A comparison of explainable artificial intelligence methods in the phase classification of multi-principal element alloys.

We demonstrate the capabilities of two model-agnostic local post-hoc model interpretability methods, namely breakDown (BD) and shapley (SHAP), to explain the predictions of a black-box classification learning model that establishes a quantitative relationship between chemical composition and multi-principal element alloys (MPEA) phase formation. We trained an ensemble of support vector machines using a dataset with 1,821 instances, 12 features with low pair-wise correlation, and seven phase labels. Feature contributions to the model prediction are computed by BD and SHAP for each composition. The resulting BD and SHAP transformed data are then used as inputs to identify similar composition groups using k-means clustering. Explanation-of-clusters by features reveal that the results from SHAP agree more closely with the literature. Visualization of compositions within a cluster using Ceteris-Paribus (CP) profile plots show the functional dependencies between the feature values and predicted response. Despite the differences between BD and SHAP in variable attribution, only minor changes were observed in the CP profile plots. Explanation-of-clusters by examples show that the clusters that share a common phase label contain similar compositions, which clarifies the similar-looking CP profile trends. Two plausible reasons are identified to describe this observation: (1) In the limits of a dataset with independent and non-interacting features, BD and SHAP show promise in recognizing MPEA composition clusters with similar phase labels. (2) There is more than one explanation for the MPEA phase formation rules with respect to the set of features considered in this work.

Accelerated HKUST-1 Thin-Film Property Optimization Using Active Learning.

A flow-coating method termed solution shearing has been shown to grow large-area thin films with no void spaces. Attaining full coverage is one of the key prerequisites for the adoption of any metal-organic framework (MOF) thin film for a variety of practical applications, including separation, membranes and sensors. However, the solution-shearing process has multiple discrete and continuous parameters that can be varied, including the metal ion and linker concentrations, solvents, substrate temperature, coating speed, and the number of coating passes. Optimization of these parameters for full coverage is a time-consuming and daunting process due to vast parameter space. Here, we incorporate an active learning approach into the solution-sheared HKUST-1 thin-film-processing parameters to control the coverage and extend the approach to gain control over the thickness. The understanding of high-quality MOF thin-film formation using solution shearing is improved by correlating the processing parameter sets and their corresponding film coverage. A large area and fully covered HKUST-1 thin film with a minimized thickness of 2.2 µm is fabricated by using guidance from active learning. To confirm full coverage, a redox-active molecule, called 7,7,8,8-tetracyanoquinodimethane (TCNQ), is incorporated along with the HKUST-1 thin film. The TCNQ@HKUST-1 thin film with a minimized thickness has the same order of magnitude of electrical conductivity as that of the TCNQ@HKUST-1 thin film created previously while reducing the film thickness by 60%. We show that active learning has the potential to rapidly navigate the vast processing space in multicomponent systems, especially when experiments are expensive and traditional computational models are not readily available for process optimization.

Machine-Learning-Enabled Prediction of Adiabatic Temperature Change in Lead-Free BaTiO3-Based Electrocaloric Ceramics.

In this paper, we develop a data-driven machine learning (ML) approach to predict the adiabatic temperature change (ΔT) in BaTiO3-based ceramics as a function of chemical composition, temperature, and applied electric field. The data set was curated from a survey of published electrocaloric measurements. Each chemical composition was represented by elemental descriptors of A-site and B-site elements. Pair-wise statistical correlation analysis was used to remove linearly correlated descriptors. We trained two separate regression-based ML models for indirect and direct measurements and found that both are capable of capturing the general trend of the temperature vs ΔT curve for various applied electric fields. We then complemented the regression models with a classification learning model that predicts the expected phase as a function of chemical composition and temperature. The combined regression and classification learning ML models predict a global maxima in ΔT near rhombohedral to cubic or tetragonal to cubic phase transition regions. An interactive, open source web application is developed to enable interested users to query our trained models and accelerate the design of novel BaTiO3-based ceramics with targeted phase and ΔT properties for electrocaloric applications.

