Iterative cluster expansion approach for predicting the structure evolution of mixed Ruddelsden-Popper oxides La2−xSrxNi1−yFeyO4±δ

Layered perovskites viz. Ruddlesden-Popper (RP) compounds have attracted a significant research interest lately due to their superior electrocatalytic activities, on top of their rich physics. Although the versatility of their compositional space is the key to tune their stability and applicability, its complexity also makes the understanding and design of new functional RP-based materials difficult. Herein by parameterizing a cluster expansion model Hamiltonian with density-functional inputs, we have successfully scanned over the complex configurational space of an RP phase, taking ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{Ni}}_{1\ensuremath{-}y}{\mathrm{Fe}}_{y}{\mathrm{O}}_{4\ifmmode\pm\else\textpm\fi{}\ensuremath{\delta}}$ as an example. This surrogate model is then used to predict the energies of unknown compositions and performing Metropolis Monte Carlo sampling for finding the ground-state structures. By analyzing these stable configurations at different $x, y$'s, and $\ensuremath{\delta}$=0, 0.125, we found that apical vacancies in the rock-salt layer are more favorable due to lesser steric forces but changes in $A$-site oxidation state due to Sr substitution can facilitate equatorial O-vacancy formation even in the perovskite layers. Our results uncover the structural evolution of RP oxides with increasing $A$-site (Sr) and $B$-site (Fe) substitutions. We find that a critical Sr concentration is required to stabilize Fe in these systems. With increasing Sr concentration, the $A$-site charge state changes gradually from ${\mathrm{La}}^{+3}$ to ${\mathrm{Sr}}^{+2}$, which facilitates both O-vacancy formation and stabilization of the $B$-site dopants. The findings further highlight the effects of configurational changes for the same composition on electronic structure. Thus, our work clearly demonstrates the importance of exploring configurational space of these complex oxides when using electronic-structure features as descriptors of their catalytic and other functional properties.