Problem: Random Displacement

     Consider an ``imperfect" crystal, where the nth atom is displaced from its ideal position, , by a random vector . We will look at the diffraction peak at around the reciprocal lattice vector . Assume that the displacement at site n is , where a is the average lattice spacing. Show that the diffraction peak intensity will change little for small , but will disappear at larger ! What is the shape of the envelope (peak height versus )?