PHZ 6426 (Solid State I) Homework 8

Due Nov. 22

1. Ashcroft and Mermin Problem 24.2.

2. A beam of thermal neutrons is incident along the [111] direction of a single crystal of gold (fcc direct lattice) with a lattice constant a = 4.08 Angstroms.

   (a) Obtain an expression for the lowest energy a neutron can have if it is to be elastically scattered backward along the [111] direction. Evaluate your expression in electron volts.

   (b) Repeat part (a) for elastic scattering along the forward (incident) [111] direction.

   (c) Due to the zero-point and thermal motion of the gold atoms, there is a difference between the intensity for the minimal energy scattering in cases (a) and (b). Which of these cases produces the greater intensity, and why?