The Miller indices of a material in a plane are proportional to

Concept:

Miller indices are the styles to designate the planes and directions in the unit cells and crystals.

Miller indices (hkl) are expressed as a reciprocal of intercepts p, q, and r made by the plane on the three rectangular axes x, y and z respectively. These are the unit distances from the origin along the three axes. Thus

\(h=\frac{1}{p},~k=\frac{1}{q},~l=\frac{1}{r}\)

where, p = intercept of the plane on the x-axis, q = intercept of the plane on the y-axis, and r = intercept of the plane on the z-axis.

Reciprocal of these intercepts are then converted into whole numbers. This can be done by multiplying each reciprocal by a number obtained after taking LCM of the denominator.

This gives the Miller indices of the required plane. The Miller indices are expressed by three smallest integers.