Li-ion site disorder driven superionic conductivity in solid electrolytes: a first-principles investigation of β-Li₃PS₄

The attractive safety and long-term stability of all solid-state batteries has added a new impetus to the discovery and development of solid electrolytes for lithium batteries. Recently several superionic lithium conducting solid electrolytes have been discovered. All the superionic lithium containing compounds (β-Li₃PS₄ and Li₁₀GeP₂S₁₂ and oxides, predominantly in the garnet phase) have partially occupied sites. This naturally begs the question of understanding the role of partial site occupancies (or site disorder) in optimizing ionic conductivity in these family of solids. We find that for a given topology of the host lattice, maximizing the number of sites with similar Li-ion adsorption energies, which gives partial site occupancy, is a natural way to increase the configurational entropy of the system and optimize the conductivity. For a given topology and density of Li-ion adsorption sites, the ionic conductivity is maximal when the number of mobile Li-ions are equal to the number of mobile vacancies, also the very condition for achieving maximal configurational entropy. We demonstrate applicability of this principle by elucidating the role of Li-ion site disorder and the local chemical environment in the high ionic conductivity of β-Li₃PS₄. In addition, for β-Li₃PS₄ we find that a significant density of vacancies in the Li-ion sub-lattice (∼25%) leads to sub-lattice melting at (∼600 K) leading to a molten form for the Li-ions in an otherwise solid anionic host. This gives a lithium site occupancy that is similar to what is measured experimentally. We further show that quenching this disorder can improve conductivity at lower temperatures. As a consequence, we discover that (a) one can optimize ionic conductivity in a given topology by choosing a chemistry/composition that maximizes the number of mobile-carriers i.e. maximizing both mobile Li-ions and vacancies, and (b) when the concentration of vacancies becomes significant in the Li-ion sub-lattice, it becomes energetically as well as entropically favorable for it to remain molten well below the bulk decomposition temperature of the solid. This principle may already apply to several known superionic conducting solids.