Elastic interaction of hydrogen in palladium studied by molecular-dynamics simulation

A simulation model for the palladium-hydrogen system is studied by Andersen’s scheme of molecular dynamics in the isothermal-isobaric ensemble. Widom’s particle-insertion method is used to determine the chemical potential of the hydrogen lattice gas. It is shown that Andersen’s Lagrangian corresponds to a lattice with a free surface (although periodic boundary conditions are used), and in agreement with this the α-α’ (‘‘gas-liquid’’) phase transition of metal-hydrogen systems is reproduced by the simulation model. A value of 3.0 A${\mathrm{̊}}^3$ is found for the partial volume ${\mathit{V}}_{\mathrm{H}}$ of hydrogen in palladium, in almost exact agreement with experiment. Further, the thermodynamic Maxwell relation (∂μ/∂p)=${\mathit{V}}_{\mathrm{H}}$ is confirmed by the simulations (i.e., classical mechanics). Finally, the effective elastic interaction of the hydrogen lattice gas is determined, and compared with the Wagner and Horner theory, which expresses this interaction in terms of phonon modes in the first Brillouin zone.