Simulation of the Melting and Cooling of Palladium Clusters

Abstract: The thermal behaviour of palladium clusters has been investigated using Monte Carlo simulation in various ensembles. Furthermore the energy transfer between palladium clusters and rare gas atoms has been calculated in simulated collisions aiming for a calculation of the cooling of clusters in a rare gas atmosphere. The internal structure of the cluster has been modeled by a Many-Body Alloy potential and the interaction between cluster and rare gas atom has been modeled by the Lennard-Jones potential. At melting, the cluster frequently switches from one phase to the other in the case of Pd₁₃. However, due to a free energy phase barrier, the simulations are quasiergodic and the simulation results are not reliable within the phase coexistence region for Pd₅₄, Pd₅₅, Pd₁₄₇ and Pd₃₀₉. In contrast to bulk, the clusters up to Pd₁₄₇ (and possibly Pd₃₀₉) show a distinct two-state behaviour and cannot be partially molten. The coexistence of the phases is instead over time or over an ensemble of clusters. The geometric properties of the clusters change at melting. For instance, the icosahedral clusters change to an on average non-spherical shape at melting. The simulation results are compared for the canonical and microcanonical ensembles as well as for constant temperature molecular dynamics simulations. The agreement between the three methods is good.

Simulations are also performed to calculate the density of states of separated solid and molten isomers. The Reference System Equilibration method proved to accurately reproduce the density of states of anharmonic systems. However, in order to estimate the melting point of a cluster, density of states calculations must be complemented by a knowledge of the number of statistically equivalent molten isomers.

In the second part of the thesis, collisions between Pd₁₃and rare gas atoms are considered. The collisions are simulated by molecular dynamics simulation. The energy transfer data obtained in the simulations were used to calculate the cooling of the cluster in a rare gas atmosphere. Furthermore, the character of the collisions was studied. At low gas temperatures, multiple encounters and even sticking were observed. By statistical models, like the Partially Ergodic Multiple Encounter Theory, energy transfer efficiency was investigated as a function of cluster and gas temperatures as well as of the kind of gas atom.