Squeeze a foreign particle into a one-dimensional crystal, and the system will readily rearrange itself to make room for the interloper. But try the same thing in two dimensions, and you will quickly find that the crystal is incapable of accommodating the change. Unless, that is, the planar surface of the two-dimensional crystal is curved — as William Irvine and colleagues have discovered, by imaging colloidal particles assembled on curved oil/glycerol interfaces (Nature Mater. http://doi.org/jh3; 2012).

Wrapping a two-dimensional crystal onto a curved surface comes with its own set of difficulties: the change in geometry induces a frustration that in turn generates topological defects, such as dislocations and disclinations. These defects ease the frustration — effectively disrupting the crystalline order to relieve compressive and shear stresses. In the case of the colloidal crystal assembled by Irvine et al., the system relaxed into a pattern scarred by a set of pleated structures.

Credit: © NPG 2012

Using optical tweezers decoupled from their imaging system, the authors then introduced interstitial particles into their hexagonal colloidal crystal, and compared the ensuing dynamics on flat and curved surfaces. In both cases, the crystal accommodated the interstitials as expected, by forming pairs of particles with either five or seven neighbours, causing a spike in the local density field.

Ordinarily, on flat surfaces, these hexagonal lattice defects would be stable: they can diffuse through the lattice, but they leave dislocations bound. On curved surfaces, however, Irvine et al. found that the dislocations broke into pairs that also moved through the crystal, thereby flattening out the density spike. The actual particle introduced with the tweezers remained in the region to which it was added, but the entire region underwent a rotation as a result of the inclusion.

It turns out that the inherent topological defects brought on by frustration in curved space are key to the fractionalization of these dislocations. Irvine et al. found that the individual defect pairs migrated through the crystal until they were absorbed by defect boundaries already existing in the curved crystal. It may be possible to trigger this fractionalization in planar crystals under certain conditions, but the phenomenon arises quite naturally in curved space. Stress that is not relieved by the initial scarring effectively drives the self-healing process missing in flat crystals — recasting interstitials as order-restoring, rather than order-disrupting, excitations.