The thermodynamics of metal–H solid solutions were studied by using a Fermi–Dirac distribution function to describe the formation of H–vacancy clusters. The H–vacancy interaction energies for clusters (decorated vacancies) containing up to six H-atoms were obtained from effective medium calculations. Various solute metals (Pd, Ni, Fe, Mo, Nb) were considered. The calculations permitted the relative fractions of clusters of a given order to be calculated as a function of the H concentration and temperature. A mathematical model was developed for the simultaneous diffusion of H atoms, vacancies and H–vacancy clusters. Numerical solution of the basic kinetic equations was based upon finite difference methods, and kinetic calculations were performed which were based upon Ni–H solutions as a model system.

The Thermodynamic and Kinetic Behavior of Metal–Vacancy–Hydrogen Systems. N.Z.Carr, R.B.McLellan: Acta Materialia, 2004, 52[11], 3273-93