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CTr*i MASm ORNL/TM-6453

Criticality Analysis of Aggregations of Actintd€s from Commercial Nuclear Waste

in Geological Storage

E. J. Allen

OAK RIDGfc NATIONAL LABORATORY 0 D E f U T t r ,BV U N I O N C A R B W - . " O P P - O R i T I O ^ C 0 R P F P A R T M E N T O F E N E R G Y

ORNL/TT-6458 Dist. Category UC-70

Contract No. W-7405-eng-26

Engineering Technology Division

CRITICALITY ANALYSIS OF AGGREGATIONS OF ACTINIDES FROM COMMERCIAL 'JCLEAR WASTE IN GEOLOGICAL STORAGE

E. J. Alien

Date Published: August 1978

y NOTICE > s j | N O S «

PORTIONS OF THIS REPORT ARE ILLEGIBLE. It has been reproduced from the best available copy to permit the broadest possible avail* e&iilty.

Prepared by the OAK RIDGE NATIONAL LABORATORY Oak Ridge, Tennessee V7R30

operated by UNION CARBIDE CORPORATION

for the ,, DEPARTMENT OF ENERGY

NOTICE Uua *epon was prepared as an account of wort tnwtsorvd by the United State* Government, Neither the (tinted States not the United Slates Department of nor anv of their employees, nor any of theu conttactort, subcontract on. <k ihetr employee*. miles any wwraniy, express or milled, or asumes any trgaf taMUty or respwoMbty fot the accuracy, complete. fss or usefulness of any taifcrnnattaa. apparatus, product of process dockaed, or represents that tts tne would not infringe pmatety owned rifhte.

or j r j^c-i iEJp: $ C N L i i m ^

iii

CONTENTS

Page

FOREWORD v ABSTRACT 1

INTRODUCTION 1

NUCLEAR WASTE REPOSITORY DESCRIPTION >• 2

•WCLEAR WASTE TYPES CONSIDERED 2

INFORMATION PERTAINING TO THE CRITICAL MASS CALCULATIONS 9 CRITICAL MASS COMPUTATIONAL MODEL 11

CALCULATTONAL RESULTS 1 9

ESTIMATED ACCURACY OF THE CALCULATIONAL RESULTS 32 DISCUSSION OF THE CALCULATIONAL RESULTS AND CONCLUSIONS 34 ACKNOWLEDGMENTS . 34 REFERENCES , 35 Appendix 1. CRITICAL MASS COMPUTATIONAL MODEL 37 Appendix 2. PLOTS AND TABLES OF CALCULATED CRITICAL MASSES .. 43

V

FOREWORD

This report was prepared by the Engineering Technology Division of Union Carbide Corporation, Nuclear Division, in cooperation with the Office of Waste Isolation for the National Waste Terminal Storage Program. The objective of this OWI program is to establish facilities in various deep geologic formations at several locations in the United States for the safe disposal of commercial nuclear waste. Thif- reported work is in support of this objective.

CRITICALITY ANALYSIS OF AGGREGATIONS OF ACTINIDES FROM COMMERCIAL NUCLEAR WASTE IN GEOLOGICAL STORAGE

E. J. Allen

ABSTRACT

An underground nuclear-waste terminal-storage facility for either spent fuel elements or high level waste from a reprocess-ing plant will contain large amounts of fissionable actinides. Such a facility must be designed to preclude the concentration of these isotopes into a criti"al mass. Information on the critical masses of the various isotopes present in spent fuel or high level waste is required as part of such a design effort. This study provides this information. The results of this study will be used, in conjunction with geologic transport rates of the actinide compounds, to estimate mass formation probabili-ties in waste repositories.

A computational model was developed as part of the study to perform criticality calculations rapidly and efficiently and to produce tables and plots of actinide concentration in geologic material versus critical mass. The criticality model uses a discrete ordinates approximation to neutron transport theory and treats sis: energy groups and spherical geometry. Neutron cross sections were obtained from ENDF/B-IV or ENDF/B-V cross section libraries. Critical masses calculated with the computa-tional model were checked against experimental values and against more detailed calculational values and wera found to be from 30% less to 10% greater.

