Quantum-mechanical calculation of the solid-state equilibrium MgO+α-Al₂O₃⇄MgAl₂O₄ (spinel) versus pressure

The ground-state crystal energies of cubic MgAl₂O₄ (spinel) and MgO (periclase) and of rhombohedral α-Al₂O₃ (corundum) have been calculated at different volumes, relaxing the corresponding structures, by all-electron periodic Hartree-Fock methods (crystal program). Basis sets of contracted Gaussian-type functions are employed for the 18 atomic (including d) orbitals representing each of the Mg, Al, and O atoms. Mulliken net atomic charges z_Mg=1.86‖e‖ (MgO), z_Al=2.30‖e‖ (α-Al₂O₃), z_Mg=1.74‖e‖, and z_Al=2.24‖e‖ (spinel) are obtained. The elastic bulk modulus, the Murnaghan equation of state p(V) at the athermal limit, the Mg-O and Al-O bond compressibilities, and the binding energy have been derived for each phase (and the elastic constants C₁₁ and C₁₂ for spinel only). Comparison with existing experimental data is discussed. The enthalpy change for spinel decomposition into the simple oxides has been computed as a function of pressure, including a correction for the electron correlation energy based on local-density-functional theory. A decomposition pressure of 11 GPa at T=0 K is predicted, against values of 8 and 13 GPa derived from experimental thermodynamic data and from direct compression experiments, respectively.