Fig. 1

The Voronoi vertex clustering algorithm for identifying the polyhedral unit structure of a an fcc single-crystal region and b a vacancy point defect is illustrated. In a(i), the unit cell of an fcc lattice is provided and in a(ii), the Voronoi polyhedron of one of the atoms is shown. Also highlighted are the Voronoi vertices, obtained by constructing the Voronoi polyhedra of all the atoms in the system. In a(iii), the VV-spheres that fall within the unit cell are shown. In a(iv), the octahedron and tetrahedron corresponding to the two distinct types of VV-spheres are depicted. In the case of the vacancy, in b(i), the fcc lattice with a vacancy is shown and the atoms surrounding the vacancy are highlighted. In b(ii), the VV-sphere that is located within the vacancy is illustrated and the atoms that have contributed to the creation of this sphere are highlighted in red. These atoms are the same as those surrounding the vacancy in b(i). The polyhedron that is obtained by triangulating the atoms in b(iii) is the cuboctahedron, which is identified as the polyhedral unit model of a vacancy in the fcc lattice