Solution

ID: past-exam-of-the-mphil-in-micro-and-nanotechnology-enterprise-course-of-the-university-of-cambridge/2020/paper-1/section-a-i/2/iii/solution

The resolved graphitic fringes indicate high-resolution phase contrast in a multi-walled carbon nanotube. Interference of transmitted and diffracted electron waves produces lattice fringes; their darkness is controlled by defocus, thickness and the contrast transfer function, so a dark fringe is not an unqualified map of individual carbon atoms. The weakly scattering central channel is lighter than the multilayer walls. Curved, roughly parallel fringes at its sides identify concentric graphitic shells; the dense fringes at the lower edge arise from overlapping graphitic material or another tube, not necessarily the wall count of the central tube.
Using the printed scale bar, the central tube has an outer diameter of roughly – and an inner channel of roughly –, depending on the cross-section selected away from the overlap. Several wall fringes are resolved on each side, with separations of order , consistent with graphitic interlayer spacing. These are approximate image measurements, not a determination of chirality, chemical purity or an exact shell count. The image alone cannot establish those quantities.

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