Visualizing dislocation nucleation by indenting colloidal crystals

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Entry by Haifei Zhang, AP 225, Fall 2009

Soft matter keywords

Colloidal Crystal, Nano-indentation, Defect Nucleation

Overview

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 space. Although thermal fluctuations are thought to play a critical role in the nucleation of these defects, it is difficult to observe them directly. Nanoindentation, during which a small tip deforms a crystalline film, is a common tool for introducing dislocations into a small volume that is initially defect-free. The authors show in the paper 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. The authors implement a new method to determine the strain tensor of a distorted crystal lattice and the authors measure the critical dislocation loop size and the rate of dislocation nucleation directly. Using continuum models, the authors elucidate the relation between thermal fluctuations and the applied strain that governs defect nucleation. Moreover, the authors 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 the results are also relevant for atomic crystals.

Experiment

Fig. 1. Laser diffraction microscopy images of defect structure.

Sample preparation

The authors grow a 43-mm-thick face-centred cubic crystal in the [100] direction by slowly sedimenting 1.55-mm-diameter silica particles onto a patterned [100] substrate11. The silica particles are suspended in a mixture of water and dimethylsulphoxide (DMSO), which matches their refractive index. The authors add a small amount of fluorescein to the solvent so that under fluorescence the particles appear as dark spots on a bright background.

Transmitted beam imaging

The authors use the transmitted beam for imaging the defect structure. LDM exploits the difference in scattering between the perfect and the distorted crystal lattices near the dislocation core, and produces a real-space image in which dislocations appear as dark lines on a bright background. The authors lower the needle at a rate of 3.4 um/h and record LDM images. Surprisingly, even before the needle touches the crystal, thermal effects produce local intensity fluctuations which last several seconds.

Four images of the indented crystal are shown in Fig. 1. About 190 min after starting lowering the needle, it is observed that two dark regions beneath the needle tip (arrows in Fig. 1b), which is associated with the strained lattice. Remarkably, these regions exhibit intensity fluctuations that last several minutes. This suggests that, in the strained lattice, thermal fluctuations become more spatially correlated, and persist over longer timescales than in the unstrained lattice. After 230 min, it is observed that a dark circular spot, about 8 mm in radius, centred 15 mm below the needle (Fig. 1c). This spot grows in size and finally detaches from the needle (Fig. 1d). These images show the nucleation of a dislocation loop and its eventual detachment from the needle. After the first event, it is observed that nucleation and propagation of many more loops, which form a complex dislocation network after 600 min (Fig. 1e). Because of the complexity of this network, its three-dimensional evolution needs to be explored on the particle scale.

Confocal imaging

Fig. 2. Defect formation on the particle scale.
Fig. 3. Strain distribution in the indented crystalline film.

The authors use confocal microscopy to image individual particles in a 60 mm by 60 mm by 30 mm section of the colloidal crystal (Fig. 2a). This technique allows us to image the dislocations and to determine the strain field caused by the indentation. To determine the full structure of the defects, three dimensional reconstructions of the unstable and stable defects are shown in Figs 2e–g.

In Fig. 3, Particle colour in a–d indicates the value of the local shear strain (see colour scale). The distribution of g in Fig. 3c shows that the negative shear strain regions (blue) inside the dislocation loop almost overlap. Because the contrast in the LDM images arises from these lattice distortions, this observation validates our interpretation that small dislocation loops appear as dark spots in Fig. 1c and d.

Soft matter details

Pushing a sewing needle into a colloidal crystal may seem a crude experiment. On the contrary, combined with laser diffraction microscopy and confocal microscopy, it provides a valuable analogy to nanoindentation and promises a deeper understanding of the mechanical response of crystalline materials.

Probe the mechanical response of surfaces

Nanoindentation is much used to probe the mechanical response of surfaces, thin films and bulk materials. In this method, a diamond tip is pressed against a surface. The resulting force and depth of penetration are monitored at resolutions of micronewtons and nanometres, respectively, and used to infer the mechanical properties of the indented material. Nanoindentation also provides a means to introduce the line defects known as dislocations into the crystal structure of a material,allowing defect nucleation and atomic-scale mechanisms of strength and failure to be studied.

