First-principles study on structure stabilities of $\alpha$-S and Na-S battery systems

To understand microscopic mechanisms of charge and discharge reactions in Na-S batteries, there has been increasing needs to study fundamental atomic and electronic structures of elemental S as well as that of Na-S phases. The most stable form of S is known to be an orthorhombic $\alpha$-S crystal at ambient temperature and pressure, and $\alpha$-S consists of puckered S$_8$ rings which crystallize in space group $Fddd$. In this study, the crystal structure of $\alpha$-S is examined by using first-principles calculations with and without the van der Waals interaction corrections of Grimme's method, and results clearly show that the van der Waals interactions between the S$_8$ rings have crucial roles on cohesion of $\alpha$-S. We also study structure stabilities of Na$_2$S, NaS, NaS$_2$, and Na$_2$S$_5$ phases with reported crystal structures. Using calculated total energies of the crystal structure models, we estimate discharge voltages assuming discharge reactions from 2Na+$x$S$\rightarrow$Na$_2$S$_x$, and discharge reactions in Na/S battery systems are discussed by comparing with experimental results.