  Using density functional theory, we investigate systematically mixed
MA(Pb:Sn)X3 perovskites, where MA is CH3NH3+, and X is Cl, Br, or I. Ab initio
calculations of the orthorhombic, tetragonal, and cubic perovskite phases show
that the substitution of lead by tin has a much weaker influence on both
structure and cohesive energies than the substitution of the halogen. The
thermodynamic stability of the MA(Pb:Sn)X3 mixtures at finite, non-zero
temperatures is studied within the Regular Solution Model. We predict that it
will be possible to create MA(Pb:Sn)I3 mixtures at any temperature. Our results
imply that mixing is unlikely for the low-temperature phase of bromide and
chloride compounds, where instead local clusters are more likely to form. We
further predict that in the high-temperature cubic phase, Pb and Sn compounds
will mix for both MA(Pb:Sn)Br3 and MA(Pb:Sn)Cl3 due to the entropy contribution
to the Helmholtz free energy.
