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Field emission patterns from multiwall carbon nanotubes with a cone-shaped tip
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16.A closed tip (i. e., a curved graphene) of a CNT is considered as a part of a fullerene cage. When twelve pentagons are evenly distributed over a fullerene cage similar to which has icosahedral symmetry, is approximately equal to the edge length of the icosahedron since pentagons are located at positions corresponding to vertices of the icosahedron. For the icosahedron with the length from its center to vertices, , where is the golden ratio , indicating is nearly equal to . Therefore, is on average approximated to a radius of curvature of a closed graphene cage (in this case, radius of curvature of a CNT cap).
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