Neutron Scattering

A straightforward method to investigate mesoscopic length scales without taking into
account the exact molecular structure ofthe samples is the small angle scattering . `Small angle'
in this case means that the mean value of the wave vector transfer IQI of the scattered beam is
much smaller than the typicalreciprocal spacing of the atours in the sample (e.g., the reciprocal
lattice vector ja * 1 for a crystal with cubic synimetry) . In this case the effects of the atomic
structure on the scattered signal are negligible . This is schematically explained in Figure 6.2 .
real
space
Fourier U transformation
Q_
space
M v~
small Q /'U \
approximation
Q_
space
Fourier U backtransformation
real
space
Figure 6.2: Principles of small angle scattering . The method is not sensitive to the exact
atomic structure but only to mesoscopic or macroscopic length scales. Therefore, samples can
be treated as continuons systems. The operator © denotes the convolution of two functions.
A more detailed explanation is given in the text.
6 .2