| In this 2-part thesis we study first study incipient plastic behavior in deformation of single crystals. We perform atomistic computer simulations to study the mechanism of homogeneous dislocation nucleation in a 2D hexagonal crystalline film during indentation with a circular nanoindenter. The nucleation process is governed by vanishing of energy associated with a single normal mode which is largely confined to a plane of adjacent atoms. For fixed film thickness, L, the spatial extent, ξ, of the critical mode grows with indenter radius, R. For fixed R/L, ξ grows with systems roughly as ξ ∼ L0.4. We, furthermore, perform a mesoscale analysis to determine the lowest energy normal mode for mesoscale regions of varying radius, rmeso, centered on the core of the critical mode. The energy of the lowest normal mode, λmeso, decays very rapidly with rmeso and λmeso ≈ 0 for rmeso ≳ ξ. The lowest normal mode shows a spatial extent, ξmeso , which has a sublinear power-law increase with r meso for rmeso ≲ ξ and saturates at rmeso ≈ 1.5 ξ. We demonstrate that the ξmeso/ξ versus r meso/ξ curve is universal and is independent of film thickness or indenter radius. Thus we have a scenario where the analysis of small regions, rmeso ≲ ξ, in the material can reveal the presence of incipient instability but gives excellent estimates for the energy and spatial extent of the critical mode only for r meso ≳ 1.5 ξ. In this sense homogeneous dislocation nucleation is a quasi-local phenomenon.;In the second part we consider the issues encountered in extracting the elasticity of colloidal crystal from displacement correlation data as measured via optical microscopy techniques. We compute the effective dispersion and density of states of two-dimensional sub-regions of fully three dimensional f.c.c. crystals. As our model is fully atomistic, it allows realistic treatment of wavevectors up to the Brillouin zone boundary. We study sub-regions of both a [111] and [100] plane. We show that for any given direction of wavevector, both [111] and [100] show an anomalous ω² ∼ q regime at low q where ω² is the energy associated with the given mode and q is its wavenumber. The ω² ∼ q should be expected to give rise to an anomalous density of states, Dω, at low ω: Dω ∼ ω³ rather than the conventional Debye result: Dω ∼ ω². The density of states for the [100] sub-region looks to be consistent with Dω ∼ ω³, while the [111] shows something closer to the conventional Debye result at the smallest frequencies. In addition to our calculations, we use a Monte Carlo method to generate the effective dispersion and density of states for these planar sub-regions and study the effects of finite sampling statistics. We show that finite sampling artifacts act as an effective disorder and bias the Dω in the same way as the finite size artifacts, giving a behavior closer to Dω ∼ ω² than D ω ∼ ω³. These results should have an important impact on the interpretation of recent studies of colloidal solids where the two-point displacement correlations can be obtained directly in real-space via microscopy. |
