Tetragonal I4$_{1}$/amd Crystal Structure of Li$_{3}$BN$_{2}$ from Dehydrogenated Li-B-N-H

We have determined the crystal structure of Li$_{3}$BN$_{2}$ formed by dehydrogenation of LiB$_{0.33}$N$_{0.67}$H$_{2.67}$ from powder x-ray diffraction (XRD) data using the Rietveld method. XRD measurements indicate unambiguously that this Li$_{3}$BN$_{2}$ polymorph is distinct from any of the previously reported Li$_{3}$BN$_{2}$ phases. We find a body-centered tetragonal I4$_{1}$/amd structure (space group No. 141 in the \textit{International Tables for X-ray Crystallography}) with a = 6.60 {\AA} and c = 10.35 {\AA}. The structure features tightly coordinated, nearly linear N--B--N units with 1.3 - 1.4 {\AA} B--N bond lengths suggesting covalently bonded (BN$_{2})^{-3}$ anions. In situ temperature-dependent XRD showed that the body-centered tetragonal Li$_{3}$BN$_{2}$ phase was present both at elevated temperature during dehydrogenation and after cooling to room temperature. We also describe the results of first principles theoretical modeling of the body-centered tetragonal Li$_{3}$BN$_{2}$ polymorph as well as the tetragonal P4$_{2}$2$_{1}$2 and monoclinic P2$_{1}$/c Li$_{3}$BN$_{2}$ structures previously reported. We obtained excellent agreement between the theoretically calculated I4$_{1}$/amd Li$_{3}$BN$_{2}$ lattice constants and atomic positions and those obtained experimentally from XRD. The approximate enthalpy of formation of the I4$_{1}$/amd Li$_{3}$BN$_{2}$ phase is $\Delta {\rm H}$ = --495 kJ/mole-formula unit.