Metals sphere

The determination of critical si2e or mass of nuclear fuel is important for safety reasons. In the design of the atom bombs at Los Alamos, it was cmcial to know the critical mass, ie, that amount of highly enriched uranium or plutonium that would permit a chain reaction. A variety of assembhes were constmcted. Eor example, a bare metal sphere was found to have a critical mass of approximately 50 kg, whereas a natural uranium reflected 235u sphere had a critical mass of only 16 kg. 

In the ARC (Figure 12-9), the sample of approximately 5 g or 4 ml is placed in a one-inch diameter metal sphere (bomb) and situated in a heated oven under adiabatic conditions. Tliese conditions are achieved by heating the chamber surrounding the bomb to the same temperature as the bomb. The thermocouple attached to the sample bomb is used to measure the sample temperature. A heat-wait-search mode of operation is used to detect an exotherm. If the temperature of the bomb increases due to an exotherm, the temperature of the surrounding chamber increases accordingly. The rate of temperature increase (selfheat rate) and bomb pressure are also tracked. Adiabatic conditions of the sample and the bomb are both maintained for self-heat rates up to 10°C/min. If the self-heat rate exceeds a predetermined value ( 0.02°C/min), an exotherm is registered. Figure 12-10 shows the temperature versus time curve of a reaction sample in the ARC test. 

Fig. 11. The Bruggeman model (BM) lakes into account the modification of the effective medium by the adjunction of metal in the medium. The net effect is a broadening of the resonance peak. The parameters of the metallic spheres in these calculations are fuHp = I eV and fiV = 0.1 eV. The insulating host is defined by ftcOp i = 1 eV and ftf = 1 eV and fidiy = 20 eV. Note that the normal Drude curve is superimposed with the Bruggeman curve with/= 1.

The relative importance of the two mechanisms - the non-local electromagnetic (EM) theory and the local charge transfer (CT) theory - remains a source of considerable discussion. It is generally considered that large-scale rough surfaces, e.g. gratings, islands, metallic spheres etc., favour the EM theory. In contrast, the CT mechanism requires chemisorption of the adsorbate at special atomic scale (e.g. adatom) sites on the metal surface, resulting in a metal/adsorbate CT complex. In addition, considerably enhanced Raman spectra have been obtained from surfaces prepared in such a way as to deliberately exclude one or the other mechanism. 

R. Ruppin, Decay of an excited molecule near a small metal sphere, J. Chem. Phys. 76, 1681-1684 (1982). 

Figi 1-4. Electrostatic potential profile near a charged metal sphere X = distance from metal surface ... 

In this section we present worked examples demonstrating application of the theory described earlier. In the first example we demonstrate a familiar simple electrostatic problem in which a metal sphere is held at a potential of 1V and is enclosed in a cubical grounded metal box (Fig. 15.5). The task at hand is to find the potential distribution in volume E between the sphere and the box. 

The iodine vapours act as transporting agent in this modified version of the van Arkel procedure ". By replacing the resistance heated dissociation wire by an induction heated metal sphere (W or Th, respectively) large samples of Th or Pa crystals can be... 

The observed darkening of the indium slides results from a shift of the absorption peak because of the coating on the particles. Because of the cumbersomeness of the expressions for coated ellipsoids (Section 5.4) this shift can be understood most easily by appealing to (12.15), the condition for surface mode excitation in a coated sphere. For a small metallic sphere with dielectric function given by the Drude formula (9.26) and coated with a nonabsorbing material with dielectric function c2, the wavelength of maximum absorption is approximately... 

Ruppin, R., 1975. Optical properties of small metal spheres, Phys. Rev., Bll, 2871-2876. 

Colloids The Thickness of the Double Layer and the Bulk Dimensions Are of the Same Order. The sizes of the phases forming the electrified interface have not quantitatively entered the picture so far. There has been a certain extravagance with dimensions. If, for instance, the metal in contact with the electrolyte was a sphere (e.g., a mercury drop), its radius was assumed to be infinitely large compared with any dimensions characteristic of the double layer, e.g., the thickness K-1 of the Gouy region. Such large metal spheres, dropped into a solution, sink to the bottom of the vessel and lie there stable and immobile. 

Referring again to the metal spheres of submicroscopic dimensions, one point becomes clear. The smaller they are ( microns), the more they react to the thermal kicks from the ions and water molecules of the electrolyte they take off on a random walk through the solution. Large ( centimeters) spheres also exchange momentum with the particles of the solution, but their masses are huge compared with those of ions or molecules, so that the velocities resulting (to the spheres) from such collisions are essentially zero. 

Once the microsphetes begin to jump about in Brownian movement in the solution, some of them collide with each other. What should happen when two approximately 105-cm metal spheres collide Many aspects of colloidal chemistry— and hence of molecular biology, including the electrochemical basis of the stability of blood and the forming of clots—are illuminated by a consideration of this subject. 

The first thing to remember is that each metal sphere sees its environment through its charged interface each sphere is enveloped in a double layer. All the concepts and pictures of the electrified interface that have been developed in this chapter are of immediate relevance76 to the microspheres rushing toward a collision. 

The total interaction between the two metal spheres can therefore be classified into two parts (1) the surface, or double-layer, interaction determined by the Gouy-Chapman potential t f0e"Krand (2) the volume, or bulk, interaction —Ar-6 + Br 12. The interaction between double layers ranges from indifference at large distances to increasing repulsion as the particles approach. The bulk interaction leads to an attraction unless the spheres get too close, when there is a sharp repulsion (Fig. 6.131). The total interaction energy depends on the interplay of the surface (double layer) and volume (bulk) effects and may be represented thus... 

This approximate formula contains information concerning what happens when two colloidal particles (the two metal spheres) collide. One has to plot this total interaction energy C/total against the distance apart of the particles. 

To account for these conclusions, we propose the following hypothesis The spots are due to molecules which rest or on protrude above the first two layers and which share electrons with the atoms in these layers. On this basis we can treat these molecules as if they were small metallic spheres or parts of spheres on a metal surface. We can then draw equipotential lines above the surface and above these spheres and deduce differences in field strength. We can also sketch probable paths for electrons from those parts of the spheres where the field strength is greatest. 

Tower Burst. If the energy of the detonation is sufficient to vaporize the entire tower mass, the particle population is like that described for the land surface burst. If, however, the entire tower is not vaporized, the particle population will consist of three identifiable components— the crystalline and glass components of the surface detonation plus a metal sphere population which arises from melted (not vaporized) tower materials resolidifying as spheres. Such spheres are metallic rather than metal oxide and exhibit the density and magnetic properties of the tower material. The size range of the spherical component is from a few microns to perhaps a few hundred microns diameter. If we indicate by... 

The constant coefficient, b, which is related to late surface deposition, is independent of particle composition hence, it is the same for the soil and the metal sphere populations. The coefficients, au are related to volume deposition and depend on chemical composition of the particles hence, they would be expected to be different for soil and metal sphere constituents. It would also be expected that the individual types of particles which make up a particular soil (e.g., quartz and feldspar) would exhibit different radionuclide compositions however, in the soil case the composition variation is independent of particle size so that a single average coefficient, 02,3, applies. However, the sphere/soil ratio in general varies with size, so that the radionuclide composition of the sphere population needs to be considered separately. 

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. 

Leva (1950) 99 H Air Glass, clay, porcelain, metal Spheres, rings, cylinders 4-18 ... 

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