  Recent experimental data on the diffusion coefficient of carbon in alpha-iron
below liquid nitrogen temperature (LNT) question the classical approach to the
observed temperature dependence. As the temperature is lowered below LNT, the
diffusion constant tends to 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 ground
state. Concommitantly, we apply an occurrence probability approach to
describing the overall temperature dependence as a single continuous rate.
Within the adiabatic approximation the electronic eigenvalue 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 of 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 to 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 alpha-iron.
