Interactive Tutorial about Diffraction
Diffuse scattering: Occupational disorder I
The third example shows the effect of replacement disorder. We are using the
identical crystal structure as in examples 1 and 2. The crystal consists of
square molecules in a primitive cubic lattice. 50% of all atoms are replaced
independently and at random by a vacancy.
The left image shows a part of the crystal, 30*30 unit cells were used
for the calculation. The right 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 essentially monotonous in reciprocal space. Note that now the diffuse scattering is more intense at shorter reciprocal vectors h a typical phenomenon of replacement disorder. Lets look again at the formula from the first example:
Now u - < u > is zero for all atoms. The term (f - < f > ) is largest near the center of reciprocal space and diminishes with the diminishing value of < f >. Note that this relationship holds only for X-ray diffraction! Since the scattering length f for neutron scattering is independent of the absolute value of h, the random replacement diffuse neutron scattering is independent of the location in reciprocal space.
|© Th. Proffen and R.B. Neder, 2003|