Colloidal crystal as physical analogues for fcc crystals

(a) Schematic representation of dislocation nucleation in an initially defectfree crystal. The location of subsurface defect nucleation is marked by the red star. The indentation load P, and penetration depth h, or equivalently the contact radius a, along with the location of defect nucleation, provide valuable information about mechanical properties of crystalline materials. (b) During a loadcontrolled indentation test, a plot of P against h for an initially perfect crystal shows a sudden displacement burst (known as a ‘pop-in’) during homogeneous defect nucleation.

The authors examine defect nucleation in real time during indentation of colloidal crystals made of silica spheres. These crystals serve as physical analogues for face centered cubic atomic crystals. Despite the complexity in interpreting results, this method could offer insights into some of the details that we need to correlate atomic-scale events with macroscopic material properties. The response of crystals to microindentation looks like a continuous rise in the plot of force, P, against indentation depth, h. During nanoindentation, however, early-stage nucleation of dislocations can result in discrete jumps and abrupt discontinuities in the P–h curve (See the figure on right). These correspond to the moments when, at a fixed load, a sudden displacement jump takes place or when a sudden drop in load occurs at a fixed displacement. During homogeneous nucleation — that is, when nucleation of dislocations occurs through breaking of the atomic bonds of an initially perfect crystal — the critical shear stress needed to activate the first such ‘pop-in’ event in fcc crystals generally correlates with the theoretical shear strength. The P–h response extracted from nanoindentation thus provides insights into the origins of defect nucleation in initially defect-free crystals. These studies led to a search for techniques whereby quantitative nanoindentation could be combined with real-time imaging of dislocations. Consequently, several atomic-scale visualization methods have been pursued.

In the colloidal crystal method, a rectangular block of a defect-free crystal, tens of micrometres along its edges, is obtained by slowly sedimenting silica microparticles onto a patterned substrate. The crystal is then indented with a sewing needle whose tip creates a strain field (the area aff ected by the indentation load in which the crystal structure becomes distorted) below the surface. Laser diffraction microscopy is used to obtain a real-time image of the dislocation loops (the circular regions inside which the crystal is distorted).

These defects appear in the subsurface region as dark lines on a light background because of the difference in the scattering of the laser beam between the perfect and defective spots in the crystal (See Fig. 1.). Confocal microscopy is then used to image the individual colloidal particles and to map out the strain field produced by the indentation. A noteworthy advantage of the colloidal crystal system is that these dislocation loops and microscopic strain fields can be obtained along with the detection of thermal fluctuations of the colloidal particles over reasonable timescales. Such quantitative results offer new information about indentation tests that could be used to develop predictive models of defect nucleation.

Dislocation differences between colloidal crystals and atomic crystals

The forces required to nucleate dislocation loops in the colloidal crystal are orders of magnitude smaller than those needed for creating homogeneous dislocations in atomic crystals. As a result, quantitative estimates of P against h cannot be obtained from the colloidal crystal model. Although thermal fluctuations reported for colloidal crystals are similar to those in atomic crystals, the bond energies between the colloidal particles are vastly different from those in atomic crystals. Despite these limitations, the defect nucleation criteria proposed in this paper provide opportunities to examine dislocation dynamics. For example, extensions of this work could explore how dislocation generation occurs beyond the first ‘pop-in’ associated with the homogeneous nucleation of dislocations and how thermal fluctuations and defect interactions continue to influence multiple ‘pop-in’ events observed in nanoindentation tests on f.c.c. crystals. Such experiments would also provide insights for the development of atomistic computational simulations of nanoindentation and for formulating theories of defect nucleation and dynamics in crystalline solids. The colloidal system could also offer a physical model to examine how dislocation nucleation at grain boundaries and grain-boundary sliding might combine or compete in influencing the strength of nanocrystalline metals. Such a model might also provide mechanistic information as to why the hardness and strength in nanocrystalline metals are so much more sensitive to the rate of loading than in microcrystalline metals.

References

[1] P. Schall, Itai Cohen, David A. Weitz, Frans Spaepen, Visualizing dislocation nucleation by indenting colloidal crystals, Nature, 440, 319 – 323, 2006.