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In this paper, four binary hard sphere crystals were numerically constructed by discrete element method (DEM) through different packing modes under three-dimensional (3D) mechanical vibration. For each crystal, a modified Voronoi tessellation method (called radical tessellation) was utilized to quantitatively investigate the topological and metrical properties of radical polyhedra (RPs). The topological properties such as the number of faces, edges, vertices per RP and the number of edges per RP face as well as the metrical properties such as perimeter, surface area, volume, and relative pore size per RP were systematically characterized and compared. Meanwhile, the mechanism of the binary hard sphere crystallization was also investigated. The results show that the packing sequence and pattern of the large spheres can determine the structure of the binary hard sphere crystal. The RP structures and their metrical and topological properties of the four binary hard sphere crystals (even the packing density of the two crystals is the same) are quite different. Each property can clearly reflect the specific characteristics of the corresponding binary hard sphere crystalline structure. The obtained quantitative results would be useful for the deep understanding of the structure and resultant properties of binary hard sphere crystals.

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