Controlling Elastic Properties in Perovskites with Polyhedral Connectivity

Using density functional theory, we investigate the effect of $B$O$_6$ octahedral face-sharing on the macroscopic mechanical properties of $AB$O$_3$ compounds ($A$=Sr, Ba) ($B$= Ti, Mn, Ni, Zr). We consider four structure prototypes of which three are hexagonal perovskites, exhibiting different ratios of corner-connected octahedra to face-connected octahedra (33\%, 50\%, \& 100\%). The fourth structure, cubic perovskite, exclusively exhibits corner-connected octahedra. We find that increasing the proportion of face-sharing to corner-sharing results in a decrease in the elastic constants independent of the $d$ orbital filling or cation size. Next, we explore the role of local and crystal structure features on this trend with a random forest regression model to identify that the volume per atom and trigonal distortion amplitude may serve as useful descriptors to predict this decrease. Finally, we propose how changing this trigonal distortion can potentially be used to engineer electronic properties such as the bandgap in these materials.