Classification of apatite structures via topological data analysis: a framework for a \u2018Materials Barcode\u2019 representation of structure maps

Scott Broderick,Tianmu Zhang,Ruhil Dongol,Krishna Rajan

doi:10.1038/s41598-021-90070-4

Scott Broderick, Tianmu Zhang + Show 2 more

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This paper introduces the use of topological data analysis (TDA) as an unsupervised machine learning tool to uncover classification criteria in complex inorganic crystal chemistries. Using the apatite chemistry as a template, we track through the use of persistent homology the topological connectivity of input crystal chemistry descriptors on defining similarity between different stoichiometries of apatites. It is shown that TDA automatically identifies a hierarchical classification scheme within apatites based on the commonality of the number of discrete coordination polyhedra that constitute the structural building units common among the compounds. This information is presented in the form of a visualization scheme of a barcode of homology classifications, where the persistence of similarity between compounds is tracked. Unlike traditional perspectives of structure maps, this new “Materials Barcode” schema serves as an automated exploratory machine learning tool that can uncover structural associations from crystal chemistry databases, as well as to achieve a more nuanced insight into what defines similarity among homologous compounds.

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This paper introduces the use of topological data analysis (TDA) as an unsupervised machine learning tool to uncover classification criteria in complex inorganic crystal chemistries
We focus on the 0thdimensional topological features of the Persistent homology (PH) ( H0), which corresponds to the connectivity of the data points in the finite parametric space represented by the barcode
Based on the concept of similarity, in this study we demonstrate how topological data analysis serves as an automated exploratory machine learning tool that can uncover structural associations from crystal chemistry databases, as well as to achieve a more nuanced insight into what defines similarity among homologous compounds

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This paper introduces the use of topological data analysis (TDA) as an unsupervised machine learning tool to uncover classification criteria in complex inorganic crystal chemistries. Homologous series of compounds are those that seem chemically diverse but appear capable of producing each chemical member in a stoichiometric relationship in a unique crystal structure “type” In this context, the use of classification maps that partition different genres of chemistry for different structural arrangements is a foundational tool in chemical crystallography and the evolution of structure maps, especially in inorganic structures. There is, a long and rich history of such maps including Mooser–Pearson plots 2, Philips and van Vechten diagrams 3,4 Goldschmidt diagrams 5 and Pettifor plots 1, just to mention a few examples Each of these mapping schemes identifies some key parameters related to electronic or crystal structure information which is usually placed on orthogonal axes and the occurrence of a given crystal chemistry is plotted . Shannon’s ionic radii of AI-site ion Shannon’s ionic radii of AII site Shannon’s ionic radii of B-site ion Shannon’s ionic radii of X-site ion Average crystal radius

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