Excluded volumes of clusters in tetrahedral particle packing

• Excluded volumes of typical clusters in tetrahedral particle packing are given.
• Influences of the size and topology of clusters on excluded volume are studied.
• Excluded volumes of dimer and wagon wheel are relatively lower.
• Excluded volume decreases when the particle approaches a wagon wheel.
• The results give an explanation to the cluster distribution in tetrahedral packings.

We investigate the excluded volumes of clusters in tetrahedral particle packing using an ideal tetrahedron model and Monte Carlo simulation. Both the influences of the size and topology of clusters on the excluded volume are studied. We find that the excluded volumes of the dimer composed of two tetrahedra and the wagon wheel composed of five tetrahedra are relatively lower than other cluster forms. For large clusters, the excluded volume decreases when the topology of a cluster approaches the wagon-wheel geometry. The results give an explanation to the cluster distribution which demonstrates that the dimer and wagon wheel are the dominative cluster forms in the packing structure of tetrahedra.