# Ground States of Crystalline Caps: Generalized Jellium on Curved Space.

@article{Li2019GroundSO, title={Ground States of Crystalline Caps: Generalized Jellium on Curved Space.}, author={Siyu Li and Roya Zandi and Alex Travesset and Gregory M. Grason}, journal={Physical review letters}, year={2019}, volume={123 14}, pages={ 145501 } }

We study the ground states of crystals on spherical surfaces. These ground states consist of positive disclination defects in structures spanning from flat and weakly curved caps to closed shells. Comparing two continuum theories and one discrete-lattice simulation, we first investigate the transition between defect-free caps to single-disclination ground states and show it to be continuous and symmetry breaking. Further, we show that ground states adopt icosahedral subgroup symmetries across…

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## References

SHOWING 1-10 OF 65 REFERENCES

### Neutral versus charged defect patterns in curved crystals.

- PhysicsPhysical review. E
- 2016

For the singular limit of zero edge forces, this work finds that scars reduce (by half) the threshold surface coverage for excess disclinations, leading to a transition between stable "charged" and "neutral" patterns that is critically sensitive to the compressive vs tensile nature of boundary forces on the cap.

### Emergent structure of multidislocation ground States in curved crystals.

- Materials SciencePhysical review letters
- 2014

It is proved that an energetic hierarchy gives rise to a structural hierarchy, whereby dislocation number and scar number diverge as a/W→0 while scar length and dislocated number per scar become independent of lattice spacing.

### Curved crystals, defects and disorder

- Materials Science
- 1989

Abstract The structure of media whose short-range order cannot be extended crystallographically in flat space (disordered metallic and covalent systems, Frank-Kasper phases, quasicrystals, blue…

### Defects in crystalline packings of twisted filament bundles. I. Continuum theory of disclinations.

- Materials SciencePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2012

The effective theory of multiple disclination defects in the cross section of bundle with a fixed twist is derived and it is shown that above a critical degree of twist, one or more fivefold disclinations is favored in the elastic energy ground state.

### Two-dimensional matter: order, curvature and defects

- Materials Science
- 2009

Many systems in nature and the synthetic world involve ordered arrangements of units on two-dimensional surfaces. We review here the fundamental role payed by both the topology of the underlying…

### Crystalline order on a sphere and the generalized Thomson problem.

- PhysicsPhysical review letters
- 2002

Predictions from the continuum theory for the ground state energy agree with numerical simulations of long range power law interactions of the form 1/r(gamma) (0<gamma<2) to four significant figures.

### Interacting topological defects on frozen topographies

- Physics
- 2000

We propose and analyze an effective free energy describing the physics of disclination defects in particle arrays constrained to move on an arbitrary two-dimensional surface. At finite temperature…

### Topological defects in twisted bundles of two-dimensionally ordered filaments.

- MathematicsPhysical review letters
- 2010

This work develops the unique, nonlinear elastic properties of twisted filament bundles that derive from generic properties of two-dimensional line-ordered materials and shows that elastic-energy ground states are extremely sensitive to the defect position in the cross section.

### Pleats in crystals on curved surfaces

- Materials ScienceNature
- 2010

This work shows that, for more general curved surfaces, curvature may be relaxed by pleats: uncharged lines of dislocations that vanish on the surface and play the same role as fabric pleats, and experimentally investigates crystal order on surfaces with spatially varying positive and negative curvature.

### Crystallography on curved surfaces

- Materials ScienceProceedings of the National Academy of Sciences
- 2006

The energetics and biased diffusion dynamics of point defects such as vacancies and interstitials are explained in terms of their geometric potential and it is found that glide diffusion of isolated dislocations is suppressed by a binding potential of purely geometrical origin.