Minimum critical volume

In adding conductive filler to an insulating resin, the volume resistivity changes slowly until a critical level of filler is reached, called the percolation point. The percolation point occurs when the resistivity drops abruptly, then continues to drop slowly (Fig. 2.11). " Almost continuous linkage of metal particles occurs at the percolation point where typical filler volumes for silver flakes are 25-30%. According to the percolation theory, there is a minimum critical volume of filler required for electrical conductivity in a polymer at which each filler particle must contact two other particles. A misconception in the use of silver flakes is that increasing the number of contacts lowers volume resistivity. Actually, the converse is true because, once the percolation point has been reached, each additional contact adds resistance. Thus, increasing the particle size can increase conductivity since the total number of contacts for a fixed volume decreases." ... 

Results of the measurements with the 11.5- and 15.2-in.-diam spheres are given in Table I. Critical e]q>eri-ments with the 14-in.-diam sphere were previously reported . Minimum critical volumes for the plutonium nitrate solution containing 4.6 wt% Pu-240. when bare and water reflected, were determined from interpolation of the data to be about 22 and 11 t, respectively, for a Pu concentration of 175 25 g Pu/f. A concrete reflector was found to be somewhat more effective than water on the 14-in. sphere, but slightly less effective on the 11.5-in. sphere where the concentration Pu was greater. Neutron-flux measurements made in the 11.5-in. and the 15.2-in. sphere were used to determine extrapolation lengths and, hence, critical bucklings for the solutions. A typical flux plot is shown in Fig. 1. The effect of a stainless-steel shell on criticality was also evaluated in several experiments by the addition of extra shells that permitted a subsequent extrapolation to zero shell thickness. 

Ugfit-water reactor hiels normally consist of natural or depleted uranium enriched with up to 8 wt% Pu. Criticality data, even on uranium systems at this low a enrichment, are sparse. For homogeneous uranium enriched with-plutonium, data are essentially nonexistent. To obtain criticality data in this area, experfinents were recently completed with a PuOz-UOa-polystyrene mixture coiAaining 7.6 wt% Pu in the Pu+U. The H Pu-i-U atomic ratio Of the fiiel mixture was 19.5, which is near the optimum concentration for minimum critical volume. 

In normal operation, plutonium nitrate solutions may be concentrated to 300 to 400 g Pu/litre. The maximum expected concentration is 600 g/litre. The nitric acid content will range from I to 10 For the criticality safety analysis, it is as.sumed that the concentrator contains plutonium nitrate. Plutonium concentration is not limited however, for the calculations, the most reactive concentration from the standpoint of criticality is assumed to be 175 g Pu/litre, as experiments have shown the minimum critical volume for Pu(N03)4 solutons to occur at about this concentration. -... 

Minimum critical volume as a function of "U enrichment in water tnoderated Znd -reflected systems. (Symbols indicate calculated data points.)... 

Minimum Critical Volume 1180 liter 825 liters Sk3 liters... 

Minimum Critical Volume 705 liters 3 6 liters 620 liters... 

The material buckling of the heavy water, natural uranium subcritical assembly, with a fixed composition and lattice spacing, is determined by measuring the spatial distribution of the neutron flux. The assembly is in a steady-state condition, multiplying neutrons which originate from a neutron source properly placed near the assembly. The buckling determination yields the minimum critical volume of a neutron-chain reactor with the same composition and structure as the exponential assembly. 

The minimum critical volume for which a cylindrical reactor with a certain Bg can be determined by the Lagrange multiplier method. The minimum value of ttR H is subject to constraint given by equation (9) and lends... 

What is the geometrical buckling for the system described in Question 7 What is the minimum critical volume for the reactor as a function of the buckling ... 

---