four metals compressed at different displacement rates. Negatively sloped lines connect two points at the beginning and end of fast slips, with springlike machine response. The Nb stress-strain curve corresponds to the pillar in (a)–(b). The “criticality slope” line is fitted to the average slope of curve 4, near the critical (failure) stress (see the text). (d) Schematic of the compression test methodology. For details, see Supplemental Material [14].Reuse & Permissions

Figure 2

Stress-integrated cumulative histograms $C(S)$ of slip sizes $S$ (i.e., the fraction of slips with sizes $>S$ plotted versus $S$) for uniaxial compression of various materials, pillar sizes, and nominal displacement rates, integrated over stress from zero to critical (failure) stress. $C(S)$ contains hundreds of points (one point per event). Error bars [from Bayesian 95% confidence bounds (see Supplemental Material [14])] are shown for histograms with the most and the least points for clarity. Fitted probability density function power-law exponents: $2.1\pm 0.1$ (Au), $1.85\pm 0.1$ (Mo), $1.8\pm 0.2$ (Cu), and $1.9\pm 0.2$ (Nb) (subtract 1 for CDF exponents). Fits were obtained from maximum likelihood estimates [32] (see Supplemental Material [14] for error bars and fitting techniques for all figures).Reuse & Permissions

Figure 3

Stress-integrated cumulative histograms $C(S)$ of slip sizes $S$ for uniaxial compression data: comparison of the impact of nominal displacement rate for Mo and Au pillars of diameter 800 nm. The nominal displacement rate impacts the apparent power laws of the cumulative slip-size histograms. The fitted probability density function exponents are $2.1\pm 0.1$, $1.45\pm 0.1$, $1.2\pm 0.2$, $1.85\pm 0.1$, $1.8\pm 0.1$, and $1.6\pm 0.3$, in the order of the legend (subtract 1 for CDF exponents). The lowest rates are used to compare with model predictions.Reuse & Permissions

Figure 4

Stress-integrated cumulative histograms $C(S)$ of the slip size $S$ for various sizes of Cu nanopillars compressed at a displacement rate of $2\mathrm{nm}/\mathrm{s}$. Larger pillars have larger maximum slip events, except for the 125 nm pillars, for which less data were taken. (For power-law distributions, the largest expected slip size increases with the total number of slips.)Reuse & Permissions

Figure 5

Main figure: Stress-binned cumulative histogram $C(S,\tau )$ of slip sizes $S$ as a function of applied stress $\tau$, using events from 7 Mo nanopillars, of approximate diameter 800 nm, compressed at $0.1\mathrm{nm}/\mathrm{s}$ nominal displacement rate. The events from each pillar are normalized according to their respective maximum stress. Inset: Scaling collapse of the same data, $f=({\tau }_c-\tau )/{\tau }_c-c^{\prime }$, where $c^{\prime }=0.14$ is an adjustable parameter that compensates for finite system size (see Supplemental Material [14]); $\kappa =1.5$ and $1/\sigma =2$ (as predicted by MFT), and the gray function is the predicted MFT scaling function, $g(x)\equiv {\int }_x^{\infty }{e}^{-At}{t}^{-\kappa }dt$.Reuse & Permissions