Quantum mechanical theory diffusion in solids. An application to H in silicon and Li in LiFePO4

• Development of a fully quantum mechanical theory of diffusion
• Observation of a zero-point energy correction to the activation energy (application to H diffusion in Si)
• Constant diffusion coefficient corresponding to tunneling in low temperature limit (H in Si)
• Application to Li diffusion in LiFePO4: Importance of cross channel diffusion intermediated by Fe anti-site vacancies

We develop a fully quantum mechanical formalism to calculate ionic transition states in solids and determine diffusion constants for H in Si and Li and Fe in LiFePO4. The formalism is quantitative and does not involve empirical parameters.From the quantum mechanical treatment we recover some quantities known from classical theory, e.g. the temperature dependent diffusion constant reflects the activation energy at high T. At low temperature however we discover a constant diffusion rate linked to the ionic tunneling. Tunneling and hopping rates are considered on an equal footing and result from the same formalism. We apply the quantum mechanical formalism to the diffusion of H in Si and discover the influence of the zero point energy of the diffusive species in the potential well. For LiFePO4 we shed some light on the importance of the cross channel diffusion probably intermediated by Fe anti-site vacancies in the understanding of the experimentally observed diffusion constant. This work opens up the possibility to study quantitatively diffusion e.g. in potential electrode materials for Li-ion batteries.