The diffusion kinetics of hydrogen in bulk palladium and in Pd nanoclusters containing up to 512 atoms was investigated theoretically at 3% loading by using ring-polymer molecular dynamics simulations. The electronic ground-state energy surfaces were modelled using an explicit many-body potential fitted to reproduce the properties of bulk palladium and palladium hydrides. The diffusion constant, calculated by integration of the velocity autocorrelation function, exhibited Arrhenius behavior. In addition, both the pre-factor and activation energy were found to exhibit approximately linear variations with inverse cluster radius for sizes exceeding 128 Pd atoms. Vibrational delocalization generally enhanced diffusion; this effect being stronger in clusters than in the bulk. An inherent structure analysis from the positions of the centroids was used to characterize the diffusion mechanisms. Quantum effects led not only to a higher coordination of hydrogen atoms both in the bulk (face-centered cubic) palladium and in clusters but also favored further softening of the outer layers.

Diffusion of Hydrides in Palladium Nanoclusters. a Ring-Polymer Molecular Dynamics Study of Quantum Finite Size Effects. Calvo, F., Costa, D.: Journal of Chemical Theory and Computation, 2010, 6[2], 508-16