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Arun posted an Question

September 26, 2021 • 15:21 pm

30 points

IIT JAM
Physics (PH)

When can we say that two planes are parallel in terms of miller indices

when can we say that two planes are parallel in terms of miller indices

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Arun

It is said that indices that are in ratio,are parallel to each other ,can anyone please throw some light on it
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Anshum Sharma

Miller indices is a set or group of three numbers that indicates the orientation of a plane or a set of parallel planes of atoms in a crystal. These miller indices form a notation system in crystallography for planes in crystal lattices. Miller indices are determined by the intersection of the plane with axes. The reciprocals of these intercepts are calculated, the fraction gives out the three miller indices (hkl)(hkl) . For instances now, a plane parallel to two axis and cuts the third axis at the length equal to one edge of a unit cell will have miller indices of (100),(010),(100),(010), or (001)(001) depending upon the axis cut. And the plane cutting all three axes at the length equal to the edges of the unit cell will have miller indices of (111)(111). As of the question, the miller indices of two parallel planes in a crystal are the same because they are equally spaced parallel planes, so therefore the miller indices of equally spaced parallel planes are the same. As we know, miller indices does not only define a particular plane but also define a set of parallel planes. The planes whose intercepts are (1,1,1)(1,1,1),(3,3,3)(3,3,3),(−2,−2,−2)(−2,−2,−2) are all represented by the same miller indices.
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