A sodium-conductive solid-state electrolyte material includes a compound of the composition Na10MP2S12, wherein M is selected from Ge, Si, and Sn. The material may have a conductivity of at least 1.0×10−5 S/cm at a temperature of about 300K and may have a tetragonal microstructure, e.g., a skewed P1 crystallographic structure. Also provided are an electrochemical cell that includes the sodium-conductive solid-state electrolyte material and a method for producing the sodium-conductive solid electrolyte material via controlled thermal processing parameters.