The Interpretation of Fractionation in Fallout Fields - Advances in

15 The Interpretation of Fractionation in Fallout Fields P. C. STEVENSON Downloaded by UNIV OF CINCINNATI on May 30, 2016 | http://pubs.acs.org Publication Date: January 1, 1970 | doi: 10.1021/ba-1970-0093.ch015

Lawrence Radiation Laboratory, University of California, Livermore, Calif.

The fractionation of fission-product radionuclides in fallout fields can be understood at least qualitatively in terms of the chemical nature and relative abundances of the short lived precursors of the observed long lived species. This consideration leads by way of reasonable assumptions detailed herein to the conclusion that the composition of any sample is specified to a defined degree of precision by the concentration of relatively few radionuclides. Identification of these species may then give insight into the physical and chemical processes of fallout phenomenology. A computerized algorithm is given for identifying the "best" nuclides for the purpose and determining the minimum number necessary.

Tyj"any of the less-understood phenomena leading to the observed fallout distribution resulting from a nuclear explosion occur on a relatively short time scale (a few tens of seconds or less). These short term phenomena lead to an initial distribution of radioactive material referred to as the "source term" i n a fallout study. M a n y predictive calculations are based on an assumed source term, which of necessity has been quite oversimplified. Two typical simplifications made for purposes of model development are: (1) that the radiochemical composition of "fallout" is well defined and uniform; (2) that the particles comprising the initial debris are uniform with respect to settling rate i n the atmosphere. The latter assumption has received considerable attention elsewhere, notably in the work of Miller (2). However, the former assumption concerning the radiochemical uniformity of the debris has received far less systematic attention. 282 Freiling; Radionuclides in the Environment Advances in Chemistry; American Chemical Society: Washington, DC, 1970.

Downloaded by UNIV OF CINCINNATI on May 30, 2016 | http://pubs.acs.org Publication Date: January 1, 1970 | doi: 10.1021/ba-1970-0093.ch015

15.

283

Fractionation in Fallout Fields

STEVENSON

Many workers have made it a practice to consider "debris" as a single uniform radioactive species, well defined by gross gamma inten sity, and with known decay properties with time—this assumption is grossly i n error. Even for consideration of external radiation effects, the variation of composition of debris with location exerts a definite and sometimes major influence, while any mechanism which depends on ingestion of a particular species into a biological food chain may be perturbed by orders of magnitude. This paper examines the origin of the source term in the light of known processes, makes some qualitative inferences regarding the results to be expected by modifying the assump tions of uniformity of debris, and examines some existing data to evaluate the results of such inferences. It has been known for many years that the "fission products" ob served in the field or in the laboratory some time after the event are i n fact not usually the species produced i n fission at all but the result of one or several consecutive beta disintegrations of shorter lived isobaric precursors which are formed directly in the fission process. F r o m the chemist's point of view this is important because the β-decay process is an actual transmutation of elements, and the time scale involved is fre quently comparable with that for the formation of fallout particles. Unfortunately, precise knowledge of the distribution of direct yield among several competing isobars is generally not available; furthermore, the radioactive half-lives involved are frequently completely unknown since the fission process gives rise directly to between 300 and 400 radio active species, and the separation of such a complex mixture usually involves a time which is quite long compared with the lifetimes of inter est. W e do know that each isobaric chain is formed directly as a number of different isobars and that the width of the isobaric yield distribution is such that to account for 90% or more of a chain one must consider at least three or perhaps four chemical elements. It is apparent, then, that to understand the physical and chemical processes which govern the distribution of a particular long lived species —e.g., B a — i n a fallout field, one must consider the properties not of barium, or not only of barium, but of cesium, xenon, and perhaps even iodine, and tellurium ( in fact i n this case the relevant species appear to be barium, cesium, and xenon ). 1 4 0

Parenthetically, it should be obvious that those radionuclides of interest which are not fission products do not suffer from this complica tion; such species either are formed directly by a nuclear reaction or are produced exclusively by a known β-decay process from a well defined precursor of (usually) known characteristics—e.g., N p formed by β-decay from U. 2 3 9

2 3 9

Freiling; Radionuclides in the Environment Advances in Chemistry; American Chemical Society: Washington, DC, 1970.

