Critical masses

Because of the high rate of emission of alpha particles and the element being specifically absorbed on bone the surface and collected in the liver, plutonium, as well as all of the other transuranium elements except neptunium, are radiological poisons and must be handled with very special equipment and precautions. Plutonium is a very dangerous radiological hazard. Precautions must also be taken to prevent the unintentional formulation of a critical mass. Plutonium in liquid solution is more likely to become critical than solid plutonium. The shape of the mass must also be considered where criticality is concerned. 

Hafnium neutron absorption capabilities have caused its alloys to be proposed as separator sheets to allow closer spacing of spent nuclear fuel rods in interim holding ponds. Hafnium is the preferred material of constmction for certain critical mass situations in spent fuel reprocessing plants where hafnium s excellent corrosion resistance to nitric acid is also important. 

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. 

Criticality Precautions. The presence of a critical mass of Pu ia a container can result ia a fission chain reaction. Lethal amounts of gamma and neutron radiation are emitted, and a large amount of heat is produced. The assembly can simmer near critical or can make repeated critical excursions. The generation of heat results eventually ia an explosion which destroys the assembly. The quantity of Pu required for a critical mass depends on several factors the form and concentration of the Pu, the geometry of the system, the presence of moderators (water, hydrogen-rich compounds such as polyethylene, cadmium, etc), the proximity of neutron reflectors, the presence of nuclear poisons, and the potential iateraction with neighboring fissile systems (188). As Httle as 509 g of Pu(N02)4 solution at a concentration Pu of 33 g/L ia a spherical container, reflected by an infinite amount of water, is a critical mass (189,190). Evaluation of criticaUty controls is available (32,190). 

A unique problem arises when reducing the fissile isotope The amount of that can be reduced is limited by its critical mass. In these cases, where the charge must be kept relatively small, calcium becomes the preferred reductant, and iodine is often used as a reaction booster. This method was introduced by Baker in 1946 (54). Researchers at Los Alamos National Laboratory have recently introduced a laser-initiated modification to this reduction process that offers several advantages (55). A carbon dioxide laser is used to initiate the reaction between UF and calcium metal. This new method does not requite induction heating in a closed bomb, nor does it utilize iodine as a booster. This promising technology has been demonstrated on a 200 g scale. 

Large quantities of fissile isotopes, U and U, should be handled and stored appropriately to avoid a criticahty hazard. Clear and relatively simple precautions, such as dividing quantities so that the minimum critical mass is avoided, following adniinisttative controls, using neutron poisons, and avoiding critical configurations (or shapes), must be followed to prevent an extremely treacherous explosion (246). 

Design of explosion suppression systems is clearly complex, since the effectiveness of an explosion suppression system is dependent on a large number of parameters. One Hypothesis of suppression system design identifies a limiting combustion wave adiabatic flame temperature, below which combustion reactions are not sustained. Suppression is thus attained, provided that sufficient thermal quenching results in depression of the combustion wave temperature below this critical value. This hypothesis identifies the need to deliver greater than a critical mass of suppressant into the enveloping fireball to effect suppression (see Fig. 26-43). 

This method employs a theoretical critical mass flow based on an ideal nozzle and isothermal flow condition. For a pure gas, the mass flow can be determined from one equation ... 

The actual mass flow rate through a pipe, G, in lbs per sec per sq ft is a function of critical mass flow G,-i, line resistance, N, and the ratio of downstream to upstream pressure. These relationships are plotted in Figure 19. In the area below the dashed line in Figure 19, the ratio of G to G,. remains constant, which indicates that sonic flow has been established. Thus, in sizing flare headers the plotted point must be above the dashed line. The line resistance, N, is given by the equation ... 

To date, there have been more than 1500 attendees and more than 500 technical papers or presentations delivered at these conferences. A critical mass of researchers, engineers, and scientists developed through the INVEN1 program in Finland, which started in 1991. These activities have expanded to include scientists, engineers, and practitioners from some 18 countries as part of the COST Action Program. 

As is standard in the development of subdisciplines, these fields arose from an intuitive perceived need. Nothing more than the ability to maintain a critical mass of jaarticipants adequately justifies the separations. Although the areas deal with different bodies of fact, this distinction is insufficient to justify a field. If it were, we might also have automotive economics or baseball economics. All involve application of economic principles to particular problems. Finding unifying analytic bases for separation is piroblematic. 

For nuclear fission to result in a chain reaction, the sample must be large enough so that most of the neutrons are captured internally. If the sample is too small, most of the neutrons escape, breaking the chain. The critical mass of uranium-235 required to maintain a chain reaction in a bomb appears to be about 1 to 10 kg. In the bomb dropped on Hiroshima, the critical mass was achieved by using a conventional explosive to fire one piece of uranium-235 into another. 

The energy produced in a nuclear reactor vessel is the result of a nuclear fission (atom splitting) process that occurs when sufficient nuclear material is brought together (critical mass). Under these circumstances, a chain reaction occurs and an external supply of neutrons is not required. A nuclear fuel control rod system raises or lowers the nuclear fuel (which is contained within fuel rods) inside the reactor vessel. 

