Electron collision and periodic crystal

[hokhani]

Ashcroft & Mermin, Solid State Physics, page 315:
"According to the Bloch theory, an electron in a perfectly periodic arrays of ions experiences no collision at all".

But how about the electron at the border of Brillouin zone? How does diffraction take place there?

 

[UltrafastPED]

Brillouin zones are just a k-space version of the unit cell. Your book is telling you that perfect crystals don't have electron scattering events.

For a nice discussion see: http://www.tf.uni-kiel.de/matwis/amat/semi_en/kap_2/backbone/r2_1_4.html

The conclusion from Ashcroft & Mermin is included. Note that Bragg reflections (diffraction patterns) are a result of interference effects between electron wave functions, not scattering of electrons.

 

[hokhani]

Note that Bragg reflections (diffraction patterns) are a result of interference effects between electron wave functions, not scattering of electrons.

Ok, Thanks. But why do electron wave functions interfere? As far as I know, it is due to scattering.

 

[UltrafastPED]

But why do electron wave functions interfere?

The "wave function" is a representation of the probability amplitude wave ... and interference is a fundamental wave property. If they _didn't_ interfere it would mean that there is no wave.