  Distinct shortcomings of individual halide perovskites for solar
applications, such as restricted range of band gaps, propensity of ABX3 to
decompose into AX+BX2, or oxidation of 2ABX3 into A2BX6 have led to the need to
consider alloys of individual perovskites. This creates a non-trivial
material-selection problem, spanning a continuum of three sets of compositions
(one for each sub lattice), and requiring control of phase-separation or
ordering in each alloyed subfield. Not surprisingly, material and structure
choices were made thus far mostly via trial-and-error explorations. We use
ideas from solid state theory of semiconductor alloys to analyze the behaviors
of the (FA,Cs)(Pb,Sn)I3 alloys system. Density functional calculations
utilizing specially constructed supercells (SQS) are used to calculate the
composition dependence of band gaps, energy of decomposition and alloy mixing
enthalpies. A number of trends are observed for A-site as well as for B-site
alloys. To understand the physical reasons that control these trends we
decompose the alloy properties into distinct physical terms: (i) the energies
associated with removing the octahedral deformations (tilting, rotations, B
site displacements), (ii) the energies of compressing the larger component and
expanding the smaller one to the alloy volume, (iii) the charge transfer
energies associated with placing the alloyed units onto a common lattice, and
finally, (iv) structural relaxation of all bonds within the cells., This
analysis clarifies the origin of the observed trends in bang gaps,
decomposition energies and mixing enthalpies. Unlike a number of previous
calculations we find that the a proper description of alloy physics requires
that even the pure, non-alloyed end-point compounds be allowed to develop local
environment dependent octahedral deformation that lowers significantly the
total energy and raises their band gaps.
