Hydrogen diffusion and tunnelling

Hydrogen ions can diffuse classically by hopping over the barrier a (1 — EJ7) in Fig. 6.2 with the attempt frequency 

The prefactor /, has also been associated with the Debye frequency of the lattice modes. The diffusion of H in the fee metals Pd, Ni, Cu and Al, reduced to the elementary hop rate between the neighbouring sites, shows classical behaviour (6.2) above room temperature . Note that many experimental methods, including neutron inelastic and quasielastic scattering, NMR line narrowing and spin-lattice relaxation, internal friction and ultrasonic damping, can give important information about the H motion on various timescales, that complements that obtained from ordinary diffusion measurements. 

There are no generally accepted theories for the basic tunnelling motion of hydrogen in metals, which is surprising after so many years of great efforts. A good theory should be able to explain from a few basic assumptions all the effects in Fig. 6.3 that differ by so many orders of 

---