Indexing a Plane
This is a 3D array of atoms in a primitive cubic lattice.
It can be represented as periodic unit cells.
Now consider a single unit cell.
The lengths of the edges are defined by distances, known as the lattice parameters:
Suppose we have a plane within this unit cell.
Taking reciprocals of these intercepts gives the Miller indices:
If the intercepts are:
1/h on the x-axis,
1/k on the y-axis,
1/l on the z-axis.
The Miller indices are (hkl)
Or, if the resulting indices contain fractions; multiply throughout to give integer values of h,k, and l.