Crystal Structures and Phase Stability of the Li$_2$S-P$_2$S$_5$ System from First Principles

The Li$_2$S-P$_2$S$_5$ pseudo-binary system has been a valuable source of promising superionic conductors, with $\alpha$-Li$_3$PS$_4$, $\beta$-Li$_3$PS$_4$, HT-Li$_7$PS$_6$, and Li$_7$P$_3$S$_{11}$ having excellent room temperature Li-ion conductivity > 0.1 mS/cm. The metastability of these phases at ambient temperature motivates a study to quantify thermodynamic accessibility. Through calculating the electronic, configurational, and vibrational sources of free energy from first principles, a phase diagram of the crystalline Li$_2$S-P$_2$S$_5$ space is constructed. Well-established phase stability trends from experiments are recovered, such as polymorphic phase transitions in Li$_7$PS$_6$ and Li$_3$PS$_4$, and the metastability of Li$_7$P$_3$S$_{11}$ at high temperature. At ambient temperature, it is predicted that all superionic conductors in this space are indeed metastable, but thermodynamically accessible. Vibrational and configurational sources of entropy are shown to be essential towards describing the stability of superionic conductors. New details of the Li sublattices are revealed, and are found to be crucial towards accurately predicting configurational entropy. All superionic conductors contain significant configurational entropy, which suggests an inherent correlation between superionic conductivity and high configurational entropy.