Phonon-assisted transport of a reactive atom in the lattice of a solid metal catalyst

The transport of a reactive atom on the surface, or dissolved in the bulk, of a metal catalyst occurs by motion of the atom between occupied and unoccupied sites in the host lattice. The energy required to surmount the potential barrier separating two such sites is obtained by the annihilation of a phonon at the Debye frequency of the lattice. We consider the Hamiltonian perturbation that stimulates this motion to involve either (1) anharmonic coupling of the reactive atom to the lattice, or (2) strain energy associated with the reactive atom entering the lattice as a hard sphere. In either case, the atomic jump rate depends upon the temperature, the mass of the metal atom, the Debye temperature of the metal, and the mass, binding energy, and local mode temperature of the reactive atom in an occupied site. Although the temperature dependence of the jump rate is the same in both cases, there is in the case of the anharmonic model an extra dependence on the binding energy, which does not appear in the case of the strain model. The temperature dependence of the jump rate successfully accounts for the curvature of Arrhenius plots of the diffusion coefficients for hydrogen atoms in various transition metals and for oxygen atoms in silver.