Carbon diffusion in α-iron: Evidence for quantum mechanical tunneling

Recent experimental data on the diffusion coefficient of carbon in α-iron below the liquid nitrogen temperature (LNT) question the classical approach to the observed temperature dependence. As the temperature is lowered below the LNT, the diffusion constant tends toward a nearly temperature-independent value rather than continuing its activated trend. The low-temperature branch is apparently characteristic of a quantum mechanical process dominated by tunneling in the ground state. Concomitantly, we apply an occurrence-probability approach to describing the overall temperature dependence as a single continuous rate. Within the adiabatic approximation, the electronic eigen value, depending parametrically on the nuclear coordinates, is taken to be the potential energy to control the motion of the nuclei. The resulting rate involves all horizontal-tunneling energy-conserving elastic transitions at the quantized energy levels of the migrating atom. A small though not negligible slope in the temperature dependence as the temperature is raised below 100 K is dealt with by complementing for the rate of a parallel one-phonon inelastic-tunneling process in excess of the basic elastic-tunneling rate. Our combined approach agrees well with the experimental data. In particular, the frequency of the coupled vibration is obtained virtually identical to the carbon vibrational frequency from inelastic neutron scattering data. The migrational barrier is also found to be within the limits expected for α-iron.