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First principles modeling techniques are used to examine the stabilities, structures, and Li ion migration properties of (thio)phosphate electrolyte materials focusing on the ``superionic" electrolyte Li7P3S11. Our simulations find a stable structure for Li7P3S11 that is in approximate agreement with X-ray and neutron diffraction experiments. The calculated formation energy predicts the structure to be unstable with respect to decomposition into Li3PS4 and Li4P2S6 plus excess S which has been observed experimentally under certain preparation conditions. The minimum activation energy for Li ion migration is estimated to EA=0.15 eV for a vacancy mechanism, a result which approximates the value of EA=0.12 eV determined from temperature-dependent conductivity measurements. Within the accuracy of the calculations, some vacancy-interstitial pair formation energies are found to be Ef ≈ 0. These low energy vacancy-interstitial pair formation processes contribute to the ``superionic" properties of this material. For comparison, simulations on hypothetical phosphate and phosphonitride materials with similar crystal structures are presented and the results are analyzed in terms of possible connections to LiPON electrolytes.