Laue Diffraction Intensity Distribution

[twosockz]

I am trying to experimentally determine the atomic scattering factors for NaCl using Laue photography. For an NaCl crystal, the intensity of the wave scattered at the unit cell is proportional to (4⋅(f_Cl+f_Na))² if h,k,l are even and to (4⋅(f_Cl-f_Na))² if h,k,l are odd. f_Na and f_Cl are the atomic scattering factors which depend on sin(θ)/λ.

Therefore, I think that if sin(θ)/λ is approximately equal for two sets of h,k,l (one all even and one all odd), then we can combine the two equations to get:
I_even+I_odd∝32⋅(f_Na²+f_Cl²)
&
I_even-I_odd∝64⋅f_Na⋅f_Cl
(Is this correct so far?)

I plan to calculate the intensity ratios using pixel values of a scanned photographic x-ray film, as shown below. As such, we can then find the ratio of the scattering factors for Sodium and Chlorine using the equations above.

Attempting to use the (3,5,1) (odd) and (4,4,2) (even) Miller indices, which both have sin(θ)/λ ~ 0.05, I noticed a problem, as the second intensity equation implies that I_even>I_odd, but, as shown below, this clearly isn't the case.

Are there any other factors affecting the intensity distribution that I am missing?

 

[Lord Jestocost]

I suppose it will be a tremendous task to determine the atomic scattering factors for NaCl using Laue photography.

Quoting from [PDF]LAUE Laue Back-Reflection of X-Rays - University of Toronto Physics:

“The size, intensity, and shape of a Laue spot depends on many factors, including the spectral intensity and angular dispersion of the X-ray beam, the perfection of the crystal, the thermal motion of the atoms in the crystal planes, the spectral absorption of beam and diffracted X-rays in the crystal, the angle of the spot,…. Only a few of these factors are discussed here; for more detail, see Cullity Ch. 4 and Preuss Ch. 2.3.”

Here is the link to Cullity’s book:
B.D. Cullity, Elements of X-ray Diffraction, Addison Wesley 1956; https://archive.org/details/elementsofxraydi030864mbp