Correlation between the ionic potential and thermal stability of metal borohydrides: First-principles investigations

Metal borohydrides are intensively studied because of their potential applications as versatile hydrogen storage. The relation between the formation enthalpy and the Pauling electronegativity established for these materials [Phys. Rev. B 74, 045126 (2006)] led to the idea of developing mixed-cation compounds that may provide a route for tuning the thermodynamic stability of metal borohydrides. We report a systematic ab initio investigation of the single-metallic and bimetallic borohydrides, and via an examination of the Born effective charges we provide insight into the physical mechanism determining their stabilities. We show that the decreasing stability of metal borohydrides follows the increasing polarizing ability of the cationic bonding component, expressed as the square root of the cation's dynamical charge divided by its radius in coordinated anion polyhedra around the cation. The charge-to-size ratio thus provides a simple yet physically sound measure of the stabilities of metal borohydrides that can be obtained in relatively simple calculations.

Figure 1

The static Bader and Born effective charges on metal cation calculated for $M\left({\mathrm{BH}}_4\right){}_n$ ($n=1$ to 4). For dual-cation borohydrides, only the Born charges are shown (open symbols). LiK(${\mathrm{BH}}_4){}_2$ (circles); NaY(${\mathrm{BH}}_4){}_2$${\mathrm{Cl}}_2$ (diamonds); NaSc(BH4)4 (triangles-right); KSc(BH4)4 (triangles-left); KAl(BH4)4 (squares). Vertical solid lines are used to separate metals of different valency (depicted by horizontal solid lines).

Figure 2

Schematic molecular orbital diagram for ${\mathrm{BH}}_4$, and partial densities of states PDOS for K-, Y-, and Zr-borohydrides. The origin of the energies corresponds to the top of valence states. Insets show the density of electronic states on ${\mathrm{BH}}_4$ related to the energy range of the bottom and top of the valence band. Electron density is plotted for isosurfaces at 0.03 and 0.0125 e/Å${}^3$, respectively. Red symbols are used to indicate the twofold and threefold symmetry axes.

Figure 3

The correlation between Pauling electronegativity ${\chi }_P$ and the square root of the metal ionic potential ${\varphi }^{0.5}$ for the single-cation borohydrides obtained using dynamical charges (a). The heat of formation $\Delta H$ of $M\left({\mathrm{BH}}_4\right){}_n$ as a function of ${\varphi }^{0.5}$ (b). The uncertainty of the calculated ionic potential results from using both the Shannon crystal and ionic radii. The ionic potentials calculated employing the Shannon crystal radii are lower than those obtained using the ionic radii. The linear and quadratic fits are shown by the dotted (red) and solid (black) lines, respectively, once they are distinguishable.

Figure 4

The experimental decomposition temperatures $T_{\mathrm{dec}}$ as a function of ${\varphi }^{0.5}$ obtained using dynamical charges on cations (cf. Fig. 3). The regression line has been fitted using second-degree polynomial.