Neutron scattering factors

The fact that neutron scattering factors are similar for all elements means that light atoms scatter neutrons as effectively as heavy atoms and can therefore be located in the crystal structure for example the X-ray scattering factors for deuterium and tungsten are 1 and 74, respectively, whereas the equivalent neutron values are 0.667 and 0.486. This... 

The technique of Rietveld profile analysis has already been mentioned in the context of X-ray powder diffraction, but it was with neutron powder diffraction that this technique originated. The fact that the neutron scattering factors are almost invariant with smOA means that the intensity of the data does not drop off at high angles of 6 as is the case with X-ray patterns, and so a neutron powder pattern tends to yield up considerably more data. 

The first term / (k) is the X-ray atomic scattering factor and the other two terms are the dispersion corrections. Similar anomalous scattering occurs for neutrons also and the neutron scattering factor is formulated in a similar way. 

An alternative approach to the problem is the isotopic substitution method. Here one uses the same alloy prepared with different isotopes having different neutron scattering factors (Mizoguchi et al., 1978 Kudo et al., 1978). In the amorphous substitution method several alloys A, are used, where x is fixed and B or A is replaced by a component of similar size and chemical affinity but different scattering factor (Chipman et al., 1978 Williams, 1982). In these methods it is tacitly assumed that the atomic distribution functions in the alloy series are the same or, at least, do not differ much. 

Much like X-rays, the interactions of neutrons with matter are atomic in nature. The difference is that neutrons are sensitive to nuclei directly, whereas X-rays interact with electrons. Hence, while X-rays are unsuitable to detect light elements because of the low atomic electron count, neutron scattering factors depend on the properties of the nucleus [206]. The most relevant consequence in the context of this discussion is that neutron-based tools are better suited for the detection of H and Li than X-rays, as H and Li are among the most highly neutron-absorbing atoms, and that they offer isotope resolution capability. In principle, they are also nondestructive. 

Because the neutron has a magnetic moment, it has a similar interaction with the clouds of impaired d or f electrons in magnetic ions and this interaction is important in studies of magnetic materials. The magnetic analogue of the atomic scattering factor is also tabulated in the International Tables [3]. Neutrons also have direct interactions with atomic nuclei, whose mass is concentrated in a volume whose radius is of the order of... 

We first examine the reiationship between particie dynamics and the scattering of radiation in the case where both the energy and momentum transferred between the sampie and the incident radiation are measured. Linear response theory aiiows dynamic structure factors to be written in terms of equiiibrium flucmations of the sampie. For neutron scattering from a system of identicai particies, this is [i,5,6]... 

The Q and ft) dependence of neutron scattering structure factors contains infonnation on the geometry, amplitudes, and time scales of all the motions in which the scatterers participate that are resolved by the instrument. Motions that are slow relative to the time scale of the measurement give rise to a 8-function elastic peak at ft) = 0, whereas diffusive motions lead to quasielastic broadening of the central peak and vibrational motions attenuate the intensity of the spectrum. It is useful to express the structure factors in a form that permits the contributions from vibrational and diffusive motions to be isolated. Assuming that vibrational and diffusive motions are decoupled, we can write the measured structure factor as... 

Figure 9 Fit of an incoherent neutron scattering structure factor, S(Q, O)), computed for iipid H atom motion in the piane of the biiayer in a simuiation of a DPPC biiayer, by the sum of an eiastic iine, a naiTow Lorentzian with width T , and a broad Lorentzian with width T2, convoiuted with a Gaussian resoiution function with AE = 0.050 meV.

Figure 10 Elastic incoherent structure factors for lipid H atoms obtained from an MD simulation of a fully hydrated DPPC bilayer, and quasielastic neutron scattering experiments on DPPC bilayers at two hydration levels for (a) motion in the plane of the bilayer and (b) motion m the direction of the bilayer normal.

The coherent tunneling case is experimentally dealt with in spectroscopic studies. For example, the neutron-scattering structure factor determining the spectral line shape is... 

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 ... 

X-ray diffraction has been used for the study both of simple molten salts and of binary mixtures thereof, as well as for liquid crystalline materials. The scattering process is similar to that described above for neutron diffraction, with the exception that the scattering of the photons arises from the electron density and not the nuclei. The X-ray scattering factor therefore increases with atomic number and the scattering pattern is dominated by the heavy atoms in the sample. Unlike in neutron diffraction, hydrogen (for example) scatters very wealdy and its position cannot be determined with any great accuracy. 

Experimentally, the stretching of block copolymer chains has been addressed in two ways by measuring L as a function of N, and by measuring the components of Rg of the block chains both parallel and perpendicular to the interface. The domain dimensions have been studied most extensively for styrene-isoprene and styrene-butadiene block copolymers X-ray and neutron scattering are the methods of choice. The predicted SSL scaling of L N2/3 has been reported for spheres, cylinders and lamellae [99,102-106], but not in all cases. For example, Bates et al. found N0 37 for styrene-butadiene spheres [100], and Hadziioannou and Skoulios observed N0 79 for styrene-isoprene lamellae [107], In the sphere case, kinetic limitations to equilibration were felt to be an important factor [100],... 

Small angle neutron scattering measurements were carried out with the PACE diffractometer at the Laboratoire Leon Brillouin, (CE Saclay, France). The q range observed was 3.4 lO" to 0.2 A l. Samples were prepared in deuterated instead of ordinary water to achieve a suitable value for the neutron contrast factor. 

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