STATICS AND DYNAMICS OF ICOSAHEDRALLY TWINNED AND SINGLE-CRYSTAL FCC CLUSTERS

Molecular-dynamics simulations were performed for isolated clusters of up to N approximately 5000 atoms interacting with Lennard-Jones potentials. Static energies for single-crystal fee clusters, with varying surface structures, were computed and compared with that of icosahedrally twinned structures. The icosahedral form was found to have the lowest static energy for clusters of a few thousand atoms or fewer. The vibrational spectrum was computed for clusters up to N = 943 in order to include zero-point motion in the free energy. Zero-point motion decreases the energy difference between the fcc and icosahedral forms for small clusters. A distinguishing feature of the icosahedral spectrum is a high-frequency local mode involving, primarily, just the motion of the central atom. Its frequency increases with increasing cluster size, corresponding to an increasing pressure transmitted, layer by layer, from the surface to the central atom. For clusters larger than N approximately 1000 the energy per atom is lower if the central site is vacant than if it is occupied. An analysis of the energies of small clusters, between 13 and 55 atoms, suggests that fcc is most likely to nucleate for N approximately 19. Possible implications for the formation of quasicrystals are discussed.