Dr Carl F. Miller, “A Theory of Decontamination of Fallout from Nuclear Detonations. Part II. Methods for Estimating the Composition of Contaminated Systems”, U. S. Naval Radiological Defense Laboratory, report USNRDL-466, 29 September 1961.
Dr Terry Triffet and Philip D. LaRiviere, “Operation Redwing. Project 2.63. Characterization of Fallout”, Nuclear Weapon test report WT-1317, 15 March 1961.
"As the temperature decreases, positive ions regain their electrons and become atoms, atoms recombine to form molecules, molecules condense to form liquid droplets, and, finally, when the temperature is low enough, the droplets solidify."
- Dr Carl F. Miller, Fallout and Radiological Countermeasures, volume 1, Stanford Research Institute, January 1963, p. 14.
"In 1954 ... we were about 20 miles away when a 10-megaton shot was detonated ... The ship [YAG 39] sailed on a pathway that led to an area directly underneath the expanding cloud, so as to be exposed to a maximum amount of fallout ... Fallout arrived about 20 minutes after detonation, at which time I collected the first few drops of 'hot' washdown water ... With most of the local fallout that we're talking about, a lot of the larger particles are fused or melted to form little glassy marbles. ... The radioactive atoms that could be absorbed into, or by, body organs were the few that are plated out on the surface of the fallout particles during the later stages of condensation in the fireball. That's why the elements iodine, strontium, ruthenium and a few other isotopes of that nature have been found in organs of animals and humans."
- Dr Carl F. Miller, fallout countermeasures research award acceptance speech, U.S. National Council on Radiological Protection (NCRP) symposium on 27-29 April 1981 in Virginia, published in The Control of Exposure of the Public to Ionising Radiation in the Event of Accident or Attack, pp. 99-100.
In the cooling of nuclear fireball, dust and dirt is continuously entering and leaving the regions of vaporized bomb debris and fission products. The gaseous fission products xenon-137 and krypton-90 cannot condense on to solid particles of fallout until their radioactive decay transforms them from rare gases into solid elements.
Hence, large fallout particles can't collect much gaseous xenon-137 or krypton-90 fission products before they leave the fireball due to gravitational settling. This is a simple example of fallout "fractionation". Xenon-137 is the precursor of cesium-137 (the well known long-lived gamma radiation emitter in fallout, which gets into food chains due to its chemical similarity to potassium) while krypton-90 is the precursor to rubidium which then decays into the well-known long-lived beta emitter strontium-90, which gets taken up and deposited into bone a little like calcium (although most food chains do discriminate against strontium relative to calcium to an impressive and helpful extent). The loss of most of the xenon-137 and krypton-90 from close-in fallout therefore reduces the long-term cesium-137 and strontium-90 radiation doses.
"As a result of radioactive decay, the gases krypton and xenon form rubidium and cesium, respectively, which subsequently condense onto solid particles. Consequently, the first particles to fall out, near ground zero, will be depleted in not only krypton and xenon, but also in their various decay (or daughter) products. ... For explosions of large energy yield at or near the surface of the sea, where the condensed particles consist of sea-water salts and water, fractionation is observed to a lesser degree than for a land surface burst. The reason is that the cloud must cool to 100 °C (212 °F) or less before the evaporated water condenses [compared a condensation temperature of 1,400 °C for Nevada silicate soil, causing a relatively] long cooling time ..."
- Samuel Glasstone and Philip J. Dolan, The Effects of Nuclear Weapons, U.S. Department of Defense, 3rd ed., 1977, p. 389.
There are also many short-lived nuclides in fallout subject to some fractionation. Iodine-131 and other isotopes of iodine are depleted from local fallout particles due to the chemical volatility of iodine and its precursors, which keeps it gaseous in the fireball for a long period. Most of these gases end up condensing so late in the fireball that most of the large fallout particles have already fallen out, and only very small particles remain, which on average take a long time to descend into the lower atmosphere from whence they can then be scavenged to the surface by rainfall.
