A universal chemical potential for sulfur vapours

The unusual chemistry of sulfur is illustrated by the tendency for catenation. Sulfur forms a range of open and closed S$_n$ species in the gas phase, which has led to speculation on the composition of sulfur vapours as a function of temperature and pressure for over a century. Unlike elemental gases such as O$_2$ and N$_2$, there is no widely accepted thermodynamic potential for sulfur. Here we combine a first-principles global structure search for the low energy clusters from S$_2$ to S$_8$ with a thermodynamic model for the mixed-allotrope system, including the Gibbs free energy for all gas-phase sulfur on an atomic basis. A strongly pressure-dependent transition from a mixture dominant in S$_2$ to S$_8$ is identified. A universal chemical potential function, $\mu_{\mathrm{S}}(T,P)$, is proposed with wide utility in modelling sulfurisation processes including the formation of metal chalcogenide semiconductors.