Packing density programs

Jiao, Nature , for details. The packing details can be found here. The determination of the densest packings of regular tetrahedra one of the five Platonic solids is attracting great attention as evidenced by the rapid pace at which packing records are being broken and the fascinating packing structures that have emerged.

Here we provide the most general analytical formulation to date to construct dense periodic packings of tetrahedra with four particles per fundamental cell. This study strongly suggests that the latter set of packings are the densest among all packings with a four-particle basis. Whether they are the densest packings of tetrahedra among all packings is an open question, but we offer remarks about this issue. Moreover, we describe a procedure that provides estimates of upper bounds on the maximal density of tetrahedron packings, which could aid in assessing the packing efficiency of candidate dense packings.

Jiao, Phys. E 81 , The Platonic and Archimedean polyhedra possess beautiful symmetries and arise in many natural and synthetic structures. Dense polyhedron packings are useful models of a variety of condensed matter systems, including liquids, glasses and crystals, granular media, and heterogeneous materials.

Understanding how nonspherical particles pack is a first step toward a better understanding of how biological cells pack. Probing the symmetries and other mathematical properties of the densest packings is a problem of interest in discrete geometry and number theory. Recently, there has been a large effort devoted to finding dense packings of polyhedra.

Although organizing principles for the types of structures associated with the densest polyhedron packings have been put forth, much remains to be done to find the maximally dense packings for specific shapes. This construction is based on a generalized organizing principle for polyhedra that lack central symmetry.

Moreover, we find that the holes in this putative optimal packing are small regular tetrahedra, leading to a new tiling of space by regular tetrahedra and truncated tetrahedra.

We also numerically study the equilibrium melting properties of what apparently is the densest packing of truncated tetrahedra as the system undergoes decompression. Our simulations reveal two different stable crystal phases, one at high densities and the other at intermediate densities, as well as a first-order liquid-crystal phase transition. See Y. Jiao and S. The PackAssistant software calculates the optimal packing arrangement of identical parts in standard containers by using 3D designs CAD.

This also works for parts with complex shapes, as the software will identify and take the individual shape of the object into account. PackAssistant users have improved the packing density of containers by up to 25 percent. This improvement also has a positive effect on other areas in the whole logistic chain: fewer containers means reduced storage space needed and lower transportation and handling costs.

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Crystallographic defects. Important types of lattice structures. Lattice structure of metals.