Systematic 3D quantification of structure, nanotexture, and texture of simulated pyrolytic carbons

Accurately characterizing a material is essential for understanding its microstructure-property correlations. Carbons with turbostratic structures hold significant technological importance. However, fully characterizing their complex microstructures remains a challenge that hinders the development of crucial structure-property relationships. In this work, we propose a consistent framework for describing the microstructure of graphenic carbons based on a single atomic-scale parameter, the atomic orientation ($\overrightarrow{AO}$). Utilizing $\overrightarrow{AO}$ and its spatial correlation, we quantify the 3D microstructure using a set of descriptors, including a structural feature, i.e., the interlayer distance ($d_{002}$), nanotextural features, i.e., the crystallite sizes ($L_a$ and $L_c$), and textural features, i.e., the anisotropy factor (${\xi }_{AF}$), the average misorientation angle between crystallites (${\varphi }_{\infty }$), and a 3D atomic equivalent of the opening angle ($O{A}_{3D}$). The proposed descriptors are applied to three sets of atomistic pyrolytic carbon (PyC) models to demonstrate their ability to discriminate and quantify the microstructure of PyCs with various accuracy and texture levels. Notably, the introduced textural parameters (${\xi }_{AF}$, ${\varphi }_{\infty }$, $O{A}_{3D}$) extend texture quantification from 2D to 3D, allowing for accurate quantification of PyCs with a broad range of texture.