First-principles study on the stability of intermediate compounds of ${\mathrm{LiBH}}_4$

We report the results of the first-principles calculation on the intermediate compounds of ${\mathrm{LiBH}}_4$. The stability of ${\mathrm{LiB}}_3{\mathrm{H}}_8$ and ${\mathrm{Li}}_2{\mathrm{B}}_n{\mathrm{H}}_n(n=5–12)$ has been examined with the ultrasoft pseudopotential method based on the density-functional theory. Theoretical prediction has suggested that monoclinic ${\mathrm{Li}}_2{\mathrm{B}}_{12}{\mathrm{H}}_{12}$ is the most stable among the candidate materials. We propose the following hydriding (dehydriding) process of ${\mathrm{LiBH}}_4$ via this intermediate compound: ${\mathrm{LiBH}}_4\leftrightarrow \frac{1}{12}{\mathrm{Li}}_2{\mathrm{B}}_{12}{\mathrm{H}}_{12}+\frac{5}{6}\mathrm{LiH}+\frac{13}{12}{\mathrm{H}}_2\leftrightarrow \mathrm{LiH}+\mathrm{B}+\frac{3}{2}{\mathrm{H}}_2$. The hydrogen content and enthalpy of the first reaction are estimated to be $10$ $\mathrm{mass}\%$ and $56\mathrm{kJ}∕\mathrm{mol}$ ${\mathrm{H}}_2$, respectively, and those of the second reaction are $4\mathrm{mass}\%$ and $125\mathrm{kJ}∕\mathrm{mol}$ ${\mathrm{H}}_2$. They are in good agreement with experimental results of the thermal desorption spectra of ${\mathrm{LiBH}}_4$. Our calculation has predicted that the bending modes for the $\Gamma$-phonon frequencies of monoclinic ${\mathrm{Li}}_2{\mathrm{B}}_{12}{\mathrm{H}}_{12}$ are lower than that of ${\mathrm{LiBH}}_4$, while stretching modes are higher. These results are very useful for the experimental search and identification of possible intermediate compounds.

Figure 1

Enthalpy of the reaction where reactants are $(1-\delta )[\mathrm{LiH}+\mathrm{B}]$ and $\delta$ mole of molecular ${\mathrm{H}}_2$. The plotted solid diamonds show the enthalpy of the reaction where the compound ${\mathrm{LiB}}_x{\mathrm{H}}_y$ (and LiH) is produced at $\delta =(y-1)∕(2x+y-1)$ mole fraction of ${\mathrm{H}}_2$ [reaction Eq. (2) in the text]. The solid line corresponds to the enthalpy of the most stable reaction.

Figure 2

(Color online) Crystal structure model of monoclinic ${\mathrm{Li}}_2{\mathrm{B}}_{12}{\mathrm{H}}_{12}$ (type 2). Large, middle, and small spheres denote Li, B, and H atoms, respectively.

Figure 3

(Color online) The total and partial DOS for ${\mathrm{Li}}_2{\mathrm{B}}_{12}{\mathrm{H}}_{12}$. The energy is measured in electron-volts relative to the top of valence states.

Figure 4

Phonon DOS for monoclinic ${\mathrm{Li}}_2{\mathrm{B}}_{12}{\mathrm{H}}_{12}$. The contribution of the TO $\Gamma$-phonon modes indicated by vertical bars is only taken into account and the Gaussian broadening with a width of $30{\mathrm{cm}}^{-1}$ is used.

Figure 5

Comparison of the formation energies, $E_f^{solid}$ and $E_f^{complex}$, corresponding to the reactions Eq. (6) and Eq. (7) in the text, respectively, where the energies are normalized by the number of B-H pairs.