= Solution
Three point-defect structures are \b[a <Stone-Wales defect>, a reconstructed <graphene monovacancy> and a reconstructed <graphene divacancy>]. The original sketch gives ring inventories rather than fitted atomic coordinates.
A <Stone-Wales defect> rotates one C–C bond, converting four hexagons into a 5–7–7–5 group without changing the number of atoms. A <graphene monovacancy> removes one carbon; a common reconstruction gives a 5–9 group with residual under-coordination. A <graphene divacancy> removes two adjacent carbons; a 5–8–5 reconstruction can eliminate dangling bonds. Other divacancy reconstructions exist, so atom loss does not uniquely select one topology.
Irradiation, energetic processing, etching and incomplete growth can create vacancies; thermally or beam-activated bond rearrangement can change their structures. Electron microscopy itself can create defects, so compare exposures before attributing a time sequence to unperturbed material.
Pentagons favor positive curvature and heptagons negative curvature. Such defects can bend tubes, help form caps or junctions, or change a local wrapping relationship. They scatter carriers and alter the local <density of states>; vacancies can add localized states and chemical reactivity. Whether a clean <band gap> appears depends on defect identity, concentration and arrangement, not merely on the presence of a defect.
\Image[/past-exam-of-the-mphil-in-micro-and-nanotechnology-enterprise-course-of-the-university-of-cambridge/2020/paper-2-carbon-defects.png]
{title=Carbon point-defect ring inventories}
{description=Original topology summaries of a Stone-Wales rearrangement and vacancy reconstructions. Atom deficits and nonhexagonal ring counts are explicit; the polygons do not represent energy-minimized atomic coordinates.}
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