## Crystal Lattice and Unit Cells

Crystal Lattice and Unit Cells

We have discussed that all crystals consist of regularly repeating array of atoms, molecules or ions. It is much more convenient to represent each particle by a point, called lattice point, or lattice site rather. This results in a three dimensional orderly arrangement of points called a space lattice or a crystal lattice.

Thus, a space lattice or crystal lattice may be defined as a regular three dimensional arrangement of identical points in space or it can be defined as an array of points showing how molecules, atoms or ions are arranged at different sites in three dimensional space.

• Each point in the lattice is known as lattice point or lattice site
• Each point in the lattice represents the constituent particle. These particles may be atoms, ions or molecules depending upon the nature of the crystalline solid.
• Lattice point s are joined together by straight lines in order to depict the geometry of the solid

## What is a Unit Cell?

A unit cell is the smallest but complete repeating unit in space lattice which when repeated over and over again in the three dimensions, generates the crystal of the given substance. Unit cell may also be defined as a three dimensional group of lattice points that generates the whole lattice on repetition.

A unit cell is characterized in terms of

Edge length and angle between edges

• Edge length: Its dimensions along the three edges, a, b and c.
• Angles between the edges, α (between b and c) β (between a and c) and γ (between a and b).

Thus, a unit cell is characterized by six parameters, a, b, c, α, β and γ.

## Types of unit cells

### Simple unit cell or Primitive unit cell

A unit cell having lattice points only at the corners is called simple, primitive or basic unit cell. A crystal lattice having primitive unit cell is called simple crystal lattice.

### Face centred cubic lattice  (FCC) –

A unit cell in which the lattice point is at the centre of each face as well as at the corner.

#### Body centred cubic lattice (bcc) –

A unit cell having a lattice point at the centre of the body as well as at the corners.

##### End – centred unit cell:

It is possible for orthorhombic and monoclinic crystal types. In an end centred there are lattice points in the face centres of only one set of faces in addition to the lattice pints at the corners of the unit cell.