Monte Carlo simulations of icosahedral quasicrystal growth and melting

Three-dimensional Monte Carlo simulations for atomic growth and melting of icosahedral quasicrystals an presented. It is supposed that the atoms can be locally ordered both icosahedrally and dodecahedrally, and the preferred ordering arises during the growth according to statistical and energetical criteria. All the waiting positions (where an atom could be in principle added) are generated on the cluster surface at every stage of the growth. The binding energies of all atoms and all waiting positions are computed with an oscillating Friedel potential. Then an object, chosen at random from the joined list of surface atoms and waiting positions, is treated according to the Metropolis criterion. The suggested growth process is completely local. It is found that the speed and sign of the process and the resulting structures depend strongly on the growth parameters. Most frequently, the main structural motif of grown clusters is the dodecahedral local ordering (DLO) whereas the icosahedral local ordering (ILO) is usually rare. However, the latter becomes dominant for rather exotic interatomic potentials or for high growth rates. The phenomenon of critical seed size is observed: for those parameters, for which large clusters grow, small enough seeds stop to grow and may even melt, The grown quasicrystals are faceted and their sizes in perpendicular space are rather close to those predicted theoretically and observed experimentally. [S0163-1829(99)11501-7].