Answer to Question #160493 in Material Science Engineering for Roshan Prasad Mallia

Question

Explain miller indices for denoting crystal planes.

Answer 1

Miller Indices are a symbolic vector representation for the orientation of an atomic plane in a crystal lattice and are defined as the reciprocals of the fractional intercepts which the plane makes with the crystallographic axes.

The method by which indices are determined is best shown by example. Recall, that there are three axes in crystallographic systems (*except sometimes in the hexagonal system adopts a convention where there are four axes). Miller indices are represented by a set of 3 integer numbers.

 Example of the (111) plane:

If you want to describe the orientation of a crystal face or a plane of atoms within a crystal lattice, then there are series of steps that will lead you to its notation using Miller indices.

1. The first thing that must be acertained are the fractional intercepts that the plane/face makes with the crystallographic axes. In other words, how far along the unit cell lengths does the plane intersect the axis. In the figure above, the plane intercepts each axis at exact one unit length.

2. Step two involves taking the reciprocal of the fractional intercept of each unit length for each axis. In the figure above, the values are all 1/1.

3. Finally the fractions are cleared (i.e., make 1 as the common denominator).

4. These integer numbers are then parenthetically enclosed and designate that specific crystallographic plane within the lattice. Since the unit cell repeats in space, the notation actually represents a family of planes, all with the same orientation. In the figure above, the Miller indice for the plane is (111)