BCC, FCC and Primitive Cubic Unit Cell

The 3D arrangement of atoms, molecules or ions inside a crystal is called a crystal lattice. It is made up of a large number of unit cells. One of the three constituent particles takes up every lattice point. A unit cell can either be primitive cubic, body-centered cubic (BCC) or face-centered cubic (FCC). In this section, we will discuss the three types of unit cell in detail.

In the primitive cubic unit cell, the atoms are present only at the corners. Every atom at the corner is shared among 8 adjacent unit cells. There are 4 unit cells in the same layer and 4 in the upper (or lower) layer. Therefore, a particular unit cell has only 1/8th of an atom. Each small sphere in the following figure represents the center of a particle which occupies that particular position and not its size. This structure is known as an open structure.

simple cubic unit cell

simple cubic unit cell

In each cubic unit cell, there are 8 atoms at the corners. Therefore, the total number of atoms in one unit cell is: 8 × 1/8 = 1 atom.

A BCC unit cell has atoms at each corner of the cube and an atom at the center of the structure. The diagram shown below is an open structure. According to this structure, the atom at the body center wholly belongs to the unit cell in which it is present.

Body centered Cubic Unit Cell

Body centered Cubic (BCC) Unit Cell

Thus, in a BCC cell, we have:

  • 8 corners × 1/8 per corner atom = 8 × 1/8 = 1 atom
  • 1 body center atom = 1 × 1 = 1 atom

Therefore, the total number of atoms present per unit cell = 2 atoms.

An FCC unit cell contains atoms at all the corners of the crystal lattice and at the center of all the faces of the cube. The atom present at the face-center is shared between 2 adjacent unit cells and only 1/2 of each atom belongs to an individual cell.

face centered cubic unit cell

face centered cubic (FCC) unit cell

Thus, in a face-centered cubic unit cell, we have:

  • 8 corners × 1/8 per corner atom = 8 × 1/8 = 1 atom
  • b) 6 face-centered atoms × 1/2 atom per unit cell = 3 atoms

Therefore, the total number of atoms in a unit cell = 4 atoms.

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Practise This Question

Select the rate law that conforms to the following data for the reaction : A+BProducts
Exp No.[A](mol L1)[B](mol L1)Initial rate(mol L1S1)10.00120.00351×10420.0240.0708×10330.0240.0351×10340.0120.0708×103