Cation Disorder of ${\text{Mg}}_{\mathbf{2}}{\text{SiO}}_{\mathbf{4}}$ 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 ${\text{Mg}}_{\mathbf{2}}{\text{SiO}}_{\mathbf{4}}$, one of the major mantle phases, may undergo the order-disorder transition (ODT) at high temperatures. However, the ODT phase boundary of ${\text{Mg}}_{\mathbf{2}}{\text{SiO}}_{\mathbf{4}}$ has not been rigorously constrained. Additionally, fundamental thermodynamic properties of the disordered ${\text{Mg}}_{\mathbf{2}}{\text{SiO}}_{\mathbf{4}}$ remain poorly investigated. Here, we develop a unified machine learning potential (MLP) for ${\text{Mg}}_{\mathbf{2}}{\text{SiO}}_{\mathbf{4}}$ of ab initio accuracy under super-Earth mantle conditions. With the efficient MLP, we extensively calculate the free energy of post-post spinel ${\text{Mg}}_{\mathbf{2}}{\text{SiO}}_{\mathbf{4}}$ 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 ${\text{Mg}}_{\mathbf{2}}{\text{SiO}}_{\mathbf{4}}$ 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.