Neutron scaling

The polymer concentration profile has been measured by small-angle neutron scattering from polymers adsorbed onto colloidal particles [70,71] or porous media [72] and from flat surfaces with neutron reflectivity [73] and optical reflectometry [74]. The fraction of segments bound to the solid surface is nicely revealed in NMR studies [75], infrared spectroscopy [76], and electron spin resonance [77]. An example of the concentration profile obtained by inverting neutron scattering measurements appears in Fig. XI-7, showing a typical surface volume fraction of 0.25 and layer thickness of 10-15 nm. The profile decays rapidly and monotonically but does not exhibit power-law scaling [70]. 

A representation of atomic structure. The various spheres are not drawn to scale. The lump of iron on the left would contain almost a million million million million (10 ) atoms, one of which is represented by the sphere in the top center of the page. In turn, each atom is composed of a number of electrons, protons, and neutrons. For example, an atom of the element iron contains 26 electrons, 26 protons, and 30 neutrons. The physical size of the atom is determined mainly by the number of electrons, but almost all of its mass is determined by the number of protons and neutrons in its dense core or nucleus (lower part of figure). The electrons are spread out around the nucleus, and their number determines atomic size but the protons and neutrons compose a very dense, small core, and their number determines atomic mass. 

A development in the 1960s was that of on-line elemental analysis of slurries using x-ray fluorescence. These have become the industry standard. Both in-stream probes and centralized analyzers are available. The latter is used in large-scale operations. The success of the analyzer depends on how representative the sample is and how accurate the caUbration standards are. Neutron activation analyzers are also available (45,51). These are especially suitable for light element analysis. On-stream analyzers are used extensively in base metal flotation plants as well as in coal plants for ash analysis. Although elemental analysis provides important data, it does not provide information on mineral composition which is most cmcial for all separation processes. Devices that can give mineral composition are under development. 

The only large-scale use of deuterium in industry is as a moderator, in the form of D2O, for nuclear reactors. Because of its favorable slowing-down properties and its small capture cross section for neutrons, deuterium moderation permits the use of uranium containing the natural abundance of uranium-235, thus avoiding an isotope enrichment step in the preparation of reactor fuel. Heavy water-moderated thermal neutron reactors fueled with uranium-233 and surrounded with a natural thorium blanket offer the prospect of successful fuel breeding, ie, production of greater amounts of (by neutron capture in thorium) than are consumed by nuclear fission in the operation of the reactor. The advantages of heavy water-moderated reactors are difficult to assess. 

Production in Target Elements. Tritium is produced on a large scale by neutron irradiation of Li. The principal U.S. site of production is the Savaimah River plant near Aiken, South Carolina where tritium is produced in large heavy-water moderated, uranium-fueled reactors. The tritium may be produced either as a primary product by placing target elements of Li—A1 alloy in the reactor, or as a secondary product by using Li—A1 elements as an absorber for control of the neutron flux. 

Production-Scale Processing. The tritium produced by neutron irradiation of Li must be recovered and purified after target elements are discharged from nuclear reactors. The targets contain tritium and He as direct products of the nuclear reaction, a small amount of He from decay of the tritium and a small amount of other hydrogen isotopes present as surface or metal contaminants. 

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... 

Analysis of neutron data in terms of models that include lipid center-of-mass diffusion in a cylinder has led to estimates of the amplitudes of the lateral and out-of-plane motion and their corresponding diffusion constants. It is important to keep in mind that these diffusion constants are not derived from a Brownian dynamics model and are therefore not comparable to diffusion constants computed from simulations via the Einstein relation. Our comparison in the previous section of the Lorentzian line widths from simulation and neutron data has provided a direct, model-independent assessment of the integrity of the time scales of the dynamic processes predicted by the simulation. We estimate the amplimdes within the cylindrical diffusion model, i.e., the length (twice the out-of-plane amplitude) L and the radius (in-plane amplitude) R of the cylinder, respectively, as follows ... 

We finish this section by comparing our results with NMR and incoherent neutron scattering experiments on water dynamics. Self-diffusion constants on the millisecond time scale have been measured by NMR with the pulsed field gradient spin echo (PFGSE) method. Applying this technique to oriented egg phosphatidylcholine bilayers, Wassail [68] demonstrated that the water motion was highly anisotropic, with diffusion in the plane of the bilayers hundreds of times greater than out of the plane. The anisotropy of... 

It should be obvious from Figure 1 that if one wishes to probe spacings on the order of atomic spacings (A) that wavelengths of the same length scale are required. Fortunately, X rays, electrons and thermal neutrons share the feature of possessing wavelengths of the appropriate size. 

More recently, simulation studies focused on surface melting [198] and on the molecular-scale growth kinetics and its anisotropy at ice-water interfaces [199-204]. Essmann and Geiger [202] compared the simulated structure of vapor-deposited amorphous ice with neutron scattering data and found that the simulated structure is between the structures of high and low density amorphous ice. Nada and Furukawa [204] observed different growth mechanisms for different surfaces, namely layer-by-layer growth kinetics for the basal face and what the authors call a collected-molecule process for the prismatic system. 

Proton capture processes by heavy nuclei have already been briefly mentioned in several of the preceding sections. The (p,y) reaction can also be invoked to explain the presence of a number of proton-rich isotopes of lower abundance than those of nearby normal and neutron-rich isotopes (Fig. 1.5). Such isotopes would also result from expulsion of a neutron by a y-ray, i.e. (y,n). Such processes may again be associated with supernovae activity on a very short time scale. With the exceptions of " ln and " Sn, all of the 36 isotopes thought to be produced in this way have even atomic mass numbers the lightest is Se... 

Phosphorus has only one stable isotope, J P, and accordingly (p. 17) its atomic weight is known with extreme accuracy, 30.973 762(4). Sixteen radioactive isotopes are known, of which P is by far the most important il is made on the multikilogram scale by the neutron irradiation of S(n,p) or P(n,y) in a nuclear reactor, and is a pure -emitter of half life 14.26 days, 1.7()9MeV, rntan 0.69MeV. It finds extensive use in tracer and mechanistic studies. The stable isotope has a nuclear spin quantum number of and this is much used in nmr spectroscopy. Chemical shifts and coupling constants can both be used diagnostically to determine structural information. 

On an industrial scale PCI3 is sprayed into steam at 190 and the product sparged of residual water and HCl using nitrogen at 165. Phosphorous acid forms colourless, deliquescent crystals, mp 70. T, in which the structural units shown form four essentially linear H bonds (O - H 155-I60pm) which. stabilize a complex 3D network. The molecular dimensions were determined by low-temperature single-crystal neutron diffraction at 15K.f - ... 

Heavy water (p. 39) is now manufactured on the multikilotonne scale for use both as a coolant and neutron-moderator in nuclear reactors its absorption cross-section for neutrons is much less than for normal water [Pg.623]

The products of nuclear fission reactions are radioactive and disintegrate according to their own time scales. Often disintegration leads to other radioactive products. A few of these secondary products emit neutrons that add to the pool of neutrons produced by nuclear fission. Very importantly, neutrons from nuclear fission occur before those from radioactive decay. The neutrons from nuclear fission are termed prompt. Those from radioacth e decay arc termed delayed. A nuclear bomb must function on only prompt neutrons and in so doing requires nearly 100 percent pure (or Pu) fuel. Although reactor... 

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