First-principles calculations of mass transport in magnesium borohydride

Mg(BH$_{4}$)$_2$ is a hydrogen storage material which can decompose to release hydrogen in the following reaction: Mg(BH$_4$)$_{2(\mathrm{solid})}$ $\rightarrow \frac{1}{6}$MgB$_{12}$H$_{12(\mathrm{solid})}$ + $\frac{5}{6}$MgH$_{2(\mathrm{solid})} + \frac{13}{6}$H$_{2(\mathrm{gas})}$ $\rightarrow$ MgH$_{2(\mathrm{solid})}$ + 2B$_{(\mathrm{solid})}$ + 4H$_{2(\mathrm{gas})}$. However, experiments show that hydrogen release only occurs at temperatures above 300 $^{\circ}$C, which severely limits applications in mobile storage. Using density-functional theory calculations, we systematically study bulk diffusion of defects in the reactant Mg(BH$_{4}$)$_2$ and products MgB$_{12}$H$_{12}$ and MgH$_{2}$ during the first step of the solid-state dehydrogenation reaction. The defect concentrations and concentration gradients are calculated for a variety of defects, including charged vacancies and interstitials. We find that neutral [BH$_3$] vacancies have the highest bulk concentration and concentration gradient in Mg(BH$_{4}$)$_2$. The diffusion mechanism of [BH$_3$] vacancy in Mg(BH$_{4}$)$_2$ is studied using the nudged elastic band method. Our results shows that the calculated diffusion barrier for [BH$_3$] vacancies is $\approx. 2$~eV, suggesting that slow mass transport limits the kinetics of hydrogen desorption.