New Tolerance Factor to Predict the Stability of Perovskite Oxides and Halides (1801.07700v2)

Abstract: Predicting the stability of the perovskite structure remains a longstanding challenge for the discovery of new functional materials for many applications including photovoltaics and electrocatalysts. We developed an accurate, physically interpretable, and one-dimensional tolerance factor, {\tau}, that correctly predicts 92% of compounds as perovskite or nonperovskite for an experimental dataset of 576 $ABX_3$ materials ($\textit{X} =$ $O^{2-}$, $F^-$, $Cl^-$, $Br^-$, $I^-$) using a novel data analytics approach based on SISSO (sure independence screening and sparsifying operator). {\tau} is shown to generalize outside the training set for 1,034 experimentally realized single and double perovskites (91% accuracy) and is applied to identify 23,314 new double perovskites ($A_2$$\textit{BB'}$$X_6$) ranked by their probability of being stable as perovskite. This work guides experimentalists and theorists towards which perovskites are most likely to be successfully synthesized and demonstrates an approach to descriptor identification that can be extended to arbitrary applications beyond perovskite stability predictions.

• The paper presents a novel tolerance factor τ that boosts prediction accuracy from 74% to 92% compared to traditional methods.
• It employs a SISSO-based, data-driven methodology that uses ionic radii and oxidation states to derive τ as a one-dimensional descriptor.
• The factor τ shows robust performance across diverse perovskite materials, enabling accelerated discoveries in photovoltaics and catalysis.

A New Tolerance Factor for Predicting Perovskite Stability

The paper introduces a novel tolerance factor, $\tau$, specifically designed for predicting the stability of perovskite structures across various ionic compounds, including oxides and halides. The conventional approach, using the Goldschmidt tolerance factor, $t$, has limitations in predictive accuracy, particularly for certain halides. The new tolerance factor, $\tau$, significantly improves upon these limitations by offering a higher classification accuracy across a diverse set of perovskite materials.

Methodology and Results

The authors deploy a data-driven methodology utilizing the Sure Independence Screening and Sparsifying Operator (SISSO) to derive the new tolerance factor, $\tau$. This approach emphasizes the usage of physically meaningful parameters such as ionic radii and oxidation states, encapsulated in a one-dimensional form. The $\tau$ factor is described by the equation:

$$\tau = \frac{r_X}{r_B} - n_A \times \left(n_A - \frac{r_A}{r_B} \ln \frac{r_A}{r_B} \right)$$

where $r$ represents ionic radii and $n$ oxidation states. By using a set of 576 experimentally characterized compounds, the paper reports a prediction accuracy of 92% with $\tau$, compared to the 74% accuracy achieved with $t$.

The systematic assessment of $\tau$ revealed uniform classification performance across different anions, with accuracy rates slightly varying between 90% (chlorides) and 94% (test set compounds). This indicates the robustness of the $\tau$ factor in capturing the stability characteristics of perovskites.

Implications and Future Directions

The implications of this paper are multifaceted. The new $\tau$ factor is computationally efficient, requiring only simple data inputs regarding ionic radii and oxidation states, making it well-suited for high-throughput screening processes. Additionally, its performance is corroborated against density functional theory (DFT) results, exhibiting a strong correlation with computed decomposition enthalpies ($\Delta H_d$). However, there are a few notable discrepancies in stability predictions when using cubic structures in DFT, highlighting an inherent limitation of structure-specific predictions that the $\tau$ factor surpasses.

From a theoretical perspective, the $\tau$ factor sets a precedent for the synthesis of more predictive descriptors in materials science that balance computational efficiency with physical interpretability. This work suggests such approaches could be extended to other material families and nonperovskite structures using similar methodologies, potentially facilitating accelerated materials discovery.

Practically, this advancement holds promise for the discovery of new perovskite materials, with applications in photovoltaics, electrocatalysis, and beyond. The identification of 23,314 candidate stable double perovskites underscores vast potential for uncovering novel compounds with desirable properties.

Conclusion

The redefined tolerance factor $\tau$ marks a significant step forward in the prediction of perovskite stability. By leveraging modern data analytics in conjunction with empirical data, this paper effectively refines a century-old metric, enhancing its prediction accuracy and applicability. Future work could potentially refine such tolerance factors further or apply analogous techniques to other complex materials, retaining focus on both simplicity and deep physical insights.