Classification of apatite structures via topological data analysis: a framework for a ‘Materials Barcode’ representation of structure maps

Abstract

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.

Topological Data Analysis for Revealing the Structural Origin of Density Anomalies in Silica Glass

“…Topological data analysis (TDA) , is an emerging and powerful tool for understanding the medium-range structural ordering of multiscale data. The possible applications of TDA range widely from cosmology to condensed matter physics. , Furthermore, in recent years, topological concepts have played an important role in materials science − and chemical engineering . Persistence diagrams (PDs) are particularly important tools in TDA.…”