Fractionation therefore works to reduce the relative long-term agricultural dangers from the close-in fallout, and to enhance these dangers in the distant fallout. Put simply, the difference in contamination levels in plants and animals in the local fallout pattern and in the global fallout pattern is much smaller than you would predict from the gamma dose rates, if you ignore fractionation. But what about the hard numbers? Exactly how much fractionation is there for any given nuclide at any given distance from any given type of nuclear explosion?
Two experts, Dr Carl F. Miller and Dr Edward C. Freiling, both originally located at the U.S. Naval Radiological Defense Laboratory in the 1950s, investigated nuclear test fallout experimentally and theoretically in an effort to get the numbers right.
Dr Freiling published a series of unclassified articles empirically analysing the nuclear test data on fractionation from nuclear tests, mainly the four well documented Operation Redwing tests in 1956 (two water surface bursts, Navajo and Flathead, and one coral island surface burst, Zuni, and one surface burst over water so shallow compared to the fireball radius that it was effectively a coral surface burst, Tewa). Freiling's first article was "Radionuclide Fractionation in Bomb Debris", in Science, v. 133 (1961), pp. 1991-8, which is based on his laboratory report Fractionation I. High Yield Surface Burst Correlations, USNRDL-TR-385 (29 October 1959). This simply plots on logarithmic graphs the ratios of the amounts of fractionation of pairs of nuclides in the fallout and cloud samples, finding straight line correlations to within a factor of 2 for all the data points. Fractionation is measured as the reduction factor of nuclide abundance in fractionated fallout, compared to the abundance in unfractionated fission products. In practice this ratio was obtained by taking a very refractory nuclide (in the 1950s this was assumed to be Mo-99, but from the early 1960s Zr-95 was preferred) as a measure of the total amount of unfractionated fission products in the sample, and then finding the relative abundances of other nuclides. The depletion factor due to fractionation, R, is then the factor by which measured abundance of a nuclide in fallout is reduced from the M-shaped fission product production curve determined for fission in a sealed sample of neutron irradiated fissionable material in a laboratory, where no fractionation occurs.
Dr Miller published an alternative approach to fractionation in January 1963 in Fallout and Radiological Countermeasures, after moving from the U.S. Naval Radiological Defense Laboratory to Stanford Research Institute. Miller formulated a theory of how molten particles of soil absorb fission products in the fireball at high temperature before falling out and solidifying. Particles entering the fireball after it has cooled blow the melting point of the soil are then not melted, and merely contaminated on their outer surfaces. Miller's theory follows experimental studies in the 1950s of fallout particles, in which individual fallout particles were sealed in solid transparent resin and then shaved into thin cross-sections which were exposed to photographic film to produce "radioautographs", x-ray like photos in which the source of the illumination is the beta radiation from the radioactivity in the particle.
Examples of such radioautographs are included in Miller's reports and the 1977 edition of Glasstone and Dolan's Effects of Nuclear Weapons. They show that small spheroidal and spherical fallout particles, which were melted from irregular sand grains by the heat of the fireball, tend to be uniformly contaminated throughout their entire internal volume. Because they were molten, the fission products condensing upon them could diffuse into the liquid interior before the fallout particle left the fireball, cooled, and solidified into glassy silica.
On the other hand, irregular shaped particles, which had not been melted by the fireball, were only contaminated on their outer surfaces, thus leaving an irregular loop shape on the radioautographs. Miller explains that these particles are generally formed at a late stage in the fireball history, when the fireball has cooled so much that it can no longer melt the debris entering it.
The problem with this theoretical model in 1963 was that most of the chemical constants for the diffusion of different fission products into molten silicate sand or other fallout materials were then unknown. Most of the research available on absorption was for the absorption of dyes into materials, and gases into activated charcoal absorbers for gas masks. There was little data available on the absorption of the various fission product vapours into molten silicate sand at the high temperatures relevant to a nuclear fireball. Miller's January 1963 report reviewed Freiling's logarithmic correlations and stated that a theoretical justification was needed. Freiling responded in the 15 March 1963 issue of Science, v. 139, pp. 1058-9, with an article called Theoretical Basis for Logarithmic Correlations of Fractionated Radionuclide Compositions.
This is easily explained with reference to the two different distributions of fission products within fallout: soil particles that enter the fireball when it is hotter than the soil melting point end up uniformly distributed throughout their volumes, while those that enter later on end up with surface contamination only.
