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Miller Indices


Miller Indices are sets of three integers, designated h, k, l, which uniquely define the orientation of a lattice plane, relative to a crystal's unit cell.

A lattice plane's orientation can be defined in terms of its intersections with the three crystallographic axes, x, y, and z. If a unit cell has edge lengths a, b, and c, and the first lattice plane from the origin cuts these axes at a/h, b/k, and c/l, then the Miller Indices of that plane are: (h k l).

Miller indices are invaluable when treating diffraction patterns of crystals, since the reflexions observed arise from the parallel and repeating lattice planes inside the crystal. Different orientations and spacings of lattice planes (i.e., different Miller Indices) give rise to different x reflexions.


Miller indices are named after a distinguished professor at the University of Cambridge in the nineteenth century. Miller was a highly accomplished academic, being a scientist and mathematician, and later becoming Professor of Classics in the university.


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