Radical Tessellation And Microstructure Characterization On The Ordered Packings Of Binary Spheres

Binary ordered hard sphere crystal with the structure of body centered cubic (BCC) was numerically constructed using the template by molecular dynamics based discrete element method (DEM) under 3D interval vibration and batch-wised feeding. Through the quantitative Radical tessellation on the generated binary ordered packings such as{111}-oriented face centered cubic ({111}-FCC), hexagonal close packed (HCP),{100}-oriented face centered cubic ({100}-FCC), BCC, and simple cubic (SC), where these binary hard sphere crystals were named according to the ordered packing of large spheres, the topological and metrical properties of the Radical polyhedra in these binary ordered packings were systematically characterized and analyzed. Here the topological properties include face number, edge number and vertice number of each polyhedron, edge number of each polyhedron face, while the metrical properties include the perimeter, area, volume of each polyhedron, perimeter and area of each polyhedron face. Meanwhile, the relative size of voids was characterized as well. The results indicate that:1. When the voids with regular tetrahedral and regular octahedral structures in{111}-FCC and HCP were concurrently filled by small particles, the packing density of the obtained two binary ordered packings can all reach 0.76. The Radical polyhedra in these two binary packings are mainly heptahedra, enneahedra, and docosanoichedra; with each polyhedron, the faces consist of triangle, petaton, and hexagon. The local packing structures of Radical polyhedra in the two binary ordered packings are different, however, the void distributions are the same which lead to the same packing density of the two packings.2. When only the regular octahederal voids in{111}-FCC and HCP binary ordered packings were filled by small particles, the packing density in these two binary ordered structures can both reach 0.79. Where the corresponding Radical polyhedra are all hexahedra and octodecahedra, and each polyhedron includes quadrilateral and hexagonal faces. The void size in these two binary ordered structures is very small with more uniform distribution, and the distribution of metrical properties is more symmetric, which makes a higher packing density than that when two types of voids are concurrently filled.3. The packing density of 0.79 can be obtained when the regular octahedral voids in {100}-FCC ordered packing were filled. The radical polyhedra all indicate hexahedra and octodecahedral, and the faces of each polyhedron are quadrangle and hexagon. The characterization on local packing structure of Radical polyhedra indicates the difference between{100}-and{111}-FCC binary ordered packings.4. When the tetrahedral voids were filled by small particles, the packing density of the obtained BCC ordered packing can reach 0.7119, where the Radical polyhedra are mainly hendecahedra and tetrahexahedra, which include quadrilateral and hexagonal faces.5. For SC ordered packing, the regular hexahedral voids were filled by small particles, therefore, the formed binary SC ordered structure has the packing density of 0.72. The Radical polyhedra with this structure are two kinds of tetrakaidecahedra with different structure, each polyhedron is mainly enclosed by quadrilateral and hexagonal faces.