Chemical gradients in human enamel crystallites.

Dental enamel is a principal component of teeth1, and has evolved to bear large chewing forces, resist mechanical fatigue and withstand wear over decades2. Functional impairment and loss of dental enamel, caused by developmental defects or tooth decay (caries), affect health and quality of life, with associated costs to society3. Although the past decade has seen progress in our understanding of enamel formation (amelogenesis) and the functional properties of mature enamel, attempts to repair lesions in this material or to synthesize it in vitro have had limited success4-6. This is partly due to the highly hierarchical structure of enamel and additional complexities arising from chemical gradients7-9. Here we show, using atomic-scale quantitative imaging and correlative spectroscopies, that the nanoscale crystallites of hydroxylapatite (Ca5(PO4)3(OH)), which are the fundamental building blocks of enamel, comprise two nanometric layers enriched in magnesium flanking a core rich in sodium, fluoride and carbonate ions; this sandwich core is surrounded by a shell with lower concentration of substitutional defects. A mechanical model based on density functional theory calculations and X-ray diffraction data predicts that residual stresses arise because of the chemical gradients, in agreement with preferential dissolution of the crystallite core in acidic media. Furthermore, stresses may affect the mechanical resilience of enamel. The two additional layers of hierarchy suggest a possible new model for biological control over crystal growth during amelogenesis, and hint at implications for the preservation of biomarkers during tooth development.

Publisher Correction: Chemical gradients in human enamel crystallites.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Conductivitylike Gilbert Damping due to Intraband Scattering in Epitaxial Iron.

Confirming the origin of Gilbert damping by experiment has remained a challenge for many decades, even for simple ferromagnetic metals. Here, we experimentally identify Gilbert damping that increases with decreasing electronic scattering in epitaxial thin films of pure Fe. This observation of conductivitylike damping, which cannot be accounted for by classical eddy-current loss, is in excellent quantitative agreement with theoretical predictions of Gilbert damping due to intraband scattering. Our results resolve the long-standing question about a fundamental damping mechanism and offer hints for engineering low-loss magnetic metals for cryogenic spintronics and quantum devices.

Experimental search for high-temperature ferroelectric perovskites guided by two-step machine learning.

Experimental search for high-temperature ferroelectric perovskites is a challenging task due to the vast chemical space and lack of predictive guidelines. Here, we demonstrate a two-step machine learning approach to guide experiments in search of xBi[Formula: see text]O3-(1 - x)PbTiO3-based perovskites with high ferroelectric Curie temperature. These involve classification learning to screen for compositions in the perovskite structures, and regression coupled to active learning to identify promising perovskites for synthesis and feedback. The problem is challenging because the search space is vast, spanning ~61,500 compositions and only 167 are experimentally studied. Furthermore, not every composition can be synthesized in the perovskite phase. In this work, we predict x, y, Me', and Me″ such that the resulting compositions have both high Curie temperature and form in the perovskite structure. Outcomes from both successful and failed experiments then iteratively refine the machine learning models via an active learning loop. Our approach finds six perovskites out of ten compositions synthesized, including three previously unexplored {Me'Me″} pairs, with 0.2Bi(Fe0.12Co0.88)O3-0.8PbTiO3 showing the highest measured Curie temperature of 898 K among them.

Multi-objective Optimization for Materials Discovery via Adaptive Design.

