Determining the orderliness of carbon materials with nanoparticle imaging and explainable machine learning

Carbon materials have paramount importance in various fields of materials science, from electronic devices to industrial catalysts. The properties of these materials are strongly related to the distribution of defects-irregularities in electron density on their surfaces. Different materials have various distributions and quantities of these defects, which can be imaged using a procedure that involves depositing palladium nanoparticles. The resulting scanning electron microscopy (SEM) images can be characterized by a key descriptor-the ordering of nanoparticle positions. This work presents a highly interpretable machine learning approach for distinguishing between materials with ordered and disordered arrangements of defects marked by nanoparticle attachment. The influence of the degree of ordering was experimentally evaluated on the example of catalysis via chemical reactions involving carbon-carbon bond formation. This represents an important step toward automated analysis of SEM images in materials science. We propose a set of features for the ordered arrangement of palladium nanoparticles that are consistent with the intuitive understanding of researchers and allow quantification of the data in terms of easily interpretable physical parameters.