Why does (100) and (010) have the shortest reciprocal lattic

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SUMMARY

The discussion clarifies that in the hexagonal close-packed (HCP) structure, the planes (100) and (010) exhibit the shortest reciprocal lattice vectors due to their geometric arrangement. The (001) plane is excluded from this consideration because its d-spacing corresponds to the distance between alternating A layers, which is greater than the d-spacing of the (100) plane that reflects the diameter of the spheres in the stacking sequence. This distinction is crucial for understanding the reciprocal lattice properties of HCP structures.

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Armani
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Can anyone explain why the two planes (100) and (010) in the HCP structure have the shortest reciprocal lattice vectors?
I mean it says {001}, but why is (001) not included?
 
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In the HCP structure you stack alternating layers in a ABAB... sequence. The (001) d-spacing is the distance between two A layers, and that is larger than the (100) d-spacing which is simply the diameter of the (hypothetical) spheres you stack.
 
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