Theoretical study of the vibrational properties of ${\rm NaAlH_4}$ with ${\rm AlH_3}$ vacancies

We investigate from first-principles calculations the vibrational properties in the presence of the ${\rm AlH_3}$ vacancy in both $\alpha$ and $\gamma$ phases of ${\rm NaAlH_4}$. When ${\rm AlH_3}$ is removed from an ${\rm AlH_4^-}$ anion, the remaining H recombines with another neighboring ${\rm AlH_4^-}$ anion and forms an ${\rm AlH_5^{2-}}$ unit with slightly deformed $D_{3h}$ symmetry. For both $\alpha$- and $\gamma$-${\rm NaAlH_4}$, the ${\rm AlH_3}$ vacancy induces several isolated phonon modes that are highly localized on the ${\rm AlH_5^{2-}}$ unit with frequencies within the band gap separating the Al-H stretching modes and Al-H bending modes in pure ${\rm NaAlH_4}$. Similar localized phonon modes also exist in the gap separating the Al-H bending modes and the modes involving the rotation of ${\rm AlH_4^-}$ anions for the $\gamma$ phase. On the other hand, for both $\alpha$ and $\gamma$ phases of ${\rm NaAlH_4}$ with charged ${\rm AlH_4^-}$ vacancies, no isolated phonon modes were found to be localized in the vacancy region with frequencies within the band gap of the pure crystal. These theoretical findings suggest further experimental studies to identify the defects that are involved in the decomposition of ${\rm NaAlH_4}$.