  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 of
Mg$_2$GeO$_4$, a post-post-perovskite (post-PPv) phase. This uncommon type of
prediction is achieved by carrying out a high-throughput sampling of atomic
configurations in a 56-atom supercell followed by a Boltzmann ensemble
statistics 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 of
super-Earths' mantles. Therefore, a similar ODT is anticipated in
$I\bar{4}2d$-type Mg$_2$SiO$_4$ as well, which should impact the internal
structure and dynamics of these planets. The prediction of this
Th$_3$P$_4$-type phase in Mg$_2$GeO$_4$ enhances further the relationship
between the crystal structures of Earth/planet-forming silicates and oxides at
extreme pressures and those of rare-earth sesquisulfides at low pressures.
