Thermodynamic stability of mixed Pb:Sn methyl-ammonium halide   perovskites
  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. 
Ksenia Korshunova, Lars Winterfeld, Wichard J.D. Beenken and Erich   Runge
cond-mat.mtrl-sci