Protocol dependence of plasticity in ultrastable amorphous solids

While perfect crystals may exhibit a purely elastic response to shear all the way to yielding, the response of amorphous solids is punctuated by plastic events. The prevalence of this plasticity depends on the number of particles $N$ of the system, with the average strain interval before the first plastic event, $\overline{\mathrm{\Delta }\gamma }$, scaling like $N^{\alpha }$ with $\alpha$ negative: larger samples are more susceptible to plasticity due to more numerous disorder-induced soft spots. In this paper we examine this scaling relation in ultrastable glasses prepared with the swap Monte Carlo algorithm, with regard to the possibility of a protocol-dependent scaling exponent, which would also imply a protocol dependence in the distribution of local yield stresses in the glass. We show that, while a superficial analysis seems to corroborate this hypothesis, this is only a preasymptotic effect and in fact our data can be well explained by a simple model wherein such protocol dependence is absent.

Figure 1

System size dependence of the average $\overline{\mathrm{\Delta }\gamma }$ interval before the first plastic event occurs. For each $T_g$ the expected scaling $N^{\alpha }$ is found, but the $\alpha$ exponent is now dependent on the preparation temperature $T_g$.

Figure 2

The rescaled pdf of $\mathrm{\Delta }\gamma$ for $T_g=0.3$ (a), $T_g=0.2$ (b), and $T_g=0.08$ (c). Data collapse takes place only at “high” (i.e., larger than $T_{\text{MCT}}$) and “low” (i.e., deeply supercooled) temperatures, but not in the intermediate regime.

Figure 3

As $c$ decreases (and therefore the glass is better annealed), the asymptotic scaling $\overline{x_{\min }}\propto {\mathcal{N}}^{-3/5}$ is pushed to larger and larger system sizes, producing an apparent change in the scaling exponent $\alpha$, which is however only a finite-size effect.

Figure 4

System size dependence of the average $\overline{\mathrm{\Delta }\gamma }$ interval before the first plastic event occurs, with added results for $N=40000$. A $T_g$-dependent crossover in the data such as the one predicted by our toy model appears to be present.

Figure 5

First panel: The dynamical structure factor $S(k,t)$ of the model simulated in the main text, for various temperatures $T$ across the onset of glassy slowdown. Second panel: The relaxation times extracted from the decay of the $S(k,t)$, plotted against the respective temperature. The dashed red line is the best power-law fit, Eq. (A1), with the parameters reported in the text.

Figure 6

A cartoon showing the behavior of $P\left(x\right)$ as $c$ is varied. The extremal cases $c=0$ and $c=1$ are plotted in grey and black respectively, with the intermediate cases plotted in color.