Intersections of a plane and the x , y and z axes, as shown in figure 3.6, are used to determine the Miller indices of the plane. The Miller Indices h, k, l are obtained as follows:
Determine the points at which a given crystal plane intersects the three axes, for example at (a, 0, 0), (0, b, 0), (0, 0, c). If the plane is parallel an axis, it is said to intersect the axis at infinity.
The Miller index for the face is then specified by (1/a, 1/b, 1/c), where the three numbers are expressed as the smallest integers (common factors are removed). Negative quantities are indicated with an over bar.
Example 2:
A plane intersects the crystallographic axes at (2, 0, 0), (0, 3, 0), (0, 0, 4).
Step 1: (1/2, 1/3, 1/4); multiply by 12 to express as smallest integers.