Fig. 2: Probability distributions of pop-in magnitudes.

a, c, e Probability distributions of the first pop-in and second and subsequent pop-in magnitudes as a function of the stress drop Δσ (Pa) for the (a) (100) and (c) (111) surfaces of BCC Fe, and (e) the (100) surface of FCC Cu, obtained by equal-width binning (5.0 × 10⁸ Pa for the first pop-in and 1.0 × 10⁷ Pa for the second and subsequent pop-ins). The solid line is drawn by using the theory, Eq. (2) (see text). b, d, f Probability distributions of subsequent pop-in magnitudes as a function of the displacement burst Δh (m) for the (b) (100) and (d) (111) surfaces of BCC Fe, and (f) the (100) surface of FCC Cu, obtained by bin-free cumulative distribution. The testing temperature is 300 K and the loading rate is 50 μNs⁻¹. The power-law exponent is estimated by least-square fitting using the data within −9.0 \(\le {\mathrm{log}\,}_{10}\Delta h\) for BCC Fe (100), −8.5 \(\le {\mathrm{log}\,}_{10}\Delta h\) for BCC Fe (111), and −8.8 \(\le {\mathrm{log}\,}_{10}\Delta h\) for FCC Cu (100). See also Supplementary Note 5 for equal-width binning and logarithmic binning plots.