Phase diagram and stability of mixed-cation lead iodide perovskites: A theory and experiment combined study

Alloying structurally similar perovskites to form mixed-cation lead iodide perovskites, e.g., ${\mathrm{Cs}}_{x}\mathrm{F}{\mathrm{A}}_{(1\ensuremath{-}x)}\mathrm{Pb}{\mathrm{I}}_{3}, \mathrm{M}{\mathrm{A}}_{x}\mathrm{F}{\mathrm{A}}_{(1\ensuremath{-}x)}\mathrm{Pb}{\mathrm{I}}_{3}$, and ${\mathrm{Cs}}_{x}\mathrm{M}{\mathrm{A}}_{y}\mathrm{F}{\mathrm{A}}_{(1\ensuremath{-}x\ensuremath{-}y)}\mathrm{Pb}{\mathrm{I}}_{3}$, could improve the performance of perovskite-based solar cells and light-emitting diodes. However, a phase diagram of them and a clear understanding of the underlying atomic-scale mechanism are still lacking. Using ab initio calculations combined with high-throughput experimentation, we demonstrate the phase diagram of mixed-cation lead iodide perovskites. Only a small proportion of monovalent cations (${\mathrm{Cs}}^{+}/{\mathrm{Rb}}^{+}/{\mathrm{MA}}^{+}$) could be incorporated into the ${\mathrm{FAPbI}}_{3}/{\mathrm{MAPbI}}_{3}$ matrix; otherwise it will be separated into \ensuremath{\delta}-${\mathrm{CsPbI}}_{3}$, \ensuremath{\delta}-${\mathrm{RbPbI}}_{3}$, MAI, etc. The smaller the radius of doping cations, the harder it is to incorporate them into a perovskite lattice and the easier it is to stabilize the perovskite phase. In ${\mathrm{FAPbI}}_{3}$-based multication perovskites, moreover, over 10 mol % alloying is needed to convert \ensuremath{\delta} phase to \ensuremath{\alpha} phase at room temperature. The combined upper and lower limits for doping concentration restrict the appropriate alloying ratio to a narrow window. We further plot the relative energy diagram for triple-cation perovskite ${\mathrm{Cs}}_{x}\mathrm{M}{\mathrm{A}}_{y}\mathrm{F}{\mathrm{A}}_{(1\ensuremath{-}x\ensuremath{-}y)}\mathrm{Pb}{\mathrm{I}}_{3}$, which reveals the ideal doping ratio for uniform stable alloying. This theory-experiment-combined study provides a clear microscopic picture of phase stability and segregation for mixed-cation perovskite solids.