Molecular dynamics simulation for the cluster formation process of Lennard-Jones particles: Magic numbers and characteristic features

Abstract

Cluster formation of Lennard-Jones particles (65 536 atoms in a unit cell with an overall number density equal to 0.0149) was simulated by molecular dynamics. The temperature was set to decrease linearly with time by various thermostats, starting from a gas state temperature and ending at zero temperature. With the Nosé–Hoover thermostat, it was found that the translational temperature of the clusters suddenly decreased almost to zero when the cluster formation drastically increased around a reduced temperature (T*) of 0.5, while the internal temperature decreased linearly. Using the Andersen thermostat, which could simulate the aggregation of particles in an inert gas, both the internal and translational temperatures decreased almost linearly with time. When these thermostats were used, cluster–cluster and cluster–atom collisions did not give any magic number peaks in the size distribution up to 250 atoms/cluster at any temperature. Careful tracing of the cluster growth of 13-atom clusters showed no difference in reactivity between icosahedral and nonicosahedral clusters. To simulate cooling in a supersonic jet, a thermostat which controlled only the translational temperature was introduced. After the clusters were formed by cooling the system with this thermostat, their internal temperature stayed at T*≊0.5, while the translational temperature decreased linearly to zero with time as it was controlled. A long-time evaporation from these high-temperature clusters gave peaks at 13 and 19 (and less significantly at 23 and 26) which are magic number sizes corresponding to single, double, triple, and quadruple icosahedra, respectively. The internal temperatures of 13- and 19-atom clusters were higher than those of other size clusters. Higher evaporation energy was observed for the clusters of 13, 19, 23, and 26 atoms than for other size clusters after the long-time evaporation, but only the 13-atom clusters had the higher evaporation energy after cooling by the Andersen thermostat. These results suggest that magic number clusters were formed by evaporation to be trapped at the magic number sizes, and not by either cluster–atom or cluster–cluster collisions. Analyses of the radial distribution functions and the overall shapes of the generated solidlike clusters consisting of many isomers revealed the following characteristic features: The clusters around 13 and 26 atoms were close to being spherical, and the clusters around 19 atoms were oblate. Clusters around 13 atoms had an icosahedron-based structure. The clusters around 55 atoms formed by the Nosé–Hoover and the Andersen thermostats were close to spherical and had an ordered structure. Clusters from 30 to 50 atoms had a disordered structure or a mixture of the different series of structures.