First-principles studies of phase stability and crystal structures in Li-Zn mixed-metal borohydrides

Abstract

We address the problem of finding mixed-metal borohydrides with favorable thermodynamics and illustrate the approach using the example of ${\mathrm{LiZn}}_{2}{({\mathrm{BH}}_{4})}_{5}$. Using density functional theory (DFT), along with the grand-canonical linear programming method (GCLP), we examine the experimentally and computationally proposed crystal structures and the finite-temperature thermodynamics of dehydrogenation for the quaternary hydride ${\mathrm{LiZn}}_{2}{({\mathrm{BH}}_{4})}_{5}$. We find the following: (i) For ${\mathrm{LiZn}}_{2}{({\mathrm{BH}}_{4})}_{5}$, DFT calculations of the experimental crystal structures reveal that the structure from the neutron diffraction experiments of Ravnsb\ae{}k et al. is more stable [by 24 kJ/(mol f.u.)] than that based on a previous x-ray study. (ii) Our DFT calculations show that when using the neutron-diffraction structure of ${\mathrm{LiZn}}_{2}{({\mathrm{BH}}_{4})}_{5}$, the recently theoretically predicted $\mathrm{LiZn}{({\mathrm{BH}}_{4})}_{3}$ compound is unstable with respect to the decomposition into ${\mathrm{LiZn}}_{2}{({\mathrm{BH}}_{4})}_{5}+{\mathrm{LiBH}}_{4}$. (iii) GCLP calculations show that even though ${\mathrm{LiZn}}_{2}{({\mathrm{BH}}_{4})}_{5}$ is a combination of weakly [$\mathrm{Zn}{({\mathrm{BH}}_{4})}_{2}$] and strongly (${\mathrm{LiBH}}_{4}$) bound borohydrides, its decomposition is not intermediate between the two individual borohydrides. Rather, we find that the decomposition of ${\mathrm{LiZn}}_{2}{({\mathrm{BH}}_{4})}_{5}$ is divided into a weakly exothermic step [${\mathrm{LiZn}}_{2}{({\mathrm{BH}}_{4})}_{5}\ensuremath{\rightarrow}2\mathrm{Zn}+\frac{1}{5}{\mathrm{LiBH}}_{4}+\frac{2}{5}{\mathrm{Li}}_{2}{\mathrm{B}}_{12}{\mathrm{H}}_{12}+\frac{36}{5}{\mathrm{H}}_{2}$] and three strong endothermic steps ($12{\mathrm{LiBH}}_{4}\ensuremath{\rightarrow}10\mathrm{LiH}+{\mathrm{Li}}_{2}{\mathrm{B}}_{12}{\mathrm{H}}_{12}+13{\mathrm{H}}_{2}$; $\mathrm{Zn}+\mathrm{LiH}\ensuremath{\rightarrow}\mathrm{LiZn}+\frac{1}{2}{\mathrm{H}}_{2}$; $2\mathrm{Zn}+{\mathrm{Li}}_{2}{\mathrm{B}}_{12}{\mathrm{H}}_{12}\ensuremath{\rightarrow}2\mathrm{LiZn}+12\mathrm{B}+6{\mathrm{H}}_{2}$). DFT-calculated $\ensuremath{\Delta}{H}_{\text{ZPE}}^{T=0\phantom{\rule{0.28em}{0ex}}\text{K}}$ values for the first three ${\mathrm{LiZn}}_{2}{({\mathrm{BH}}_{4})}_{5}$ decomposition steps are $\ensuremath{-}19$, $+$37, $+$74 kJ/(mol ${\mathrm{H}}_{2}$), respectively. The behavior of ${\mathrm{LiZn}}_{2}{({\mathrm{BH}}_{4})}_{5}$ shows that mixed-metal borohydrides formed by mixing borohydrides of high and low thermodynamics stabilities do not necessarily have an intermediate decomposition tendency. Our results suggest the correct strategy to find intermediate decomposition in mixed-metal borohydrides is to search for stable mixed-metal products such as ternary metal borides.