We have studied the ferrous (Fe2+) and ferric (Fe3+) iron concentrations in
Al-free Fe containing Mg-silicate perovskite (Mg-Pv) at pressure (P),
temperature (T), and oxygen fugacity (fO2) conditions related to the lower
mantle using a thermodynamic model based on ab-initio calculations. We consider
the oxidation reaction and the charge disproportionation reaction, both of
which can produce Fe3+ in Mg-Pv. The model shows qualitatively good agreement
with available experimental data on Fe3+/{\Sigma}Fe ({\Sigma}Fe = total Fe in
system), spin transitions, and equations of state. We predict that under
lower-mantle conditions Fe3+/{\Sigma}Fe determined by the charge
disproportionation is estimated to be 0.01-0.07 in Al-free Mg-Pv, suggesting
that low Al Mg-Pv in the uppermost pyrolitic mantle (where majoritic garnet
contains most of the Al) and in the harzburgitic heterogeneities throughout the
lower mantle contains very little Fe3+. We find that the volume reduction by
the spin transition of the B-site Fe3+ leads to a minimum Fe3+/{\Sigma}Fe in
Mg-Pv at mid-mantle pressures. The model shows that configurational entropy is
a key driving force to create Fe3+ and therefore Fe3+ content is highly
temperature sensitive. The temperature sensitivity may lead to a maximum
Fe3+/{\Sigma}Fe in Mg-Pv in warm regions at the core-mantle boundary region,
such as Large Low Shear Velocity Provinces (LLSVPs), potentially altering the
physical (e.g., bulk modulus) and transport (e.g., thermal and electrical
conductivities) properties of the heterogeneities