Magic numbers of Coulomb and Lennard-Jones crystals and quasicrystals

Abstract

With the help of molecular dynamics computer simulations we study the equilibrium configurations at low temperature of large systems of strongly correlated particles either under the influence of their mutual long-range Coulomb forces and a radial harmonic external confining force or of the short-range Lennard-Jones potential. The former is a model for charged particles in ion traps and the latter for clusters. For the Coulomb plus harmonic force, the particles arrange in concentric spherical shells with hexagonal structures on the surfaces. The closed shell particle numbers agree well with those of multilayer icosahedra (mli). A Madelung (excess) energy of −0.8926 is extracted which is larger than the bcc value.

For the Lennard-Jones force we employ various initial configurations like multilayer icosahedra or hexagonal closed packed (hcp) spheres. Cohesive (volume) and surface energies per particle are extracted and compared to the energies of scaled mli quasicrystals and of spherical scaled crystals with N up to 36 000. It is shown that relaxed mli are the dominant structures for N < 5 000 and hcp spheres for larger particle numbers. For N < 22 000, hcp crystals have about the same closed shell numbers as mli quasicrystals but smaller ones for N > 22 000. The same magic numbers obtain with other short range Mie potentials.