We have conducted a detailed electron-microscopic investigation of the structure and morphology of alpha-hexathienyl (alpha-6T), a hexameric homologue of polythiophene that shows great promise as a thin-film-transistor material. In ordinary films for device applications prepared by vacuum sublimation, alpha-6T crystals are very small (<100 nm), irregular, and preferentially oriented parallel to the substrate. By crystallization from the melt, very broad (tens of micrometers) and thin lamellar crystals are obtained, with their molecules perpendicular to the lamellar surfaces. Single-crystal electron-diffraction patterns from a variety of zones allow resolution of the main-chain repeat at 2.38 nm, recording of over 30 orders of intramolecular reflections, discrimination among the four proposed unit cells, and determination of the preferred crystal-growth direction (which corresponds to the unique b-axis of the monoclinic cell). In addition, we have shown that the lamellae undergo splaying and warping about an axis corresponding to their growth direction, as well as very extensive fractures perpendicular to that axis. These fractures are explained based upon poor interdigitation of the flat extended-chain molecules between their densely packed (020) planes. By introducing such extensive internal disruptions to the lattice, these cleavage planes are expected to have severe negative implications on single-crystal transistor characteristics.