Heats of solution and lattice-expansion and trapping energies of hydrogen in transition metals

The heat of hydrogen solution in a metal at infinite dilution {Δ}H_∞ is shown to depend on (1) the distance R between a hydrogen atom and its metallic nearest neighbors, (2) the characteristic band-structure energy {Δ}E=EF-Eₛ, where EF is the Fermi energy and Eₛ basically the center of the lowest conduction band of the host metal, and (3) the width Wd of the d band of the host metal. The semiempirical relation {Δ}H_∞={α}{Δ}E Wd1/2 ? [with {α}=18.6 (kJ/mol H)(A⁴ eV^-3/2) and {β}=-90 kJ/mol H if {Δ}E, Wd, and R are given in units of eV and A{}, respectively] reproduces the experimental values of {Δ}H_∞ remarkably well. It also reproduces the volume expansion accompanying hydrogen absorption and predicts the correct interstitial site occupancy of hydrogen in a transition metal. Furthermore, it makes it possible to estimate the binding energy of hydrogen to a vacancy.