Design Rules and Discovery of Face-Sharing Hexagonal Perovskites

Hexagonal perovskites with face-sharing octahedral connectivity are an underexplored class of materials. We propose quantitative design principles for stabilizing face-sharing ABX3 hexagonal perovskites based on a comparative analysis of oxides and sulfides. By mapping structural preferences across a phase-space defined by an electronegativity-corrected tolerance factor and the Shannon radius of the A-site cations, we identify distinct thresholds that separate hexagonal phases from competing cubic polymorphs having corner-sharing octahedral connectivity. Our analysis reveals that sulfides differ significantly from oxides due to the increased covalency of the transition metal-sulfur bonds, which enables broader compositional flexibility. Applying these principles, we predict a set of thermodynamically formable ABO3 and ABS3 compounds that are likely to adopt face-sharing octahedral connectivity. These findings establish a predictive framework for designing hexagonal perovskites, highlighting sulfides as promising candidates for obtaining quasi-one-dimensional materials having transition-metal cations for novel ferroic phenomena.

💡 Research Summary

This paper addresses the scarcity of face‑sharing hexagonal perovskites (ABX₃, X = O, S) by establishing quantitative design rules that predict when the face‑sharing octahedral connectivity will be thermodynamically favored over the conventional corner‑sharing cubic perovskite. The authors begin by highlighting the limitations of the classic Goldschmidt tolerance factor (τ) for distinguishing structural motifs, especially in sulfides where the electronegativity difference between cations and anions dramatically alters bond lengths. To overcome this, they introduce two key modifications: (1) updated Shannon ionic radii specifically calibrated for sulfur‑based environments, and (2) an electronegativity‑corrected tolerance factor τ⁺ (denoted τ*), which scales the cation‑anion bond length by the relative electronegativity difference Δχ with respect to oxygen. For oxides τ* reduces to the traditional τ, while for sulfides τ* typically falls between 1 and 2 for realistic compositions.

Using these descriptors, the authors systematically generate a chemical space comprising 790 hypothetical AB O₃ and 790 AB S₃ compositions, selecting A‑site cations (alkali, alkaline‑earth, post‑transition, rare‑earth) and B‑site cations (transition metals, selected post‑transition and rare‑earth elements). They restrict the search to τ* > 1, where face‑sharing polytypes (2H, 4H, 6H) become plausible, and for sulfides also include the edge‑sharing “needle‑like” chain structure. Density‑functional theory (DFT) calculations are performed with VASP (PAW‑PBE, 520 eV cutoff, Γ‑centered k‑mesh) to fully relax each candidate in all considered polymorphs, followed by magnetic ordering tests for spin‑active compounds. Formation energies are compared against competing phases using Materials Project hull analyses to obtain ΔE_hull values, providing a thermodynamic stability metric.

The results are organized by charge families: A³⁺B³⁺X₃, A²⁺B⁴⁺X₃, and A¹⁺B⁵⁺X₃. For the A³⁺B³⁺X₃ family, small A‑site radii (0.82–1.38 Å) keep τ* below the face‑sharing threshold, leading to orthorhombic or hexagonal manganite structures rather than face‑sharing chains, both for oxides and sulfides. In contrast, the A²⁺B⁴⁺X₃ family exhibits larger A‑site radii that push τ* into the 1.05–1.15 window. Phase maps in τ*–R_A space reveal a sharp boundary separating corner‑sharing cubic/orthorhombic phases from face‑sharing hexagonal phases at τ*≈1.05 for oxides and τ*≈1.07 for sulfides. Notably, sulfides display a broader τ* distribution due to the Δχ correction, and the increased covalency of TM–S bonds expands the compositional flexibility, allowing many more candidates to satisfy the face‑sharing criterion.

From the DFT screening, the authors identify 29 previously unreported AB O₃ and AB S₃ compositions that lie on or very close to the convex hull and fall within the face‑sharing stability region. Many of these sulfide candidates have not been synthesized before, suggesting a rich, untapped landscape for quasi‑one‑dimensional materials. The paper discusses how the shortened B–B distances in face‑sharing chains can foster strong electron‑phonon coupling, charge‑density‑wave tendencies, and geometric magnetic frustration, potentially giving rise to spin‑liquid behavior, colossal birefringence, and chiral multiferroicity—phenomena already observed in a few known hexagonal perovskites such as BaTiS₃.

In conclusion, the study provides a unified, electronegativity‑aware tolerance factor τ* combined with A‑site ionic radius as a robust predictor for face‑sharing hexagonal perovskite formation. It demonstrates that sulfides, owing to their more covalent bonding and larger τ* window, are especially promising for discovering new functional materials. The authors propose that this design framework can guide experimental synthesis and further computational exploration aimed at exploiting the unique electronic, optical, and magnetic properties of face‑sharing perovskites for next‑generation devices.