Scattered neutrons, wavelength

For the calculation of the hydrodynamic thickness we divide the profile artificially into elementary layers, the result being independent of the division chosen provided it is sufficiently fine. The s.a.n.s. data is obtained as a function of Q, the wave vector (4it/A sin(0/2), where X is the neutron wavelength and 0 the scattering angle. The Q resolution corresponds in real space to a fraction of a bond length which is small enough for defining an elementary layer. 

The momentum transfer hQ, respectively the wave vector, is given by Q= k -kf where k and kf are the wave vectors of the incoming and outgoing (scattered) neutrons. They relate to the neutron wavelength k j=2Tt/Aij. The neutron momenta a.rep ij=m Vi f=fikif. Therefore ... 

One of the most serious difficulties for experimentally accessing the dynamics in the low Q plateau is the presence of multiple scattering [210]. In order to assess this effect, NSE spectra were taken above and below the multiple scattering threshold. For neutron wavelengths A 14 A the first structure factor peak cannot be seen with neutrons and therefore multiple scattering contributions... 

Figure 16-15. Time-dependent intensity profile of the (200) reflection of (AgBr + NaBr) mixtures measured during interdiffusion at 621 K. Wavelength of the scattered neutrons Xn = 2.36 A (after [G. Eckold (1992)]).

Pulsed sources may use a wide range of neutron wavelengths in the beam incident on the sample. The velocity of individual scattered neutrons is determined by the detector electronics, from the time delay between the burst of neutrons leaving the uranium target, and the detection of the scattered neutron by the detector. 

The coherent scattered amplitude F(r) of neutrons, wavelength X, at a displacement r from a nucleus j of coherent scattering amplitude (or scattering length) h is... 

A scattering angle of order X/R is needed to observe a feature of size R, where X is the X-ray or neutron wavelength, and hence small angle scattering is needed to observe large features. Fig. 2.13 shows X-ray data for a-Si H and a-Si C H alloys in the form of a Guinier plot (Mahan, Nelson, Crandall and Williamson 1989),... 

What appears below is a brief discussion of neutron scattering formalism (for an in depth exposition see, for example, the classic paper by van Hove). We assume the scattering is from point particles, which is reasonable, because thermal neutron scattering involves wavelengths on the order of 1A and the length scale of the interaction between an atomic nucleus and the neutron is around five orders of magnitude smaller. If we consider an individual particle j at position rj at time t, the number density can be expressed as... 

Fig. 4 The geometry of a small-angle neutron scattering experiment. Neutrons of wavelength X are scattered by the atomic nuclei in the sample. A fraction of the neutrons, are scattered through an angle 9 and are detected by a 2-dimensional (2-D) detector at a distance L d from the sample. The wave vectors of the incident and scattered neutrons are ki and respectively. (Reproduced from Ref...

SANS measurements were made using the PAXE instrument installed at the Orphe reactor, Laboratoire Leon Brillouin, Gif-sur-Yvette, France. Measurements were made on intact membranes (47 mm diameter) which were oriented either perpendicular or parallel to the incident neutron beam. SANS was measured at sample/detector distances of 1.5 m with a neutron wavelength, X, of 6 A and at 3.5 m with A. of 15 A, respectively. Analysis of the scattering, measured on a 2D detector, was carried out using procedures described previously... 

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