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We perform atomistic computer simulations to study the mechanism ofhomogeneous dislocation nucleation in two dimensional (2D) hexagonalcrystalline films during indentation with a circular nanoindenter. Thenucleation process is governed by the vanishing of the energy associated with asingle normal mode. This critical mode is largely confined to a single plane ofadjacent atoms. For fixed film thickness, L, the spatial extent, \xi, of thecritical mode grows with indenter radius, R. For fixed R/L, the spatial extent\xi, grows roughly as \xi ~ L^0.4. We, furthermore, perform a mesoscaleanalysis to determine the lowest energy normal mode for mesoscale regions ofvarying radius, r_{meso}, centered on the critical mode's core. The energy,\lambda_{meso}, of the lowest normal mode in the meso-region decays veryrapidly with r_{meso} and \lambda_{meso} ~= 0 for r_{meso} >~ \xi. The lowestnormal mode shows a spatial extent, \xi_{meso}, which has a sublinear power-lawincrease with r_{meso} for r_{meso} <~ \xi, and saturates at r_{meso} \gtrsim1.5\xi. We demonstrate a universal relationship between \xi_{meso}/ \xi versusr_{meso}/ \xi: independent of film thickness or indenter radius. The scenariothat emerges is one where the analysis of small regions, r_{meso} <~ \xi, inthe material \emph{can} reveal the presence of incipient instability even whenthe region being probed is much smaller than the spatial extent of the criticalmode. However, the mesoscale analysis gives good estimates for the energy andspatial extent of the critical mode \emph{only} for r_{meso} >~ 1.5 \xi. Inthis sense homogeneous dislocation nucleation should be understood as aquasi-local phenomenon.

Mesoscale harmonic analysis of homogenous dislocation nucleation