In the current work, we study inorganic solid-state electrolytes for lithium-ion batteries. These materials, unlike the traditional liquid electrolytes, could lead to a breakthrough in battery lifetime and safety, since the use of flammable organic solvents is no longer needed. Our aim is to study the ways in which the ionic conductivity can be tuned. We propose to perform PND studies to obtain a definitive model of the crystal structure, on a series of LiAlX4 (X = Cl, Br, I) samples, in parallel with a complementary, variable-temperature dynamics experiment on MuonSR. This data will be crucial for gaining insight into the structure-conductivity relationships.