Theoretical prediction of different decomposition paths for $\text{Ca}{\left({\text{BH}}_4\right)}_2$ and $\text{Mg}{\left({\text{BH}}_4\right)}_2$

We have studied the decomposition pathways of both Ca- and Mg-borohydride using density-functional theory (DFT) calculations of the free energy (including vibrational contributions) in conjunction with a Monte Carlo-based crystal-structure prediction method, the prototype electrostatic ground-state (PEGS) search method. We find that a recently proposed ${\text{CaB}}_2{\text{H}}_2$ intermediate [M. D. Riktor, M. H. Sørby, K. Chłopek, M. Fichtner, and B. C. Hauback, J. Mater. Chem. 19, 2754 (2009)] is energetically highly unfavorable and hence very unlikely to form. We systematically search for low-energy structures of ${\text{CaB}}_2{\text{H}}_n$ compounds with $n=2$, 4, and 6 using PEGS simulations, refining the resulting structures with accurate DFT calculations. We find that the lowest-energy ${\text{CaB}}_2{\text{H}}_2$ and ${\text{CaB}}_2{\text{H}}_4$ crystal structures do not lie on the thermodynamically stable decomposition path but rather are unstable with respect to a decomposition pathway involving the previously proposed ${\text{CaB}}_{12}{\text{H}}_{12}$ phase. We also predict a ${\text{CaB}}_2{\text{H}}_6$ compound which forms a low-energy intermediate in the calcium borohydride decomposition pathway. This new reaction pathway is practically degenerate with decomposition into the ${\text{CaB}}_{12}{\text{H}}_{12}$ phase. Similar calculations for magnesium borohydride show that a recently predicted ${\text{MgB}}_2{\text{H}}_6$ phase does not form a stable intermediate in the decomposition pathway of $\text{Mg}{\left({\text{BH}}_4\right)}_2$.

Figure 1

(Color online) Schematic of ${\text{B}}_2{\text{H}}_6$ molecular geometry in the gas phase (left) and an ethanelike structure under a charged $\left(-2e\right)$ background (right). Gray spheres and small spheres represent B atoms and H atoms, respectively.

Figure 2

(Color online) Schematic view of the ${\text{CaB}}_2{\text{H}}_2$ experimental crystal structure (the left panel) and corresponding DFT fully relaxed structure (the right panel). The former one has the $Pnma$ space group with lattice constants $a=12.81\text{Å}$, $b=4.08\text{Å}$, $c=3.90\text{Å}$. While the latter one after the relaxation shows $a=14.92\text{Å}$, $b=3.88\text{Å}$, $c=3.71\text{Å}$. Big spheres, gray spheres and small spheres represent Ca atoms, B atoms, and H atoms, respectively.

Figure 3

(Color online) Schematic view of the lowest-energy structures of ${\text{CaB}}_2{\text{H}}_n$ $\left(n=2,4,6\right)$ by $\text{PEGS}+\text{DFT}$ predictions. Detailed structural information, lattice parameters, and atomic positions are given in Table .

Figure 4

(Color online) Theoretical prediction of decomposition pathways in $\text{Ca}{\left({\text{BH}}_4\right)}_2$ (upper panel) and $\text{Mg}{\left({\text{BH}}_4\right)}_2$ (lower panel) based on the calculated reaction enthalpies in Table . The black circle/line, the red square/line, and the blue diamond/line represent the convex hulls of static enthalpies at $T=0\text{K}$, enthalpies including the vibrational energies at $T=0\text{K}$ and $T=300\text{K}$, respectively. The black dashed line is the convex hull without involving ${\text{CaB}}_2{\text{H}}_n$ reactions in at the static energy case.

Figure 5

(Color online) Schematic view of ${\text{MgB}}_2{\text{H}}_6$ structures from MD annealing simulations of Ref. 15 (the left panel) and from our $\text{PEGS}+\text{DFT}$ (the right panel). The big red spheres represent Mg atoms. We find our $\text{PEGS}+\text{DFT}$ structure is $\sim 13\text{kJ}/\left(\text{mol}\text{f}\text{.u}\text{.}\right)$ lower in energy than the structure proposed in Ref. 15 but neither forms a stable intermediate in the decomposition of $\text{Mg}{\left({\text{BH}}_4\right)}_2$.