MILLER INDICES:- Definition:

Definition:

          Miller indices is a system of notation of planes within a crystal of space lattice. They are based on the intercepts of plane with thee three crystal axes, i.e. edges of the unit cell. The intercepts are measured in terms of the edge lengths or dimensions of the unit cell which are unit distance from the origin along three axes.

          Miller evolved a method to designate a set of parallel planes in a crystal by three numbers h, k, and l, usually written within brackets thus (h, k, l) known as Miller indices of the plane.

Procedure for finding miller indices

The miller indices of a crystal plane are determined as follows:

STEP 1    :  Find the intercepts of the plane along the axes x, y, z ; Ex: 2, 2, 3.

STEP 2    :  Take reciprocals of the same ratio. Ex: 1/2, 1/2, 1/3.

STEP 3    :  Convert into smallest integers in the same ratio. Ex: 3, 3, 2.

STEP 4    :  Enclose in parentheses. Those are in the form of (h, k, l). Ex: (3, 3, 2).

Salient features of miller indices of crystal planes

1. All the parallel planes have the same miller indices. Thus the Miller indices defined a set of parallel planes.
2. A plane parallel to one of the co-ordinate axes has an intercept of infinity.
3. If the miller indices of the two planes have the same ratio [i.e., 841 and 422 or 211] then the planes are parallel to each other.