Why Does Bragg Diffraction Occur for Bound Electrons in a Crystal?

[hokhani]

As far as I know, Bragg diffraction happens for incident particles which are free; for example free electrons or X-ray are Bragg-reflected under the special conditions. Why the Bragg diffraction happens for electrons which are not free in a crystal?

 

[M@2]

As far as I know, Bragg diffraction happens for incident particles which are free; for example free electrons or X-ray are Bragg-reflected under the special conditions. Why the Bragg diffraction happens for electrons which are not free in a crystal?

Bragg diffraction happens for WAVES.
Waves can be of any nature and spread in any medium. Electron wave in ion's lattice is a WAVE with ions as diffracting screen.

 

[hokhani]

If we consider the diffraction classically, incident waves are in direction of k and reflected waves are in direction of k^\prime and G=k-k^\prime. But for electrons in crystals direction of motion is not direction of wave vector.

 

[M@2]

If we consider the diffraction classically, incident waves are in direction of k and reflected waves are in direction of k^\prime and G=k-k^\prime. But for electrons in crystals direction of motion is not direction of wave vector.

If we consider the diffraction classically

In classical physics electrons are not WAVES, so you could not bragg diffract electrons.