On the Formation of XLi$_{3}$N$_{2}$ Compounds (X = Sc-Zn)

Ternary lithium nitrides XLi$_{3}$N$_{2}$ are known to form for the 3d transition elements X = Sc, Fe. We explore the formation of such compounds for other 3d elements by means of density functional theory using the crystal structures of ScLi$_{3}$N$_{2}$ and FeLi$_{3}$N$_{2}$ as templates. Enthalpies of formation including electronic and phonon contributions are calculated for the most stable structures. Thermodynamic stability with respect to known binary and ternary compounds is investigated in order to assess prospects for phase formation. In the case of FeLi$_{3}$N$_{2}$ we find an antiferromagnetic state lower in energy than the ferromagnetic state previously identified.