First principles computational techniques are used to study properties of promising Li ion electrolytes, recently developed at Oak Ridge National Laboratory, based on alloys having the composition Li3+xAs1-xGexS4. The crystal structure of pure Li3AsS4 is found to be characterized by the Pmn2(1) space group. Based on modifications of this structure, reasonable models of the x = 1/4 and x = 1/3 alloys are found to be in good agreement with the experimental X-ray diffraction patterns and to be consistent with the measured trends in Li ion conduction. As a consequence of their Pmn2(1)-based structures, interstitial and interstitialcy mechanisms are found to be important for the Li ion conduction processes in these systems. (C) The Author(s) 2016. Published by ECS. All rights reserved.