284

RADIONUCLIDES IN T H E E N V I R O N M E N T


Mechanism

of Inclusion

of Activity

in

Fallout

A relatively crude physicochemical model can give a basis for understanding fallout formation. It is assumed first that the preponderance of material comprising the fallout forms an inert condensed matrix in which the active species are included as impurities in such low concentrations that the vapor pressure of the matrix is not perturbed. One then considers the behavior of each trace impurity in terms of a distribution ratio between the matrix phase and the vapor phase. The behavior of such a ratio with temperature can be described roughly as a step function. A t a high enough temperature, assuming there is a high enough partial pressure of matrix material to permit the existence of a condensed phase, the trace impurity w i l l be largely in the vapor phase, while at a low temperature, the trace impurity w i l l be largely in the condensed phase. Intermediate behavior w i l l be governed by Raoult's or Henry's law, depending on the possibility of compound formation between the impurity and the matrix; for our present discussion the transition range may be neglected until later. In actual practice, of course, there is a well defined temperature above which a condensed phase does not exist since the amount of matrix material is limited. This leads to a logical (though oversimplified) threestage division of the process of fallout formation from the very high temperature gas resulting from a nuclear explosion: Stage 1—the earliest stage—ends when condensed matrix formation occurs; Stage 2 ends far less sharply, when the temperature reaches an equilibrium with the surroundings; Stage 3 includes all subsequent processes. Based on our simple model, one may divide the elements into three classes: (1) refractory species, which becomes condensable at or before the end of Stage 1 and consequently condense as soon as matrix material appears; (2) semivolatile species, which are not condensed into the matrix at high temperatures but are absorbed or adsorbed by the particles as the temperature approaches ambient; (3) volatile species, which condense only below ambient temperature, the extreme examples being the noble gases. It should be apparent that the allocation of a particular element to a particular class is a function of both the matrix material (considering condensation temperature and compound formation) and the conditions of the event. A nuclear explosion in the atmosphere gives rise to a cloud of debris which within a few minutes cools to the temperature of the tropopause; a nuclear explosion conducted underground, for example to loosen up a gas-bearing formation, cools rapidly only to the melting point of the surrounding rock. A further complication ensues when the time scale of radioactive decay is compared with the time scale of debris condensation. If con-


15.


STEVENSON

285

d e n s a t i o n is r a p i d c o m p a r e d w i t h a l l the h a l f lives i n a p a r t i c u l a r i s o b a r i c c h a i n , the isobars w i l l d i s t r i b u t e a c c o r d i n g to their n a t u r e , a n d

those

c h e m i c a l species that r e m a i n v o l a t i l e into the t h i r d stage of d e b r i s f o r m a t i o n w i l l c o n d e n s e o n l y after t r a n s m u t a t i o n via

β-decay.

the half-lives are of the same o r d e r of m a g n i t u d e

as the

If,

however,

condensation

times, the c h a n g i n g n a t u r e o f the species d u r i n g c o n d e n s a t i o n c a n m a k e the process q u i t e c o m p l i c a t e d . I n the extreme case, i n w h i c h a l l half-lives are short c o m p a r e d w i t h c o n d e n s a t i o n t i m e , the a c t i v i t y w i l l s h o w h a v i o r characteristic of the e n d - p r o d u c t

be

species.


T h i s series of p h e n o m e n a exerts a p r o f o u n d influence o n the c o m p o s i t i o n a n d d i s t r i b u t i o n of r a d i o a c t i v e m a t e r i a l i n fallout, the effect d e p e n d i n g o n the e n v i r o n m e n t of the n u c l e a r e x p l o s i o n .

A n e x p l o s i o n i n the

a t m o s p h e r e , h i g h e n o u g h so that the u n d e r l y i n g t e r r a i n does not

affect

the d e b r i s , results i n particles w h i c h b e g i n to f o r m at the e n d of Stage 1 a n d i n c o r p o r a t e the r e f r a c t o r y species present at that t i m e .