Critical mass calculations were made for five waste types, five waste ages, five actinide elements, and four geologic compositions. Minimum critical masses were calculated for over 400 combinations of the above variables. The relative importance for criticality of the various actinides and waste types is pre-sented in terms of the number of possible critical masses per waste container.

Key words: nuclear waste, critical mass, actinides, calcu-lations, computer codes.

INTRODUCTION >

A nuclear waste repository for spent fuel or high level wastes from a fuel reprocessing plant will contain large amounts of the actinide elements U, Np, Pu, Am, and Cm. Since many of the isotopes of these elements are

' • - i' - ' ' 1 - i . fissionable, the repository must be designed to prevent a,-critical mass

being formed as a result of selective leaching and/or selective transport and selective deposition of one or more of the fissionable actinides.

Tile results cf considerations to date indicate very low possibilities of an assembly of actinides being formed which would meet all of the requirements for criticality; namely, required amounts of actinides, purity, geometric shape and size, and neutron moderation and reflection.1

To help in further assessments of the criticality possibilities, criti-cal ity calculations were made for a wide range of assumed repository onditions for the actinides in nuclear wastes from each of several dif-ferent fuel cycles.

NUCLEAR WASTE REPOSITORY DESCRIPTION

Preliminary waste repository designs indicate that the high-level waste canisters will be placed in vertical holes in underground chambers. The holes containing the canisters will be placed in a single or double row down the center of each chamber and spaced to 3 meters apart. There will be several high-level waste chambers in each repository. A similar design will result if fuel elements rather than High Level Waste (HLW) canisters are stored.

Geologic structures considered suitable for terminal storage of nuclear waste include structures composed of salt, granite, or shale. The repository structure and site are selected partially for long-term stability properties. These include infrequency of earthquakes, low probability of groundwater intrusion, and absence of surface drillings.

A more complete description on nuclear-waste terminal-storage facilities is presented in Ref. 2.

NUCLEAR WASTE TYPES CONSIDERED

Five nuclear waste types were considered in this study. The waste types are summarized in Table 1 and will be specified througliout this paper as being of types 1—5 as in the table.

All five waste types were assumed to be from light-water reactor fuel since most of the nuclear waste generated for the first terminal- w

storage facility will come from such reactors. The fuel was assumed,, to

Table 1. Descriptions of the nuclvar waste types considered

Nuelear waste type Desoript ion'

1 Spent fuel Hi^h level waste (HLl-C) trosi

fresh uranium fuel HLW from plutonium re'-yc-led

fuei HLW from fresh uranium fuel

hut with a l l the plutonium remaining in the waste

HLW from 2/3 fresh uranium fuel and 1/3 plutonium reeve led fuel

Note that a l l f ive nuclear waste types originate from PWR fuel hurne-d to 33,000 MWD/MT.

have undergone a burnup of 33,000 MWD/MT. For the waste types other than spent fuel, reprocessing was assumed to occur one year after discharge from the reactor. In waste types 2 through 5, 99.5% of the uranium was assumed to be removed during reprocessing. In type four waste, the plutonium was not removed during reprocessing and remained in the waste. In types 2, 3, and 5 waste, 99.5% of the plutonium1! was removed. Type 5 waste is representative high-level waste of a pressurized-water.reactor (PWR) operating with plutonium recycle of the Plutonium to the reactor.

Since the critical mass of a particular actinide with a particular moderator and reflector is dependent on the isotopic composition of the actinide, the isotopic compositions of the five most important actinides were calculated for the five waste types and for five waste ages. The,, isotopic compositions change with time due to decay of the nuclides in \ the waste. The decay calculations were performed by the Office of Waste Isolation in their fiscal year 1977 projections with the isotope generation and depletion code 0RIGEN.3

In Tables 2—6, the isotopic weight fractions of five actinide element for the five waste types are presented. Note that the isotopic weight fractions are given for oxides of the actinides. The time periods or ages of the waste refer back to when the fuel was discharged from the reactor.

