Homogeneous Dislocation Nucleation

We perform atomistic computer simulations to study the mechanism of homogeneous dislocation nucleation (HDN) in a 2D hexagonal crystalline film under circular indentation. The nucleation process is governed by vanishing of energy associated with a single normal mode. For fixed film thickness, $L$, the spatial extent, $\xi$, of the critical mode grows with indenter radius, $R$. For fixed $R/L$, $\xi$ scales roughly as $\xi\sim L^{0.4}$. We perform a \emph{mesoscale} analysis to determine the lowest energy normal mode for regions of varying radius, $r_{\rm meso}$, centered on the critical mode's core. The energy of the lowest normal mode $\lambda_{\rm meso} \to 0$ rapidly as $r_{\rm meso}\to \xi$. The lowest mode shows a spatial extent, $\xi_{\rm meso}$, which increases sublinearly for $r_{\rm meso}\leq \xi$ and saturates at $r_{\rm meso} \approx 1.5\; \xi$. We demonstrate that the $\xi_{\rm meso}/ \xi$ versus $r_{\rm meso}/ \xi$ curve is \emph{universal} (independent of $L$ or $R$). Hence small regions, $r_{\rm meso}\leq \xi$, \emph{can} reveal the presence of incipient instability but give excellent estimates for the critical mode's energy and spatial extent \emph{only} for $r_{\rm meso} \geq 1.5\; \xi$. Thus HDN is a \emph{quasi-local} phenomenon.