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Physics
Atomic and Condensed Matter
Miller indices for hexagonal crystal systems
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[QUOTE="M Quack, post: 5818393, member: 396278"] The 4 Miller indices often used with hexagonal crystals are just a convenience. The 3rd index can be dropped. 4 indices are used to make planes with the same symmetry also "look alike" in the 4-notation. The physical reason is that the a- and b- axes form a 120 degree angle. There is a third axis within the basal plane that has the exact same symmetry. You get this axis, let's call it "d", by rotating the b-axis by another 120 degrees. So instead of using a and be as basis vectors, you could just as well use b and d, or d and a. Absolutely nothing would change, as the 120 degree rotation is the defining feature of a hexagonal crystal. The redundant 3rd Miller index corresponds to the reciprocal space "d*" axis. The 4th index is along the c-axis. [/QUOTE]
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Miller indices for hexagonal crystal systems
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