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The Development of New Perovskite-Type Oxygen Transport Membranes Using Machine Learning
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Applications of Machine Learning to the Study of Crystalline Materials

Hartmut Schlenz
1,2,* and
Stefan Sandfeld
Forschungszentrum Juelich, Institute of Energy and Climate Research (IEK), IEK-1: Materials Synthesis and Processing, Wilhelm-Johnen-Strasse, D-52425 Juelich, Germany
Institute of Geoscience, Division of Geochemistry and Petrology, University of Bonn, Meckenheimer Allee 139, D-53115 Bonn, Germany
Forschungszentrum Juelich, Institute of Advanced Simulation—Materials Data Science and Informatics (IAS-9), Wilhelm-Johnen-Strasse, D-52425 Juelich, Germany
Faculty 5, RWTH Aachen University, D-52062 Aachen, Germany
Authors to whom correspondence should be addressed.
Crystals 2022, 12(8), 1070;
Submission received: 27 July 2022 / Accepted: 28 July 2022 / Published: 30 July 2022
This Special Issue, “Applications of Machine Learning to the Study of Crystalline Materials”, is a collection of seven original articles published in 2021 and 2022 and dedicated to applications of machine learning in materials research.
Machine learning (ML) is rapidly revolutionizing many fields and is starting to change landscapes for physics, chemistry, materials science, and structural research. With its ability to solve complex tasks autonomously, ML is being exploited as a radically new way to help find material correlations, understand materials chemistry, analyze crystal structures and related properties, and generally accelerate the discovery of new materials. Thus, one goal of this special issue is to demonstrate available, practical machine learning techniques that can be used to study crystalline materials today by means of the application of different ML techniques (including deep learning), as well as by the demonstration of best practices.
The focus of this Special Issue is the practical application of ML in materials research in order to inspire more materials scientists and crystallographers to use ML as a powerful tool in research and also to demonstrate the potential benefits of ML, as well as to improve communication between theoretically and more practically working scientists, in order to reduce any inhibitions that may exist. In this context, one goal may be to establish ML as a way to usefully extend existing analytical procedures and also to obtain results that cannot be obtained by experiments and standard procedures, or only at a disproportionately high cost.
The development of new ceramic gas separation membranes for the production of pure oxygen is demonstrated by Schlenz et al. [1]. For this work, mainly experimental data were used to generate training data for ML, where the training data contained information on both crystal structures and the microstructures of selected ceramic phases. The use of artificial neural networks (ANNs) for optimizing the fabrication and alloying processes of Al75O75-TiC composites is demonstrated by Alam et al. [2]. Using ANNs, the crystallite sizes and lattice strains of the composites could be predicted. An alternative approach is taken by Shu et al. [3] for the prediction of microstructures of polycrystalline phases. For this purpose, grain knowledge graphs were used, and a new heterogeneous grain graph attention model (HGGAT) is presented. The operation of HGGAT is demonstrated using the prediction of magnesium alloy microstructures as an example. Even Gómez-Peralta et al. [4] used ANNs for materials research, this time, however, in order to classify crystal structures. In this work, different halite, fluorite, ilmenite, spinel, and perovskite phases could be distinguished with an average precision of about 94%, by means of crystal-site-based features. Spinel represents the focus of the work of Lin et al. [5]. They applied ML to the development of new photocatalytic phases, based on highly entropic spinels. Predictions for this promising class of materials are demonstrated using the system ( C o , C r , F e , M n , N i ) 3 O 4 as an example. As in the work of Schlenz et al. [1] and Gómez-Peralta et al. [4], perovskite is the focus of interest in the work of Li et al. [6]. Here, ML was used for the successful prediction of specific properties, for example, formation energies, thermodynamic stability, crystal volume, and oxygen vacancy formation energies, where the latter again provides important information for the first contribution [1]. Li et al. [6] tested different ML algorithms for this purpose and compared their results. Finally, Trampert et al. [7] used deep neural networks for image analysis. Microscopy images were analyzed with Convolutional Neural Networks (CNNs), but with a special feature: synthetic image data were generated for training the CNNs, which makes it possible to train neural networks in a meaningful way in the case of insufficient image data.
We hope that the contributions in this Special Issue will be especially helpful for further progress in materials research and for the establishment of ML methods as a standard tool, and we would also like to express our sincere thanks to all the authors who have made their contributions to this issue.

