Miller indices are integer sets
that were created to distinguish directions and planes in a lattice
. They are used primarily in crystalline
structures because they describe plane
s in relation to a larger lattice
terms, as opposed to absolute
terms. An example of this is describing planes in a building, Miller indices would distinguish the floor from the walls, and north wall from west wall, however it would not distinguish the 4th floor from the 5th floor. This is useful in crystal lattice
s because the planes are the same in many direction
s (like floors in a tall building).
Calculating Miller Indices
To calculate Miller indices take the reciprocal of the x, y, z intercepts and reduce the result down to lowest integers. If the xyz intercepts of a plane are (1,0,2) the reciprocal is (1,0,1/2) and the Miller Indices are 2 0 1.
Negative intercepts can be shown by placing a bar over the corresponding index. Common notation is to put the indices in brackets when they describe the form of a crystal and to leave them without brackets if they describe a face of the crystal. Named after British mineralogist William H. Miller.