First-principle calculations of thermodynamic stability of CsPb(Br1-xClx)3 perovskites in phase-separated and phase-homogenized conditions. (a) Structures of phase-separated and phase-homogenized CsPb(Br1-xClx)3 perovskites involved in the calculations. The phase-homogenized structure corresponds to the random alloy. The cubic-phase perovskite structure is adopted, and for clarity only, the corner-sharing octahedral framework is shown. (b) Calculated formation energies (Ef) with respect to decomposition into phase-pure CsPbBr3 and CsPbCl3. (c) Strain field (upper panels) and charge transfer (lower panels) distribution of one octahedral layer perpendicular to the  direction for the phase-separated and phase-homogenized cases. The strains are calculated in terms of Pb-Br/Cl bond lengths (see Materials and Methods). The charge transfer values (in unit charge) are evaluated by the difference in the charge at Br/Cl sites between CsPb(Br1-xClx)3 and CsPbBr3/CsPbCl3 (see Materials and Methods). The cases with the Br content of 0.1875 in (b) are selected for presentation. (d) Calculated formation energies of CsPb(Br1-xClx)3 perovskites in the whole component-variation range. The CsPb(BrxCl1-x)3 structures were generated by the cluster expansion (CE) approach with the constraint of up to 20 atoms per unit cell (see Materials and Methods). The red triangles are the structures calculated by the density functional theory (DFT-calculated), and the blue line represents the stable ground states (ground states).