Revealing a Vacancy Analog of the Crowdion Interstitial in Simple Cubic Crystals

Abstract

Vacancies in simple cubic crystals of hard cubes are known to delocalize over one-dimensional chains of several lattice sites. Here, we use computer simulations to examine the structure and dynamics of vacancies in simple cubic crystals formed by hard cubes, right rhombic prisms (slanted cubes), truncated cubes, and particles interacting via a soft isotropic pair potential. We show that these vacancies form a vacancy analog of the crowdion interstitial, generating a strain field which follows a soliton solution of the sine-Gordon equation, and diffusing via a persistent random walk. Surprisingly, we find that the structure of these "voidions" is not significantly affected by changes in density, vacancy concentration, and even particle interaction. We explain this structure quantitatively using a one-dimensional model that includes the free-energy barrier particles have to overcome to slide between lattice sites and the effective pair interaction along this line. We argue that voidions are a robust phenomenon in systems of repulsive particles forming simple cubic crystals.

Multilayer Diffraction Reveals That Colloidal Superlattices Approach the Structural Perfection of Single Crystals

“…crowdions-voidions pair). 37,38 Second, the sensitivity to the atomic planes periodicity d revealed an anisotropic 3.4% expansion of the CsPbBr3 structure in going from N=13 nanocubes to N=2 in nanoplatelets, indicating that the approximate d = 5.8 Å value often used to estimate the thickness of a single [PbBr6] 2octahedron is imprecise for thin nanostructures. Third, the superlattice periodicity fluctuation (σL) establishes a figure of merit for the superlattice structural perfection and its upper boundary can be quickly estimated from the Eq.…”

Defects in crystals of soft colloidal particles

“…The one exception observed was the SC phase in the Hertzian model whose vacancies were extended in two dimensions, in contrast to the one-dimensional distortions seen in the previous studies of SC crystal of repulsive particles. 5 We did, however, observe a number of other “one-dimensional” defects, including voidions in the hexagonal (H) crystal of Hertzian spheres and crowdions in BCC crystals of both models, with the concentration of the latter reaching up to 0.01 interstitials per lattice site.…”

“…However, relatively recent work on simple cubic (SC) lattices have shown that at least for some colloidal crystals, even simple point defects can extend over large areas and occur in high concentrations. [3][4][5] In particular, it was found that these SC crystals contain large numbers of vacancies, up to 0.06 per lattice site, that cause one-dimensional lattice distortions along the three main crystalline lattice directions. These one-dimensional deformations are aptly named voidions, as a counterpart to the crowdion -a largely one-dimensional lattice distortion caused by an interstitial.…”

Sculpting crystals one Burgers vector at a time: Toward colloidal lattice robot swarms

“…Unlike more common interstitials and vacancies, the extra or missing particle(s) is (are) not localized to a single site, but instead effectively spread out over many sites with fractional occupancy. Ensembles of cubes simulated with thermal agitation have been shown to display vacancy-type crowdions as an emergent behavior (48,49). This suggests that stochastic versions of cube-type lattice robots might display crowdion-type mass transport without careful algorithmic control of neighbor bonding and only mild module compressibility.…”