Accelerated search for BaTiO ₃ -based piezoelectrics with vertical morphotropic phase boundary using Bayesian learning

Abstract

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 BaTiO 3 -based piezoelectrics with the desired target of a vertical morphotropic phase boundary. We predict, synthesize, and characterize a solid solution, (Ba 0.5 Ca 0.5 )TiO 3 -Ba(Ti 0.7 Zr 0.3 )O 3 , with piezoelectric properties that show better temperature reliability than other BaTiO 3 -based piezoelectrics in our initial training data.piezoelectric materials | materials informatics | Bayesian learning | morphotropic phase boundary | Pb-free materials A ccelerating the process of materials design and discovery is an emerging theme in materials science (1). The emphasis has so far largely been on screening databases or using datadriven approaches that infer predictions directly from the data, be it from high-throughput calculations or experimental measurements (2-6). However, a distinguishing aspect of materials science is that in addition to data there exists a substantial body of knowledge in the form of phenomenological models and physical theories that could be used to constrain the inference models. Hence, a key challenge in materials informatics is to incorporate knowledge to make predictions that are more robust than would be possible by using data alone. Although such knowledge is used in choosing features or descriptors for materials informatics (7-9), it has seldom been used to encode prior information in the form of probability distributions and uncertainties for predicting novel materials with desired properties. Bayesian inference, which permits integration of prior knowledge or beliefs with the observed data, has shown considerable promise in cancer genomics (10) using metabolic pathway information, and in systems biology (11), but has been little explored in materials science. Our objective is to combine empirical data and materials knowledge within a Bayesian approach coupled to the results of Landau-Devonshire theory (12, 13) to design better BaTiO3-based lead-free piezoelectrics.Piezoelectric materials, such as the solid solutions of BaTiO3, are best suited for exploring Bayesian inference methods because historically they are well modeled by Landau-Devonshire theory (12-14) and equations exist for describing some of the key characteristics that determine the functional response, such as the morphotropic phase boundary (MPB) (15, 16). These equations serve as "constraints" that encode prior knowledge within our Bayesian formalism. Furthermore, BaTiO3-based solid solutions represent an important class of potential substitutes for Pb-based materials, which suffer from environmental concerns. Akin to the Pb-based piezoelectrics, MPBs can be established in BaTiO3-based solid solutions that enable polarization and structural inst...

A Critical Review of Machine Learning of Energy Materials

“…Subsequently, Xue et al have applied Bayesian learning framework with uncertainties estimation and took linear regression as surrogate model to guide the discovery of new BaTiO 3 ‐based materials with desirable temperature reliability (see Figure 16 ). The authors used the atomic, crystal, and electronic structure properties of the tetragonal and rhombohedral ends of composition‐temperature phase diagram as features and the change of composition dx along each MPB when temperature decreases by 100 K from room temperature (298 K) as the target.…”

“…Similarly, Yuan et al have used Bayesian learning to lead the synthesis of the piezoelectric (Ba 0.84 Ca 0.16 )(Ti 0.90 Zr 0.07 Sn 0.03 )O 3 compound with largest electrostrain of 0.23% in the BaTiO 3 ‐based family and (Ba 0.85 Ca 0.15 ) (Ti 0.91 Zr 0.09 )O 3 compound with “optimal” d 33 of 362 pC N −1 . While these studies paved a way in accelerating the discovery of targeted piezoelectric materials, one objective optimization may sometimes lead to the expense of other properties not in the optimized targets or failure in reproducing the best available results …”

“…The loop is repeated until the material with the desired response is discovered. Reproduced with permission . Copyright 2016, National Academy of Sciences.…”

Bayesim: A tool for adaptive grid model fitting with Bayesian inference

“…[5,16] However, the use of Bayesian inference in materials science and related contexts is much more recent, having only emerged in the past few years. [1, 19,21] We have previously demonstrated the value of a BPE approach in using automated high-throughput temperatureand illumination-dependent current-voltage measurements (JV T i) to fit material/interface properties and defect recombination parameters in photovoltaic (PV) absorbers [1,9], i.e. as a replacement for direct experimental characterization via probabilitistic inversion of a forward model.…”

Multi-objective Bayesian materials discovery: Application on the discovery of precipitation strengthened NiTi shape memory alloys through micromechanical modeling

“…In later work, Seko et al [25] employed BO based on the GPR model and PI acquisition function to discover low thermal conductivity compounds. While most approaches have been implemented over a computational space, Xue et al [20], [21] used BO to accelerate the experimental and computational discovery of NiTi-based SMAs (Ti50.0Ni46.7Cu0.8Fe2.3Pd0.2) with very low thermal hysteresis and BaTiO3based piezoelectrics with vertical morphotropic phase boundary. In [20], Xue et al performed BOED using the EGO framework and KG while utilizing various probabilistic models (GPR, Support Vector Regression (SVR) with a radial basis function kernel and with a linear kernel and using bootstrap uncertainty estimates).…”