T h e debris

c l o u d is so d i l u t e that the particles f o r m e d are s m a l l a n d d o not separate f r o m the v a p o r d u r i n g Stages 2 a n d 3, so that the o v e r - a l l c o m p o s i t i o n of the d e b r i s at the e n d of a l l c o n d e n s a t i o n , say 20 b u r s t , is u n i f o r m .

m i n u t e s after

the

It is still true that the r e f r a c t o r y species t e n d to

d i s t r i b u t e d t h r o u g h the b u l k of the debris particles a n d that the

be

semi-

volatile species a n d c o n d e n s a b l e descendants of volatile species t e n d to b e o n the p a r t i c l e surfaces,

so that particles w i t h different

v o l u m e ratios w i l l differ i n c o m p o s i t i o n .

surface-to-

T h e r e f o r e , a n y m e c h a n i s m that

tends to segregate particles o n the basis of size w i l l separate a n o n r e p r e sentative

sample.

I n a n explosion that i n c l u d e s c o n d e n s a b l e matter f r o m the e n v i r o n m e n t , the t i m e scale is r e d u c e d ; i n p a r t i c u l a r , the rate of t i o n segregation m e c h a n i s m s is a c c e l e r a t e d e n o r m o u s l y .

post-condensa

I n bursts at v e r y

l o w a l t i t u d e or at the surface, large a m o u n t s of dust, g r a v e l , rocks, a n d w a t e r v a p o r at r e l a t i v e l y l o w t e m p e r a t u r e are s w e p t into the d e b r i s c l o u d , p r e s u m a b l y to exert a s c r u b b i n g a n d s c a v e n g i n g a c t i o n o n those species c o n d e n s a b l e at that time. condensed,

T h e volatile radioéléments,

a n d their r a d i o a c t i v e descendants

the s u s p e n d e d

fine

l u m p s a n d droplets.

of course, are n o t

deposit p r e f e r e n t i a l l y

on

particles that r e m a i n after the settling of the gross O n e m i g h t expect c l o s e - i n fallout u n d e r s u c h c o n -

ditions to b e h i g h l y e n r i c h e d i n r e f r a c t o r y r a d i o n u c l i d e s a n d d e p l e t e d i n r a d i o n u c l i d e s w i t h volatile p r e c u r s o r s , w h i l e the d e b r i s r e m a i n i n g a i r borne w o u l d be

expected

to consist p r i m a r i l y of

those n u c l i d e s

with

volatile p r e c u r s o r s . T o estimate the effect of s u c h e n r i c h m e n t a n d d e p l e t i o n , one m u s t k n o w the f r a c t i o n of a g i v e n i s o b a r i c c h a i n f o r m e d as a volatile c h e m i c a l species or its v e r y short l i v e d p r e c u r s o r s ; this k n o w l e d g e , as m e n t i o n e d before, is c u r r e n t l y i n a c c u r a t e a n d i n c o m p l e t e .



