3.1 Exploring phase stability at high oxygen fugacities: MgO-O system and stable peroxide MgO$_2$

It is well known that monovalent (H-Cs) and divalent (Be-Ba and Zn-Hg) elements are able to form not only normal oxides, but also peroxides and even superoxides 186 (for instance, BaO$_2$ has been well studied at both ambient and high pressure 187; 188). Our structure prediction calculations identified the presence magnesium peroxide with Pa3 symmetry and 12 atoms in the unit cell at ambient pressure, which is in good agreement with experimental results 189. In this cubic phase, Mg is octahedrally coordinated by oxygen atoms (which form O$_2$ dumbbells), see Fig. 6.2a. However, Pa3 MgO$_2$ ($c$-MgO$_2$ from now on) is calculated to have a positive formation enthalpy from Mg and O$_2$, and is therefore metastable. The calculation shows that on increasing pressure, $c$-MgO$_2$ transforms into a tetragonal form with the space group I4/mcm. In the $t$-MgO$_2$ phase (Fig. 6.2b), Mg is 8-coordinate. Here we see the same trend of change from 6-fold to 8-fold coordination as in the predicted B1-B2 transition in MgO. but in MgO$_2$ it happens at mere 53 GPa, compared to 490 GPa for MgO. Most remarkably, above 116 GPa the $t$-MgO$_2$ structure has a negative enthalpy of formation from MgO and O$_2$, indicating that $t$-MgO$_2$ becomes thermodynamically stable. Furthermore, its stability is greatly enhanced by pressure and its enthalpy of formation becomes impressively negative, -0.43 eV/atom, at 500 GPa! We also examined the effect of temperature on its stability by performing quasiharmonic free energy calculations. Thermal effects tend to decrease the relative stability of MgO$_2$ by 0.008 meV/(atom$\cdot $K, which is clearly insufficient to change the sign of the formation free energy ($\Delta $$G$), and MgO$_2$ remains stable at high temperatures.

Figure 6.1: (a) Convex hull for the MgO-O system at high pressures; (b) the enthalpy of formation of MgO$_2$ as a function of pressure. For oxygen, we used the earlier predicted structures in Chapter 6. For MgO, B1 and B2 phases were considered. $c$-MgO$_2$ was considered at 50 GPa, while $t$-MgO$_2$ was used at pressures higher than 50 GPa.
Figure 6.2: Crystal structures of (a) $c$-MgO$_2$ phase at 50 GPa, space group Pa3, a=4.524 , Mg(0, 0, 0), O(0.4074, 0.4074, 0.4074); (b)$t$-MgO$_2$ at 500 GPa, space group I4/mcm, a=3.377 , c=3.985 , Mg(0, 0, 0.75), O(0.1260, 0.3740, 0.5). The green polyhedra are drawn to show the coordination environment of Mg atoms (6-fold in $c$-MgO$_2$, and 8-fold in $t$-MgO$_2$).