Experimental evidence of librational vibrations determining the stability of calcium borohydride

The high energy of hydrogen vibrations in solids is the origin of their strong impact on thermodynamic properties. The peculiar structure of complex hydrides amplifies this impact. We shed light on the vibrational properties of three allotropes of Ca(${\mathrm{BH}}_4$)${}_2$ using density-functional theory calculations, infrared spectroscopy, and inelastic neutron scattering. We show that the vibrational properties of Ca(${\mathrm{BH}}_4$)${}_2$ depend on the specific phase and are hitherto the origin of their differences in stability.

Figure 1

Calculated density of phonons states $g(E)$ of the three polymorphs of Ca(BH${}_4$)${}_2$. The continuous lines are plots of the function $\ln (1-e^{\frac{-E}{\mathit{kT}}})$ with $T=400$, 550 K illustrating the impact of the partition function on the free energy of the system.

Figure 2

Calculated free energy $F$ of the three polymorphs of Ca(BH${}_4$)${}_2$ as a function of temperature. The inset shows the difference in free energy with respect to the $\alpha$ phase.

Figure 3

X-ray diffraction of Ca(BH${}_4$)${}_2$ as prepared ($\gamma$ phase) and after heat treatments yielding the $\alpha$ and $\beta$ phases.

Figure 4

Normalized NMR spectra (${}^{11}\mathrm{B}$ resonance line) of the $\alpha$ and $\beta$ phases of Ca(BH${}_4$)${}_2$.

Figure 5

INS at $T=15$ K (bottom curves) and IR spectra at $T=300$ K (top curves) of the $\alpha$ and $\beta$ phases, respectively.

Figure 6

INS spectra as measured and as calculated of the $\gamma$, $\alpha$, and $\beta$ phases, respectively.

Figure 7

Simplified visualization of the librational modes $n$ and $r$. The $n$-vibrations may be described by a “nick” movement with one hydrogen atom standing still, and the $r$-vibrations by a constrained rotation around the $c_3$ axis. The complete movements of all atoms involved are visualized as movies found in the Supplemental Information.[20]

Figure 8

Comparison of the hydrogen phonon density of states of the stable polymorphs of Ca(BH${}_4$)${}_2$, i.e., $\alpha$ and $\beta$ phases, respectively, as measured (bottom curves) and as calculated (top curves). The opening of the gap between the two characteristic librational modes $n$ and $r$ is indicated.