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Here we present an ab initio prediction of an order-disorder transition (ODT)from $I\bar{4}2d$-type to a Th$_3$P$_4$-type phase in the cation sublattices ofMg$_2$GeO$_4$, a post-post-perovskite (post-PPv) phase. This uncommon type ofprediction is achieved by carrying out a high-throughput sampling of atomicconfigurations in a 56-atom supercell followed by a Boltzmann ensemblestatistics calculation. Mg$_2$GeO$_4$ is a low-pressure analog of$I\bar{4}2d$-type Mg$_2$SiO$_4$, a predicted major planet-forming phase ofsuper-Earths' mantles. Therefore, a similar ODT is anticipated in$I\bar{4}2d$-type Mg$_2$SiO$_4$ as well, which should impact the internalstructure and dynamics of these planets. The prediction of thisTh$_3$P$_4$-type phase in Mg$_2$GeO$_4$ enhances further the relationshipbetween the crystal structures of Earth/planet-forming silicates and oxides atextreme pressures and those of rare-earth sesquisulfides at low pressures.

Ab initio prediction of an order-disorder transition in Mg$_2$GeO$_4$: implication for the nature of super-Earth's mantles