Uniform contamination corresponds therefore to unfractionated or refractory (non-volatile) fission products, that can condense even at very high temperature. Thus, most of the unfractionated fission product radioactivity condenses uniformly throughout the internal volumes of large particles, making this radioactivity mostly insoluble (trapped in glass), if the soil is silicate in nature (calcium carbonate soils like coral or limestone produce more soluble early fallout than silicate soil).
If the radius of a spherical fallout particle is r, then the total uniformly distributed unfractionated activity throughout its volume is proportional to r3. By contrast, the highly fractionated fission products condense at late times after the fallout particle has cooled and solidified, so they just land on the solid outer surface and are unable to diffuse throughout the volume. The total amount of this fractionated activity which condenses upon a fallout particle is therefore proportional to the particle's surface area, which varies with particle size in proportion to r2.
Hence, the ratio of fractionated to unfractionated fission products in a fallout particle of radius r is directly proportional to the ratio of surface area to volume or r2/r3 = 1/r. Hence, you would expect the fractionation depletion factor R to vary inversely with the radius of the particle: bigger particles show greater depletion in volatile nuclides, because they fall out of the fireball sooner and get less volatile gaseous fission products condensed upon them, relative to the refractory metallic fission products with high boiling points that are always unfractionated in fallout.
So for severely fractionated fission products, the depletion factor R varies with fallout particle radius, r, according to the rule R ~ 1/r, whereas for unfractionated fission products R = 1.
Freilings logarithmic correlations can then be seen as a simple unification and interpolation between these two extremes: R ~ r-n, where n = 0 for unfractionated (refractory) nuclides and n = 1 for the most highly fractionated nuclides. For intermediate degrees of fractionation, n is between 0 and 1. This explains Freilings logarithmic correlations: he called it the "radial distribution model" of fractionation.
There are a couple of very deep insights to be gained from applying this theory to the interpretation of nuclear test data on fractionation. First, Freilings original correlations were log-log plots of depletion factors, R (relative to unfractionated Mo-99 or to unfractionated Zr-95), comparing the fractionation of two different fission product beta decay chains, for example the R factor for nuclides of mass number 91 versus that for nuclides of mass number 89. Freiling's correlations were straight lines through the data points on the log-log axes, but he originally allowed two variables: the intercept of the line and the gradient of the line. His "radial distribution model" later led to the abandoning of the first variable, since the intercept of the line on either R axis cannot be a variable but must always be equal R = 1 for both of the decay chains.
Hence Freiling's original correlation of the Cs-137 depletion factor R137 compared to the Sr-89 depletion factor R89 was:
log R137 = a + (b log R89)
containing two adjustable parameters, a and b, which his later theoretical radial distribution model of fractionation reduced to a single variable, b, by showing that the log-log intercept value a = 0:
log R137 = b log R89,
which yields the simple relationship:
R137 = R89b,
which is exactly what Freiling's radial distribution model of fractionation gives.
In the original papers by Freiling and others, R89 is written r89,95. We're using upper case R for the fractionation depletion factor because lower case r is being used for the radius of the fallout particle, and we are dropping the "95" from the subscript which tells you that Nb-95 was used as the "unfractionated" standard nuclide in working out the depletion factor for Sr-89. This was important when the standard nuclide was switched from Mo-99 in the 1950s to Nb-95 in the 1960s. Precise definition:
"The fractionation ratio [R89,95] is the ratio of the number of fissions required to produce the amount of the mass-89 [beta decay] chain found in a sample to the number of fissions which would be required to produce the amount of the mass-95 chain found in the same sample."
- E. C. Freiling and S. C. Rainey, Fractionation II. On Defining the Surface Density of Contamination, USNRDL-TR-631, 13 March 1963, p. 9.
The absence of a variable intercept implies that where R = 1 for one decay chain (say mass number 89) in a sample, R must also equal 1 for all of the other decay chains in fallout particles leaving the fallout at the same time, i.e. in a sample which has left the fireball at a particular time after detonation. If for Sr-89, R = 1 in a sample, then the "radial distribution model" of fractionation predicts that all other nuclides in the sample are also unfractionated, having R = 1.
