🔬 materials science

Design Rules and Discovery of Face-Sharing Hexagonal Perovskites

This paper establishes quantitative design rules based on electronegativity-corrected tolerance factors and cation radii to predict and stabilize face-sharing hexagonal perovskites, revealing that sulfides offer greater compositional flexibility than oxides for creating novel quasi-one-dimensional materials.

Original authors: M. J. Swamynadhan, Gwan Yeong Jung, Pravan Omprakash, Rohan Mishra

Published 2026-02-09

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CC BY 4.0

Original authors: M. J. Swamynadhan, Gwan Yeong Jung, Pravan Omprakash, Rohan Mishra

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a world built out of tiny, interlocking LEGO bricks. In the world of chemistry, these bricks are atoms, and the way they snap together determines the properties of the material—whether it conducts electricity, glows, or acts like a magnet.

For decades, scientists have been obsessed with a specific shape called a perovskite. Think of this as a standard, perfect cube made of these atomic bricks. In this "cubic" world, the bricks usually touch only at their corners, like a neat, open grid. This is the most common way these materials are built.

However, there is a rare, exotic cousin to this cubic structure called the hexagonal perovskite. In this version, the atomic bricks don't just touch at the corners; they smash their flat faces directly against each other, forming tight, face-to-face chains. It's like stacking coins perfectly on top of one another versus arranging them in a scattered grid. This "face-sharing" arrangement creates unique superpowers, like strange magnetic behaviors or the ability to twist light in unusual ways.

The Problem: Finding the Right Recipe
The problem is that these face-sharing structures are incredibly rare and hard to find. It's like trying to bake a specific type of cake that only rises if you use exactly the right amount of flour and sugar, but you don't know the recipe. Scientists have a rough idea called the "tolerance factor" (a mathematical formula based on the size of the atoms), but it works well for the common corner-sharing cubes and fails miserably when trying to predict these rare face-sharing hexagons.

The Discovery: A New Rulebook
In this paper, the researchers acted like master architects who finally cracked the code. They didn't just look at the sizes of the atoms; they looked at how "sticky" the atoms are to each other (a property called covalency).

They discovered that the rules are different depending on whether the material is an oxide (containing oxygen) or a sulfide (containing sulfur).

The Oxygen Team (Oxides): These are picky. To build a face-sharing hexagonal tower, you need very large "A-site" atoms (the big bricks holding the structure together) and specific charge combinations. If the atoms are too small or the charges are wrong, the structure collapses back into the common corner-sharing cube.
The Sulfur Team (Sulfides): These are much more flexible. Because sulfur atoms form "stickier," more covalent bonds, they can handle more variation. The researchers found that sulfur allows for a much wider range of sizes and charges to still form those rare face-sharing chains. It's like sulfur is a more forgiving glue that lets you build the exotic shape even when the ingredients aren't perfect.

The Solution: Tuning the Dial
The authors created a new "design rulebook." They mapped out a specific zone on a graph where these face-sharing structures are stable.

For Oxides: You need big atoms and a specific ratio.
For Sulfides: You have a bigger playground. If you have a mix of atoms that doesn't quite fit the face-sharing shape, you can "tune" it. Imagine mixing two different types of sand to get the perfect grain size. By mixing different elements (like swapping Hafnium for Germanium in a sulfur compound), they can dial the structure into the perfect "face-sharing" zone.

The Results: A Treasure Map
Using these new rules, the researchers didn't just explain the past; they predicted the future. They identified 29 new chemical compounds (a mix of oxides and sulfides) that they are confident will form these rare face-sharing hexagonal structures.

They compared their predictions to what is already known in the lab and found they were spot on for many existing materials. They also pointed out that while some materials should be face-sharing based on their rules, they might not show up that way in a lab yet because of how they were made (like the pressure or temperature used during cooking).

Why It Matters
The paper concludes that these face-sharing materials are special because they create "one-dimensional" chains of atoms. This is like having a highway for electrons instead of a parking lot. This structure could lead to new types of magnets, materials that change shape with electricity, or optical devices that manipulate light in new ways.

In short, the authors have moved from guessing to knowing. They have provided a clear, quantitative map for scientists to stop searching blindly and start building these exotic, face-sharing atomic structures on purpose.

Technical Summary: Design Rules and Discovery of Face-Sharing Hexagonal Perovskites

Problem Statement
Hexagonal perovskites with face-sharing octahedral connectivity represent an underexplored class of materials with unique electronic, magnetic, and optical properties, such as quasi-one-dimensional electronic pockets, geometric frustration, and chiral multiferroicity. Despite their functional potential, these materials remain scarce; the Inorganic Crystal Structure Database (ICSD) contains only 78 face-sharing $ABO_3$ and 10 $ABS_3$ compounds, compared to thousands of corner-sharing variants. Existing design tools, specifically the Goldschmidt tolerance factor ( $\tau$ ) and A-site cation radius ( $R_A$ ), are effective for screening corner-sharing oxide perovskites but fail to distinguish hexagonal face-sharing phases from competing cubic or orthorhombic polymorphs. Furthermore, these descriptors do not adequately capture the stability trends in sulfides, where increased covalency alters bonding environments. There is a critical need for quantitative design principles that can predict and stabilize face-sharing hexagonal $ABX_3$ structures across both oxide and sulfide chemistries.

