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When x-ray falls on an atom,the atom scatters it in all 4pi solid angles. In case of a crystal also the atoms sitting in different planes scatter light in all 4pi direction. But when it comes to Bragg equation, we always consider the forward direction only. Bragg equation can also be satisfied on all points of a circle which lies on an outer plane that is parallel to the crystal plane which is considered ie when the incident and reflected beams and the normal to the surface are not in same plane.

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  • $\begingroup$ It does. Look at Laue diffraction, for example, which is often used in a backscattering geometry. Or did you mean non-specular? $\endgroup$ – Pieter Oct 1 '19 at 8:55
  • $\begingroup$ Yes, I mean non specular Or when the incident and reflected beams and the normal to the diffracting planes are not in the same plane. Thanks $\endgroup$ – user103515 Oct 1 '19 at 10:29
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Yes, individual atoms scatter in all directions. But they add upp in phase when the scattered wave comes from a plane only for the specular direction.

The Bragg conditions is the next step, adding reflections from many planes with the same orientation and distance.

Crystals have many such planes in many directions. And in reality, of course, there are no planes that the atoms "sit on". There are just 3D arrays of scattering centers. One can understand Laue diffraction by considering the response of these scattering centers to a pulse (not a wave).

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  • $\begingroup$ My question is not on lau diffraction. I need to know why the incident ray, diffracted ray and normal to the plane need to lie on same plane in Bragg diffraction. $\endgroup$ – user103515 Oct 3 '19 at 17:59
  • $\begingroup$ @user103515 I will say it again: only for the specular direction, the scattered waves add upp in phase when the scattered wave comes from a plane. $\endgroup$ – Pieter Oct 3 '19 at 20:01
  • $\begingroup$ Dear Sir, I want know why this happens? Would you please elaborate why they add up in phase in specular direction only. In fact this is my question. $\endgroup$ – user103515 Oct 5 '19 at 2:04
  • $\begingroup$ @user103515 One way to see this is to use Fermat's principle, the principle of least time. Near the minimum, the phases are approximately constant. $\endgroup$ – Pieter Oct 5 '19 at 7:53

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