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bragg vs diffuse

Here is a classical example showing the difference between the Bragg peaks and the diffuse scattering. Here we simulated three 2D binary crystals, all of which have an average structure A0.7B0.3. In the left case, the A and B atoms do not care about their neighbors - random distribution. In the middle case, both A and B like to form clusters locally (phase separation), a type of short-range order. A and B perfer to form pairs in the right case - locally creating 2*2 supercells. All three cases will generate the identical Bragg reflection patterns because they have the same average structure. However, the diffraction patterns in the reciprocal space are very different. It is a merely 2D lattice with point-like Bragg peaks for the random distribution case. The other two show distinct and structured diffuse scattering patterns. Therefore, by studying the diffuse scattering pattern, one can know more detailed information about the atoms' arrangement in the crystals.

the wonderland rule

This simulation illustrates a simple relationship between the real space and the reciporcal space - big in the real space <==> small in the reciprocal space.

the size effect

Simulated diffse scattering pattern from a binary array with two different ionic sizes.