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

Abstract

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 are 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.

Figures (4)

• Figure 1: Images of rhombi arrangements generated by the LASC algorithm for an individual layer of the (a) single perovskite $\mathrm{A_2Cu^{II}Cl_4}$ and (b) double perovskite $\mathrm{A_4Cu^{I}In^{III}Cl_8}$. In both (a) and (b), the cross sections of the Jahn-Teller distorted Co21$\mathrm{Cu^{II}Cl_6}$, $\mathrm{Cu^{I}Cl_6}$, and $\mathrm{In^{III}Cl_6}$ units within the plane of the layer are respectively depicted by yellow, cyan, and red rhombi, and the solid black square denotes the boundary of the periodic simulation cell. The centers of the rhombi are located on the pervoskite B-sites. The A-sites are centered on the interstitial spaces between the B-sites but are located out of the plane of the layer. Note that the vertices of the aforementioned rhombi correspond to the positions of the $\mathrm{Cl}$ ligands. The antiferrodistortive and rock-salt arangements of (a) and (b), respectively, are consistent with those observed in the experimentally obtained crystal structures for these materials reported in Ref. Co21. For the simulation of (a), we fix the Jahn-Teller elongated axis of $\mathrm{Cu^{II}Cl_6}$ in the plane of the layer as is observed experimentally Co21. The structures in (a) and (b) consist of $N=100$ rhombi total with $L=10$ rhombi per side.
• Figure 2: (a) A schematic depicting a row within a layer of the double perovskite crystal $\mathrm{A_4Cu^{I}In^{III}Cl_8}$ during a LASC simulation in which the nearest-neighbor rhombi interact via potential \ref{['eqn:pot']}. Here, the third and fourth rhombi from the left have been swapped, resulting in an unfavorable gap $r_{ij}>0$ between the nearest-neighbor vertices of the adjacent $\mathrm{In^{III}Cl_6}$ units (second and third from the left), and an unfavorable overlap $r_{ij}<0$ between the nearest-neighbor vertices of the adjacent $\mathrm{Cu^{I}Cl_6}$ units (fourth and fifth from the left) within the plane of the layer. By contrast, the nearest-neighbor $\mathrm{Cu^{I}Cl_6}$ and $\mathrm{In^{III}Cl_6}$ units have no such packing mismatches (i.e., $r_{ij}=0$) because their $\mathrm{M-Cl}$ bond lengths are consistent with the lattice constant $a$. (b) A schematic depiction of the (left) trial Monte Carlo swap and rotational moves, (middle) isotropic cell compression moves employed by the LASC algorithm, as well as the (right) resulting densified system. In (a), the gray lines represent the grid of the underlying square lattice. In (b), the magnitude of the trial compression is much greater than what is normally applied in the algorithm to facilitate visualization.
• Figure 3: (a) A portion of a LASC simulated $\mathrm{(Ag^{I}Fe^{III}) Fe^{II}_2}$ structure consisting of phase segregated domains of $\mathrm{Fe^{II}Cl_4 }$ and $\mathrm{Ag^{I}Fe^{III}Cl_8}$. (b) Plots of the ensemble averaged integrated compositional mixing metric \ref{['eqn:sigma']} as a function of $\chi_{\mathrm{Fe(II)}}$ for $\mathrm{Fe^{III}Cl_6}, \mathrm{Ag^{I}Cl_6},$ and $\mathrm{Fe^{II}Cl_6}$ octahedra. The dashed black line marks the value of the mixing metric for an uncorrelated B-site mixture (UM), which one can show is $\approx0.8033$ for all compositions $0<\chi_i<1$To22a. Note that $\Sigma_{\mathrm{Fe(III)}}$ and $\Sigma_{\mathrm{Ag(I)}}$ are roughly equivalent across $\chi_{\mathrm{Fe(II)}}$ values since these octahedra are always co-localized in the rock-salt pattern of the double perovskite $\mathrm{Ag^{I}Fe^{III}Cl_8}$. In (a), the $\mathrm{Fe^{III}Cl_6}$, $\mathrm{Ag^{I}Cl_6}$, and $\mathrm{Fe^{II}Cl_6}$ octahedra within the layer are respectively represented as orange, gray, and green rhombi. In (b), the error-bars represent the standard deviation of the ensemble. Each composition is averaged over 250 realizations of a $200\times200$ lattice system.
• Figure 4: (a) An example image of a LASC simulated $\mathrm{(Cu^{I}In^{III}) Cu^{II}_2}$ structure, in which polycrystalline grains of the $2\times2$ motif shown in the inset are observed. Note the horizontal and vertical grain boundaries near the bottom and right of the structure, respectively. (b) Plots of the ensemble averaged integrated compositional mixing metric \ref{['eqn:sigma']} as a function of $\chi_{\mathrm{Cu(II)}}$ for $\mathrm{In^{III}Cl_6}, \mathrm{Cu^{I}Cl_6},$ and $\mathrm{Cu^{II}Cl_6}$ octahedra. The dashed black line marks the value of the mixing metric for an uncorrelated B-site mixture (UM). In (a), the $\mathrm{In^{III}Cl_6}$, $\mathrm{Cu^{I}Cl_6}$, and $\mathrm{Cu^{II}Cl_6}$ octahedra within the layer are respectively represented as red, cyan, and yellow rhombi. In (b), the error-bars represent the standard deviation of the ensemble. Each composition is averaged over 250 realizations of a $200\times200$ lattice system.