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  1. Abstract We perform ab initio simulations of beryllium (Be) and magnesium oxide (MgO) at megabar pressures and compare their structural and thermodynamic properties. We make a detailed comparison of our two recently derived phase diagrams of Be (Wu et al 2021 Phys. Rev. B 104 014103) and MgO (Soubiran and Militzer 2020 Phys. Rev. Lett. 125 175701) using the thermodynamic integration technique, as they exhibit striking similarities regarding their shape. We explore whether the Lindemann criterion can explain the melting temperatures of these materials through the calculation of the Debye temperature at high pressure. From our free energy calculations, we find that the melting line of both materials is well represented by the Simon–Glazel fit T m ( P ) = T 0 (1 + P / a ) 1/ c , where T 0 = 1564 K, a = 15.8037 GPa and c = 2.4154 for Be, while T 0 = 3010 K, a = 10.5797 GPa and c = 2.8683 for the MgO in the B1. For the B2 phase, we use the values a = 26.1163 GPa and c = 2.2426. Both materials exhibit negative Clapeyron slopes on the boundaries between the two solid phases that are strongly affected by anharmonic effects, which also influence the location of the solid–solid–liquid triple point. We find that the quasi-harmonic approximation underestimates the stability range of the low-pressure phases, namely hcp for Be and B1 for MgO. We also compute the phonon dispersion relations at low and high pressure for each of the phases of these materials, and also explore how the phonon density of states is modified by temperature. Finally, we derive secondary shock Hugoniot curves in addition to the principal Hugoniot curve for both materials, and study their offsets in pressure between solid and liquid branches. 
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