Small-angle neutron differential scattering cross section

Figure 5 - Small angle neutron differential scattering cross section (ooo) measured from a sample consisting of sheets of PIP (N = 23000) and deuterated 1,2-PBD (N = 3200) which were in contact for 162 hours at 52°C. The scattering contrast significantly exceeds the incoherent background (—) determined from measurements on the individual polymers, evidencing the thermodynamic miscibility of the blend.

The scattered intensity is defined in terms of the normahzed differential scattering cross-section per unit volume, dX((2)/dQ (expressed in units of cm ), where dE((2) (neutrons s ) represents the number of neutrons scattered per second into a small solid angle, dfi. In general,... 

S A N S can be employed to study both homogeneous as well as heterogenous blends and various information can be derived by analysis of the differential scattering cross-section, d2(Q)/dQ (cm ), where d2(Q) (neutron s ) is the number of neutrons scattered per second into a small solid angle, dQ. The measured intensity, I Q), is related to d 2(Q)/d Q and depends on various parameters such as the incident flux, resolution of the detector, detector efficiency, and so on. It is also a function of the contrast factor (Ag), which is defined as the square of the difference of the scattering length density of the scattering centers, for example, the particle and the matrix. This quantity is calculated from ... 

When analysing the results of a neutron experiment we shall need to relate the number of neutrons seen in a detector of small area, dA, as it is positioned at different scattering angles around the sample, see Fig. 2.1. The detector subtends a small solid angle, di2, at the sample. The number of neutrons per unit time, or flux, scattered to the detector, Jf, is directly proportional to the incident neutron flux, Ji. It is also proportional to the size of the detector but inversely proportional to the square of the distance, d, between the sample and the detector, also df2= 6A / d. The differential cross section, dcr/d/2, is the constant of proportionality. 

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