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The Geometric Blueprint of Perovskites
Marina R. Filip, Feliciano Giustino
TL;DR
The paper asks how many and which perovskites remain undiscovered across a vast compositional landscape. It maps geometric formability using Goldschmidt’s no-rattling principle, inferential statistics, and web data extraction, finding roughly 80% predictive fidelity and nearly 100,000 apparently new compounds. The resulting library supports systematic exploration of possible perovskite compositions.
Problem
The study addresses which of 3,658,527 hypothetical compositions can form perovskite crystals, a scale too large for currently unscalable ab initio screening alone.
Method
The paper formalizes Goldschmidt’s no-rattling principle into geometric stability criteria, evaluates classification with inferential statistics, and checks predicted compounds through large-scale web data extraction.
Results
79.7±4.0% classification success was achieved for samples of at least 100 compounds at 95% confidence, and 94,232 candidate perovskites were predicted with an expected formation probability of 80%.
Takeaways & Limitations
The study provides a mathematically rigorous structure map and a library of almost 100,000 hitherto-unknown perovskites awaiting discovery.
Abstract
from arXiv · showhide
Perovskite minerals form an essential component of the Earth's mantle, and synthetic crystals are ubiquitous in electronics, photonics, and energy technology. The extraordinary chemical diversity of these crystals raises the question on how many and which perovskites are yet to be discovered. Here we show that the "no-rattling" principle postulated by Goldschmidt in 1926, describing the geometric conditions under which a perovskite can form, is much more effective than previously thought, and allows us to predict new perovskites with a fidelity of 80%. By supplementing this principle with inferential statistics and internet data mining we establish that currently known perovskites are only the tip of the iceberg, and we enumerate ninety thousand hitherto-unknown compounds awaiting to be studied. Our results suggest that geometric blueprints may enable the systematic screening of millions of compounds, and offer untapped opportunities in structure prediction and materials design.
I. INTRODUCTION
Perovskites are structurally related crystals with broad importance across Earth science, electronics, photonics, and energy technology. Their common network topology accommodates substantial chemical and structural variation.
- Perovskite crystals are widespread in nature and central to many areas of current research.Silicate perovskites are abundant Earth minerals, while synthetic oxide and halide perovskites support diverse technologies.
- Synthetic oxide perovskites serve as ferroelectrics, ferromagnets, multiferroics, superconductors, sensors, spin filters, conductors, and catalysts.
- Halide perovskites are promising for solar cells, light-emitting diodes, and lasers, while double perovskites function as scintillators for radiation detection.
- Cubic ABX3 perovskites contain A- and B-site cations and X anions, with BX6 octahedra forming a corner-sharing network occupied by A-site cations.
- All perovskites share this network topology but vary in octahedral tilting and distortion; the term also includes quaternary A2BB′X6 compounds.
RESULTS
A geometric model extending Goldschmidt’s no-rattling principle predicts perovskite formability across a broad chemical space. It classifies known compounds with about 80% accuracy and identifies tens of thousands of largely unreported candidate perovskites.
- Chemical landscape: 3,658,527 hypothetical compounds define the screened chemical space after considering combinations of ions with known ionic radii.The paper considers combinations of three cations and one anion, excluding elements without known ionic radii.
- Geometric model: The model extends tolerance and octahedral factors to include octahedral mismatch, producing a closed three-dimensional stability region for double perovskites.The generalized descriptors are average octahedral factor, tolerance factor, and octahedral mismatch.
- Prediction test: 2,291 ternary and quaternary compounds were used to evaluate whether the geometric inequalities distinguish perovskites from non-perovskites.The dataset contains 1,622 perovskites, 592 non-perovskites, and 77 compounds capable of adopting either structure.
- Prediction test: 79.7±4.0% classification accuracy was obtained for samples of at least 100 compounds at 95% confidence.Formability is estimated from the fraction of an uncertainty cuboid inside the perovskite region, with repeated sampling used to quantify statistical uncertainty.
- Predicted compounds: 94,232 new perovskites and double perovskites were predicted from all 3,658,527 quaternary combinations, with an expected formation probability of 80%.Internet searches found that fewer than 1%—786 of 94,232—were already known.
- Chemical landscape: Predicted compounds comprise 68% oxides, 16% halides, 12% chalcogenides, and 4% nitrides, while fewer than eighty nitride perovskites occur across the Periodic Table.The model’s applicability is limited because geometric formability does not include thermodynamic stability against decomposition.
CONCLUSION
The study validates Goldschmidt’s no-rattling principle quantitatively, using inferential statistics and large-scale web data extraction to map existing and future perovskites. It predicts perovskite stability with 80% fidelity and identifies almost one hundred thousand unknown compounds for further study.
- 80% fidelity: the geometric structure map predicts the stability of perovskites.The map formalizes Goldschmidt’s no-rattling hypothesis into mathematical criteria for perovskite design and discovery.
- Almost one hundred thousand hitherto-unknown perovskites were generated in a library awaiting discovery.The library is released as database S2.1 for future experimental and computational research.
- The stability range is represented as a volume in (¯µ, t, ∆µ) space for ternary and quaternary perovskites.Figure 2 distinguishes perovskites from non-perovskites using blue and red markers and slices of the stability volume.
- The predicted landscape combines density maps with crystallographic site preferences across ternary and quaternary perovskites.Database S2 contains 59 binary, 2834 ternary and 90,606 quaternary perovskites.
- For ternary oxides, the geometric model correctly classifies 354 of 383 experimentally observed compounds (92%).The figure compares the model with DFT/GGA calculations and experimental data.
SUPPLEMENTARY INFORMATION
The supplementary methods define geometric formability limits, assemble known-compound databases, screen hypothetical compositions, and validate predictions through classification and internet searches. The workflow identifies 93,447 predicted perovskites never previously reported while documenting pressure-related scope limitations.
- Databases: Known-compound databases comprise perovskites, non-perovskites, and compositions reported in both structural forms, with database S1.1 containing 1,622 distinct perovskites.The databases draw on ICSD records and published compilations, with duplicate removal and cross-checking of compositions.
- Geometric limits: The geometric model defines stability through extremal contacts among A-A*, A-B, A-X, and X-X* ions, alongside stretch, octahedral, tilt, and chemical limits.The construction assumes ideal corner-sharing BX6 octahedra and treats B-X contact as fixed while other contacts define bounds.
- Classification: Formability represents the fraction of each compound’s uncertainty cuboid inside the stability region, with fc = 0.34 yielding 79.7% accuracy for both perovskites and non-perovskites.The cuboid incorporates minima and maxima of generalized geometric descriptors calculated from available ionic radii.
- High-throughput screening: 3,658,527 hypothetical compositions are reduced by charge neutrality and Pauling’s valency rule to 1,131,737 structures, of which 94,232 pass the formability threshold as distinct predicted compounds.The final set excludes known perovskites and double perovskites already present in databases S1.1 and S1.3.
- Validation and novelty: The internet-search validation procedure has a 74% success rate on known compounds and identifies 93,447 predicted perovskites as never previously reported after manual review.Internet searches found 92,899 formulas without online presence; manual investigation classified 786 found compounds, including 555 perovskites, before removal.
- Scope boundary: The geometric analysis does not distinguish compounds synthesizable at ambient pressure from high-pressure phases, as illustrated by Fe2O3 perovskite predictions.The comparison notes a 12% unit-cell-volume change from 0 to 200 GPa and a 14% range in Fe3+ ionic radius across coordinations.