Tible J. Isotonic *.*eii;i>t fractions <>t uranium in nuclear wnstt

Kei^it fraction of uranium Kilograms uranium >iot«et» in ur.iiiiur.) >>:-. iiie per metric ton oi

- fuel charged ••'T •' " r • ' "r

1 lO 0.0001b 0.0074 3 0.00379 0.87098 955.3 ] 100 0.00022 0.00744 0.00380 0.S7089 955.4 ] 1 .000 0.00027 0.00756 0.00398 0-87054 955.8 1 10.000 0.0002. .-'0.00862 0.00507 0.86839 958.2 1 100,000 0.00022 0.01201 0.00576 0.S644.; 962.6 2 10 0.00018 0.00743 ':00379 0.87095 4.77 j 100 0.00039 0.00745 0.00384 0.87067 4.77 i 1.000 0.00068 0.00759 0.00438 0.86970 l* . 78 J 10,000 0.00067 0.00998 0.00770 0.86400 4.81 • } 100,000 0.00052 0.02587 0.00969 0.84632 4.91 i 10 0.00049 0.00290 0.00068 0.87S28 4.65 3 100 0.00346 0.00291 0.00164 0.87435 4.67 3 1.000 0.01035 0.00342 0.01259 0.85599 r"' A.77 3 10,000 0.00927 0.02493 0.07345 0.77470 5.27 3 100,001) 0.00569 0.17423 0.09002 0.61246 6.69 4 10 0.00379 0.00839 0.00750 0.86-67 4.80 4 100 0.02789 0.01055 0.01082 0.83310 4,. 97 4 1 ,000 0.04730 0.03186 0.04096 0.76225 5143 U 10,000 0.03199 0. 1,3768 0.Ih332 0.52937 7.83 4 100,000 0.01367 0.37095 0.15817 0.33761 12.44"

10 0.00028 0.00595 0.00277 -0.87 335 4.73 5 100 0.00140 0.00596 0-00312 0.87188 4.74 5 1,000 0.00390 f1;. 00620 0.00711 ,0.86514 4.78 5 10,000 0.00371 rj.01527 0.03098' 0.83239 4.96 5 100,000 0.00261 0.08596 0.04222 0.75161 5.50

Xuc1 ear a * * t vpe

A*e (ve.irs)

5

Tahl«- 5. Isotropic weight : r . i f t ions of neptunium in nuclear vnstv

•Nuclear wiiste tvjie

A^e (vt i rs)

Wight fraction of neptunium isotopes in neptunium oxide

:V"Np

Kilograms neptunium per metri.- ton of

flit.-1 ri.ar

1 10 0.882 1 100 1 0.882 1 1.000 0.882 1 10,000 0.882 •> 10 0.882

100 0.882 ) 1,000 0.88s 2 10,000 0.882 3 10 0.SS2 J 100 0.882 3 1,000 0.882 i 10.000 0.882 4 10 0.882 4 loo 0.882 4 , 1.000 0-. 882 4 10,000 0.882 5 10 0.S82 5 100 0.882

1,000 0.882 10,000 0.882

0.467 0.614 1. 47 1.'/ j 0.464 0.478 0.347 0.367

0.176 0.276 0.77] 0.964

0.968 1j.11 , 1.94 2 . 2 0

0. 368f:; 0.411 0.622 0.699.,

'V „•

;sates

Tabic 4. Isotypic weight fracLions of pluloniuni in nuclear waste

Nuclear waste type

Age (years)

