Medium-range order in molecular materials: Fluctuation electron microscopy for detecting fullerenes in disordered carbons

During a fluctuation electron microscopy (FEM) study of disordered carbons, we found that samples containing C₆₀ exhibit a normalized variance peak at 7.1 nm^-1 that appears to be a unique indicator of tight curvature in layered materials. This peak is associated with the characteristic in-plane carbon-carbon bond distance of ∼0.14 nm in graphene. Diffraction from this spacing is normally forbidden in planar graphene (and graphite), but becomes allowed when the layer structure is interrupted. Such interruptions arise at the edges of graphite fragments and also when 5-rings are incorporated into a layer. We show that the curvature induced by a high density of 5-rings, such as that in C₆₀, can dominate the variance peak at 7.1 nm^-1. FEM simulations reveal that the variance peak at ∼7.1 nm^-1, which we label F₁, is one of several fullerene-signature peaks, with others occurring at Q values of 10.6 nm^-1 (F₂) and 12.4 nm^-1 (F₃). We conclude that FEM is a sensitive method for detecting dilute quantities of highly curved pentagon-rich fullerenes, such as C₆₀, when dispersed within disordered graphitic carbon.