Interactive guide to diffraction ..

Interactive Tutorial about Diffraction
Diffuse scattering: Occupational disorder II

Diffuse scattering
Thermal I
Thermal II
Occupational I
Occupational II
Longitudinal waves
Transversal waves
Short range order
Stacking faults

Interactive examples
Displacement waves
Short range order
Stacking faults

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The second example modifies the effect of replacement disorder. Now the crystal consists of rigid square molecules in a primitive cubic lattice. Instead of replaceing the atoms at random by the vacancies, we always replace a whole molecule by four vacancies. The left image shows a part of the crystal, 30*30 unit cells were used for the calculation. The middle image shows one quadrant of reciprocal space.

The Bragg reflections are shown as black dots, most of them are overexposed. Diffuse scattering results that is modulated in reciprocal space since the atoms are no longer replaced independently. Note that the diffuse scattering is more intense at shorter reciprocal vectors h. The modulation of the diffuse scattering can be explained by calculating the Fourier transform of a single rigid square molecule (right image above). This Fourier transform shows the same modulation as that of the diffuse scattering observed from the disordered crystal. In real space randomly occupied and empty points on a cubic primitive lattice are convoluted with the molecule. In reciprocal space the monotonous Laue scattering is multiplied by the Fourier transform of a single molecule. Since the monotonous Laue scattering is strongest near the origin of reciprocal space, the diffuse scattering of this crystal is strongest at the origin of reciprocal space as well.