Quantifying Curvature in High-Resolution Transmission Electron Microscopy Lattice Fringe Micrographs of Coals

The observation of high-resolution transmission electron microscopy (HRTEM) lattice fringe images for coals has aided the rationalization of structure and order. Within the hundreds of lattice fringes (edge-on view of the aromatic structures) in a typical micrograph, apparent curvature is common. Traditional image analysis approaches do not appropriately quantify curvature. Tortuosity is functional for the quantification of single-inflection-point smooth lines but poor for complex or undulating lines. Here we present an image analysis method that can identify the points of inflection, angles, and segment lengths that constitute curved lattice fringes. Four coals from the Argonne Premium suite (Pocahontas No. 3, Upper Freeport, Illinois No. 6, and Beulah-Zap) and example anthracites were examined, and curvature was present in 17-24% of the fringes. These curved fringes were further classified as having low (<45 degrees), medium (45-90 degrees), or high curvature (>90 degrees) on the basis of cumulative angle changes. For the Argonne Premium coals, Pocahontas had the greatest portion of fringes with low curvature (74%), with the other coals being between 55 and 65%. In all cases, low curvature was the predominant class. High curvature contributed between 8 and 19%. The majority of the curved fringes (84 to 87%) were located in the range defined by fringes with lengths of 6.0-12.5 angstrom and cumulative angles of 4-125 degrees. The Argonne Premium coals examined have similar distributions of angle change between adjacent segments. Angle changes of 10-20 degrees account for the largest contribution. The coals had similar tortuosity distributions with fringe length. The majority of curved fringes for Argonne Premium coals (>90%) were defined by fringes with lengths of 6.0-22.5 angstrom and tortuosities of 1.001-2.0, while the curved fringes of anthracite with lengths of 6-52.5 angstrom and tortuosities of 1.001-1.5 accounted for 90%. These observations have implications for the frequency and placement of non six-membered rings in aromatic structures.