The Search for BaTiO₃-Based Piezoelectrics With Large Piezoelectric Coefficient Using Machine Learning

Abstract

We employ a data-driven approach to search for BaTiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> -based piezoelectrics with large piezoelectric coefficient d <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">33</sub> . Our approach uses a surrogate model to make predictions of d <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">33</sub> with uncertainties, followed by a design step that selects the next optimal compound to synthesize. We compare several combinations of choices of the model and design selection strategies on the training data assembled from many experiments that we have previously performed, and we choose the best two performers for guiding new experiments. This adaptive design strategy is iterated five times and in each iteration, four new compounds are synthesized based on the two different design selection criteria. The best new compound found in this work is (Ba <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0.85</sub> Ca <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0.15</sub> )(Ti <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0.91</sub> Zr <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0.09</sub> )O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> with a d <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">33</sub> of 362 pC/N, compared to the best compound BCT-0.5BZT in the training data with a d <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">33</sub> of ~610 pC/N. Our conclusion from this study is that although our model describes well most of the available d <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">33</sub> data, the especially large value for BCT-0.5BZT is difficult to fit with any surrogate model and emphasizes the need to combine a physics-based approach with a pure data-driven approach used in this study.