N , V -1 Li , and Li +1 i . The total concentration of V -1 Li and Li +1 i , which mediate Li di↵usion, is 5.43 ⇥ 10 15 cm 3 . This agrees well with experimental findings that Li 3 N is a good Li-ion conductor. Under the most Li-poor condition (Figure ), E Fermi,eq is at 1.32 eV. The dominant defect is Li +1 i , with a very low E D,q of 0.47 eV. Li vacancy (V -1 Li ) that forms at one of the two unique Li Wycko↵ sites is the next dominant defect, with E D,q of 0.48 eV. These two defects mediating Li di↵usion have a total concentration of 6.60 ⇥ 10 14 cm 3 , indicating a lower Li-ion conductivity than that under Li-rich conditions. The free carrier (electron) concentration is 1.64⇥10 4 cm 3 , which is substantially lower than that under Li-rich conditions. E D,q changes linearly as the elemental chemical potentials are varied. The moderate Li condition (Figure ) represents a scenario where µ Li is between the most Li-rich (0.0 eV) and most Li-poor (-0.78 eV) conditions. Compared to the Li-rich condition, E Fermi,eq is now inside the band gap and located at 1.71 eV. The total concentration of the two dominant defects, Li +1 i and V - 1 Li , are nearly identical to those under the Li-poor conditions. The net free electron concentration is 5.82 ⇥ 10 10 cm 3 . Expectedly, this concentration is higher than that under the Li-poor condition and lower than that under the Li-rich condition.