Dynamic free energy surfaces for sodium diffusion in type II silicon clathrates

Earth abundant semiconducting type II Si clathrates have attracted attention as photovoltaic materials due to their wide band gaps. To realize the semiconducting properties of these materials, guest species that arise during the synthesis process must be completely evacuated from the host cage structure post synthesis. A common guest species utilized in the synthesis of Si clathrates is Na (metal), which templates the clathrate cage formation. Previous experimental investigations have identified that it is possible to evacuate Na from type II clathrates to an occupancy of less than 1 Na per unit cell. This work investigates the energetics, kinetics, and resulting mechanism of Na diffusion through type II Si clathrates by means of biased molecular dynamics and kinetic Monte Carlo simulations. Well-tempered metadynamics has been used to determine the potential of mean force for Na moving between clathrate cages, from which the thermodynamic preferences and transition barrier heights have been obtained. Kinetic Monte Carlo simulations based on the metadynamics results have identified the mechanism of Na diffusion in type II Si clathrates. The overall mechanism consists of a coupled diffusive process linked via electrostatic guest-guest interactions. The large occupied hexakaidechedral cages initially empty their Na guests to adjacent empty large cages, thereby changing the local electrostatic environment around the occupied small pentagonal dodecahedral cages and increasing the probability of Na guests to leave the small cages. This coupled process continues through the cross-over point that is identified as the point where large and small cages are equally occupied by Na guests. Further Na removal results in the majority of guests residing in the large cages as opposed to the small cages, in agreement with experiments, and ultimately a Na free structure.