Aluminum spheres

In transmission studies of small aluminum spheres, Batson (22) has shown details of the generation of surface plasmons in the aluminum and in the thin coating oxide layer. Marks (23) and Cowley (24) have examined the surface plasmons and surface state excitations of small MgO smoke crystals. It is clearly evident that these excitations may be produced by electron beams passing the crystal in the vacuum, 3 nm or more away from the surface. 

The calculated extinction spectrum of a polydispersion of small aluminum spheres (mean radius 0.01 jam, fractional standard deviation 0.15) is shown in Fig. 11.4 both scales are logarithmic. In some ways spectral extinction by metallic particles is less interesting than that by insulating particles, such as those discussed in the preceding two sections. The free-electron contribution to absorption in metals, which dominates other absorption bands, extends from radio to far-ultraviolet frequencies. Hence, extinction features in the transparent region of insulating particles, such as ripple and interference structure, are suppressed in metallic particles because of their inherent opacity. But extinction by metallic particles is not without its interesting aspects. 

Figure 11.4 Calculated extinction by a polydispersion of aluminum spheres (top) compared with the bulk absorption spectrum of aluminum (bottom).

There are some notable differences apparent in Fig. 11.14 between the extinction curves for aluminum spheres and those for water droplets. For example, av is still constant for sufficiently small aluminum particles but the range of sizes is more restricted. The large peak is not an interference maximum aluminum is too absorbing for that. Rather it is the dominance of the magnetic dipole term bx in the series (4.62). Physically, this absorption arises from eddy current losses, which are strong when the particle size is near, but less than, the skin depth. At X = 0.1 jam the skin depth is less than the radius, so the interior of the particle is shielded from the field eddy current losses are confined to the vicinity of the surface and therefore the volume of absorbing material is reduced. 

As an example of extinction by spherical particles in the surface plasmon region, Fig. 12.3 shows calculated results for aluminum spheres using optical constants from the Drude model taking into account the variation of the mean free path with radius by means of (12.23). Figure 9.11 and the attendant discussion have shown that the free-electron model accurately represents the bulk dielectric function of aluminum in the ultraviolet. In contrast with the Qext plot for SiC (Fig. 12.1), we now plot volume-normalized extinction. Because this measure of extinction is independent of radius in the small size... 

Figure 12.3 Calculated extinction per unit volume of aluminum spheres.

At energies on either side of 8.8 eV a small aluminum sphere presents a much smaller target to incident photons. At 5 eV, for example, the absorption efficiency of a sphere with x = 0.3 is about 0.1 as far as absorption is concerned, the sphere is much smaller than its geometrical cross-sectional area. The field lines of the Poynting vector, shown in Fig. 12.46, are what are to be... 

Figure 12.4 Field lines of the total Poynting vector (excluding that scattered) around a small aluminum sphere illuminated by light of energy 8.8 eV (a) and 5 eV (b). The dashed vertical line in (a) indicates the effective radius of the sphere for absorption of light.

Figure 12.6 Calculated absorption spectra of aluminum spheres, randomly oriented ellipsoids (geometrical factors 0.01, 0.3, and 0.69), and a continuous distribution of ellipsoidal shapes (CDE). Below this is the real part of the Drude dielectric function.

Extinction calculations for aluminum spheres and a continuous distribution of ellipsoids (CDE) are compared in Fig. 12.6 the dielectric function was approximated by the Drude formula. The sum rule (12.32) implies that integrated absorption by an aluminum particle in air is nearly independent of its shape a change of shape merely shifts the resonance to another frequency between 0 and 15 eV, the region over which e for aluminum is negative. Thus, a distribution of shapes causes the surface plasmon band to be broadened, the... 

Figure 12.20 Extinction spectra calculated for small aluminum spheres and a continuous distribution of ellipsoids (CDE) in air (---) and in a medium with c = 2.3 (—). The circles show data...

Campbell and Huntington (1952) 99 H, C Air, natural gas (82 % CH4) Glass, alumina, aluminum Spheres, cylinders 5-25 ... 

An aluminum sphere, S.O cm in diameter, is initially at a uniform temperature of 50°C. It is suddenly exposed to an outers pace radiation environment at 0 K (no convection). Assuming the surface of aluminum is blackened and lumped-capacity analysis applies, calculate the time required for the temperature of the sphere to drop to -110°C. 

