Supercon

Nov 21, 2023

Abstract Data-driven methods, in particular machine learning, can help to speed up the discovery of new materials by finding hidden patterns in existing data and using them to identify promising candidate materials. In the case of superconductors, the use of data science tools is to date slowed down by a lack of accessible data. In this work, we present a new and publicly available superconductivity dataset (‘3DSC’), featuring the critical temperature TC of superconducting materials additionally to tested non-superconductors. In contrast to existing databases such as the SuperCon database which contains information on the chemical composition, the 3DSC is augmented by approximate three-dimensional crystal structures. We perform a statistical analysis and machine learning experiments to show that access to this structural information improves the prediction of the critical temperature TC of materials. Furthermore, we provide ideas and directions for further research to improve the 3DSC. We are confident that this database will be useful in applying state-of-the-art machine learning methods to eventually find new superconductors. Background & Summary Superconductors are materials in which the electrical resistance is zero when the temperature drops below a critical temperature Tc. Furthermore, superconductors are perfect diamagnets that expel magnetic fields via the Meissner effect. These properties make superconductors very useful for many high-power applications such as efficient electric power conversion, lossless power transmission, and ultra-strong magnets, as well as high-sensitivity sensor materials e.g. superconducting quantum interference devices and photon detectors 1 , 2 . The discovery of new superconducting materials with optimized properties will enable e.g. the use of cheaper coolants due to increased critical temperatures, stronger magnets due to improved magnetic properties, and simpler production of superconducting wires due to improved mechanical properties. The critical temperature Tc can be very sensitive to small changes in the crystal structure, for example to changes in the interatomic distances via mechanical pressure or chemical pressure 3 , i.e. the deformation of the lattice by replacing one atom with another element with same valency but different size. Despite the success of understanding the mechanism behind superconductivity within a microscopic theory, such as the theory by Bardeen, Cooper and Schrieffer 4 and strong-coupling generalizations thereof, it is to date difficult to faithfully predict the critical temperature Tc of new materials. Even though the prediction of the critical temperature has improved a lot over the last years and decades for well-understood classes of superconductors, the predictability of the superconducting onset temperature remains a major challenge in the material’s research endeavour, in particular in view of exploring new material candidates. This is largely caused by the dependence of Tc on subtle details of atomic arrangements in the crystal structure. Input parameters of the microscopic, low-energy theories, such as the electronic density of states at the Fermi level, the phonon spectrum, and the electron-lattice coupling, are not easily related to the chemical formula. Thus, when predicting the critical temperature Tc with machine learning, a first step to narrow this gap is to have access not only to the chemical composition of the material, but also to the exact 3D structure of the crystal. Machine learning has been widely used for the prediction of materials properties. Saal et al. 5 collected and reviewed a big number of machine learning generated predictions which have been confirmed experimentally afterward in applications ranging from organic LEDs over new binary and ternary crystal structures, perovskites, metallic glasses and metal-organic-frameworks to superhard materials. Furthermore, machine learning was used to predict the critical temperature Tc of superconductors using the SuperCon database 6 as training data, which is the largest and most commonly used dataset of superconductors. Previous papers have also made preprocessed subsets of the data available for further research 7 , 8 . There have been many attempts to predict the critical temperature Tc of a material using the SuperCon database. Hamidieh 8 used a gradient boosting model (XGB 9 ) trained on MAGPIE features 10 to predict Tc. Aketi et al. 11 used gradient-boosted decision trees, Matsumoto et al. 12 used random forests and Le et al. 13 used Bayesian neural networks on very similar features, while Gaikwad et al. 14 compare multiple machine learning models. Konno et al. 15 and Zeng et al. 16 used a convolutional neural network (CNN) and represented the chemical formula as elements on a grid. Li et al. 17 used a hybrid neural network consisting of a CNN and a recurrent neural network (RNN) which is trained on Atom2Vec features 18 . Dan et al. 19 use a convolutional gradient boosting decision tree (ConvGBDT). Sizochenko et al. 20 found that an often-used subset of the SuperCon contained a lot of duplicate entries and repeated their analysis with the cleaned dataset. Meredig et al. 21 showed that random splits for the cross-validation give overly confident model evaluations. Roter et al. 22 trained a bagged tree model on the chemical composition and argued that physical features such as the Fermi energy would be helpful for increasing the performance of their model if they were available for more materials. Data availability is the most important prerequisite for the development of (supervised) machine learning models for materials property prediction. In particular, informative and complete information on the materials is essential for the training of accurate machine learning models. All of the studies discussed above were based on representing materials only by their chemical composition, which is not a unique and complete