The Coordination number of bcc, fcc, ccp, hcp

Understanding Crystal Structures and Coordination Numbers

To determine the coordination number of crystal structures, let’s first understand the basics of unit cells. A unit cell is the simplest repeating unit in a crystal lattice, defined by lattice points where particles vibrate in a fixed pattern. There are 14 distinct types of crystal unit cell structures, known as Bravais lattices, but the most common types in metals and many other solids include body-centered cubic (bcc), face-centered cubic (fcc), and hexagonal close-packed (hcp).

Coordination Number

The coordination number is the number of atoms directly surrounding a central atom in a crystal structure. In covalent molecules and polyatomic ions, this is simply the number of atoms bonded to the central atom. In metal atoms, however, bonding is delocalized, and atoms arrange themselves as closely as possible without forming distinct pairs.

Body-Centred Cubic (bcc): In a bcc structure, each atom is in contact with 8 neighboring atoms, so the coordination number is 8.

Face-Centred Cubic (fcc): In an fcc structure, each atom is in contact with 12 neighboring atoms, so the coordination number is 12.

Cubic Close-Packed (ccp): This arrangement is essentially the same as fcc, with a coordination number of 12.

Hexagonal Close-Packed (hcp): In hcp structures, each atom also has 12 nearest neighbors, so the coordination number is 12.

Additional Information

Packing Efficiency: This refers to the percentage of space filled by the atoms within a unit cell. Higher coordination numbers generally correspond to greater packing efficiency.

Note: The coordination number should not be confused with the number of atoms per unit cell. For example, an fcc structure has 4 atoms per unit cell, but a coordination number of 12.