Ab-initio predictions of potassium partitioning between Fe and Al-bearing MgSiO3 perovskite and post-perovskite

Partitioning of radioactive isotopes in the Earth’s interior is of great importance to the thermal and dynamic state and evolution of the Earth as radioactive decay provides an important source of energy for mantle dynamics. As a consequence, enriched (or depleted) reservoirs in the mantle can influence the energy balance in geodynamics. The recently discovered phase transition in MgSiO₃ from perovskite (pv) to post-perovskite (ppv) in the lowermost mantle provides the possibility for an enriched or depleted zone at the base of the mantle. Here we take a first step in addressing this issue by considering potassium (K) incorporation in pv and ppv by means of ab-initio computations.
We have set up computations for a coupled substitutions of K and Al or Fe³⁺ (M ion) for 2 Mg on the A site, and evaluate the energetics of a (Mg₃₀,K,M)Si₃₂O₉₆ composition in the pv and ppv structure. We compute the enthalpy of formation of the following reaction: (Mg₃₀,K,M)Si₃₂O₉₆ (ppv)+ Mg₃₂Si₃₂O₉₆ (pv) → (Mg₃₀,K,M)Si₃₂O₉₆ (pv)+ Mg₃₂Si₃₂O₉₆ (ppv).
We use the VASP package with the projector augmented wave (PAW) method for the static lattices of the respective high pressure phases and the generalized gradient approximation (GGA) to the exchange and correlation potential. Structures are optimized fully at constant volume, and we assume that the M and K ions are at A positions directly adjacent to one another. Computations are performed for a wide compression range, corresponding to pressures up to that of the CMB.
The distribution coefficient of potassium between pv and ppv can be computed from the energy difference of the reaction and the temperature T. We find that regardless of the M ion K partitions preferentially into the pv phase, making potassium-enriched lowermost mantle layer based on the stability of ppv is unlikely.