Neutrons (mass: M = 1:675.1e-27) with a wavelength of λ= 1:8 Å are scattered at a LiF crystal (sodium chloride structure with lattice parameter a = 4:02Å) and leave the crystal with a wavelength of λ' = 1:15Å . The incident neutron beam travels along the [100] direction (in terms of the crystal coordinate system) and is scattered within the (001) plane by 30°.

Question

Neutrons (mass: M = 1:675.1e-27) with a wavelength of  λ= 1:8 Å are scattered at a LiF crystal (sodium chloride structure with lattice parameter a = 4:02Å) and leave the crystal with a wavelength of λ' = 1:15Å . The incident neutron beam travels along the [100] direction (in terms of the crystal coordinate system) and is scattered within the (001) plane by 30°.

a) Are phonons destroyed or created in the crystal?
b) What are the magnitudes of the incident wavevector k and the scattered wavevector k'? What is the frequency of the involved phonon in Thz?
c) Which reflection is involved (i.e., Laue or Miller indices)? Hint: You have 2 wavelengths. Check them both and decide what reflection fits best and is most realistic. What is the magnitude of the corresponding reciprocal lattice vector (g_hkl = 2π/d_hkl with d_hkl the net plane distance)?
d) Draw a sketch of the scattering process!
e) What is the magnitude of the wave vector of the phonon?