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When doing electron diffraction on graphite (a popular experiment for students at universities) always diffraction at these two planes with distances $d_1$ and $d_2$ are observed:

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But a plane parallel to the ones with distance $d_2$ can also be formed with a distance of the atom spacing $s$. When looking through crystal diffraction databases there's also no data about diffraction on these "$s$" planes.

Why is it not possible that electrons or X-Rays scatter at the planes with distance $s$ or some multiple of it?

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You can make two parallel planes a distance $s$ apart in the way you describe, but you need an infinite stack of them $s$ apart to get diffraction.

The reason there are no such stacks even though the distance between sites is $s$, is because the honeycomb is actually a triangular tiling, where the corners of the triangle are every other atom. So the vector which connects the two adjacent is not actually a symmetry of the crystal (i.e. it is not a Bravais lattice vector).

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