Disadvantage factor

Last but not least, the degree of comminution also plays a part in keeping drugs in the best possible condition too fine a degree of comminution increases the surface area and allows disadvantageous factors to operate more strongly and rapidly than in the case of the whole drug. 

In general, hot melts offer production advantages in cleanliness of operation and the elimination of solvent extraction problems. Hot melts can also be modified to contribute to the barrier properties of the laminate. Control of heat and cost are the main disadvantageous factors. 

The ordinary two region formula for the resonance absorption factor must be modified to include the fact that there are two metal surfaces exposed to good moderating materials, and that the disadvantage factor is rather more complicated than before. It may be shown that the proper generalization of for the three region problem is... 

Herein d = ni/no is called the overall disadvantage factor it is the ratio of the average neutron densities in moderator and U. Similarly, ds = ni/us is the disadvantage factor of the surface of the lump. Mq is the total mass of the lump, and... 

The overall disadvantage factor, d, and the surface disadvantage factor, d, are related by F is the metal disadvantage factor)... 

We can obtain an expression for the characteristic numbers Aj in terms of the disadvantage factors by integrating (26) over the moderator and applying Green s theorem to the left side. This gives, since the gradient of Zi vanishes over the cell boundaxy. 

The i can be expressed in terms of the metal absorption and the i-th disadvantage factor according to (29). A further simplification is possible if we normalize the characteristic functions to / Z dV = 1, the integral to be extended over the... 

The higher terms in the expansion of qi represent transients which die away much more rapidly than the fundamental, i = 1, Hence the fact that di (a constant) is a good approximation to the true average disadvantage factor means that the neutron distribution reaches its stationary shape very little below the top of the resonance band. The actual computation of the dj, or equivalently, the computation of A,, is performed by solving the characteristic equation (29). The form of this equation will depend on the particular function Zj, and these functions depend, in turn, on the geometry of the system. 

In order to compare the calculation of the disadvantage factor based on a Gaussian slowing down model (section 5) with its calculation based on an exponential model (section 4) we shall recalculate the neutron distributions of section 4 by expanding them in terms of the characteristic functions of section 5. 

One can obtain an accurate expression for the surface disadvantage factor ds in terms of the a,-. It is, per definition... 

In addition to 1 /p2 it is interesting to note the factor by which the absorption in the carbon is increased by having the uranium concentrated in lumps, rather than spread out uniformly. Since the U has a higher absorption coefficient than the carbon, the neutron density will be larger in the carbon than in the U and we shall call the ratio of these densities the disadvantage factor d. It can be calculated from p2 as follows. 

If only the first two terms of (14) were present, the disadvantage factor would be just 1, i.e., the thermal utilization would be just as good as in a homogeneous mixture. Actually, however. 

In the case of the resonance absorption, p2 is very far from 1 (about. 16) and the above approximation becomes very poor. It continues to be possible, however, to use (11a) for both (/C2 2) and ( o o) and obtain in this way a manageable expression for the disadvantage factor d. One obtains... 

The graphite density was taken to be 1.63. Table 2 gives the disadvantage factors in the same way. 

Table 2. Disadvantage factor for the thermal region with oxide spheres of density 6...

Table 3 gives the disadvantage factors for the resonance absorption in an oxide sphere of density 6. 

The disadvantage factor can be factored into two factors the average density in the C, divided by the average density in the U can be written as... 

Again, (4) and (5) contain two terms. The first corresponds to fast neutrons and in this c(E) = 1/( E) where is the slowing down power of the material (.158 for carbon). The second term refers to thermal neutrons. In this / c E) dE is the ratio of total scattering cross section and total absorption cross section per unit cell, multiplied by the thermal disadvantage factor (about 1.4 in the usual arrangement). (This means, of course, that the f c(E)dE of this term is the number of collisions a neutron suffers while it is thermal.)... 

The best method for analyzing the errors and possibly for correcting them would seem to be by a Monte Carlo analysis of selected cases. Methods for achieving this have been developed by Richtmyer, et al. [23]. Before such calculations have been made with sufficient accuracy, it would seem best not to introduce any special disadvantage factors. The successful application of the old method is attributable to the fact that the available data were analyzed in terms of a theory which used disadvantage factors, and thus led to larger values of the resonance integrals than later measurements. 

Detailed flux distribution measurements throughout a representative cell have yielded a value of 1.10 0.02 for the disadvantage factor for a single fuel pin in a li-in. triangular lattice. Similar measurements in the clustered geometry gave 1.4. 

The tabulated data are not corrected for fuel self-shielding and flux depression. E]q[>eri-ments performed at Livermore indicate a disadvantage factor of 0.79 0.07 for the room temperature experiment. 

Using the methods described, the effective multipUca4 tlon factor (kg), U-235 fission cadmiu ratios (Cis)r U-238 cadmium ratios (Cnl, and thermal disadvantage factors, the dm/ F Assemblies I tiumugh VI were calculated and compared with experiment. Table H presents this comparison. 

Either ratio, Ra or pa, can be related to the resonance escape probability or the conversion ratio. Microscopic (intracellular) flux distributions can be measured, and values of disadvantage factors and thermal utilisation can be obtained from them, b lattices of slightly enriched uranium rods in ordinary water it has also been possible to determine, indirectly, the migration area or age, and thus to obtain an experimental link between the macroscopic and microscopic properties of such lattices. 

The slab-lattice disadvantage factors were measured in a miniature lattice. This is a small rectangular exponential assembly measuring 16 inches high by 12 inches wide by 12 inches long contained in an aluminum tank surrounded on all sides, except the top, by a -inch of cadmium sheet and 3 inches of paraffin. Hie whole assembly wu exposed in the animal tunnel btcility of the Brook-haven Gmphite Reactor which supplied a flux of 10 neutrons/sec-cnf. 

The disadvantage factors were determined from intracellular flux distributions measured with 0.007-in.-thick, jt-ind) in diameter, 93% Al/7% Dy foils. Seven or five foilsi depending on the volume ratio, were supported in the water by O.Ol inch-thick Lucite foil holders. One fuel element contained a -inch-diameter i -inch -thick uranium disk insert. This disk was split in half, and... 

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