In this research, an order-disorder transition in its cation sublattice of Mg₂GeO₄ between I-42d-type and Th₃P₄-type phases is predicted using ab initio calculations to occur at high temperatures. This type of uncommon 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. Mg₂GeO₄ is a low-pressure analogue of I-42d-type Mg₂SiO₄, a predicted major planet-forming phase of super-Earths’ mantles. Therefore, a similar order-disorder transition is anticipated in I-42d-type Mg₂SiO₄, which should impact these planets’ internal structure and dynamics.

Many candidates of super-Earths, terrestrial exoplanets much larger than the Earth, have been discovered recently. Internal pressures and temperatures in super-Earths should be much higher than those of the Earth. Despite remarkable developments in experimental techniques, these pressure-temperature conditions are still very challenging to experiments making ab initio predictions of phase-transition phenomena in planet-forming phases critical to advancing planetary modelling. So far, several ab initio calculations have predicted that MgSiO₃ post-perovskite (PPV), which is the final form of MgSiO₃ (a major constituent of the Earth’s lower mantle) in the Earth, should undergo the pressure-induced three-stage dissociations: MgSiO₃ PPVà I-42d-type Mg₂SiO₄ + P2₁/c-type MgSi₂O₅ à I-42d-type Mg₂SiO₄ + Fe₂P-type SiO₂ à CsCl-type MgO + Fe₂P-type SiO₂. However, these predictions were based on structural searches at the static condition, i.e., any effect of temperature on the phase transitions has not been considered explicitly. Since the temperature in super-Earths is very high, phase transitions induced by temperature as well as pressure should be investigated.

In this research, a temperature-induced order-disorder transition (ODT) was predicted by ab initio calculations for I-42d-type Mg₂GeO₄, which is a good candidate for a low-pressure analogue of Mg₂SiO₄. In I-42d-type Mg₂GeO₄, local atomic environments around the Mg and Ge sites are very similar, both being surrounded by eight O ions. Due to the similarity, all cations are expected to be distributed randomly over these sites by entropy at high temperatures, leading to the ODT. Once the ODT occurs and all cation sites become equivalent, the resultant structure is identical to that of Th₃P₄.

The ODT critical temperature, T_c, was calculated using a statistical treatment. To represent the disordered Th₃P₄-type phase, an ensemble of 125 configurations was generated for a supercell consisting of 56 atoms. Then, the partition function was obtained by taking the summation of Boltzmann factors, whose total energies were by ab initio calculations, over the 125 configurations. From the partition function, the heat capacity, C_P (P, T), can be calculated. The peak temperature of C_P gives T_c. Since T_c gradually increases with pressure, the phase boundary has a positive Clapeyron slope. With the ODT predicted, a new sequence of the post-PPV dissociation should occur at high temperatures: MgGeO₃ PPV à Th₃P₄-type Mg₂GeO₄ + pyrite-type GeO₂. Since Mg₂GeO₄ is an analogue of Mg₂SiO₄, a similar ODT should also occur in I-42d-type Mg₂SiO₄ at high temperatures and impact the internal structure and dynamics of super-Earths.