Communication: Modeling layered mosaic perovskite alloy microstructures across length scales via a packing algorithm.

Layered "mosaic" metal-halide perovskite materials display a wide-variety of microstructures that span the order-disorder spectrum and can be tuned via the composition of their constituent B-site octahedral species. Such materials are typically modeled using computationally expensive ab initio methods, but these approaches are greatly limited to small sample sizes. Here, we develop a highly efficient hard-particle packing algorithm to model large samples of these layered complex alloys that enables an accurate determination of the geometrical and topological properties of the B-site arrangements within the plane of the inorganic layers across length scales. Our results are in good agreement with various experiments and, therefore, our algorithm bypasses the need for full-blown ab initio calculations. The accurate predictive power of our algorithm demonstrates how our minimalist hard-particle model effectively captures complex interactions and dynamics like incoherent thermal motion, out-of-plane octahedral tilting, and bond compression/stretching. We specifically show that the composition-dependent miscibility predicted by our algorithm for certain silver-iron and copper-indium layered alloys is consistent with previous experimental observations. We further quantify the degree of mixing in the simulated structures across length scales using our recently developed sensitive "mixing" metric. The large structural snapshots provided by our algorithm also shed light on previous experimentally measured magnetic properties of a copper-indium system. The generalization of our algorithm to model 3D perovskite alloys is also discussed. In summary, our packing model and mixing metric enable one to accurately explore the enormous space of hypothetical layered mosaic alloy compositions and identify materials with potentially desirable optoelectronic and magnetic properties.