Neutron reflectivity reflected beam intensity

Due to the wave-particle duality of neutrons, they can be reflected and refracted in a manner similar to light. Reflected neutron beams can interfere with each other to produce a reflected beam intensity that is characteristic of the reflecting material (Lekner, 1987). Detailed analysis of the reflectivity is able to able to provide information on the structural organization normal to the surface on which the beam is incident. Neutron reflectometry is particularly useful (vis a vis x-ray reflectometry), since selective isotopic labeling can be used to highlight particular regions of interest in a surface structure. This is especially valuable for monolayers on surfaces. 

NR In NR, a beam of neutrons is directed at the interface at an incident angle. The reflected beam intensity, R, is measured as a function of the scattering vector Q ... 

The technique that is commonly used nowadays for the investigation of the structure of adsorption layers is the specular neutron reflection. Neutron reflection studies are based on the measurement of the intensity of a reflected beam, generated from a collimated beam of neutrons with the wavelength X falling on the air-solution interface at a grazing angle 0. The quantity that is measured is referred to as the reflectance, R, which is given by the ratio of the reflected intensity to the intensity of the incident beam [17]. From reflectance measurements one can estimate the adsorption and obtain information on the orientation of molecules in the adsorption layer. 

Neutron reflection from fluid interfaces has revealed detailed arrangements of molecules in adsorbed layers (Lu et al., 2000). Basically neutrons can be totally reflected from interfaces in a manner similar to the total internal reflection of light at interfaces where a suitable refractive index distribution exists. Qose to the critical angle for total reflection, the intensity of the weak scattered beam provides information on the refractive index distribution normal to the interface. For neutrons, a refractive index can be defined in terms of the density of the various nuclei present and their scattering cross sections. As in neutron scattering, the use of ordinary and deuterated compounds is a powerful tool in identifying the location and arrangement of molecules. 

However, the low intensity of the neutron beam and the coarse resolution compared to x-rays often result in quite large error bars. The flux of a neutron beam is typically more than 5 orders of magnitude smaller than the photon flux of a synchrotron radiation source with up to 10 photons/sec on an area of (0.2x2)mm. From Eq. 1 it is known that the specularly reflected intensity at least falls with 1/ /. Thus, the low intensity of a neutron beam restricts the acc sible -range (a neutron reflectivity almost never exceeds a -value of qz,muF 0.2A" ). This means a relatively coarse resolution Az in real space via Azoc27i/ niax- In contrast, an x-ray reflectivity easily covers about 9 orders of magnitude which corresponds to a range of 0.7A to l.OA This yields a 4 times better resolution in real space if x-rays are used. 

With the new VME/UNIX control system on the polarised hot-neutron normal-beam diffractometer D3 at ILL, each measurement cycle for both peak and background intensities lasts 2 s, and the (+)/(-) counting-time fractions are defined with a 1 MHz clock. There are two detector scalers and two monitor scalers ((+) and (-) states). In Table 1, we compare the flipping ratio measured for the strong 200 and the weak 600 Bragg peak reflections of a CoFe sample. As expected, the standard deviation cr (if) is improved in the case of the strong reflection (16%). 

The intensities of diffracted beams, or reflections as they ate commonly called, depend upon the strength of the scattering that the material inflicts upon the radiation. Electrons are scattered strongly, neutrons weakly and X-rays moderately. The basic scattering nnit of a crystal is its unit cell, and we may calculate the scattering at any angle by mnltiplying... 

Other systematic errors include absorption, extinction, and multiple reflection. Absorption effects and the required corrections are well understood. When a monochromatic beam of X rays or neutrons with incident intensity / passes through a crystal, the intensity is reduced exponentially... 

The advantage of using polarized neutrons to determine weak magnetic reflections is clearly apparent. For example, if T =0.01 then the magnetic contribution to the intensity in an unpolarized beam experiment is 0.01 percent, but R Ri 1.04, i.e., there is a 4 percent effect on changing the incident neutron polarization. It is necessary to know the nuclear scattering amplitude accurately if an accurate magnetic amplitude is to be obtained and extinction corrections in particular must be accurately performed. 

The concepts of coherence and incoherence are related to the way in which the neutron, both as a wave and as a particle, interacts with the scattering sample. Wave-like representations of the neutron view its interaction with solids as occurring simultaneously at several atomic centres these atoms become the sources of new wavefronts. Since the scattering occurs simultaneously from all of these atoms the new wavefronts will spread out spherically from each new source and remain in phase. Provided the lattice is ordered, the coherence of the incident wave has been conserved. Constmctive interference between the new wavefronts leads to the generation of distinctive diffraction patterns with well-defined beams, or reflections, appearing only in certain directions in space and no intensity in other directions. 

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