Concentric metal spheres

If uniform mixing of the fission product vapors and volatilized materials results, the recondensed particles might be expected to have a constant specific activity of elements having similar boiling points. Note parenthetically that studies of fission-product incorporation into the metal and oxide products of vaporized iron wires (in which iron-metal spheres and iron-oxide irregulars are formed) indicate no simple relationship between specific activity and size. For example, a refractory element like zirconium is found most enriched in particles of intermediate size. This is probably in part caused by a concentration effect—i.e.y in these experiments the zirconium represented a mole fraction of about 10"9. As indicated earlier, the fission products are a minor constituent in the fireball, and a very complex pattern of incorporation can be anticipated, especially if coagulation with melted but unvaporized particles ensues. 

A spherical model was used in Ref. [15] in order to obtain the shape of the domains, reversed under the fdb conditions. This model was widely applied for studies of different processes that take place in the field of afm tip (see Ref. [65]), including ferroelectric polarization reversal [66-69], In this model the field of the tip apex is supposed to coincide with a field of a metallic sphere, the radius of which is equal to the radius of curvature of the tip apex. Using a simple approximation it may be supposed that the tip charge is concentrated in the center of the sphere [15,64-69], We will take into account a more general model and check the accuracy of the simple spherical model application to the ferroelectric domain breakdown condition. 

What does happen as the concentration of A becomes very high (and this can be shown very clearly with a mechanical model in which metal spheres of different kinds are agitated in a moving tray) is that pairs of B molecules tend to become hemmed in by the surrounding crowd of solvent molecules and caused to pommel one another repeatedly instead of wandering off to collide with new adversaries. But, as both theory and the mechanical model indicate, the total number of B, B collisions remains sensibly constant, although the... 

The average density of the metal.assemblles ranges from 17.7 to 18.0 g/cm. The uraqyl nitrate solution concentrations used are 11.0, 21.3, and 104.9 gU/Uter. Critical masses and radii of the metal spheres are given in Table I for solution cylinders having.51.1- and 38.4-cm diameters and various thicknesses. 

Critically measurements and calculations on enriched (93,2 wt% ) uranium metal spheres symmetrically immersed in enriched (93.2 wt% U) uranyl nitrate solution, have been presented previously. The present Interpretation of the same data considers the criticality safety of an enriched uranium metal sphere immersed, initially, in nonflssile liquid (e.g., acid). As the metal dissolves, the fissile concentration of the solution in-creases until. the two interacting fissile regions together achieve criticality. Here, the uranium in solution is assumed homogeneously distributed. 

This interpretation of the data was made by calcula-tionally converting each critical ejqierimental system to an ideal one in which the uranium spheres have the full crystal density (18.664 g/cm ) and the solution is a uranium-water mixture. These conversions (and all subsequent calculations) use the DTF computer code in the Sis approximation with Hansen-Rc ch cross sections. Then, two end points are calculated for the data analysis plots the first is the critical mass of a full metal sphere reflected by water the second Is the critical uranium concentration tor a metal/water mixture. An example of the results obtained at this stage of the analysis is pre-... 

The LLL version of the MORSE neutron Monte Carlo code was used to generate plutonium metal-array-criticality data. We used a 92-group neutron cross-section set derived from Howerton s compilation. Thermal data for water were derived by the FLANGE code. Validation of the computational methods was done by calculating (a) a single water-reflected metal sphere, (b) the limiting critical concentration of plutonium in water, (c) the arrays of 3- and 6-kg plutonium cylinders, and (d) the lattices of Pu-Al rods in water. ... 

Classical percolation is a very familiar concept. Anyone who has tried to cross a stream by stepping from rock to rock knows that a minimum density of rocks is needed to prevent wet feet. A more relevant, but still easily visualized model system, is a collection of glass and metal spheres in a box. One asks, How does the electrical conductivity of such an assembly depend on the relative proportions of metal and nonmetal The answer is that the conductivity tends continuously to zero at a critical concentration of metal. This is the classical percolation transition. This behavior can be verified experimentally by simple physical models (see, e.g., Last and Thouless, 1971) or by computer simulations (Kirkpatrick, 1971,1973). Near the transition, the conductivity depends on the fraction of metal according to a power law... 

The equilibrium between the complexes formed according to Equation (80) depends both on the concentration of fluorine ions and on the potential of interionic interactions, namely the nature of the outer-sphere cations [358]. The influence of the concentration of fluorine ions and of the nature of the outer-sphere cations on the equilibrium in Equation (80) can be demonstrated by the spectral transformations observed at 850°C for M2TaF7 - MF systems, where M = alkali metal [358]. 

A determination of dimethyl sulphoxide by Dizdar and Idjakovic" is based on the fact that it can cause changes in the visible absorption spectra of some metal compounds, especially transition metals, in aqueous solution. In these solutions water and sulphoxide evidently compete for places in the coordination sphere of the metal ions. The authors found the effect to be largest with ammonium ferric sulphate, (NH4)2S04 Fe2(S04)3T2H20, in dilute acid and related the observed increase in absorption at 410 nm with the concentration of dimethyl sulphoxide. Neither sulphide nor sulphone interfered. Toma and coworkers described a method, which may bear a relation to this group displacement in a sphere of coordination. They reacted sulphoxides (also cyanides and carbon monoxide) with excess sodium aquapentacyanoferrate" (the corresponding amminopentacyanoferrate complex was used) with which a 1 1 complex is formed. In the sulphoxide determination they then titrated spectrophotometrically with methylpyrazinium iodide, the cation of which reacts with the unused ferrate" complex to give a deep blue ion combination product (absorption maximum at 658 nm). 

In mixtures of nonpolar solvents with little water, surfactants form spherical reverse micelles. They have a reversed orientation of the molecules with the hydrophilic groups in the interior and a drop of enclosed water in the middle. Starting from a precursor material, metal oxides in the form of uniform nanosized spheres can be obtained by hydrolysis under controlled conditions (pH, concentration, temperature). For example, titanium oxide spheres are obtained from a titanium alkoxide, Ti(OR)4 + 2 H20 —t Ti02 + 4 ROH. 

Calculations of the capacitance of the mercury/aqueous electrolyte interface near the point of zero charge were performed103 with all hard-sphere diameters taken as 3 A. The results, for various electrolyte concentrations, agreed well with measured capacitances as shown in Table 3. They are a great improvement over what one gets104 when the metal is represented as ideal, i.e., a perfectly conducting hard wall. The temperature dependence of the compact-layer capacitance was also reproduced by these calculations. 

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