Display a Lattice Plane

CrystalMaker X lets you display any number of lattice planes, slicing through your crystal structures. You can select a plane and move it through the structure (along the direction of its plane normal); you can also displays sets of parallel planes (good for teaching).

You can use a single lattice plane as a guillotine, to hide atoms on one side of the structure - or to insert space in a crystal lattice. You can use a pair of planes to isolate an oriented slab of material.

To display a lattice plane:

Navigate to the Volume Inspector and locate the Lattice Planes group.
Double-click in an empty Lattice Planes list row to add a dummy plane.
Edit the Miller Indices and choose the colour and opacity.

Lattice Plane Position

There is a common misconception that the Miller Indices of a lattice plane, e.g., "(200)" somehow fix the lattice plane at a particular point in space - e.g., half-way up the unit cell's "a" axis. This is wrong!

Miller Indices define the orientation of a plane's normal and, if one is referring to a set of lattice planes, their relative spacing. However, they provide no information about the absolute position of the planes in space.

Miller Indices were derived long before scientists understood about the atomic structures of crystals. They were used for specifying the relative orientations of crystal faces; the ratios of the three indices, h, k and l giving the orientation of a single plane, relative to the crystal.

The origin of the "fixed-in-space" misconception probably stems from an over-simplistic approach when teaching crystallography. It is usual to start with a block model of a "unit cell", and to demonstrate Miller Indices in terms of the first intercepts from the origin made by a particular plane. However, that does not mean that the plane has to be fixed in space. After all, most crystals have billions of unit cells - so which unit cell would the plane be fixed to? Furthermore, the "origin" can be anywhere within the crystal lattice - and it is common to shift the origin for convenience. That does not mean that the Miller Indices of planes suddenly change: (100) doesn't suddenly become (200) or some other value!

Summary:

For a single lattice plane, the Miller Indices define only the orientation of its plane normal - not its absolute position.
When dealing with a set of parallel planes, the Miller Indices also define the separation (d-spacing) of the planes. Thus, a set of (200) planes would have one-half the d-spacing of a set of (100) planes.