Leaky cell model of hard spheres

We study packings of hard spheres on lattices. The partition function, and therefore the pressure, may be written solely in terms accessible free volume, i.e., volume space that a sphere can explore without touching another sphere. compute these volumes using leaky cell model, which accounts for possibility escape from local cage lattice neighbors. describe how elementary geometry used to calculate exactly this model two- three-dimensional compare results well-known Carnahan–Starling Percus–Yevick liquid models. provide formulas various lattices use common tangent construction identify several phase transitions between them regime, indicating coexistence crystalline materials.