286

R A D I O N U C L I D E S IN

THE

ENVIRONMENT

When the amount of surrounding or entrapped material is very large, as in a buried explosion, the scrubbing and scavenging effect is completely predominant. A deeply buried event releases no activity whatever; one buried at a somewhat shallower depth releases only those radionuclides that can pass through a thick filter bed of cool material; these consequently consist almost exclusively of noble gases and their decay products. A n explosion buried to produce a crater w i l l liberate nuclides able to pass through a filter bed that is both thinner and more diffuse, but the emergent debris is still highly enriched in volatile species; those condensable elements that emerge are probably attached to the relatively coarse dust that is blown through the filter and may be ex pected to be enriched in the close-in fallout and severely depleted i n the long range airborne cloud. Again, for full understanding, it is necessary to know the isobaric yield distribution and nuclide lifetimes in each β-decay chain of interest. In any case, this simple model indicates that the distribution of long lived activities in fallout debris should be the result of not more than three different mechanisms—not, in fact, more than two different mecha nisms if there is no separation of the vapor and condensed phases until after a time that is long compared with all precursor half-lives. This in turn signifies that one should be able to predict the entire radioactive composition of a particular fallout sample, whatever the mechanism of fractionation may be, given an analysis for only two or three consituents of sufficiently different behavior, and given full knowledge of the relative isobaric yields and half lives and the condensation time scale of the events. As mentioned previously, such knowledge is not yet available; however, this simple approach can be tested by examining the available data to see whether it is possible to express the compositions of all samples from a given event in terms of a small number of radionuclides. Measurements have been made (see Figures 1-4) on sets of samples obtained with aircraft from debris clouds resulting from atmospheric explosions. In many cases it has been observed that the behavior of the active products was determined by the behavior of two and only two different radionuchdes and that for an entire set of samples from a single event, the amount of nuclide i in sample j was given, usually to within 1 0 % , by an equation such as Ajj = k A j + k A n

1

i2

(1)

2j

where Nuclide 1 was a radionuclide that had one or more volatile or semivolatile precursors, and Nuclide 2 was a radionuclide having only refractory precursors. In practice, this relationship has usually been expressed in terms of ratios by dividing by A or A and using suitable normalizing factors to convert the resulting activity or atom ratios to the 1S

2 j



15.

STEVENSON


Eu / Mo" 156

287

(RELATIVE)

Figure 1. Correction of the ratio Ba/"Mo with the ratio Eu/"Mo in a set of airborne-debris samples from a nuclear event. Eu has only refractory species for precur sors; the mass-99 chain exhibits volatile behavior, perhaps owing to the volatility of MoO . The strong negative corre lation indicates that Ba has at least some volatile pre cursors. 140

156

156

s

140

s o - c a l l e d " R v a l u e s , " w h i c h are e q u i v a l e n t to a c t i v i t y ratios for c o u n t e r sensitivity.

corrected

E q u a t i o n 1 is c l e a r l y a m a t r i x e q u a t i o n that c a n

b e w r i t t e n c o n v e n i e n t l y as: A = K«

(2)

w h e r e α is a s u b m a t r i x of A consisting of the first two r o w s . B y the o r d i n a r y rules of m a t r i x a l g e b r a , it is o b v i o u s m a t r i x of r a n k not greater t h a n two

that A is a

since b o t h Κ a n d a are of r a n k t w o .

It is clear that this simplest case is a selected set of samples f r o m the debris that r e m a i n s a i r b o r n e for r e l a t i v e l y l o n g p e r i o d s .

taken One

m i g h t therefore expect that a n y e a r l y t i m e s e p a r a t i o n processes that w o u l d separate debris c o n d e n s e d d u r i n g Stage 2 f r o m that to b e c o n d e n s e d later i n Stage 3, s u c h as p r o m p t filtration or " s c r u b b i n g " b y h e a v y e a r l y f a l l o u t , w o u l d exert a constant bias o n a l l samples r e m a i n i n g a i r b o r n e , so that the p r e s e n c e or absence of a t h i r d m e c h a n i s m w o u l d n o t b e a p p a r e n t i n the selected d a t a . H o w e v e r , it is not u n r e a s o n a b l e to a t t e m p t to evaluate activities i n d e b r i s fields i n terms of a r e l a t i v e l y s m a l l n u m b e r of species, a n d the d a t a f r o m l a r g e sets of samples c o u l d b e r e p r e s e n t e d b y a m a t r i x



288

RADIONUCLIDES

IN

THE

ENVIRONMENT

equation of the form of Equation 2, where the rank of the matrix A is small compared with the number of species of interest. Our simple theory says the rank should not be greater than three, but it is now time to abandon our simplifications and to realize that actual distributionfunction/time (or temperature) curves may depart quite widely from step functions and that we should give up the arbitrary division of all elements into three classes. The question is: i n the data from a real experiment, where many radionuclides are measured i n many samples collected under a wide vari ety of conditions, what is the least number of classes of chemical behavior that w i l l describe the observed results to the desired precision? O r , i n mathematical terms, what is the rank of the matrix A , and what nuclides should be selected to make up the submatrix a? Finally, can any physical significance be attached to the combination of coefficients making up the elements of K , and can these elements of Κ or quantities thus derived be carried over from one event to the next? 2

