Improved quantification of curvature in high-resolution transmission electron microscopy lattice fringe micrographs of soots

Soot affects climate change and human health. Its structure is influenced by fuel and combustion conditions. Image analysis of high-resolution transmission electron microscopy lattice fringes indicates curvature is common and impacts reactivity. Here an improved curvature quantification determined the distributions of segment frequency, segment lengths, angles between segments, frequency of inflection points, relative inflection point locations, and overall angle changes for each fringe for three soots and a carbon black. Curvature was present in 28–49% of the fringes. Low curvature (<30°) account for the largest portion (61–76%). The most common inflection angles were 10–20°. Geometry optimized (ab initio) atomistic models containing centrally located pentagon rings or Stone-Thrower-Wales defects had angle changes 19–77° depending on viewing angle and molecule. The majority of curved fringes (71–78%) had a singular inflection point. Fringes were primarily within the range 6–15.0 Å length 4–100° cumulative angle. Tortuosity data demonstrated this commonly used parameter was limited for the evaluation of undulating curvature. Linking these data to structural defects will enhance linking reactivity to structure, capturing and improving structural features in atomistic representations. Changes in segment angles <45° however are not likely to be associated with centrally placed isolated pentagon rings.