Crystal structure and phonon instability of high-temperature $\ensuremath{\beta}\text{-Ca}{({\text{BH}}_{4})}_{2}$

Crystal structure and phonon instability of high-temperature $β -Ca {({BH}_{4})}_{2}$

Young-Su Lee, Yoonyoung Kim, Young Whan Cho, Daniel Shapiro, Chris Wolverton, and Vidvuds Ozoliņš

Phys. Rev. B 79, 104107 – Published 13 March 2009

Abstract

$Ca {({BH}_{4})}_{2}$ is an interesting candidate for high-density hydrogen storage since it contains a large amount of hydrogen by weight and volume, and has been shown to reversibly release and absorb hydrogen, albeit at moderately high temperatures. $Ca {({BH}_{4})}_{2}$ undergoes a polymorphic transformation around 400–440 K from a low-temperature $α -Ca {({BH}_{4})}_{2}$ phase to a high-temperature $β -Ca {({BH}_{4})}_{2}$ phase. The crystal structure of $β -Ca {({BH}_{4})}_{2}$ has only recently been resolved, and its thermodynamic phase stability is still not well understood. Using a combined experimental and theoretical approach, we have independently determined the structure of $β -Ca {({BH}_{4})}_{2}$ and assessed its thermodynamic stability in the quasiharmonic approximation. The space-group $P 4_{2} / m$ gives an excellent agreement between experiment and theory, confirming the result of a recent study [Buchter et al., J. Phys. Chem. B 112, 8042 (2008)]. Using density-functional theory (DFT), we obtained a value of 10.9 kJ/mol for the static total-energy difference between the $β -Ca {({BH}_{4})}_{2}$ and the $α -Ca {({BH}_{4})}_{2}$ phases at $T = 0 K$ (without vibrations). Using DFT linear-response calculations, we find that the $[\frac{1}{2} \frac{1}{2} ξ]$ acoustic phonon branch of $β -Ca {({BH}_{4})}_{2}$ is dynamically unstable on the Brillouin-zone boundary at the $T = 0 K$ lattice parameters predicted from static DFT calculations. This phonon branch is very sensitive to the lattice parameters and can be stabilized by including lattice expansion due to zero-point vibrational contributions in the quasiharmonic approximation. This expanded stable $β -Ca {({BH}_{4})}_{2}$ structure has a room-temperature vibrational entropy that is $16 J / mol K$ higher than that of the $α -Ca {({BH}_{4})}_{2}$ phase, qualitatively consistent with the observed stabilization of the former at elevated temperatures. The main contribution to the entropy difference between the $α -Ca {({BH}_{4})}_{2}$ and $β -Ca {({BH}_{4})}_{2}$ phases comes from the low-frequency region dominated by translational and rotational phonon modes.