I

1

1

1

SAMPLE: 6

ol 0 1

1

1

1

1

4

1 •

» 1 •

1

1

12

3

l1

ι

2 3 4 5 6 E u / M o " (RELATIVE)

ι

I

5

II11— 7

8

9

1 5 6

Figure 2. Correction of the ratios Nd/"Mo and Ce/ "Mo with the ratio Eu/"Mo. Slight positive correlation indicates that both the mass-144 and mass-147 chains are somewhat less volatile than the mass-99 chain. 147

144

156


15.


1

SAMPLE:

J υ

289


STEVENSON

I

Ο

1

1

1

I

I

1

1

1I

I

li

4

6

1

1

2

Γ

12

3

3 4 5 6 E u / Mo" (RELATIVE)

I

5

H ll

7

8

9

156

Figure 3. Correlation of the ratio Y/"Mo with the ratio Eu/"Mo. Negative correlation indicate volatile behavior in the mass-91 chain. 91

156

These questions have practical importance. The number of radio nuclides contributing significant radiation to a fallout field is large; furthermore, some of the chemical elements that contribute a small frac tion of the total radiation may be of biological importance out of a l l proportion, owing to efficient biological concentration mechanisms. If an accurate survey of all radionuclides could be accomplished by, for example, surveying a set of samples with a gamma spectrometer of ade quate resolution, such as a hthium-drifted germanium diode ( I ) , the reduction in total work load would be enormous. The variation i n com position of fallout samples is significant; a survey for total y-radiation in the close-in fallout pattern is practically useless for giving a measure of the source term for further predictions unless it is interpreted i n terms of the radiochemical composition of the fallout as a varying function of


290

RADIONUCLIDES IN

THE

ENVIRONMENT

position and especially so if it is reduced to an essentially meaningless term like "kilotons/unit area" or "fraction of fissions released." The determination of the rank of a matrix is fairly simple and straight-forward. Unfortunately, the orthodox methods applied to a matrix such as A in Equation 2 give an answer which is exact mathe matically but useless physically, namely that the rank of A is the number of radionuclides measured or the number of samples analyzed, whichever is less. This unfortunate result arises from presence of experimental imprecision in the elements of A . One must therefore rewrite Equation 2 in the form Downloaded by UNIV OF CINCINNATI on May 30, 2016 | http://pubs.acs.org Publication Date: January 1, 1970 | doi: 10.1021/ba-1970-0093.ch015

A - Κα = Ε

Eu / M o " 156

(3)

(RELATIVE)

Figure 4. Correlation of the ratios ^Sc^Mo, Cm/ "Mo and Tb/"Mo with the ratio Eu/"Mo. Positive corrections with intercept at the origin indicate refractory behavior. 242

161

156


15.

STEVENSON

Fractionation

in Fallout

291

Fields

where Ε is a matrix whose elements are not significantly different from zero, the significance being judged in terms of the known imprécisions of the elements of A and a. The algorithm used is attributed to J. B. J . Read. For many manipulations on large matrices it is only practical for use with a fairly large computer. The data are arranged i n two matrices by sample i and nuclide j : one matrix, V , contains the amount of each nuclide in each sample; the other matrix, E , contains the variances of these numbers, as estimated from counting statistics, agreement between replicate analyses, and known analytical errors. It is also possible to add an arbitrary term F to each variance to account for random effects between samples not considered in the model; this is usually done in terms of an additional fractional error. Zeroes are inserted for missing data in cases i n which not all nuclides were measured in every sample. The "best nuclide" is selected from the two matrices, the selection criteria being: (1) the nuclide must be one of those for which the largest number of samples were analyzed; and (2) that of these species, the one is selected for which the measurements are most precise, that is for which


i k

(4) has the largest value. The other columns of V are then made orthogonal to the fcth ("best") column by adding an appropriate multiple of the Jfcth column to each. (Zero elements must be skipped.) The same operation is also performed on a unit matrix M having the same number of columns as V . The resulting transformed V matrix now has all other columns orthogonal to the pivot column k; the matrix M has been converted into the matrix which, multiplied into the original V matrix from the right, transforms it into the new V matrix, V —i.e., 1

