14 WORLDWIDE EFFECTS OF ATOMIC WEAPONS ORIGIN AND NATURE OF RADIOACTIVE DEBRIS of ZrO,(g) would be 10°* atm. We may estimate the vaporization temperature at 10° atm pressure to be 1300°K.In the case of FeO (assuming and growth must be proceeding simultaneously to give the observed range of particle sizes. If nucleation were slow and the subsequent growth the whole bomb structure to be Fe), the partial pressure of FeO(g) would be 10°* atm. At this partial pressure a condensed phase of FeO would start to form at 2300°K. For aluminum at pa artial pressure of 10-° atm a condensed phase might be expected at 2700°K. Uranium oxide would have a partial pressure of 3 X 10°° atm and would be expected to condense at 1600°K. From these considerations we see that, even assuming equi- librium (i.e., no supersaturation), the first condensed phase expected is Al,O, in the case of an aluminum bombstructure and FeO for an iron structure. Cooling through the temperature range where condensation takes place occurs at the rate of about 10° deg/sec for a 20-KT bomb,so that consid- erable supersaturation is possible, particularly in view of the very low partial pressures of most of the oxides. This supersaturation may tend to favor the initial condensation of those materials present in larger amounts, thus again indicating that the major components, such as aluminum or iron, probably condense first. Supersaturation may also lead to the simultaneous formation of a larger number of condensation nuclei, since fewer molecules are needed to form a nucleus, with the result that very small particles would be formed. Several species condense simultaneously, so that each small sample contains a mixture of the condensable materials present at the instant of condensation. Some general statements may be made about the nucleation process: 1. The solid material present in the air engulfed by the fireball cannot be an important source of nuclei, since all of this material would be vaporized and mixed with the gaseous bomb materials. 2. The ions produced by the very intense radioactivity may serve to collect a few gaseous molecules and thus form condensation nuclei. It seems likely that this mechanism would be very important in the later stages of the condensation when the degree of supercooling ts large, so that two or three molecules would be enough to form a stable condensation nucleus. 3. The material may be self-nucleating by statistical fluctuations in the number of many-bodycollisions. From the experimental data that exist one can conclude that nucleation 15 process very fast, the particles would have an extremely narrow distribu- tion in size about the mean. If nucleation were fast compared with growth, then essentially all the material would go into such nuclei and the particles would be very small and all very nearly the samesize. The experimental data on particle-size distribution have one thing in common: they all indicate in the region where the measurements are best that the number of particles of a given diameter decreases exponentially as the diameter increases. The experimental data also show a decrease in the number of particles at low diameters. The maximum number, however, occurs at a diameter that ts very dependent on the method of sampling and sizing. For example, optical microscope results indicate a maximum in the number distribution at a particle diameter of 1 micron (yz) or greater, while electron microscope results indicate that this maximum occurs below 0.1 p. It seems quite clear that this decrease in the number of particles having small diameters is not real, but is a result of the sample collection efficiency and of the resolution of the microscope. In the absenceof better measurements the most reasonable assumption seemsto be that the exponential increase actually continues down to very small particles of 0.01 p or less in diameter. With the assumption that the number distribution is given by N,= WN, exp (—D/6), the fraction of the particles of diameter less than a given diameter D” is given by f, == 1 — exp (—D’/6). The fraction of the mass that resides in particles of diameter less than D’ is given by penorale(+49)+81] 2 Figure 2 shows a plot of these two functions. It may be pointed out, for example, that 50 per cent of the particles has D’/b less than 0.693 and and hence (assuming constant specific activity) only 2 per cent of the activity. On a mass basis, 50 per cent of the mass is contained in particles with D’/b = 4 and these particles constitute only 2 per cent or 3 per cent of the total number of particles.