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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.

We can define a set of axes, x, y and z, that describe the edges of this unit cell.

The lengths of the edges are defined by distances, known as the lattice parameters:

*a* on the x-axis,

*b* on the y-axis,

*c* on the z-axis.

Suppose we have a plane within this unit cell.

This plane intercepts:

the x-axis at *a*/2,

the y-axis at *b*/1,

the z-axis at *c*/2,

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*.