(5)

V! = VM

If each row of V is considered as a separate row vector, then it can be shown (3) by transposing the matrices that the variances of the elements of V are the diagonal elements of the matrices obtained by 1

1

(β)

where E symbolizes the Zth column of the matrix E . This gives a matrix E , whose elements are the variances of the elements of V . One then evaluates S again, using the new V and E to find the second pivot column ( other than the kth column ) having the largest number of nonzero elements and the highest value of S . Again a unit matrix, M , and V are operated on to orthogonalize the remaining columns in V (since z

1

1

m

2

1

1

m

2

1

1


292

RADIONUCLIDES IN

THE

ENVIRONMENT

the kth column is already orthogonal, it is not altered by this operation ) ; the column of the twice-altered V matrix (other than the two previously used) that has the largest number of non-zero elements and the highest new value of S- is then used as the third pivot, and so on until each column of the matrix, except the last, has been used as a pivot column for orthogonalization. The resulting transformed V matrix now has all columns mutually orthogonal, and we may calculate a quantity X j for each column of V 2

1


X j

2=viMl

(7)

which is analogous to S of Equation 4; in fact, for the original pivot column the two quantities are identical. For the other columns (nuclides) X is equivalent to a χ test of the assumption that the data for each nuclide can be fitted, within statistics, by a linear expression only in those significant radionuclides which were previously used as pivots. The reliability with which one concludes that each nuclide must be used is then evaluated from a χ significance table, using for the number of degrees of freedom the number of non-zero elements in the column, less the number of previously used significant pivot columns. 2

2

2

2

Results This technique has been applied to data from a set of 42 samples from a nuclear detonation. Samples were taken both from fallout col lectors and from airborne-debris samplers. Twenty-seven radionuclides could be identified and measured with acceptable precision (better than 10% ) in at least some of the samples. The results are presented in Table I. This calculation was performed without the added variance term F . The nuclides include both fission and activation products. i k

From Table I it is essentially certain that four radionuclides must be used to interpret the data, these being T e (the original pivot spe cies), B a , A u , and P b . The two nuclides U and N d , which also show a level of significance greater than 5 % , can almost certainly be disregarded since they were detected in only a few samples, and the appreciable value of X is probably caused by an erroneous value on one or two samples. If we disregard these two nuclides, it is a reliable con clusion at the 9 7 % confidence level that no more than four nuclides are necessary, and at a confidence level of greater than 9 9 % that no more than five are needed. It is worth noting that two nuclides which are clearly fractionated from each other, B a and T e , are major con tributors to the gamma field but have very different lifetimes. 132

140

1 9 6

2 0 3

2 3 7

1 4 7

2

1 4 0

132


15.


STEVENSON

Table I.

Data for 27 Species Analyzed in 42 Samples Collected from a Nuclear Event

Nuclide 132

T e

"OBa 196

A u

2 0 3

Pb

108 122

A

u

Sb

131J 1 4 1

Ce


237TJ

10S i)9 1 4 7

R u

M o

Nd

187\y 2 4 5 4

Na Mn

88γ

»iSr Zr Zr Sb Sb 95

97

124

127

133J 1351 1 3 7

Cs

139 1 4 3

B a

Ce

293

23,088 1,533 418 141 11.8 9.71 8.73 3.25 1.44 0.819 0.425 0.411 0.261 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Degrees of Freedom

Level of Significance, %

42 34 40 36 22 25 30 28 4 11 15 1 19 0 0 0 0 0 0 0 0 0 0 0 0 0 0

100 (Original Pivot) 99 + 99 + 99 +

The Interpretation of Fractionation in Fallout Fields - Advances in

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