Why Does n=2 Not Produce an Equally Strong Peak in X-ray Diffraction?

[thcommj]

1. In satisfying the Bragg's law, $$n\lambda=2d\sin\theta$$, n is typically assumed to be one, which explains why we see only one peak for a particular plane (say [400] plane for silicon). But I really don't see why n=2 should not appear as an equally strong peak..?

2. Is the Fourier transform effect of X-ray scattering comparable to that of a Fraunhoffer diffraction by multiple slits?

3. In calculating the Fourier transform of the original lattice, how is the origin of the r vectors determined? Or it doesn't matter?

Thanks!

 

[bpsbps]

(1) Purely according to Bragg's law it should be an equally strong peak. However there is also a matter of the structure factor and atomic scattering factors. See B.D. Cullity chapter 4.

(2) I don't know

(3) It doesn't matter. The lattice vectors describe the translational periodicity of the crystal. Sometimes it is conceptually convenient to define one of the atoms as the origin, but this isn't necessary.