The formation of dislocations is central to our understanding of yield, work hardening, fracture, and fatigue1 of crystalline materials. While dislocations have been studied extensively in conventional materials, recent results have shown that colloidal crystals offer a potential model system for visualizing their structure and dynamics directly in real space2. Although thermal fluctuations are thought to play a critical role in the nucleation of these defects, it is difficult to observe them directly. Nano-indentation, during which a small tip deforms a crystalline film, is a common tool for introducing dislocations into a small volume that is initially defect-free3,4,5,6,7,8,9,10. Here, we show that an analogue of nano-indentation performed on a colloidal crystal provides direct images of defect formation in real time and on the single particle level, allowing us to probe the effects of thermal fluctuations. We implement a new method to determine the strain tensor of a distorted crystal lattice and we measure the critical dislocation loop size and the rate of dislocation nucleation directly. Using continuum models, we elucidate the relation between thermal fluctuations and the applied strain that governs defect nucleation. Moreover, we estimate that although bond energies between particles are about fifty times larger in atomic systems, the difference in attempt frequencies makes the effects of thermal fluctuations remarkably similar, so that our results are also relevant for atomic crystals.
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We thank R. Christianson and D. Blair for their help with the image analysis, M.L. Falk for discussions about the strain algorithm, and D. Bonner for help with programming the strain algorithm. This work was supported by a Lynen Fellowship from the Alexander von Humboldt Foundation (P.S.), and by NSF and Harvard MRSEC grants.
This movie shows laser diffraction microscopy images of the nucleation and growth of dislocations during indentation of a colloidal crystalline film. The time lapse covers a period of 10 h, during which we slowly move the indenting tip into the crystalline sediment at a rate of 3.4µm/h and subsequently pull it back at a rate of 20µm/min. After the initial emergence of a strain field depicted as a two-armed contrast profile and the nucleation of a first dislocation loop depicted as a dark circular spot, a complex dislocation structure evolves. This structure relaxes and partially heals when the needle moves back up. These images also show local intensity fluctuations in both the strained and unstrained crystal lattice that correspond to thermally excited fluctuations in the particle configurations.
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The coupling interaction of a screw dislocation with a bimaterial interface and a nearby circular inclusion
Archive of Applied Mechanics (2015)