Cation Disorder of Mg₂SiO₄ in Super-Earth Mantles

Understanding the mineralogy of exoplanets is essential for unraveling their interior structures, dynamics, and evolution. For large super-Earths, the post-post spinel (Formula presented.), one of the major mantle phases, may undergo the order-disorder transition (ODT) at high temperatures. However, the ODT phase boundary of (Formula presented.) has not been rigorously constrained. Additionally, fundamental thermodynamic properties of the disordered (Formula presented.) remain poorly investigated. Here, we develop a unified machine learning potential (MLP) for (Formula presented.) of ab initio accuracy under super-Earth mantle conditions. With the efficient MLP, we extensively calculate the free energy of post-post spinel (Formula presented.) via the thermodynamic integration method. The results are used to constrain the ODT phase boundary. Furthermore, we report the P-V-T equation of state and Grüneisen parameters for post-post spinel (Formula presented.) across various degrees of disorder. These thermodynamic properties are further applied to update the adiabatic thermal profiles and the mass-radius relation of super-Earths.