Low Speed Crack Propagation via Kink Formation and Advance on the Silicon (110) Cleavage Plane

We present density functional theory based atomistic calculations predicting that slow fracturing of silicon is possible at any chosen crack propagation speed under suitable temperature and load conditions. We also present experiments demonstrating fracture propagation on the Si(110) cleavage plane in the $\sim 100\mathrm{m}/\mathrm{s}$ speed range, consistent with our predictions. These results suggest that many other brittle crystals could be broken arbitrarily slowly in controlled experiments.

Figure 1

Minimum energy paths (MEPs) obtained with the nudged elastic band (NEB) method at the Griffith critical load $2\gamma$ on the Si(110) cleavage plane for (a) crack advance by simultaneous advance of all $N_{\text{sites}}=10$ bonds along the crack front and (b) crack advance by sequential bond rupture. Solid blue circles are minima and black crosses the positions of replicas. Schematic insets show broken (white) and intact (black) bonds along the crack front.

Figure 2

Dependence of kink-pair energy barriers calculated with the modified SW potential on $G/2\gamma$. Vertical dotted lines correspond to the loads $G_{+}^{\mathrm{adv}}$ and $G_{+}^{\mathrm{form}}$ at which the kink advance and formation barriers fall to zero.

Figure 3

Estimated DFT energy barriers for crack growth processes (left vertical axis) overlaid with experimental Si(110) and classical MD crack speed data (right vertical axis). The $G$ axis has been rescaled to align with DFT $G_{+}^{\text{simul}}$, and the dashed purple and blue lines show simple analytical models relevant in the low and high speed limits (see text).