Weight f ract ions of the plutonium isotopes in plntonliim oxide

'I'u ! f I'u »i'u 1 I'll I'll

K i 1 o>;rams p lutuni um per metric ton of

fuel chaiv.eil

1 10 0.0129 0.531 0. 219 0.0704 0.04 37 8. Mb 1 J 100 0. 0071/7 0.585 0. 240 0,00118 0.048 5 . li 1 1 ,000 o.oo'joi 0.001 0. 2'l 0.0 0.0507 7.71 1 10,000 0.0 0. 078 0. 132 0.0 0.0720 5. 55 2 10 0.0374 0.448 0. 290 0.0044 0.0 109 0.0532 ) 100 0.0.71 0.379 0. 4 5 5 0.00074 0.0 no 0.0040 2 1 ,000 o.oo/jn 0.44 5 0. 407 0.00001 0.0J09 0.00 71 2 10,000 0. o 0.720 0. 130 0.0 0.02 59 (1.079 , 3 10 0.00ll7 0. 138 0. 575 0.0400 0.059 5 0. 5 59 3 100 0.0222 0.0700 0. 754 0.00040 0.0290 0. 78(i 3 1 ,000 0.00047 0.184 0. 004 0.00015 0.0338 0,831 3 10,000 0.0 0.038 0. 212 0.00000 0.0318 1 .04 4 10 0.02h5 0.531 0. 213 0.0720 0.0 595 9,20 4 100 0.0140 0.587 0. 230 0.00113 0.04 59 8. 28 4 1 ,000 0.00001 0.008 0. 227 0.0 0.0400 7.80 4 10,000 '0.0 0.080 0. 131 0.0 0.000 1 5.41 5 10 0.0377 0.209 0. 511 0.0502 0.0541 0, 1 5') 5 100 0.0215 . 0. 119 0. 712 0.00050 0.(1298 0. 305 5 1 ,000 0.00043 0. 220 0. 029 0.00013 0.03 34 0. 522 5 10,000 0.0 0.049 0. 202 0.00005 0.0310 0. 3'i'j

/

Table 5. Isotopic weight fractions of americium in nuclear waste

Nuc1 ear was t u type

Aye (years)

Weight fractions of americium isotopes in

americium oxide ? u l Am 22ra 'Am ' <4 3

Kilograms americium per metric ton of

fuel charged Am

1 10 0.750 0.00105 0.131 0.601 1 100 0.SIS 0.00034 0.0640 2.2 2 1 1,000 0.677 0.00002 0.205 0.351 1 10,000 0.00014 0.0 0.882 0.0361 2 10 0.471 0.00327 0.4 OS 1.93 0 100 0.450 0.00231 0.431 0. 181 2 1,000 0.1S7 0.00007 0.695 0.103 9 10,000 0.00014 0.0 0.882 0.0361 3 10 0.297 0.0146 0.571 2.20 3 100 0.278 0.0102 0.594 2.08 3 ] , 000 0.096S 0.00024 0.785 1.45 3 10,000 0.00316 0.0 0.879 0.575 4 10 0.760 0.00105 0.121 0.579 4 100 0.823 0.00034 0.0590 1.18 4 1,000 0.691 0.00002 0.191 0.336 4 10,000 0.0'»014 0.0 0.882 0.0321 5 10 0.323 0.0129 0.546 0.860 5 100 0.304 0.00905 0.370 0.814 5 1,000 0.108 0.00022 0.774 0.552 5 10,000 0.00282 0.0 0.880 0.216

>

8

].!.') U- . • . Isi't.'j'i Weight ; r.ii-t ien.s < * i 1 111 i um i n nui' U-.ir K.^ti'

- t .• A v t i Vf,i )

Ke i i

;ht 1 r.H't ion ol" itiipt-s in i tir itin

<nr i ikh oxid»- Kilncraras curium

pi-r netrit ton • " Cn u 'Cm ' * "Cm •' ~ Cm '

ui Cm of fuel charged

i 10 0.00004 0 OOJh 7 0.8(i 5 0.0124 0. 00154 0.0169 1 lull u.ooi24 0 <10792 0. 574 0.267 0.0316 0.000813 1 1.11(1(1 11.00007 0 0 0.0 0.744 0.0888 0.000254 1 10.0(10 0.0 0 0 0.0 0.S30 0.052", 0.000114 J lit (,. 000(H) 0 00267 0.865 0.0129 0.00154 0.0169 - 100 0.00124 0 00792 0. 574 0.267 0.0316 0.000813 2 1 .000 0.00007 0 I1 0.0 0. 794 0.0888 0.000254

10.001) 0.0 0 0 0.0 0.830 0.0525 0.000114 10 (I.OUOU II .00075 0. 728 0. 1 38 0.0152 0.564

' 100 0.000-4*, 0 .00053 o. ;i<i 0.690 0.07S4 0.112 i 1 ,000 o.oonoi 0 0 0.0 0.800 0.0826 0.0898 i 10.000 o.o 0 0 0.834 0.0488 0.0405 4 11) o.oooio 0 002 82 0.865 0.0126 0.001 A3 0.0144 4 100 0.001 AL' 0 00845 0. 580 0.263 0.0297 0.0006S4 4 1 ,000 o.oooox 0 0 n.o 0.797 0.0848 0.000209 a 10,<>00 0.0 0 .0 0.0 0.832 0.0502 0.0000943 » 10 0.00013 0 0008(i 0.736 0. 131 0.0145 0.199

loo 0.000i7 0 000hi 0. 123 0.684 0.0748 0.0380 » 1 ,000 0.00001 0 0 0.0 0.800 0.0827 0.0301

