Crystal Structure Prediction and its Application in Earth and Materials Sciences: Exploring phase stability at high oxygen fugacities: MgO-O system and stable peroxide MgO

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.

$\includegraphics[scale=1.0]{chapter6/pdf/fig1-MgO-O.png}$

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.

$\includegraphics[scale=0.6]{chapter6/pdf/fig2-MgO2.png}$

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 $_2$ ).