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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:

   (212)

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.