This theoretical conclusion simplified Freilings logarithmic correlations by reducing the correlation of the degree of fractionation to a single variable, the slope of the line on the log-log plot of reduction factors, R. In Figure 4 of Glenn R. Crocker, Francis K. Kawahara and Edward C. Freiling's paper "Radiochemical-Data Correlations of Debris from Silicate Bursts" (in Alfred W. Klement, Jr., Radioactive Fallout from Nuclear Weapons Tests, U.S. Atomic Energy Commission, Symposium Series 5, Proceedings of the Second Conference, Germantown, Maryland, November 3-6, 1964, CONF-765, page 78), a Freiling log-log plot of R factors for fission product mass number 91 is plotted against the R factor for fission product mass number 89 for the 1962 1.65 kt Nevada surface burst Small Boy. Freiling plots data from three different laboratories which were employed to determine the fractionation debris from 43 fallout collection stations within 8.7 miles of ground zero.
Each of the three laboratories produced data with an an almost identical slope, but with greatly different intercepts values, due to systematic measurement errors in the laboratory analyses. Freiling could easily identify the most accurate laboratory from the data which gave similar intercept values of about R = 1 for both nuclides, thus using the theoretical elimination of one variable as a means to identify and discard inaccurate laboratory data!
Table 1 of that report by Crocker, Kawahara and Freiling summarizes the fractionation slopes for the 1962 Nevada surface bursts Small Boy (1.65 kt) and Johnie Boy (0.5 kt) and the 1956 coral surface burst Zuni (3.53 Mt). Before we repeat these data, it is important to quote what they say on pp. 73-5 about the samples from the July 1962 Nevada near-surface burst nuclear tests:
"Small Boy was a low-yield shot fired from atop a 10-ft high wooden tower above alluvial soil ... NRDL [U.S. Naval Radiological Defense Laboratory] collected many fallout samples of debris at 43 stations within 8.7 miles of ground zero ... The discussion in this report is mainly restricted to samples from within 8.7 miles of ground zero and from the cloud samples ... A total of about 187 samples is dealt with here, all of which were analyzed for Sr-89, Sr-90, Y-91, and Zr-95. In addition, about one-third of them were analyzed for Mo-99, Ru-103, Ru-106, Cs-136, Cs-137, Ba-140, Ce-141, Ce-144, Np-239, and Pu-239. Some of this last group of samples were also analyzed for I-131 and Te-132. The numbers quoted do not include a fairly large number of radiochemical analyses on samples used for solubility studies. ...
"... Johnie Boy was a low-yield burst 23 in. below the surface of basaltic material ... Forty-four fallout samples from the area out to about 1.25 miles from ground zero and two cloud samples were studied radiochemically. All of these were analyzed for Sr-89, Sr-90, Y-91, and Zr-95, and about one-third of them were analyzed for the long list of nuclides previously given for the Small Boy samples. ...
"... The Small Boy [deposited fallout] field was the cigar-shaped downwind area typically associated with such shots. The Johnnie Boy field was very, perhaps atypically, narrow with a very [radioactive] hot line down the centre, which was visible on the ground as a darkened streak. For Johnie Boy a weighted average for this [Sr-89 depletion R ratio due to fractionation relative to unfractionated fission products, determined from the abundance of the unfractionated nuclide Nb-95] for the hot-line stations is around 0.03, indicating very severe fractionation. For Small Boy the values for most stations are in the range 0.1 to 0.2, indicating more moderate fractionation."
[Insert fractionation correlation summary data table here]
There is also a problem with the way that some of the nuclear test data on fractionation has been analyzed to check this theory. It is clear that the fallout particles do not fall out of the hot fireball in a perfectly size-ordered way, largest first and smallest last. There is a toroidal circulation with an updraft in the centre carrying the dusty mushroom stem up into the cloud head, and there are downdrafts around the periphery of the edge of the mushroom cloud, where the ascending air column has collided with cool high altitude air, been cooled, and started to flow back downwards.
