Disentangling Intra- and Interlayer Disorder in Disordered Carbons via Pair-Angle Distribution Function Analysis

Highly sp 2 -hybridized disordered carbons stand out because of their versatile and often complex extended-range order, characterized by curved layers with rings of varying sizes, stacking disorder, and other defects. Understanding this extended-range order is crucial for grasping its role in numerous applications. In this study, we demonstrate the use of the pair-angle distribution function (PADF) analysis to address this challenging task. The three-dimensional aspect of the PADF enables the extraction of a wide range of information, including the ability to separately study intra- and interlayer disorder─a difficult task with other methods like one-dimensional pair distribution functions. Using PADF analysis thus improves our understanding of the extended-range order, which is essential for customizing carbons for specific applications. The proof-of-concept demonstration of separating inter- and intraplane disorder in layered materials also introduces a powerful new approach for studying other materials, including MXenes and layered double hydroxides.