Emergence of Rigid Polycrystals from Atomistic Systems with Heitmann–Radin Sticky Disk Energy

Abstract We investigate the emergence of rigid polycrystalline structures from atomistic particle systems. The atomic interaction is governed by a suitably normalized pair energy, where ‘sticky disk’ potential models atoms as hard spheres that interact when they are tangential. discrete energy frame invariant and no underlying reference lattice on configurations assumed. By means $$\Gamma $$ Γ -convergence, we characterize asymptotic behavior with finite surface scaling in infinite limit. effective continuum theory described terms piecewise constant field delineating local orientation micro-translation configuration. limiting concentrated grain boundaries, is, boundaries zones microscopic configuration has parameters. corresponding density depends relative two grains, their translation misfit, normal to interface. further provide fine analysis energies at both for vacuum–solid solid–solid phase transitions. latter relies fundamentally structure result showing that, due extremely brittle setup, interpolating boundary layers near cracks energetically not favorable.