Potential-induced breathing model for the elastic moduli and high-pressure behavior of the cubic alkaline-earth oxides

Abstract

A parameter-free model is presented for the elastic constants and high-pressure behavior of the alkaline-earth oxides MgO, CaO, SrO, and BaO. The model is based on a Gordon-Kim-type calculation for the short-range energy of a crystal. Spherically symmetric relaxation of ion charge density in response to the Madelung potential, termed potential-induced breathing (PIB), is incorporated into the model as a function of strain. This charge relaxation is accomplished by the use of a Watson-sphere calculation to obtain the interaction energy of pairs of ions as a function of both interatomic distance and Coulomb potential. By this technique many-body effects, which are particularly important for the prediction of crystal elasticity, are included. The model successfully reproduces both the sign and magnitude of the deviation (Δ=$C_{12}$-$C_{44}$) from the Cauchy relation measured at zero pressure for the cubic alkaline-earth oxides. Static compression curves calculated in both the B1 and B2 phases of these compounds are found to be within 5% of the available room-temperature data. From a calculation of the pressure dependence of the elastic moduli, the role of many-body effects at high pressure is determined. The B1-B2 phase transition pressures are calculated within the PIB model to be 251 GPa (MgO), 55 GPa (CaO), 36 GPa (SrO), and 21 GPa (BaO), in very good agreement with available experimental data for these compounds.