This is confirmed experimentally by the small spread of fractionation values in the large distribution of particle sizes collected in sequentially exposed fallout collection trays at fixed ground stations under mushroom clouds. Fallout particles of different sizes that arrive at the same place, at the same time after detonation, must have originated from different locations in the mushroom cloud, due to their different settling rates. In kiloton Nevada tests where the vertical extent of the cloud was far greater than its relatively small horizontal radius, it generally follows that the larger particles in such samples originated from higher altitudes than the smaller particles.
This implies that the smaller particles in such samples left the fireball sooner than the larger particles, which is the exact opposite of the overall fractionation trend with particle size within the downwind fallout pattern, hence offsetting the usual fractionation variation with size, and explaining discrepancies in the degree of fractionation as a function of particle size in individual samples of fallout obtained at a fixed time and location.
To give a specific example of this error in experimental data analysis, Glenn R. Crocker, Francis K. Kawahara and Edward C. Freiling in Figure 5 of a paper called "Radiochemical-Data Correlations of Debris from Silicate Bursts" (in Alfred W. Klement, Jr., Radioactive Fallout from Nuclear Weapons Tests, U.S. Atomic Energy Commission, Symposium Series 5, Proceedings of the Second Conference, Germantown, Maryland, November 3-6, 1964, CONF-765, page 80) plot a range of data on the depletion factor R for Sr-89 as a function of fallout particle radius for the 1.65 kt Nevada nuclear surface burst Small Boy. But because most of the data used was collected for similar locations and times after detonation, the data points for the fractionation R factor is mostly in the range of 0.1-0.2 and shows only very weak evidence of a dependence upon particle size. Because of the relatively small cloud radius in this low yield test, most of the variation in the sizes of fallout particles deposited at close in locations was due to variation in altitude from which the particles originated, so this effect wiped out much of the anticipated radial distribution model fractionation with particle size! The same misleading graph is reproduced, with a poorly fitting fractionation prediction curve, as Figure 10 on page 26 of Freiling's symposium proceedings book Radionuclides in the Environment (1970).
In order to properly determine the fractionation depletion factor of a given nuclide as a function of particle size, it is therefore necessary to take account of the altitude from which individual particles originated. If particles originate from only one altitude, then to see a significant radial distribution in fractionation in fallout samples it is necessary to utilise samples from widely varying downwind distances, or the fractionation effect will be largely suppressed by differences in the altitude of origination of the fallout particles deposited at one location.
Effect of fractionation on the gamma ray spectrum of fallout
Glenn R. Crocker's 287 pages long report Radiation Properties of Fractionated Fallout; Predictions of Activities, Exposure Rates and Gamma Spectra for Selected Situations, U.S. Naval Radiological Defense Laboratory, USNRDL-TR-68-134, 27 June 1968 (mentioned previously on the post linked here) does not appear to be listed in any online database, although it is cited in the experimental report linked here, so we have created a PDF file which tabulates some of Crocker's most important gamma spectra data, linked here. This shows that for the fission of U-238 in a H-bomb by thermonuclear neutrons, the mean gamma ray energy for unfractionated fission products is 0.81 MeV at one hour and 0.48 MeV at 1 week after detonation, while for fission products in which 90% of the Sr-89 is depleted (i.e. where only 10% of the Sr-89 expected - from the abundance of unfractionated Nb-95 - is present), the mean gamma ray energy is just 0.71 MeV at 1 hour and 0.44 MeV at one week after detonation.
Hence, the depletion of volatile fission products due to fractionation does cause a shift in the spectrum to lower gamma ray energy. As explained in more detail in a previous post, this shift is due to the fact that the most highly volatile fission products are shell structures for both electrons and nuclear properties via the exclusion principle which result in higher than average gamma ray energy emissions. The loss of these high gamma ray energies from fallout due to fractionation results in a downward shift in the mean gamma ray energy. This is quite apart from the additional effect of very low energy gamma ray contributions from non-fission neutron captures in U-238 which produce large quantities of Np-239, U-237, U-240, etc., in the fallout, causing an additional massive reduction in the mean gamma ray energy and making shielding against fallout (at least for low to moderate protection factors, where the low energy gamma rays are easily filtered out, leaving only the smaller proportion of higher energy gamma rays to continue).
(To be continued.)
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