Guiding experiments to find materials with targeted properties is a crucial aspect of materials discovery and design, and typically multiple properties, which often compete, are involved. In the case of two properties, new compounds are sought that will provide improvement to existing data points lying on the Pareto front (PF) in as few experiments or calculations as possible. Here we address this problem by using the concept and methods of optimal learning to determine their suitability and performance on three materials data sets; an experimental data set of over 100 shape memory alloys, a data set of 223 M2AX phases obtained from density functional theory calculations, and a computational data set of 704 piezoelectric compounds. We show that the Maximin and Centroid design strategies, based on value of information criteria, are more efficient in determining points on the PF from the data than random selection, pure exploitation of the surrogate model prediction or pure exploration by maximum uncertainty from the learning model. Although the datasets varied in size and source, the Maximin algorithm showed superior performance across all the data sets, particularly when the accuracy of the machine learning model fits were not high, emphasizing that the design appears to be quite forgiving of relatively poor surrogate models.

Accelerated Discovery of Large Electrostrains in BaTiO3 -Based Piezoelectrics Using Active Learning.

A key challenge in guiding experiments toward materials with desired properties is to effectively navigate the vast search space comprising the chemistry and structure of allowed compounds. Here, it is shown how the use of machine learning coupled to optimization methods can accelerate the discovery of new Pb-free BaTiO3 (BTO-) based piezoelectrics with large electrostrains. By experimentally comparing several design strategies, it is shown that the approach balancing the trade-off between exploration (using uncertainties) and exploitation (using only model predictions) gives the optimal criterion leading to the synthesis of the piezoelectric (Ba0.84 Ca0.16 )(Ti0.90 Zr0.07 Sn0.03 )O3 with the largest electrostrain of 0.23% in the BTO family. Using Landau theory and insights from density functional theory, it is uncovered that the observed large electrostrain is due to the presence of Sn, which allows for the ease of switching of tetragonal domains under an electric field.

Predicting displacements of octahedral cations in ferroelectric perovskites using machine learning.

In ferroelectric perovskites, displacements of cations from the high-symmetry lattice positions in the paraelectric phase break the spatial inversion symmetry. Furthermore, the relative magnitude of ionic displacements correlate strongly with ferroelectric properties such as the Curie temperature. As a result, there is interest in predicting the relative displacements of cations prior to experiments. Here, machine learning is used to predict the average displacement of octahedral cations from its high-symmetry position in ferroelectric perovskites. Published octahedral cation displacements data from density functional theory (DFT) calculations are used to train machine learning models, where each cation is represented by features such as Pauling electronegativity, Martynov-Batsanov electronegativity and the ratio of valence electron number to nominal charge. Average displacements for ten new octahedral cations for which DFT data do not exist are predicted. Predictions are validated by comparing them with new DFT calculations and existing experimental data. The outcome of this work has implications in the design and discovery of novel ferroelectric perovskites.

Learning from data to design functional materials without inversion symmetry.

Accelerating the search for functional materials is a challenging problem. Here we develop an informatics-guided ab initio approach to accelerate the design and discovery of noncentrosymmetric materials. The workflow integrates group theory, informatics and density-functional theory to uncover design guidelines for predicting noncentrosymmetric compounds, which we apply to layered Ruddlesden-Popper oxides. Group theory identifies how configurations of oxygen octahedral rotation patterns, ordered cation arrangements and their interplay break inversion symmetry, while informatics tools learn from available data to select candidate compositions that fulfil the group-theoretical postulates. Our key outcome is the identification of 242 compositions after screening ∼3,200 that show potential for noncentrosymmetric structures, a 25-fold increase in the projected number of known noncentrosymmetric Ruddlesden-Popper oxides. We validate our predictions for 19 compounds using phonon calculations, among which 17 have noncentrosymmetric ground states including two potential multiferroics. Our approach enables rational design of materials with targeted crystal symmetries and functionalities.

Accelerated search for BaTiO3-based piezoelectrics with vertical morphotropic phase boundary using Bayesian learning.

