Bulk rare medium

B. Electric Field Components in Bulk Rare (Optically Thin) Medium... 

Equations (4)-(6) hold for a bulk (non- or weakly absorbing) rare medium 2 (case (a) in Fig. 3). In the case of a thin film with thickness <7<<7p in contact with the IRE (case (b) in Fig. 3), the thin-layer approximation gives good results (5). Here it is assumed that the electric field is determined by the IRE and the bulk medium above the thin film. The thin film is then considered as a dielectric in this field, and equations similar to Eqs. (4)-(6) can be derived. 

Fig. 3. Various situations encountered in ATR spectroscopy. Medium 1 represents the IRE. (a) Bulk rare (optically thin) medium 2. (b) Thin film with thickness d much less than the penetration depth dp. (c) General case with N layers of different optical properties and thickness. The electric field depicted schematically on the left decays exponentially into the rare medium. This situation applies for case (a). In the more general case (c), the electric field does not decay smoothly.

The term pore-scale implies behavior or analysis performed at a resolution where the void phase and solid phase can be distinguished. At this scale, the void phase is conceptually divided into pores (the larger voids, which provide its volume) and pore throats (constrictions that connect the pores), though the distinction is rarely black and white. In contrast, the continuum-scale approach is usually adopted in engineering practice. Continuum techniques treat the bulk porous medium as a single phase, which in turn requires spatially averaged parameters to be introduced that are intended to capture relevant characteristics of the pore-scale structure. 

Although bulk polymerization of acrylonitrile seems adaptable, it is rarely used commercially because the autocatalytic nature of the reaction makes it difficult to control. This, combined with the fact that the rate of heat generated per unit volume is very high, makes large-scale commercial operations difficult to engineer. Lastiy, the viscosity of the medium becomes very high at conversion levels above 40 to 50%. Therefore commercial operation at low conversion requires an extensive monomer recovery operation. 

All these effects are probably responsible for the discrepancies of reported photoelectron results in actinide oxides. Often, especially for the more radioactive and rare heavy actinides, dioxide samples are prepared for photoemission by growing oxide layers on top of the bulk actinide metal. These samples may then display features of trivalent sesquiox-ides since the underlying metal acts as a reducing medium. 

In this subsection we examine the mechanism of the very fast diffusion. In the bulk medium the vacancies and interstitial site play a primary role in accelerating the diffusion. However, these diffusion mechanisms are not relevant in microclusters. It is well known that the vacancies created inside the cluster are immediately pushed to the surface. Indeed in our simulation the creation of vacancies inside the cluster is a very rare event even at the temperature close to the melting temperature. Moreover, we cannot find any evidence that the interstitial deformation takes place inside the cluster, and therefore neither of them is responsible for the rapid diffusion into the cluster. The key feature of the cluster that distinguishes the cluster from the bulk medium is that it is surrounded by the surface beyond which no atoms exist. In other words, the outside of the cluster is occupied by vacancies. As a result, the atoms on the surface move very actively along the surface. Such an active movement along the surface will be responsible for the rapid diffusion in the radial direction of the cluster. We focus our attention to the details of the active diffusive motion along the surface of the cluster, and we present a direct evidence that the surface activity controls the radial diffusion. A direct measure of the surface motion is the diffusion rate of the surface atoms... 

The kinetics of H2 formation (and other surface reactions) via the Langmuir-Hinshelwood (diffusive) mechanism can be treated by rate equations, as in Eq. (1.52), or by stochastic methods.There are two main objections to the former approach it does not handle random-walk correctly and it fails in the limit of small numbers of reactive species. The latter objection is a far more serious one in the interstellar medium because dust particles are small, and the number of reactive atoms and radicals on their surfaces can be, on average, less than unity. Nevertheless, with rare exceptions, the few large models of interstellar chemistry that include surface processes as well as gas-phase chemistry do so via the rate equation approach, so we discuss it here. In the treatment below, we do not use the ordinary units of surface chemistry — areal concentrations or mono-layers — but instead refer to nmnbers of species on the mantle of an individual but average grain. Numbers can be converted to bulk concentrations, as used in Eq. (1.52), by multiplication by the grain number density n. ... 

The conventional separation scheme is to leach the primary ore or concentrates and use the resulting solution containing the rare earth mixtures as the feedstock to the solvent extraction plant. Solvent extraction of the rare earth mixture in the leached solution separates them into bulk concentrates of light (La, Ce, Pr, Nd, etc.), middle (Sm, Eu, Gd, etc.) and heavy (Tb, Dy, Ho, Er, Tm, Yb, Lu, Y) rare earths. A typical solvent extraction of rare earths in a HCl medium is with di-2-ethylhexyl phosphoric acid, HDEHP, in a kerosene diluent. The individual rare earth is separated from the bulk light, middle, and heavy rare earth solution mixtures by additional individual rare earth solvent extraction streams. The number of stages for solvent extraction cascades or batteries increases with the increase in purity of each individual rare earth produced. Further purification... 

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