First-principles thermodynamics study of phase stability in inorganic halide perovskite solid solutions

Halide substitution gives rise to a tunable band gap as a function of composition in halide perovskite materials. However, photoinduced phase segregation, observed at room temperature in mixed halide $A\text{Pb}{({\mathrm{I}}_{x}{\mathrm{Br}}_{1\ensuremath{-}x})}_{3}$ systems, limits open circuit voltages and decreases photovoltaic device efficiencies. We investigate equilibrium phase stability of orthorhombic $Pnma\phantom{\rule{4pt}{0ex}}\ensuremath{\gamma}$-phase $\text{Cs}M{({X}_{x}{Y}_{1\ensuremath{-}x})}_{3}$ perovskites where $M$ is Pb or Sn, and $X$ and $Y$ are Br, Cl, or I. Finite-temperature phase diagrams are constructed using a cluster expansion effective Hamiltonian parameterized from first-principles density-functional-theory calculations. Solid solution phases for $\text{Cs}M{({\mathrm{I}}_{x}{\mathrm{Br}}_{1\ensuremath{-}x})}_{3}$ and $\text{Cs}M{({\mathrm{Br}}_{x}{\mathrm{Cl}}_{1\ensuremath{-}x})}_{3}$ are predicted to be stable well below room temperature while $\text{Cs}M{({\mathrm{I}}_{x}{\mathrm{Cl}}_{1\ensuremath{-}x})}_{3}$ systems have miscibility gaps that extend above 400 K. The height of the miscibility gap correlates with the difference in volume between end members. Also layered ground states are found on the convex hull at $x=2/3$ for ${\mathrm{CsSnBr}}_{2}\mathrm{Cl},{\mathrm{CsPbI}}_{2}\mathrm{Br}$, and ${\mathrm{CsPbBrCl}}_{2}$. The impact of these ground states on the finite temperature phase diagram is discussed in the context of the experimentally observed photoinduced phase segregation.