1 0, (MM) 0.0 0 0 0.0 0.834 0.0488 0.0136

Five actinides were considered in this study. These were uranium, neptunium, plutonium, americium, and curium. Heavier actinides were not considered as they were not discharged in enough abundance to cause a criticality problem. Of the five actinides considered, uranium had to be followed for a longer time than the others because of the long half-lives of the uranium isotopes and because the isotope 2 3 5U continued to increase in relative abundance. Critical mass calculations for uranium were per-formed to a waste age of 100,000 years; the other actinides were only considered to a waste age of 10,000 years.

In Tables 2—6, the heavy metal masses in the nuclear waste per metric ton of heavy metal charged to the reactor are presented in addition to the isotopic weight fractions. There are two types of waste containers; the spent fuel element of waste type 1 and the HLW container of the other waste types. There are approximately 0.523 metric tons of heavy-metal oxide initially present in each spent fuel element and 2.38 metric tons of

9

heavy-metal oxide reprocessed per HLW container-u Using this information and the information in Tables 2—6, the heavy—metal oxide masses per waste container can be calculated and are presented in Table 7-

r.iMi' Ma - i S i S i>t V irii-u. .let initio oxides r nu<-le.ir v.iM i- font a i m r

KMI--

M. i S S ot' a c t i n i d e i'X:<.!<•• p e r • is t t' > o n t a i r i e r ( k p )

t Afce - . - - . . . _ . . . . . . . - - - - - -

•'|H tyvars) Iran i un N .•ptunium P l u t o n i u m Aneri.-ium Curium Iota!

1 HI 4*)9. 5 0.244 4.h9 0. 314 0.0089 504.8 1 10(1 40a, 0. 31'] 4.24 O . M 7 0.000423 "i 04 . 8 1 ) .000 499. S 0. 7b9 4.0 3 0. 183 0.00013 3 304.8 1 10.000 501.0 0.903 J . 80 0.0189 0.000060 504.7 I 100.000 503.4 0. 3b2

10 1 1. lb 1. 10 0.1 '7 0.4^9 0.0403 13.09 > 100 U . 36 1.14 0. 1 54 0.431 0.00193 13. OS t 1.000 11.37 1. 30 0. 160 0.24h 0.00060 3 13.08 > 10,000 11.45 1. 15 0. US9 0.0859 0.000271 13.07 \ 100,000 1 l .69 0.0262

3 10 11.07 0.419 0.854 3.22 " 1.34 IS. 91 3 100 11. 12 0.657 1.87 4. 3 0.267 18.87 * 1,000 1 1. 36 1.84 1 .98 3.45 0.214 If*. 84 3 10,000 12.35 -» Q 2.47 1. 37 0.09f>5 18.78 3 100,000 15.91 0. 370 ^ 10 11. '.2 2. 30 2 1 .89 1 .38 0.0342 37.02 4 100 11.82 2.64 19.71 2.81 0.00163 36,98 4 1 , 000 12.92 4.62 18.37 0.799 0.000498 36.91

10,000 IS. 64 5.24 12.86 0.0764 0.000224 36. ei 4 100,000 29.61 1.60

3 10 11.2( 0.876 0. 369 2.05 0.474 15.03 3 100 11.28 0.977 0.726 1.94 0.0904 15.01 5 1,000 11.37 1.48 0.766 1.31 0.0716 15.00 5 10,000 11.81 1.66 0.948 0.513 0.0223 14.97 5 100. )00 13.09 0.141

INFORMATION PERTAINING TO THE CRITICAL MASS CALCULATIONS

Information pertinent to the critical mass calculations is presented in this section. In the discussion which follows, the moderator is defined to be the material with which the actinide compounds are mixed, whether it is water, brine, granite, or salt. The reflector is the outer shell or

10

annulus of material which does not contain actinide compounds but may be the same material as the moderator.