Methodology
The authors employed a high-throughput computational approach combining Density Functional Theory (DFT) with materials informatics to establish design rules:

Dataset Generation: A systematic chemical space of 790 hypothetical $ABO_3$ and 790 $ABS_3$ compositions was generated by combining elements with specific oxidation states ( $A^{1+}B^{5+}$ , $A^{2+}B^{4+}$ , $A^{3+}B^{3+}$ ).
Descriptor Refinement: To address the limitations of the classical tolerance factor in sulfides, the study utilized an electronegativity-corrected tolerance factor ( $\tau^*$ ). This metric scales cation-anion bond lengths based on the relative electronegativity difference ( $\Delta\chi$ ) compared to oxygen, alongside updated Shannon ionic radii specific to sulfur environments.
DFT Calculations: Using the Vienna Ab initio Simulation Package (VASP), the formation energies of approximately 134 oxides and 323 sulfides were calculated. The study compared the energetics of four representative polymorphs: corner-sharing cubic/orthorhombic, face-sharing 2H, 4H, and 6H stackings, and edge-sharing "needle-like" phases.
Stability Analysis: The lowest-energy polymorphs were identified by comparing total energies and constructing energy-hull diagrams ( $\Delta E_{hull}$ ). For magnetic compounds, various spin configurations were evaluated to determine the magnetic ground state.
Physical Mechanism Investigation: To explain the divergence between oxides and sulfides, the authors calculated Coulombic forces between B-cations ( $F_{B-B}$ ) and analyzed Crystal Orbital Hamilton Population (ICOHP) values to quantify covalency and charge distribution.

Key Contributions and Results
The study successfully mapped the stability of face-sharing hexagonal phases within a phase space defined by $\tau^*$ and $R_A$ , leading to the following findings:

Distinct Stability Thresholds: The authors identified specific thresholds separating face-sharing hexagonal phases from corner-sharing cubic polymorphs:
- Oxides: Face-sharing stability requires $\tau^* > 1.04$ and $R_A \geq 1.4$ Å.
- Sulfides: Face-sharing stability requires $\tau^* > 1.07$ and $R_A \geq 1.7$ Å.
Oxidation State Selectivity: The study reveals a strong dependence on cation charge states. In oxides, only the $A^{2+}B^{4+}O_3$ family stabilizes face-sharing hexagonal structures; $A^{3+}B^{3+}O_3$ and $A^{1+}B^{5+}O_3$ families favor corner-sharing or edge-sharing motifs due to high electrostatic repulsion between highly charged B-cations in face-sharing geometries. In contrast, sulfides ( $A^{2+}B^{4+}S_3$ and $A^{1+}B^{5+}S_3$ ) readily stabilize face-sharing phases.
Role of Covalency: The preference for sulfides is attributed to the increased covalency of transition metal–sulfur (TM–S) bonds compared to TM–O bonds. This covalency reduces the effective charge on B-cations and increases B–B interionic distances, thereby mitigating the electrostatic repulsion that destabilizes face-sharing octahedra in oxides.
Tunability via Solid Solutions: The authors demonstrated that the broader range of $\tau^*$ values in sulfides allows for the stabilization of face-sharing phases through compositional tuning. As a proof of concept, the study predicted that solid solutions of $BaHf_{(1-x)}Ge_xS_3$ could be tuned into the face-sharing stability window ( $1.07 < \tau^* < 1.4$ ), even though the end members ( $BaHfS_3$ and $BaGeS_3$ ) adopt corner-sharing and edge-sharing structures, respectively.
New Predictions: Applying these rules, the authors predicted 29 new $ABO_3$ and $ABS_3$ compounds likely to adopt face-sharing hexagonal geometries. Many of these candidates, particularly sulfides like $CsVS_3$ , $RbVS_3$ , and $RbTaS_3$ , exhibit $\Delta E_{hull}$ values indicating thermodynamic formability.

Significance and Claims
The paper establishes a predictive framework for designing hexagonal perovskites, moving beyond the limitations of classical geometric descriptors. The authors claim that their derived design rules provide a quantitative method to expand the chemical space of face-sharing materials, highlighting sulfides as particularly promising candidates due to their structural flexibility and covalent bonding nature.

The significance of this work lies in its ability to guide the synthesis of materials with specific functional properties:

Ferroic Phenomena: Compounds with $d^0$ cations (e.g., $BaTiS_3$ analogs) are identified as potential candidates for novel ferroic phenomena, including coupled ferroelectricity and chirality.
Magnetic Interactions: Systems with partially filled $d$ shells are suggested as fertile ground for exploring exotic magnetic interactions and spin-liquid behaviors driven by geometric frustration.
Anisotropic Properties: The quasi-one-dimensional nature of the predicted face-sharing chains is noted as a source of highly anisotropic physical properties, such as optical birefringence and thermal transport.

The authors maintain a modest stance regarding the immediate synthesis of these materials, acknowledging that experimental realization depends on synthesis conditions (pressure, temperature, oxygen partial pressure) which may override thermodynamic preferences. However, they assert that the identified stability windows offer a robust starting point for the rational discovery of new quasi-one-dimensional materials.

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