Atomic packing factor

Atomic packing factor is the fraction of a crystal unit cell’s volume occupied by its constituent atoms, modeled as hard spheres. It compares geometric packing efficiency across crystal structures.

Unit cell: The smallest repeating volume that generates a crystal lattice by translation. The packing factor is calculated within this repeating volume.
Face-centered cubic crystal structure: A cubic crystal structure with lattice points at each face center and each corner. Its hard-sphere packing factor is about 0.74.
Theoretical density: The density calculated from a crystal structure, unit-cell contents, and atomic or molecular mass. Packing geometry and atomic volume help relate a unit cell to its material density.
Packing fraction: The fraction of a region’s volume occupied by specified objects. This broader geometric measure uses the same occupied-volume ratio as atomic packing factor.
Coordination number: The number of nearest neighboring atoms or ions surrounding a particle in a structure. Neighbor contacts constrain how spheres fit together in common crystal structures.
Body-centered cubic crystal structure: A cubic crystal structure with lattice points at the cube corners and its center. Its packing factor is about 0.68, below close-packed cubic arrangements.
Crystal structure: The ordered arrangement of atoms, ions, or molecules in a crystalline solid. Packing factor summarizes one geometric property of a crystal structure.
Mass density: Mass per unit volume of a substance. Atomic packing factor measures occupied hard-sphere volume, not mass per volume.
Lattice parameter: A length or angle that specifies the dimensions and shape of a crystal unit cell. Cell dimensions connect atomic radius to the volume used in the ratio.
Simple cubic crystal structure: A cubic crystal structure with lattice points only at the cube corners. Its packing factor is about 0.52, illustrating relatively loose sphere packing.

Linked from 1 page