Space Lattice (crystal Lattice)

SPACE LATTICE (CRYSTAL LATTICE)

A crystal is an array of atoms in three dimensions. As a matter of convenience, these atoms can be associated with a set of imaginary points in space.

These points are arranged in such a way that every point has an identical surrounding as any other point in three dimensions and it is known as a space lattice or simply lattice.

Lattice is an imaginary geometrical concept. It is a large assembly of points in which each point represents the position and orientation of an atom in the crystal.

Note: In 2 dimensions, the arrangement of points is only in 2D (X & Y).

Definition - Space lattice is an array of points in space to represent atoms in a crystal in which the environment about each point is the same i.e., every point has identical surroundings as that of every other point in the array.

Explanation

The collection of points in two dimensions is shown in fig. 1.3 (a) and (b)

It is found that in fig 1.3 (a) the environment (position of neighbouring points) about any two points is same. Hence, it is a 2D lattice.

The mathematical representation of a 2D lattice is T = la + mb where l and m are integers, a and b are the translation vectors in X and Y directions.

For example T = AB = 2a + 2b as shown in fig 1.3(a)

On the other hand, in fig. 1.3 (b) the environment about any two points is not the same. So, it is not a proper lattice.

A similar argument is extended to three-dimensional space lattice. For 3D, T = la + mb + nc such that a, b and c are the translation vectors.

Lattice points

The points in a space lattice are called points (Fig. 1.4).

Lattice lines

The lattice points are joined with lines as shown in fig. 1.4. These lines are known as lattice lines.

Lattice plane

A plane containing lattice points is known as lattice plane. (fig. 1.4)