Quantitative structural and textural characterization of natural disordered sp ² carbon using transmission electron microscopy image discretization

This work presents an algorithm developing a methodology for the quantitative characterization of the complex structure of disordered sp2 carbon based on the mathematical processing of high-resolution transmission electron microscopy (HRTEM) images. The mathematical processing algorithm includes HRTEM image discretization, differentiation of the structure by three degrees of order using information-theoretical entropy as a metric within the discretized image fragments, and an assessment of the parameters of neighborhood homogeneity and anisotropy. Neighborhood anisotropy characterizes the textured and blocky nature of the sample structure, while a combined analysis of the degree of order and homogeneity measure enables a comparative analysis of the structure’s orderliness. All studies were performed using natural carbon-rich shungite and anthraxolite samples as examples. The proposed algorithm for HRTEM image analysis can be applied to various disordered materials for the quantitative characterization of their structure and can also be used to predict physicochemical properties.