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Roo2

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What I don't understand is why only maximal-intensity waves are observed. Unless the two waves are π radians out of phase, there should still be some constructive interference that gives rise to amplitude at the detector plate. Therefore, there should be some intensity at almost any value of θ. The wikipedia page on Bragg's law acknowledges this fact:

It should be taken into account that if only two planes of atoms were diffracting, as shown in the pictures, then the transition from constructive to destructive interference would be gradual as the angle is varied. However, since many atomic planes are interfering in real materials, very sharp peaks surrounded by mostly destructive interference result.

Unfortunately, I don't see a clear and unbroken line of reasoning in the explanation. So many atomic planes means more complex interference... why is that guaranteed to produce mostly destructive interference? For help, I turned to Gale Rhodes' Crystallography made Crystal Clear. He explains it as follows:

For other angles of incidence θ' (where 2d(hkl) sinθ does not equal an integral multiple of λ), waves emerging from successive planes are out of phase, so they interfere destructively, and no beam emerges at that angle. Think of it this way: If X-rays impinge at an angle θ' that does not satisfy the Bragg conditions, then for every reflecting plane p, there will exist, at some depth in the crystal, another parallel plane p' producing a wave precisely 180° out of phase with that from p, and thus precisely cancelling the wave from p.

This is starting to approach an answer but I don't think it's complete. Why must there exist some parallel plane that produces a 180 degree phase shift? Why do such cancelling planes not exist for the set of planes that comply with Bragg's equation?

Thanks for any help!