Scattering length neutron

The data taken is normally presented as the total structure factor, F(Q). This is related to the neutron scattering lengths hi, the concentrations C , and the partial structure factor Sy(Q) for each pair of atoms i and j in the sample, by Equation 4.1-1 ... 

Sears VF (1984) Thermal-neutron scattering lengths and cross-sections for condensed matter research. Chalk River Nuclear Laboratories, Chalk River... 

Fig. 2.54 Neutron reflectivity profile for a symmetric PS-dPMMA diblock (Mw 30 kg moP1) as a function of incident wavevector (Russell 1990). The inset shows the scattering length density (b/V, the neutron scattering length per unit volume) profile normal to the film surface that was used to calculate the reflectivity profile shown as the solid line, This is typical of a block copolymer film containing a multilayer stack, with lamellae parallel to the surface.

Neutron scattering is also useful for the study of adsorbed material on hydrosol particles. The neutron scattering length densities of hydrogen and deuterium differ considerably. By preparing a hydrosol in an appropriate H20/D20 mixture, it is possible to match the neutron scattering length densities of the dispersion medium and the core particles. The neutron beam thus sees only the adsorbed layer, the thickness of which can be estimated. Alternatively, the dispersion medium can be matched to the adsorbed layer to permit estimation of the core-particle size. 

Pore masking is not always easy in an X-ray s.a.s. experiment because certain supports have such high electron densities that it is impossible to find a fluid which can match them.47 It is here that neutron s.a.s. can be particularly useful since it is relatively easy to find a suitable fluid with the same neutron scattering length density as a chosen catalyst support. 

Table 4a Neutron scattering-length densities (n.s.l.d.) of some supports and maskants...

Fig. 6. Mass (top and right-hand y axis) and neutron scattering length (bottom and left-hand y axis) density increments for AMDH as functions of the respective solvent densities. From Zaccai et al. (1989), with permission.

The measured reflectivity, R(Q), depends upon the neutron refractive index profile perpendicular to the interface, defined as the z-direction. The neutron refractive index is a function of the scattering length density, Nb, which is the product of the number density N, in units of nuclei per cm3, and the neutron scattering lengths, b, of the nuclei present. Since the neutron scattering length varies from nucleus to nucleus, chances in the nature and composition of the surface result in changes in reflectivity. 

In the simplest case of the interface between two bulk media, the reflectivity is related to the refractive index difference across the interface, and is described by Fresnel s Law [18]. The refractive index, n, is related to the neutron scattering length density, such that... 

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