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Thermodynamics

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Miller Indices

In a crystal, lattice points are systematically arranged in parallel planes. An aggregate of a set of parallel equidistant planes passing through the lattice points represents a crystal lattice. The parallel planes are called lattice planes. In fig. (a), (b), (c) etc. represent three different sets of a lattice planes.

Consider that the intercepts of the given lattice plane (i) along the x-axis is ra, (ii) along the y axis is sb (iii) along the z-axis is tc.

Here, a, b and c are the primitives (vectors, of a unit cell) along the three coordinate axes x, y and z. Here r, s and t are mere numbers only (small integer or a simple fraction).

Let h, k and l represent the smallest possible integers satisfying the condition

h : k : l = 1/r : 1/s : 1/t

Here, h, k and l are called Miller indices for a given set of planes and the plane is designated as (h, k, l).