For those interested I came across a more in-depth derivation of the Von Laue condition and the structure factor.
physics.valpo.edu/courses/p440/Diffraction_Crystal_Structure.ppt
By treating the incident waves as plane waves and the atoms as point scatterers, the scattered waves take the form of isotropic spherical waves. One can then work through and derive the total scattered wave as a sum of the contributions of all the atoms.
By calculating the related intensity of this scattered wave the Laude condition falls out trivially. The derivation up to this point is slightly more complicated then that done in class, however it is mathematically more appealing and concrete.
To derive the structure factor the amplitude of the scattered wave is considered, and the the structure factor Sk is defined from it. Its nice to see how this measure can fall out from a relatively quick derivation.
If I'm given lambda and theta, the angle at which diffraction peaks occur. I can work out the sum of (h_square + k_square + l_square). However, I'm not quite sure how to determine the type of lattice form that.
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