Reaction energetics and crystal structure of Li 4 BN 3 H 10 from first principles

Using density functional theory we examine the crystal structure and the finite-temperature thermodynamics of formation and dehydrogenation for the quaternary hydride ${\mathrm{Li}}_{4}{\mathrm{BN}}_{3}{\mathrm{H}}_{10}$. Two recent studies based on x-ray and neutron diffraction have reported three bcc crystal structures for this phase. While these structures possess identical space groups and similar lattice constants, internal coordinate differences result in bond length discrepancies as large as $0.2\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$. Geometry optimization calculations on the experimental structures reveal that the apparent discrepancies are an artifact of x-ray interactions with strong bond polarization; the relaxed structures are essentially identical. Regarding reaction energetics, the present calculations predict that the formation reaction $3{\mathrm{LiNH}}_{2}+{\mathrm{LiBH}}_{4}\ensuremath{\rightarrow}{\mathrm{Li}}_{4}{\mathrm{BN}}_{3}{\mathrm{H}}_{10}$ is exothermic with enthalpy $\mathrm{\ensuremath{\Delta}}{H}^{T=300\phantom{\rule{0.3em}{0ex}}\mathrm{K}}=\ensuremath{-}11.8\phantom{\rule{0.3em}{0ex}}\mathrm{kJ}∕(\mathrm{mol}\phantom{\rule{0.2em}{0ex}}\mathrm{f.u.})$, consistent with reports of spontaneous ${\mathrm{Li}}_{4}{\mathrm{BN}}_{3}{\mathrm{H}}_{10}$ formation in the literature. Calorimetry experiments have been reported for the dehydrogenation reaction, but have proven difficult to interpret. To help clarify the thermodynamics we evaluate the free energies of seventeen candidate dehydrogenation pathways over the temperature range $T=0\char21{}1000\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. At temperatures where ${\mathrm{H}}_{2}$ release has been experimentally observed $(T\ensuremath{\approx}520\char21{}630\phantom{\rule{0.3em}{0ex}}\mathrm{K})$, the favored dehydrogenation reaction is ${\mathrm{Li}}_{4}{\mathrm{BN}}_{3}{\mathrm{H}}_{10}\ensuremath{\rightarrow}{\mathrm{Li}}_{3}{\mathrm{BN}}_{2}+{\mathrm{LiNH}}_{2}+4{\mathrm{H}}_{2}$, which is weakly endothermic $[\mathrm{\ensuremath{\Delta}}{H}^{T=550\phantom{\rule{0.3em}{0ex}}\mathrm{K}}=12.8\phantom{\rule{0.3em}{0ex}}\mathrm{kJ}∕(\mathrm{mol}\phantom{\rule{0.2em}{0ex}}{\mathrm{H}}_{2})]$. The small calculated $\mathrm{\ensuremath{\Delta}}H$ is consistent with the unsuccessful attempts at rehydriding reported in the literature, and suggests that the moderately high temperatures needed for H desorption result from slow kinetics.