Theory , Experiment , and Computations Sodium Diffusion in Type II Silicon Clathrates , JASON

Sodium Diffusion in Type II Silicon Clathrates, JASON G. SLINGSBY, NICHOLAS A. RORRER, LAKSHMI KRISHNA, ERIC S. TOBERER, CAROLYN A. KOH, and C. MARK MAUPIN (Chemical and Biological Engineering Department, Colorado School of Mines, 1500 Illinois Street, Golden, CO 80401; Physics Department, Colorado School of Mines, 1500 Illinois Street, Golden, CO 80401; [email protected]). Earth abundant semiconducting type I and II silicon clathrates have attracted significant attention as photovoltaic materials due to their wide band gaps. To realize the semiconducting properties of these materials guest species, present during the synthesis process, must often times be completely evacuated from the host cage structure post synthesis. A common guest species utilized in the synthesis of silicon clathrates is sodium, which templates the clathrate cage formation. Previous experimental investigations have identified that it is possible to evacuate sodium from type II clathrates to an occupancy of less than 1 sodium per unit cell, but any significant sodium removal from type I has not been achieved. This work investigates the energetics, kinetics, and resulting mechanism of sodium diffusion through type II silicon 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 sodium 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 sodium diffusion and eventual evacuation from type II silicon clathrates. The overall mechanism consists of a coupled diffusive process, where the large occupied hexakaidechedral cages empty their sodium guests to adjacent empty large cages. This migration of sodium guests changes the local environment around the occupied small pentagonal dodecahedral cages increasing the ability of sodium guests to leave the small cages. This coupled process continues through the critical cross-over point that is identified as the point where large and small cages are equally occupied by sodium guests. Further sodium removal results in the majority of sodium guests residing in the large cages as opposed to the small cages, in agreement with experiment, and ultimately a sodium free structure