An outstanding challenge in the nascent field of materials informatics is to incorporate materials knowledge in a robust Bayesian approach to guide the discovery of new materials. Utilizing inputs from known phase diagrams, features or material descriptors that are known to affect the ferroelectric response, and Landau-Devonshire theory, we demonstrate our approach for BaTiO3-based piezoelectrics with the desired target of a vertical morphotropic phase boundary. We predict, synthesize, and characterize a solid solution, (Ba0.5Ca0.5)TiO3-Ba(Ti0.7Zr0.3)O3, with piezoelectric properties that show better temperature reliability than other BaTiO3-based piezoelectrics in our initial training data.

Accelerated search for materials with targeted properties by adaptive design.

Finding new materials with targeted properties has traditionally been guided by intuition, and trial and error. With increasing chemical complexity, the combinatorial possibilities are too large for an Edisonian approach to be practical. Here we show how an adaptive design strategy, tightly coupled with experiments, can accelerate the discovery process by sequentially identifying the next experiments or calculations, to effectively navigate the complex search space. Our strategy uses inference and global optimization to balance the trade-off between exploitation and exploration of the search space. We demonstrate this by finding very low thermal hysteresis (ΔT) NiTi-based shape memory alloys, with Ti50.0Ni46.7Cu0.8Fe2.3Pd0.2 possessing the smallest ΔT (1.84 K). We synthesize and characterize 36 predicted compositions (9 feedback loops) from a potential space of ∼800,000 compositions. Of these, 14 had smaller ΔT than any of the 22 in the original data set.

Adaptive Strategies for Materials Design using Uncertainties.

We compare several adaptive design strategies using a data set of 223 M2AX family of compounds for which the elastic properties [bulk (B), shear (G), and Young's (E) modulus] have been computed using density functional theory. The design strategies are decomposed into an iterative loop with two main steps: machine learning is used to train a regressor that predicts elastic properties in terms of elementary orbital radii of the individual components of the materials; and a selector uses these predictions and their uncertainties to choose the next material to investigate. The ultimate goal is to obtain a material with desired elastic properties in as few iterations as possible. We examine how the choice of data set size, regressor and selector impact the design. We find that selectors that use information about the prediction uncertainty outperform those that don't. Our work is a step in illustrating how adaptive design tools can guide the search for new materials with desired properties.

Materials Prediction via Classification Learning.

In the paradigm of materials informatics for accelerated materials discovery, the choice of feature set (i.e. attributes that capture aspects of structure, chemistry and/or bonding) is critical. Ideally, the feature sets should provide a simple physical basis for extracting major structural and chemical trends and furthermore, enable rapid predictions of new material chemistries. Orbital radii calculated from model pseudopotential fits to spectroscopic data are potential candidates to satisfy these conditions. Although these radii (and their linear combinations) have been utilized in the past, their functional forms are largely justified with heuristic arguments. Here we show that machine learning methods naturally uncover the functional forms that mimic most frequently used features in the literature, thereby providing a mathematical basis for feature set construction without a priori assumptions. We apply these principles to study two broad materials classes: (i) wide band gap AB compounds and (ii) rare earth-main group RM intermetallics. The AB compounds serve as a prototypical example to demonstrate our approach, whereas the RM intermetallics show how these concepts can be used to rapidly design new ductile materials. Our predictive models indicate that ScCo, ScIr, and YCd should be ductile, whereas each was previously proposed to be brittle.

Polarization screening-induced magnetic phase gradients at complex oxide interfaces.

Thin-film oxide heterostructures show great potential for use in spintronic memories, where electronic charge and spin are coupled to transport information. Here we use a La0.7Sr0.3MnO3 (LSMO)/PbZr0.2Ti0.8O3 (PZT) model system to explore how local variations in electronic and magnetic phases mediate this coupling. We present direct, local measurements of valence, ferroelectric polarization and magnetization, from which we map the phases at the LSMO/PZT interface. We combine these experimental results with electronic structure calculations to elucidate the microscopic interactions governing the interfacial response of this system. We observe a magnetic asymmetry at the LSMO/PZT interface that depends on the local PZT polarization and gives rise to gradients in local magnetic moments; this is associated with a metal-insulator transition at the interface, which results in significantly different charge-transfer screening lengths. This study establishes a framework to understand the fundamental asymmetries of magnetoelectric coupling in oxide heterostructures.

