A comparative study on the linear scaling relations for the diffusion of S-vacancies on MoS2 and WS2.

Abstract

This work uses density functional theory (DFT) calculations and kinetic Monte Carlo (kMC) simulations to compare the diffusion of S-vacancies on defective MoS2 and WS2, two structures that are often discussed as catalysts. Similar to what has been discussed for MoS2, the vacancy diffusion barriers on WS2 also follow Brønsted-Evans-Polanyi (BEP) type linear scaling relations. The vacancy diffusion kinetics is discussed at the example of a large vacancy cluster consisting of 37 unoccupied sites in direct vicinity and how its structure changes with time. Using barriers estimated via linear scaling relations as input for the kMC simulations yields results that qualitatively agree with results calculated self-consistently at DFT level. As the diffusion barriers for WS2 are significantly higher than those for MoS2, the vacancy diffusion on WS2 is poorly described by the linear scaling relations derived from MoS2 and vice versa. This work further shows that one needs DFT level barriers of about 40% of all S-vacancy diffusion processes on a material to derive sufficiently reliable linear scaling relations. This means that computational costs for future studies may be reduced by only explicitly computing one fraction of the diffusion barriers while estimating the remaining ones via linear scaling. However, in this case, one would lack information about the partition function of the transition states, which are needed for calculating the rate constants. Thus, we have also proposed a scheme to estimate the contribution of the partition functions based only on the initial state's vibrational modes.