  Understanding geometric frustration of ordered phases in two-dimensional
condensed matters on curved surfaces is closely related to a host of scientific
problems in condensed matter physics and materials science. Here we show how
two-dimensional Lennard-Jones crystal clusters confined on a sphere resolve the
geometric frustration and lead to pentagonal vacancy structures. These
vacancies, originated from the combination of curvature and physical
interaction, are found to be topological defects and they can be further
classified into dislocational and disclinational types. We analyze the dual
role of these crystallographic defects as both vacancies and topological
defects, illustrate their formation mechanism, and present the phase diagram.
The revealed dual role of the topological vacancies may find applications in
the fabrication of robust nanopores. This work also suggests the promising
potential of exploiting the richness in both physical interactions and
substrate geometries to create new types of crystallographic defects, which
have strong connections with the design of crystalline materials.