Additionally, the surfactant properties of filmers reduce the potential for stagnant, heat-transfer-resisting films, which typically develop in a filmwise condensation process, by promoting the formation of condensate drops (dropwise condensation process) that reach critical mass and fall away to leave a bare metal surface (see Figure 11.2). This function, together with the well-known scouring effect on unwanted deposits keeps internal surfaces clean and thus improves heat-transfer efficiencies (often by 5-10%). 

Green (G3) has proposed an alternate approach based on the concept of a critical mass-velocity required to produce a Mach number of 1 in a constant-area channel. Green showed this approach was able to correlate the erosive-burning data he obtained for both a double-base propellant and a composite propellant. 

Neutrons produced in a chain reaction are moving very fast, and most escape into the surroundings without colliding with another fissionable nucleus. However, if a large enough number of uranium nuclei are present in the sample, enough neutrons can be captured to sustain the chain reaction. In that case, there is a critical mass, a mass of fissionable material above which so few neutrons escape from the sample that the fission chain reaction is sustained. If a sample is supercritical,... 

Nuclear energy can be extracted by arranging for a nuclear chain reaction to take place in a critical mass of fissionable material. with neutrons as the chain carriers. A moderator is used to reduce the speeds of the neutrons in a reactor that uses fissile material. 

CH3(CH2)3CH3 + CH3CH=CH2. critical mass The mass of fissionable material above which so few neutrons escape from a sample of nuclear fuel that the fission chain reaction is sustained a greater mass is supercritical and a smaller mass is subcritical. 

Examples electron proton neutron, subcritical Having a mass less than the critical mass. sublimation The direct conversion of a solid into a vapor without first forming a liquid, sublimation vapor pressure The vapor pressure of a solid. 

Fe(CN)6]3-(aq) + 6 H20(1). substrate The chemical species on which an enzyme acts, superconductor An electronic conductor that conducts electricity with zero resistance. See also high-temperature superconductor. supercooled Refers to a liquid cooled to below its freezing point but not yet frozen, supercritical fluid A fluid phase of a substance above its critical temperature and critical pressure. supercritical Having a mass greater than the critical mass. 

Every fission reaction releases some neutrons, and these neutrons can be recaptured by other nuclei, causing more fission reactions. When the amount of fissionable material is small, most neutrons escape from the sample, and only a few neutrons are recaptured. Increasing the amount of material increases the likelihood that neutrons will be recaptured and cause additional fission reactions. The critical mass is defined as the amount of material that is just large enough to recapture one neutron, on average, for every fission reaction. 

As long as the amount of fissionable material is less than the critical mass, the rate of fission events does not grow, and the rate of energy release remains low. In contrast, a sample behaves quite differently when the amount of fissionable material is larger than the critical mass. Above the critical mass, more than one neutron, on average, is recaptured for every fission that occurs. Now the number of fission reactions grows rapidly. As an illustration, consider what happens when two neutrons are recaptured from each fission reaction. As shown in figure 22-11 on... 

The recapture ratio does not have to be 2 for this effect to occur. Any recapture value larger than 1.0 results in explosive growth of the fission chain. The critical mass is called critical because any mass greater than this value sustains a chain reaction and may explode. 

Subcritical portions of this fissionable nuclide must be combined into a critical mass. 

The critical mass must be held together long enough for the chain to multiply to immense size. 

The moderator component of a reactor slows neutrons without capturing them. Moderators are used because the neutrons released in fission have such high kinetic energies that they are difficult to capture. The critical mass of a nuclear fuel is much smaller for slow neutrons than for fast neutrons, so considerably less fuel is needed in a... 

A hydrogen bomb, which uses nuclear fusion for its destructive power, is three bombs in one. A conventional explosive charge triggers a fission bomb, which in turn triggers a fusion reaction. Such bombs can be considerably more powerful than fission bombs because they can incorporate larger masses of nuclear fuel. In a fission bomb, no component of fissionable material can exceed the critical mass. In fusion, there is no critical mass because fusion begins at a threshold temperature and is independent of the amount of nuclear fuel present. Thus, there is no theoretical limit on how much nuclear fiiel can be squeezed into a fusion bomb. 

The polyperoxidation of 1,3-dienes is even more dangerous because they are more reactive and some of their polyperoxides are insoluble. With butadiene, the polyperoxidation takes place at temperatures lower than -113 C the oxygen is absorbed very quickly and forms insoluble polyperoxides that precipitate. It was estimated that at a temperature of 25°C the critical mass of such a compound consists of a sphere of diameter 9 cm. This diameter decreases quickly with the temperature. Isoprene behaves in the same way, but its polyperoxide is soluble, in these conditions, the monomer can absorb any temperature rise which would be caused by the beginning of a decomposition, thus reducing risks. If the monomer evaporates, a gum that detonates at 20°C is formed if the medium is stirred. With cyclopentadiene, polyperoxide is more stable and only detonates at a high temperature. 

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