The effect of equilibrium vacancy formation on the solubility of H in metals was derived. The treatment was based on a Fermi–Dirac distribution function so that problems which arise at low temperatures in Maxwell–Boltzmann formulations were obviated. Using input data for Ni, the effect of vacancy formation on the validity of Sieverts' law was

calculated and the (pT)-region in which the thermodynamic functions of the solute (H) atoms could be easily extracted from measured solubility was mapped.

Vacancy Concentrations in Metals in Equilibrium with H2-Gas at High Pressures. J.Mao, R.B.McLellan: Journal of Physics and Chemistry of Solids, 2003, 64[3], 527-30