The Principles of Neutron Scattering

Polymer Spectroscopy. Edited by Allan H. Fawcett 1996 John Wiley Sons Ltd 

It is first useful to recall that the neutrons can be considered as either particles or waves the connection between the two descriptions is provided by the de Broglie relationships  

The calculation of scattering patterns is based on the summation of amplitudes or intensities scattered from all components. The intensity I of a wave described in the usual notation of complex variables is given by 

This is known as the Bom approximation for scattering from weak potentials. It is seen that the scattered wave is spherically symmetric and decreases in intensity as l/ r, which is the usual inverse square law. For a distribution of scattering lengths described by a density p(r) the resulting amplitude is 

The quantity p r)p r ) is the spatial correlation function of the scattering length density, and the integral with is equivalent to a Fourier transform. It 

---

Even though TEM and SEM played major roles in the study of IPN morphological features, there are various shortcomings, such as staining artifacts, difficulties in sample preparation for very rubbery materials, and the two-dimensional viewing limit for the former. Recently, various scattering techniques have been applied to measure the phase dimensions of IPN s via statistical treatment. The principles of neutron scattering theory as applied to the phase separated materials have been described in a number of papers and review articles [33-36]. 

The principles of neutron scattering theory as applied to the solution of polymer problems have been described in a number of papers and review articles (8-23). The coherent intensity in a SANS experiment is given by the scattering cross-section dl/dG, which is the probability that a neutron will be scattered into a solid angle, for unit volume of the sample. The quantity d /dG expresses the neutron scattering power of a sample and is the counterpart of the Rayleigh ratio, R(0), used in lightscattering. 

---