1) 40 points total with 8 points for each question: Sodium hydride has the same crystal structure as the table salt NaCl is shown in the figure with the positions of the ions in the cubic unit cell as the followings: Nat (0 0 0) (1/2 1/2 0) (1/2 0 1/2) (0 1/2 1/2) H- (0 1/2 0) (1/2 0 0) (0 0 1/2) (1/2 1/2 1/2). Chloride ion Sodium ion Approximate the Debye-Waller factor as 1, a) Calculate the squared structure factor |F(T)² at T =(hkl) in analytic form for neutron Bragg diffraction when common 'H is contained in the hydride. b) Repeat to get the analytic squared structure factor when ID is used to synthesize the hydride. c) Calculate the Bragg powder diffraction intensity mF(T)² at T =(111) and (200) for NaH and NaD. Pay attention to the multiplicity of the Bragg peaks. d) Take the diffraction patterns on page 10 of the Lecture 6, now take 30min to count each data point, what will be the peak counts at (111) and (200) for NaH and NaD and what will be their standard deviations? e) Similarly, estimate the background intensity with the error bar at (111) and (200), then give the peak intensity (peak value-background) of them with the error bar for NaH and NaD. Are the intensity ratio I(111)/(200) consistent with your theoretic values for the two materials?

Fig: 1