Direct visualization of dislocation dynamics in grain-boundary scars

Abstract

glide constant is extracted directly from the experimental data and is found to be moderately faster than single particle diffusion. We are also able to determine the parameters of the Peierls potential induced by the underlying crystalline lattice.There is considerable need for the rational design of new functional materials. One promising strategy is to build such materials from the bottom up by assembling mesoscale units which can then be linked into larger structures. The characteristics of such materials on the fundamental scale of the building blocks must be understood before they can be intelligently assembled into novel materials. In many cases the units in question possess surfaces with ordered arrays of particles; liposomes, colloidosomes, fullerenes and nanotubes provide prominent examples of such materials [1][2][3] . As in traditional 3D materials, the static structure and dynamic behaviour of defects, such as dislocations, is crucial in determining the response to mechanical, electrical and thermal stimuli 4 . In the ground state of planar 2D systems (flat space) all such defects are tightly bound. The role of thermally excited or mechanically induced defects has been thoroughly studied from both the theoretical and experimental side 5,6 .

Deformation and failure of curved colloidal crystal shells

“…Thin-shell structures are often conceived for encapsulation purposes at various scales (i.e., as delivery vehicles of different kinds of cargo, from drugs to flavors and cosmetics) and arise naturally in biological systems. Examples include crystalline and glassy colloidosomes, capsules of Janus and patchy particles, nematic vesicles, and viral capsids.Theoretical considerations indicate that arranging a colloidal crystal into a curved geometry involves elastic deformation and the presence of geometrically necessary disclinations showed by simulations to be attached to extended grain boundary scars (13-15), as also confirmed in several experiments (5,9,16,17). Thus, grain boundary scars are different from standard grain boundaries in that they have a nonzero disclination charge, which makes them more costly.…”

“…Theoretical considerations indicate that arranging a colloidal crystal into a curved geometry involves elastic deformation and the presence of geometrically necessary disclinations showed by simulations to be attached to extended grain boundary scars (13-15), as also confirmed in several experiments (5,9,16,17). Thus, grain boundary scars are different from standard grain boundaries in that they have a nonzero disclination charge, which makes them more costly.…”

“…Deviatoric strain can be induced by changing the shape of the spherical shell into a prolate spheroid, centered at the origin and with principal semiaxes R × aðtÞ and R × cðtÞ, keeping either its volume or its surface constant. This can be achieved by a force field F = −KðdðtÞ − RÞ r dðtÞ , [5] where d = ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi ðx 2 + y 2 Þ=a 2 + z 2 =c 2 p , cðtÞ grows in time with a deformation velocity v def [i.e., cðtÞ = 1 + t v def ], and aðtÞ varies, so that the surface or the volume of the spheroid are conserved. Here, we discuss in detail the case where we preserve the surface area of the crystal.…”

“…For example, the Gaussian curvature of a sphere demands the presence of geometrically necessary rotational defects (disclinations) such as the 12 pentagons in a soccer ball. Disclinations can be found in thin shell structures at different length scales: from the world of carbon allotropes (1) [as in fullerenes, nanotubes, and graphene (2)] to biological systems [such as in lipid membranes (3), solid domains on vesicles (4,5), or in viral capsids (6)(7)(8)], and in synthetic structures such as colloidosomes, colloidal particle shells lying at the interface between two fluids (9)(10)(11)(12). Thin-shell structures are often conceived for encapsulation purposes at various scales (i.e., as delivery vehicles of different kinds of cargo, from drugs to flavors and cosmetics) and arise naturally in biological systems.…”

Emergent perversions in the buckling of heterogeneous elastic strips

“…The spontaneous formation of the perversion line from individual perversions (as shown in Fig. 5C), which are defects themselves in an otherwise uniform helical structure, is strongly analogous to the self-organization of individual disclinations to form ordered compound defects like scars and pleats over curved crystals (27)(28)(29). Note that the coalescence of perversions is not observed when their separation exceeds about two helical periods in the surveys of typical bistrip systems.…”