Lithium nitride is a solid electrolyte with a high Li+-conductivity at ambient temperatures and attractive properties for an application in a primary battery. The proposed presence of a polarizable ion N3- in the unique hexagonal structure could be proved by measurements of Czochralski-grown single crystals applying the methods of modern solid state science, particular X-ray diffraction. A model for the conduction mechanism of the Li+-ions is presented. Using crystal-chemical considerations a material for application at higher temperatures could be found among the lithium-nitride-halides.