1 Introduction

Light weight metal borohydrides have recently received much attention owing to their high gravimetric and volumetric hydrogen densities compared to other complex hydrides 123; 124; 125. Of these, magnesium borohydride, Mg(BH$_4$)$_2$, is a prominent lightweight solid-state hydrogen storage material with a theoretical hydrogen capacity of 14.8 wt %. Mg(BH$_4$)$_2$ at ambient condition has been extensively studied. To improve the reversible hydrogen absorption or desorption kinetics or get new metastable polymorphs, recent interest are foucusing on the stabilization of the high-pressure phase of Mg(BH$_4$)$_2$ at ambient pressure. For example, $\gamma $-Mg(BH$_4$)$_2$ is one of the hydrogen-richest solids, reported to be capable of storing guest species, such as hydrogen 126. Most recently, new $\delta $, $\delta ’$, and $\epsilon $ phases of Mg(BH$_4$)$_2$ were successfully synthesized under pressure 126. Many of them turned out to retain their structure upon decompression to ambient conditions. Crystal structures of $\gamma $ and $\delta $ phases were, apparently convincingly, resolved using powder x-ray diffraction data obtained with synchrotron radiation 126. Unexpectedly, theoretical phonon calculations showed the $P4_2nm$ structure ($\delta $ phase) to be dynamically unstable at ambient pressure, which means that the exact crystal structure of $\delta $ phase is still unresolved, even for such a simple structure only with 22 atoms per cell, and still less for the unknown $\delta ’$ and $\epsilon $ phases 126. Therefore, the polymorphism and phase diagram of this important compound require further investigation.