Planes

Planes in a crystal are identified by their Miller indices. The system involves;

1. Writing the intercepts on the three axes;

2. Taking the reciprocals;

3. Reducing these to the lowest set of integers in the same ratio;

4. Enclosing in parentheses.

EXAMPLE PROBLEM AI.1: Write the Miller indices of the two planes shown in Figure AI.1.

Solution: For plane a:

1. The intercepts on the three axes are 1, ∞, and 1. Note that the y intercept is taken as ∞ because the plane does not intercept the y axis.

2. Reciprocals are 1, 0, and 1.

3. These are already reduced to lowest set of integers in same ratio.

4. The plane is (101).

For plane b:

1. The intercepts on the three axes are 1, −1, and 1/2. Note that the plane has to be extended out of the cubic element to intercept the y axis at −.

2. Reciprocals are 1, −1, and 2.

3. These are already reduced to lowest set of integers in same ratio.

4. The plane is (112). Note that the minus sign is indicated by an over bar and that no commas are used.

Directions

Directions are indicated by their components parallel to the three axes reduced to the lowest set of integers and enclosed in brackets, [].