# Structure and dynamics of spherical crystals characterized for the Thomson problem

@article{Wales2006StructureAD, title={Structure and dynamics of spherical crystals characterized for the Thomson problem}, author={David J. Wales and Sidika Ulker}, journal={Physical Review B}, year={2006}, volume={74}, pages={212101} }

Candidates for global minima of the Thomson problem for N charges on a sphere are located for N 400 and selected sizes up to N=972. These results supersede many of the lowest minima located in previous work, with particularly large improvements for N 400. Our analysis reveals interesting topological defects, which are likely to play an important role in determining the mechanical and electrical properties of systems confined to a spherical geometry. We also find low-energy rearrangements for…

## 110 Citations

Parameter-free shell model of spherical Coulomb crystals.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2008

An accurate shell model of spherical Coulomb crystals is presented. Employing intrashell angular particle positions that correspond to the global energy minima of the pertinent Thomson problems, it…

Correspondences between the Classical Electrostatic Thomson Problem and Atomic Electronic Structure

- Physics
- 2013

Properties of Coulomb crystals: rigorous results.

- PhysicsThe Journal of chemical physics
- 2008

The leading term in the asymptotic expression for the shell capacity that appears in the recently introduced approximate model of Coulomb crystals is obtained, providing in turn explicit large-N asymPTotics for e(N) and the mean crystal radius.

Modified Thomson problem.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2009

The modified Thomson problem, which concerns an assembly of N particles mutually interacting through a Coulombic potential and subject to a Coul Lombic-harmonic confinement, is introduced and the perturbed spherical Coulomb crystal regime emerges.

Two and three electrons on a sphere: A generalized Thomson problem

- PhysicsPhysical Review B
- 2018

Generalizing the classical Thomson problem to the quantum regime provides an ideal model to explore the underlying physics regarding electron correlations. In this work, we systematically investigate…

The Structure of Metastable States in The Thomson Problem

- Mathematics
- 2015

A practical numerical method for the effective solution of the Thomson Problem is proposed. The developed iterative algorithm allows to conduct theoretical researches such as study of the number of…

Topological defect motifs in two-dimensional Coulomb clusters.

- Materials ScienceJournal of physics. Condensed matter : an Institute of Physics journal
- 2011

The minima hopping algorithm based on molecular dynamics is used to efficiently locate the ground- and low-energy metastable states, and their structure is analysed by means of the Delaunay triangulation.

Magic numbers for vibrational frequency of charged particles on a sphere

- PhysicsPhysical Review B
- 2021

Finding minimum energy distribution of N charges on a sphere is known as the Thomson problem. Here, we study the vibrational properties of the N charges in the lowest energy state within the harmonic…

## References

SHOWING 1-10 OF 40 REFERENCES

Global minimum for Thomson's problem of charges on a sphere.

- MathematicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2005

This work explicitly finds that analogues of the tetrahedral and dihedral configurations for N larger than 306 and 542, respectively, are not global minima, thus helping to confirm the theory of Dodgson and Moore that as N grows, dislocation defects can lower the lattice strain of symmetric configurations and concomitantly the energy.

Symmetric patterns of dislocations in Thomson’s problem

- Mathematics
- 1999

Determination of the classical ground state arrangement of $N$ charges on the surface of a sphere (Thomson's problem) is a challenging numerical task. For special values of $N$ we have obtained using…

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.

Defect-free global minima in Thomson's problem of charges on a sphere.

- MathematicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2006

This work shows that for N approximately same or greater than 500-1000, adding dislocation defects to a symmetric icosadeltahedral lattice lowers the energy, and gives a complete or near complete catalogue of defect free global minima.

Possible Global Minimum Lattice Configurations for Thomson`s Problem of Charges on a Sphere

- Mathematics
- 1997

What configuration of N point charges on a conducting sphere minimizes the Coulombic energy? J.J. Thomson posed this question in 1904. For N{le}112, numerical methods have found apparent global…

Grain Boundary Scars and Spherical Crystallography

- Materials Science, PhysicsScience
- 2003

Experimental investigations of the structure of two-dimensional spherical crystals find that crystals develop distinctive high-angle grain boundaries, or scars, not found in planar crystals above a critical system size.

Crystalline Particle Packings on a Sphere with Long Range Power Law Potentials

- Physics
- 2006

The original Thomson problem of “spherical crystallography” seeks the ground state of electron shells interacting via the Coulomb potential; however one can also study crystalline ground states of…

Investigation on the ground states of a model thin-film superconductor on a sphere

- Physics
- 1996

We consider the problem of finding the ground state of a model type-II superconductor on the two-dimensional surface of a sphere, penetrated by N vortices. Numerical work shows the ground states to…

Grain boundary scars on spherical crystals.

- Materials ScienceLangmuir : the ACS journal of surfaces and colloids
- 2005

The introduction of fluorescently labeled particles enables us to determine the location and orientation of grain boundary scars and it is found that the total number of scars and the number of excess dislocations per scar agree with theoretical predictions.