Journal
PHYSICAL REVIEW LETTERS
Volume 112, Issue 22, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevLett.112.225502
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Funding
- NSF [09-55760]
- Alfred P. Sloan Foundation
- Division Of Materials Research
- Direct For Mathematical & Physical Scien [0955760] Funding Source: National Science Foundation
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We study the structural features and underlying principles of multidislocation ground states of a crystalline spherical cap. In the continuum limit where the ratio of crystal size to lattice spacing W/a diverges, dislocations proliferate and ground states approach a characteristic sequence of structures composed of radial grain boundaries (neutral scars), extending radially from the boundary and terminating in the bulk. Employing a combination of numerical simulations and asymptotic analysis of continuum elasticity theory, we prove 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 dislocation number per scar become independent of lattice spacing. We characterize a secondary transition occurring as scar length grows, where the n-fold scar symmetry is broken and ground states are characterized by polydisperse, forked-scar morphologies.
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