Author Contributions

Conceptualization, methodology, validation, formal analysis, investigation, resources, H.S. and S.S.; writing—original draft preparation, H.S.; writing—review and editing, H.S. and S.S.; project administration, funding acquisition, H.S. All authors have read and agreed to the published version of the manuscript.


This research was funded by the Helmholtz Innovation Fund (Project No. DB001840), and it also received publication funding by MDPI, both of which are gratefully acknowledged.


We thank the Helmholtz Association of German Research Centers and Forschungszentrum Juelich for providing the time and infrastructure necessary to perform the presented work. The contribution of all authors is gratefully acknowledged. The authors would also like to express their thanks to the Crystals Editorial Office, and on top of that to Autumn Du for her excellent communication and support, and for her always friendly, patient, and professional attitude.

Conflicts of Interest

The authors declare no conflict of interest.


  1. Schlenz, H.; Baumann, S.; Meulenberg, W.A.; Guillon, O. The Development of New Perowskite-Type Oxygen Transport Membranes Using Machine Learning. Crystals 2022, 12, 947. [Google Scholar] [CrossRef]
  2. Alam, M.A.; Ya, H.H.; Azeem, M.; Yusuf, M.; Soomro, I.A.; Masood, F.; Shozib, I.A.; Sapuan, S.M.; Akhter, J. Artificial Neural Network Modeling to Predict the Effect of Milling Time and TiC Content on the Crystallite Size and Lattice Strain of Al7075-TiC Composites Fabricated by Powder Metallurgy. Crystals 2022, 12, 372. [Google Scholar] [CrossRef]
  3. Shu, C.; He, J.; Xue, G.; Xie, C. Grain Knowledge Graph Representation Learning: A New Paradigm for Microstructure-Property Prediction. Crystals 2022, 12, 280. [Google Scholar] [CrossRef]
  4. Gómez-Peralta, J.I.; García-Peña, N.G.; Bokhimi, X. Crystal-Site-Based Artificial Neural Networks for Material Classification. Crystals 2021, 11, 1039. [Google Scholar] [CrossRef]
  5. Lin, C.C.; Chang, C.W.; Kaun, C.C.; Su, Y.H. Stepwise Evolution of Photocatalytic Spinel-Structured (Co, Cr, Fe, Mn, Ni)3O4 High Entropy Oxides from First-Principles Calculations to Machine Learning. Crystals 2021, 11, 1035. [Google Scholar] [CrossRef]
  6. Li, R.; Deng, Q.; Tian, D.; Zhu, D.; Lin, B. Predicting Perovskite Performance with Multiple Machine-Learning Algorithms. Crystals 2021, 11, 818. [Google Scholar] [CrossRef]
  7. Trampert, P.; Rubinstein, D.; Boughorbel, F.; Schlinkmann, C.; Luschkova, M.; Slusallek, P.; Dahmen, T.; Sandfeld, S. Deep Neural Networks for Analysis of Microscopy Images—Synthetic Data Generation and Adaptive Sampling. Crystals 2021, 11, 258. [Google Scholar] [CrossRef]
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Schlenz, H.; Sandfeld, S. Applications of Machine Learning to the Study of Crystalline Materials. Crystals 2022, 12, 1070.

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Schlenz H, Sandfeld S. Applications of Machine Learning to the Study of Crystalline Materials. Crystals. 2022; 12(8):1070.

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Schlenz, Hartmut, and Stefan Sandfeld. 2022. "Applications of Machine Learning to the Study of Crystalline Materials" Crystals 12, no. 8: 1070.

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