Computer Simulations for Hydrogen Loaded Palladium Clusters

Abstract

In this work, a new expression for the chemical potential μ of H in Pd is used, which relies on an extension of Widom's particle insertion method. Being an exact expression, this μ contains a term that agrees with the configurational entropy of the ideal solution model, and a term which describes the energy gain in the system when adding an extra H atom. This latter term is due to direct hydrogen-hydrogen interactions, deformations of the lattice by the absorbed hydrogen atoms, the energy gain from lattice relaxation and the binding energy E of H in Pd. The calculation of μ is carried out in bulk Pd and in a 923 Pd-atoms cuboctahedral cluster within a hybrid monte carlo - molecular dynamics (MC-MD) procedure. Also E is determined as function of the hydrogen concentration x in bulk and in cluster. In order to perform the calculations a set of interaction potentials are applied to describe the Pd-Pd, H-Pd and the H-H interactions. For the Pd-Pd interaction several models were tested, which include a first, second or third shell of neighbours. The H-Pd interaction is a first neighbour model. For the H-H interaction a next neighbour model and next nearest neighbour model are used. The chosen Pd-Pd interaction describes the equilibrium lattice constant of pure Pd. The H-Pd interaction model was constructed to reproduce the elastic properties of the H atoms in the metal and its relationship to the relative volume change under H loading, and also the binding energy E at dilute concentrations. The H-H interaction potential describes the appearance of the two phase region in PdH bulk. Binding energy E calculations are carried out with 1 H atom to test sites at the surface and in the cluster. Energies are found for different surface-like and bulk-like sites, in agreement with experimental results. E calculation in cluster shows no directional dependence, but one that follows the geometry of the system. Also E as function of x, at low x concentrations, is in qualitative good agreement with experimental results. The discrepancy at higher x concentrations is due to the missing electronic band structure effects or due to very strong H-H repulsive interactions that were not taken into account. Also at low x concentrations, the relative volume change reproduces the experimental results. It is found that, with the interaction potential set ppI-HH**-HPdmod, it is possible to describe μ in bulk at 300 K. The presence of a α-α' phase transition was established. In cluster, μ at 300 K, was also calculated. It was possible to identify an α-α' phase transition. Sievert's law limit was estimated in good agreement with the experiment, for both bulk and cluster. In cluster it is shifted to higher x concentrations when compared to bulk in agreement with the experiments. Using the Maxwell construction, the phase solubility limits were determined both in cluster and bulk. Also, in agreement with the prediction from the lattice-Green's function formalism, our results demonstrates that two hydrogen atoms in next nearest (NN) neighbour (100) configuration show a rather strong attractive lattice mediated interaction, while the nearest (N) neighbour pairs (110) have a repulsive lattice mediated coupling. This predicts that in the α-phase regime at moderate temperatures (100) chain-like H distributions shall be preferred in the structure.