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

[thcommj]

1. In satisfying the Bragg's law, [tex]n\lambda=2d\sin\theta[/tex], 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.

 

[charng]

1. The value of n in Bragg's law represents the order of the diffraction peak and is typically assumed to be one because it corresponds to the most intense diffraction peak. This is because the diffraction intensity decreases with increasing order due to factors such as the atomic arrangement and the wavelength of the X-rays. However, it is possible for higher order peaks to appear, but they will typically be weaker and may not be as easily detected.

2. The Fourier transform effect of X-ray scattering is similar to Fraunhofer diffraction by multiple slits in that both involve the interference of waves. However, X-ray scattering involves the interaction of X-rays with the periodic arrangement of atoms in a crystal, while Fraunhofer diffraction involves the interaction of light with a series of parallel slits. Therefore, there are some differences in the mathematical equations used to describe these phenomena.

3. In calculating the Fourier transform of the original lattice, the origin of the r vectors is typically chosen to be the center of the unit cell. However, this choice may vary depending on the specific crystal structure and the purpose of the calculation. In general, the origin of the r vectors does not significantly affect the resulting Fourier transform, but it may be important to consider for some applications.