Massive band gap variation in layered oxides through cation ordering.

The electronic band gap is a fundamental material parameter requiring control for light harvesting, conversion and transport technologies, including photovoltaics, lasers and sensors. Although traditional methods to tune band gaps rely on chemical alloying, quantum size effects, lattice mismatch or superlattice formation, the spectral variation is often limited to <1 eV, unless marked changes to composition or structure occur. Here we report large band gap changes of up to 200% or ~2 eV without modifying chemical composition or use of epitaxial strain in the LaSrAlO4 Ruddlesden-Popper oxide. First-principles calculations show that ordering electrically charged [LaO](1+) and neutral [SrO](0) monoxide planes imposes internal electric fields in the layered oxides. These fields drive local atomic displacements and bond distortions that control the energy levels at the valence and conduction band edges, providing a path towards electronic structure engineering in complex oxides.

Electronically driven structural transitions in A10(PO4)6F2 apatites (A = Ca, Sr, Pb, Cd and Hg).

It is shown that there is a dynamic lattice instability in the aristotype P63/m structure of A10(PO4)6F2 apatites containing divalent A-site Cd or Hg cations with (n - 1)d(10)ns(0) electronic configurations. The distortion to a low-symmetry P\bar{1} triclinic structure is driven by an electronic mechanism rather than from ionic size mismatch. Our theoretical work provides key insights into the role of the electronic configurations of A cations in fluorapatites.

Thickness-dependent crossover from charge- to strain-mediated magnetoelectric coupling in ferromagnetic/piezoelectric oxide heterostructures.

Magnetoelectric oxide heterostructures are proposed active layers for spintronic memory and logic devices, where information is conveyed through spin transport in the solid state. Incomplete theories of the coupling between local strain, charge, and magnetic order have limited their deployment into new information and communication technologies. In this study, we report direct, local measurements of strain- and charge-mediated magnetization changes in the La0.7Sr0.3MnO3/PbZr0.2Ti0.8O3 system using spatially resolved characterization techniques in both real and reciprocal space. Polarized neutron reflectometry reveals a graded magnetization that results from both local structural distortions and interfacial screening of bound surface charge from the adjacent ferroelectric. Density functional theory calculations support the experimental observation that strain locally suppresses the magnetization through a change in the Mn-eg orbital polarization. We suggest that this local coupling and magnetization suppression may be tuned by controlling the manganite and ferroelectric layer thicknesses, with direct implications for device applications.

Crystal-chemistry guidelines for noncentrosymmetric A2BO4 Ruddlesden-Popper oxides.

Noncentrosymmetric (NCS) phases are seldom seen in layered A2BO4 Ruddlesden-Popper (214 RP) oxides. In this work, we uncover the underlying crystallographic symmetry restrictions that enforce the spatial parity operation of inversion and then subsequently show how to lift them to achieve NCS structures. Simple octahedral distortions alone, while impacting the electronic and magnetic properties, are insufficient. We show using group theory that the condensation of two distortion modes, which describe suitable symmetry unique octahedral distortions or a combination of a single octahedral distortion with a "compositional" A or B cation ordering mode, is able to transform the centrosymmetric aristotype into a NCS structure. With these symmetry guidelines, we formulate a data-driven model founded on Bayesian inference that allows us to rationally search for combinations of A- and B-site elements satisfying the inversion symmetry lifting criterion. We describe the general methodology and apply it to 214 iridates with A(2+) cations, identifying RP-structured Ca2IrO4 as a potential NCS oxide, which we evaluate with density functional theory. We find a strong energetic competition between two closely related polar and nonpolar low-energy crystal structures in Ca2IrO4 and suggest pathways to stabilize the NCS structure.