Random close pack crystal lattices have maximum densities equal to this upper limit. Random close packing does not have a precise geometric definition. It is defined statistically, and results are empirical. A container is randomly filled with objects, and then the container is shaken or tapped until the objects do not compact any further, at this point the packing state is RCP. The definition of packing fraction can be given as: "the volume taken by number of particles in a given space of volume". In other words, packing fraction defines the packing density. It has been shown that the filling fraction increases with
Close-packing of equal spheres a common radius, "r". Therefore two centers would simply have a distance 2"r". To form an A-B-A-B-... hexagonal close packing of spheres, the coordinate points of the lattice will be the spheres' centers. Suppose, the goal is to fill a box with spheres according to hcp. The box would be placed on the "x"-"y"-"z" coordinate space. First form a row of spheres. The centers will all lie on a straight line. Their "x"-coordinate will vary by 2"r" since the distance between each center of the spheres are touching is 2"r". The "y"-coordinate and z-coordinate will be the same. For simplicity,