Breaking the Aristotype: Featurization of Polyhedral Distortions in Perovskite Crystals

Abstract

While traditional crystallographic representations of structure play an important role in materials science, they are unsuitable for efficient machine learning. A range of effective numerical descriptors have been developed for molecular and crystal structures.We are interested in a special case, where distortions emerge relative to an ideal highsymmetry parent structure. We demonstrate that irreducible representations form an efficient basis for the featurisation of polyhedral deformations with respect to such an aristotype. Applied to a dataset of 552 octahedra in ABO 3 perovskite-type materials, we use unsupervised machine learning with irreducible representation descriptors to identify four distinct classes of behaviour, associated with predominately corner, edge, face, and mixed connectivity between neighbouring octahedral units. Through this analysis, we identify SrCrO 3 as a material with tuneable multiferroic behaviour. We further show, through supervised machine learning, that thermally activated structural distortions of CsPbI 3 are well described by this approach.

Insights into Cation Ordering of Double Perovskite Oxides from Machine Learning and Causal Relations

“…In the community of materials science with a focus on ML, double perovskites have gained much attention in recent years. Several reports − exist on combinatorial and systematic searches conducted over a wide compositional space throughout the periodic table to judiciously shortlist formable perovskites of different forms such as ABO 3 , A 2 BB′O 6 , AA′B 2 O 6 , AA′BB′O 6 , and ABX 3 with energy-related applications, including solar cells and photovoltaics. , The design capabilities of thermodynamic stability, formation energy, and synthesizability are explored using high-throughput screening and first-principles computations combined with various ML algorithms . Out of different electronic properties, bandgap and its tuneability have been the key functionalities of interest because of their direct relationships to applications mentioned above. − Our study of cation ordering falls right in this regime, where we are interested in formation of cation ordering driving functionalities such as switchable polarization and magnetization in AA′BB′O 6 , by comparing energies between different A-site ordering arrangements.…”

Physics-Guided Descriptors for Prediction of Structural Polymorphs

“…On the basis of this analysis, the X 5 − mode along ab is the most important feature, and as expected, the Γ 4 − modes are also significant. However, surprisingly, modes corresponding to 40-atom supercells, such as T 2 (24) or Δ 5 − (24), are also crucial for the model to predict the energy of various structures, demonstrating the importance of including these less often discussed modes. We further evaluate the extrapolative power of our model by removing all the structures that contain only one distortion mode (1922 points) from the training set before predicting their energies.…”

“… 8 , 22 , 23 More recently, polyhedral distortions have been used as descriptors to explain trends in behaviors across perovskites. 24 …”

“…8,22,23 More recently, polyhedral distortions have been used as descriptors to explain trends in behaviors across perovskites. 24 In this work, we explore the idea of using the distortion modes as descriptors in ML. Our method utilizes distortion modes to explore the Born−Oppenheimer potential energy surface (PES) and identify local minima corresponding to metastable phases (polymorphs).…”

“…A natural approach to representing a crystal structure is to use the concept of irreducible representations (irreps), in which the distortions from a higher symmetry reference structure are decomposed into a set of normal modes that describe the transformation of the reference structure into the considered one. , This approach has been used to understand and explain various phenomena such as thermopower anisotropy, negative thermal expansion, proper and improper ferroelectricity, and antiferroelectricity. − Furthermore, in the context of phase transitions in transition-metal compounds, the distortion modes have been used as features in statistical analysis of the correlation between distortions and functionalities. ,, More recently, polyhedral distortions have been used as descriptors to explain trends in behaviors across perovskites …”