Abstract
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.
Highlights
Solid solution alloys and multi-phase crystalline materials are widely existed in the fields of metallurgy, physics, chemistry, biology and various other engineering applications, and their superior properties like high strength, heat resistance and anti-corrosion can satisfy different requirements.[1,2,3,4,5] the unique and enhanced material performance is mainly determined by its microstructure
Richard and Gervois[51,52,53,54] presented topological and metrical analyses on the random binary sphere packings with different packing fractions ranging from 0 - 0.6 by radical tessellation (RT), the results revealed that the differences between different disordered packings can be seen from very simple quantities like the edge number distribution per radical polyhedron (RP) face; and the weak local segregation existed in the packings with high packing fraction and the size ratio of particles as well as building algorithm had large effects on the topological and metrical properties
Once the first ordered layer with specific packing mode is established within the container, one batch of small spheres with a certain number are added to the position where the specific pores exist, and periodical mechanical vibration is conducted to help these small spheres find their stable positions after the collision between the small and large spheres
Summary
Solid solution alloys and multi-phase crystalline materials are widely existed in the fields of metallurgy, physics, chemistry, biology and various other engineering applications, and their superior properties like high strength, heat resistance and anti-corrosion can satisfy different requirements.[1,2,3,4,5] the unique and enhanced material performance is mainly determined by its microstructure. It is well known that the materials structure and properties are significantly influenced by the packing behavior of the constituent atoms which can be regarded as particles, while directly studying the materials states and their transitions in-situ from the atomic scale is rather difficult due to the complexity of materials dynamics and thermo-kinetics. This research gap can be filled by the packing of particles because it can be used as an effective starting point to model the structure of liquids,[6,7,8] amorphous metals and alloys,[9] and crystalline granular materials.[10,11,12,13,14,15,16] constructing new types of packings and studying their macro/microscopic structural properties and formation mechanisms have increasingly attracted more and more researchers’ interests. In addition to some global quantities like material apparent density and mechanical properties, the proper description of material microstructural properties (or microstructures) such as CN
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