A 12-mm-diameter aluminum sphere is heated to a uniform temperature of 400°C and then suddenly subjected to room air at 20°C with a convection heat-transfer coefficient of 10 W/m2 °C. Calculate the time for the center temperature of the sphere to reach 200°C. 

FIGURE 19.13 (a) The target chamber of Nova, a 16-foot-diameter aluminum sphere inside of which ten powerful laser beams converge. 

Dry bulk resistivity, O-cm 0.005-0.008 (silver-coated products of PQ), 0.0017 (silver coated solid and hollow glass spheres - Conduct-O-Fil), 0.004 (silver coated glass fiber - Conduct-O-Fil), 0.0005-0.0006 (silver coated copper powder - Conduct-O-Fil), 0.0012 (silver coated copper flake - Conduct-O-Fil), 0.0007 (silver coated aluminum sphere - Conduct-O-Fil), 0.003 (silver coated inorganic flake - Conduct-O-Fil), 0.006 (silver coated nickel granules - Conduct -O-Fil), 0.0000016 - pure silver... 

Materials for sintering and melting are plastics, metals, or ceramics. Plastics may be unfilled or filled with glass or aluminum spheres or egg-shaped geometries to improve properties like durability and thermal resistance. Also nanoscale particles are used. Unfilled plastics are mostly commodities like semicrystalline polyamides from the PAl 1 or PA12 type or amorphous plastics like polystyrene (PS). Engineering plastics like PEEK are available. 

Diameter Container Reactor 69.2 (computed from volume) 0.32 cm aluminum sphere Fuel Fissile U H O N... 

Critical experiments were completed with plutonium nitrate solutions in a large 4-ft-dlam aluminum Sphere. This identical sphere was previously used iii critical experiments at the Oak Ridge National Laboratory fo the measurement of eta for uranium in critical aqueous solutions. The plutonium used in the current e rl-ments. was selected for its low Pu content, which was only 2i52 wt% Pu. The sphere volume was 949.1 litres. For low plutonium concentrations in aqueous solutions, the neutron leakage from a sphere of this size. 11 be no more than several percent. Measurements were made with Pu(NOs)4 water solutions with Pu concentrations ranging from 11 g Pu/litre to <8 g Pn/litre wtth nitric acid molarity at about one. 

The peak detonation pressure upon arrival of the detonation front at the surface of the aluminum sphere was 740 kbar. The calculated experimental positions of the shock were the same, within experimental error, as in Figures 2.50 and 2.51. 

Figure 2.51 Initial and final foil radii and shock wave density for the system described in Figure 2.50 at 1.63 //sec after detonation wave arrived at surface of aluminum sphere.

To illustrate the parameter estimation process, a numerical example is considered here. For a direct-central impact of two identical aluminum spheres, a coefficient of restitution of 0.7 and a duration of contact of 135 fis were recorded from experiment [. Both spheres had equal and opposite impact velocities of 0. IS m/s, and each had a radius of 0.02 m. 

Figure 4. A Hertzian contact force model with permanent indentation for the impact of two identical aluminum spheres with impact velocities of 0.15 m/s each.

Figure 5. Results from a continuous analysis of the two aluminum-spheres impact.

A solid aluminum sphere has amass of 85 g. Use the density of aluminum to find the radius of the sphere in inches. 

An aluminum sphere contains 8.55 x 10 " aluminum atoms. What is the sphere s radius in centimeters The density of aluminum is 2.70 g/cm. ... 

In these experiments, reported in December 1940 [1], 112 liters of heavy water mixed with varying amounts of UsOg powder were used inside an aluminum sphere 60 cm in diameter, which was immersed in about one ton of heavy mineral oil to serve as a reflector. (Mineral oil was chosen to avoid contamination of the D2O in case of a leak in the sphere.) By measuring neutron fluxes at varying distances from a neutron source located in the center of the sphere, Halban and Kowarski calculated a multiplication factor of 1.18 0.07 for this system when the ratio of deuterium atoms to uranium atoms was 380 to 1, and 1.09 0.03 when the D/U ratio was 160 to 1. 

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