Cluster and constraint analysis in tetrahedron packings.

The disordered packings of tetrahedra often show no obvious macroscopic orientational or positional order for a wide range of packing densities, and it has been found that the local order in particle clusters is the main order form of tetrahedron packings. Therefore, a cluster analysis is carried out to investigate the local structures and properties of tetrahedron packings in this work. We obtain a cluster distribution of differently sized clusters, and peaks are observed at two special clusters, i.e., dimer and wagon wheel. We then calculate the amounts of dimers and wagon wheels, which are observed to have linear or approximate linear correlations with packing density. Following our previous work, the amount of particles participating in dimers is used as an order metric to evaluate the order degree of the hierarchical packing structure of tetrahedra, and an order map is consequently depicted. Furthermore, a constraint analysis is performed to determine the isostatic or hyperstatic region in the order map. We employ a Monte Carlo algorithm to test jamming and then suggest a new maximally random jammed packing of hard tetrahedra from the order map with a packing density of 0.6337.