representation of materials. Yet, most SuperCon entries contain only the chemical formula and critical temperature Tc of each material. Structural data such as space group and crystal system are only sparsely recorded and the full three-dimensional crystal structure is never given. Therefore, all of the aforementioned predictions of the critical temperature using the SuperCon database were limited to representations of the chemical composition of each material. One notable exception of using only chemical formulas to predict critical temperatures is the work of Stanev et al. 7 . They developed a superconductivity classifier based on matching the chemical compositions of materials in the SuperCon with the chemical compositions of materials in the AFLOW database and used tabular structural and electronic features such as the space group and the energy per atom as additional features. In this pioneering work, 1500 materials could be matched, half of them being superconductors. Stanev et al. argued that structural information is helpful in predicting superconductivity, yet realized the issue of severely reducing the size of the dataset when doing this matching. As of today, the matched crystal structures were not published. Recently, two more databases dealing with superconductors were presented in the literature. The SuperMat 23 database and the SC-CoMIcs 24 database are corpora of manually annotated texts from papers about superconductors. The annotations consist of different entities such as chemical formula and critical temperature with which certain phrases in the texts have been labeled. These corpora can be used for tasks such as training a named entity recognition model such as SciBERT 25 on automatically labeling new papers, which was demonstrated by Yamaguchi et al. 24 Foppiano et al. 23 also publicly provide their annotation procedure to encourage others to continue this work. So far, these annotated corpora are not publicly available. In the future, they might be useful to automatically extract information about superconductivity from literature. Court et al. 26 used the already trained ChemDataExtractor 27 to extract information of superconductors and magnetic materials from literature. They found approximately 20,400 superconductors and magnetic materials together with their chemical compositions and respective phase transition temperatures. The focus of the study was the prediction of the phase diagram of magnetic and superconducting materials. Furthermore, some of the entries were paired with crystal structures from the Crystallographic Open Database (COD) 28 . The authors provide a link to an interactive web app and the data, yet, the provided link is currently inactive. Another recently initiated superconductor database is the Superconducting Research Database 29 . In this online database, superconductors can be submitted with their exact three-dimensional crystal structure and critical temperature Tc. This database currently contains 14 superconductors which limits its usefulness for machine learning processes. In this work, we extended the structure matching approach by Stanev et al. 7 to build a new database (called 3DSC) of experimentally tested superconducting and non-superconducting materials 30 . This database is made publicly available. The 3DSC database features the critical temperature of superconductors as well as the approximated 3D crystal structure of each material. The core idea is to match materials in the SuperCon database with (modified) crystal structures of the Materials Project 31 , 32 and the Inorganic Crystal Structure Database 33 , 34 , 35 (ICSD). In addition to matching only exact chemical compositions (as in Stanev et al. 7 ), we employ a systematic adaptation algorithm that approximates the three-dimensional crystal structures of materials without perfect match by artificial doping of similar crystal structures. For example, the crystal structure of the SuperCon entry CuLa1.95Nd0.05O4 (which has no perfect match in the Materials Project database) is approximated by taking the 3D crystal structure of CuLa2O4 and partially replacing La with Nd at the respective crystal positions. This step is important to maximize the number of matched materials since the SuperCon contains many entries with doped materials, which otherwise would mostly be discarded. In this paper, we introduce and analyze two different 3DSC databases. Both are based on the SuperCon database, but one uses structures from the Materials Project (3DSCMP) and one uses structures from the ICSD (3DSCICSD). Using our matching and adaptation algorithm, we are able to match 5,759 (3DSCMP) and 9,150 (3DSCICSD) superconducting and non-superconducting materials from the SuperCon. We publicly provide the full 3DSCMP dataset on figshare 30 including the critical temperature Tc and approximate three-dimensional crystal structures. However, structures from the ICSD must not be (re-)published. Therefore, we refrain from publishing the 3DSCICSD. The subset of the 3DSCICSD that we provide under this link only contains the ICSD IDs necessary for reproducing the full dataset. The necessary structures can be downloaded with an ICSD license and artificially doped using our code in the aforementioned repository. However, despite not being able to publish this database, we have decided to present the 3DSCICSD in this paper along with the 3DSCMP, since it contains more structures and slightly different information than the 3DSCMP. Methods Overview of 3DSC data generation In this section, we describe our algorithm to match entries of the SuperCon database based on their chemical formula with 3D structures from crystal structure databases (see Fig. 1 ). We use and compare two different crystal structure databases, the Materials Project and the ICSD. We furthermore use the copy of the SuperCon database published by Stanev et al. 7 . All databases are cleaned as described in Sec. ‘Data and dataset cleaning’. Fig. 1