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

Abstract

We use a combination of first-principles density functional theory (DFT) calculations and the recently developed prototype electrostatic ground state (PEGS) method to predict low-energy crystal structures and study phase stability of Li-Zn and Na-Zn mixed-metal borohydride compounds [i.e., NaZn(BH${}_{4}$)${}_{3}$, NaZn${}_{2}$(BH${}_{4}$)${}_{5}$, LiZn(BH${}_{4}$)${}_{3}$, and LiZn${}_{2}$(BH${}_{4}$)${}_{5}$]. We find the following: (i) DFT $+$ PEGS successfully predicts low-energy structures in these mixed-metal borohydride systems. (ii) DFT calculations show negative mixing energies in both the Li-Zn and Na-Zn borohydride systems, consistent with the observation of mixed-metal ordering in these systems. (iii) Our DFT calculations of the recently reported experimental crystal structures of NaZn${}_{2}$(BH${}_{4}$)${}_{5}$ and NaZn(BH${}_{4}$)${}_{3}$ show that the former has a negative mixing energy, while the latter has a positive mixing energy. (iv) Using the PEGS approach, we predict a new crystal structure of NaZn(BH${}_{4}$)${}_{3}$ with negative mixing energy and find that the experimental structure of NaZn${}_{2}$(BH${}_{4}$)${}_{5}$ and the PEGS obtained structure of NaZn(BH${}_{4}$)${}_{3}$ lie on the ground state convex hull. (v) In the Li-Zn borohydride system, we have used the PEGS $+$ DFT approach to predict a stable crystal structure of new, previously unobserved stoichiometry, LiZn(BH${}_{4}$)${}_{3}$. As a consequence of this predicted low-energy compound, DFT calculations of the experimentally reported structure of LiZn${}_{2}$(BH${}_{4}$)${}_{5}$ show that it is unstable with respect to decomposition into LiZn(BH${}_{4}$)${}_{3}$ $+$ Zn(BH${}_{4}$)${}_{2}$. (vi) In addition, we also elucidate the ground state crystal structure of NaBH${}_{4}$, and confirm that reorientation of (BH${}_{4}$)${}^{\ensuremath{-}}$ units is the driving force behind the order-disorder phase transition in NaBH${}_{4}$. (vii) Finally, we predict a new low-energy crystal structure of Zn(BH${}_{4}$)${}_{2}$, and illustrate its similarities with the crystal structure of Mg(BH${}_{4}$)${}_{2}$.