# Body-Centered Cubic (BCC)

## Definition - What does Body-Centered Cubic (BCC) mean?

Body-centered cubic (BCC) is the name given to a type of atom arrangement found in nature. A body-centered cubic unit cell structure consists of atoms arranged in a cube where each corner of the cube shares an atom and with one atom positioned at the center.

The atom at the corners of the cube are shared with eight other unit cells. As such, each corner atom represents one-eighth of an atom. Therefore, the BCC structure is said to have a coordination number of 8.

The center of the unit cell consists of 1 full atom, therefore the total number of atoms in the BCC unit cell structure is 2; one at the center plus eight one-eighth atoms at the corners.

1 atom + (1/8 atoms x 8 corners) = 2 atoms

The atoms in the BCC unit cell arrangement are not packed as closely as other arrangements (such as the face-centered cubic, FCC). However, due to their arrangement, it is more difficult for the atoms to slip past each other. This attribute makes BCC structures harder and less malleable than closer packed materials such as gold. This may be important when selecting materials for specific applications.

Some metals that possess this crystalline structure include chromium, tantalum, molybdenum, tungsten and alpha iron.

## Corrosionpedia explains Body-Centered Cubic (BCC)

Metal atoms naturally pack themselves in a close arrangement to form the strongest metallic bond possible. In nature, several packing arrangements are found, including the body-centered cubic (BCC) arrangement.

One of the defining features of BCC is the directions in which the atoms are touching. The atoms do not touch along the edges of the cube. Instead, the atoms touch along the cube’s diagonal. In other words, the central atom touches all of the corner atoms.

**Packing Density in the Body-Centered Cubic**

One of the other parameters used to define the BCC structure is packing density. The packing density, also known as the atomic packing factor (APF), is essentially the fraction of the volume of atoms that occupy a crystal structure.

The APF of a BCC structure is equal to the volume of the atoms in the unit cell divided by the volume of the unit cell.

Therefore:

APF_{BCC} = V_{atoms}/V_{unit sphere}

Because there are two atoms in the BCC unit cell, each with a radius, r, the total volume of atoms in the cell is:

2 x 4/3πr^{3}

The volume of the cube is a^{3}. However, to get the volume in terms of r, we can use Pythagoras’ Theorem to get:

a^{2} + a^{2} + a^{2} = (4r)^{2}

Solving for a:

a = (4/√3)⋅r

Therefore, the volume of the cube in terms of r is

(4/√3⋅r)^{3}

Substituting the expressions for V_{atoms} and V_{unit} sphere:

APF_{BCC} = 2 x 4/3πr^{3} / (4/√3)^{3}⋅r^{3}

= 0.68

Therefore, the packing factor of a BCC unit cell is always 0.68. By contrast, the packing factor for a face-centered cubic unit cell is 0.74. This means that BCC cells are not as closely packed as their FCC counterparts.