First-principles study of the formation and migration of native defects in ${\text{NaAlH}}_4$

We present a first-principles study of native defects in ${\text{NaAlH}}_4$. Our analysis indicates that the structure and energetics of these defects can be interpreted in terms of elementary building blocks, which include $V_{{\text{AlH}}_4}^{+}$, $V_{\text{Na}}^{-}$, $V_{\text{H}}^{+}$, ${\text{H}}_i^{-}$, and ${\left({\text{H}}_2\right)}_i$. We also calculate migration barriers for several key defects, in order to compare enthalpies of diffusion to experimentally measured activation energies of desorption. From this, we estimate activation energies for the diffusion of defects and defect pairs. We suggest that $V_{{\text{AlH}}_4}^{+}$ and ${\text{H}}_i^{-}$, or $V_{\text{Na}}^{-}$ and $V_{\text{H}}^{+}$, may be responsible for diffusion necessary for desorption. We discuss the possible role of $V_{\text{H}}^{+}{\text{-H}}_i^{-}$ complex formation. The values we find are in the range of activation energies reported for catalyzed desorption.

Figure 1

(Color online) The body-centered tetragonal structure of ${\text{NaAlH}}_4$. Sodium is represented by large (gray) spheres, aluminum (at center of tetrahedra) is small (dark blue), and hydrogen is small (red). A [001] plane is drawn in gray in order to help illustrate depth.

Figure 2

Formation energy of hydrogen-related native defects in ${\text{NaAlH}}_4$ plotted as a function of Fermi level with respect to the valence-band maximum. Atomic chemical potentials were chosen to reflect equilibrium with ${\text{Na}}_3{\text{AlH}}_6$, ${\text{NaAlH}}_4$, and Al.

Figure 3

(Color online) The structures of (a) ${\text{H}}_i^{-}$, (b) $V_{\text{H}}^{+}$, (c) $V_{\text{H}}^{-}$, (d) ${\left({\text{H}}_2\right)}_i$, and (e) ${\text{H}}_i^{+}$. In the case of ${\text{H}}_i^{-}$ and $V_{\text{H}}^{-}$, an isosurface of the highest occupied orbital is shown, in order to illustrate the defect character of this orbital. The electron density at the isosurfaces is $0.06\text{electrons}/{\text{Å}}^3$. All of the structural diagrams are of sodium and aluminum atoms in a [010] plane (and coordinated hydrogens), except for the case of ${\left({\text{H}}_2\right)}_i$ in panel (e), where a [001] plane is shown.

Figure 4

Formation energy of aluminum-related native defects in ${\text{NaAlH}}_4$ plotted as a function of Fermi level with respect to the valence-band maximum. Atomic chemical potentials were chosen to reflect equilibrium with ${\text{Na}}_3{\text{AlH}}_6$, ${\text{NaAlH}}_4$, and Al.

Figure 5

(Color online) The structures of (a) $V_{{\text{AlH}}_4}^{+}$, (b) $V_{\text{Al}}^{+}$, (c) $V_{\text{Al}}^{3-}$, (d) $V_{\text{Al}}^{-}$, and (e) $V_{{\text{AlH}}_3}$. The structural diagrams in panels (a), (b), and (e) are of sodium and aluminum atoms in a [010] plane (and coordinated hydrogens). For the cases of and $V_{\text{Al}}^{3-}$ (c) and $V_{\text{Al}}^{-}$ (d), we show the atoms from two [010] planes in order to illustrate the differences upon reduction of the aluminum vacancy.

Figure 6

(Color online) Energy versus reaction coordinate along the migration path for $V_{{\text{AlH}}_4}^{+}$ (equivalently, ${\text{AlH}}_4^{-}$) as modeled with the NEB method. The local lattice structures of the initial, saddle-point, and final configurations are shown as (I), (II), and (III), respectively.

Figure 7

Formation energy of sodium-related native defects in ${\text{NaAlH}}_4$ plotted as a function of Fermi level with respect to the valence-band maximum. Atomic chemical potentials were chosen to reflect equilibrium with ${\text{Na}}_3{\text{AlH}}_6$, ${\text{NaAlH}}_4$, and Al.

Figure 8

(Color online) The structures of (a) $V_{\text{Na}}^{-}$ and (b) $V_{\text{NaH}}$. The structural diagrams are of sodium and aluminum atoms in several [010] planes (and coordinated hydrogens).