Scattering on random alloys ↩

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created: 2021-11-01 00:56:15
modified: 2022-01-10 04:13:03

Let's consider scattering on a Bravais lattice where the atoms sitting in the positions of lattice vectors are of type or type by random chance. In this case the atomic form factors of the atoms in lattice vectors are independent, discrete random variables. The form factor will be with probability and with probability .

We can get the expectation value by considering these:

The intensity for a given change in wavenumber :

Averaging it out for the randomness of the atoms:

We can see that the intensity has an incoherent contribution that gives a constant background to the scattering pattern and it also has a coherent contribution that just modulates the Bragg peaks.