All calculations in this study assumed a spherical geometry. For a giv^n composition of actinide compounds in a moderator material, the critical mass is least for a sphere of the composition.

For a given moderator, reflector, and actinide compound, there exists a specific concentration of actinide compound in moderator at which the critical mass is minimum. Several interacting effects, described in Ref. 5, result in a minimum in tlie curve of critical mass versus actinide concentration in moderator. This minimum for each moderator, reflector, and a -.tinide compound will be referred to as the minimum critical mass throughout this paper.

The critical masses were calculated for homogeneous spherical mixtures of actinide compounds in moderator material. Heterogeneous mixtures were not studied. However, if high concentrations of resonance absorbers such as *-3f,U or 2-nPu are present, it is possible that a heterogeneous mixture of lower critical mass can be formed than that calculated for a homo-geneous mixture of same actinide compounds in moderator.

Four geologic materials were considered; water, brine, granite or shal<2, and salt. The elemental compositions of granite and shale are similar but vary from one site to another. A reasonable overall com-position was selected and this material will be referred to as granite throughout the remainder of the paper. Water may te present in a granite repository but water in a salt repository will result in brine. Some properties of each of these materials are presented in Table 8.

The moderator-reflector material arrangements studied were water-water, brine-brine, granite-granite, and salt-salt. Test cases were calculated for water-granite and brine-salt systems. The results of these test cases indicate that for low concentrations of actinide com-pound in moderator the reflector composition has only a small effect on the calculated critical mass. For high concentrations of actinide com-pounds, granite and salt reflected systems generally have lower critical masses. Mixtures of water and granite or brine and salt for moderator or reflector materials were not studied.

1".

Table 8. Scne properties of the moderator and reflector materials

Moderate c or , _ . , . , ^ „ , , Chemical composition (weight percent) Densitv (g/cm ) reflector material

Water Hydrogen (11.11), oxygen (88.89) 1.00 Brine Hydrogen (8.17), oxygen (65.36), 1.18

souium (10.42), chlorine (16.06) Granite and Oxygen (52.02), gluminum (10.58), 2.91 shale silicon (37.40)"

Salt Sodium (39.34), .hlorine (60.66) 2.165

'Composition of brine was assumed to be that of a saturated solution of salt in water at 23°C.

^Composition of shale and granite was assumed to be SiOj (80.0) and A1?03 (20.0). Oxygen, aluminum, and silicon are the most abundant elements in many granites and shales.

There are five actinides abundant enough in nuclear waste to consider either separately or in combination as forming critical masses in waste repositories. These five actinides are uranium, neptunium, plutonium, americium, and curium. Critical mass calculations were made for the oxide state of each of these actinides and for a mixture of the five actinide oxides.

The calculated critical mass is dependent on the isotopic composition of the actinide. Isotopic compositions vary from one waste type to another and also change with time due to decay of the waste. As a result, five waste types and five waste ages were considered in this study.

CRITICAL MASS COMPUTATIONAL MODEL

A computational model was developed to perform the criticality cs iculations and to produce plots of critical mass versus actinide com-pound concentration in moderator. The discrete-ordinate code XSDRNPM6

was used to check computational model development. Use of conventional

12

computer codes to perform the survey calculations was abandoned early in the study because conventioual computer codes are programmed to perform one criticality search (a search on the radius until the multiplication factor is unity) at a time. It was estimated that approximat. _y 4000 search calculations wculd be required to complete the survey. The data Manipula-tion for input and output of conventional computer codes would have been unwieldy.

The computational nodel was developed co perform progressive radial search calculations until a curve of critical mass versus actinide com-pound concentration in mixture was generated. The model was programmed to be fast and efficient. The computational model uses a discrete-ordinates approximation to neutron transport theory and treats six neutron groups and spherical geometry. Little input is required and output consists of tables and curves of actinide compound concentration in moderator versus critical mass and critical radius. More details on the computational model are presented in Appendix 1.

Most of the neutron cross sections used by the computational model were taken from a 218-neutron-group cross-section library' developed for use in criticality calculations from ENDF/B-IV8 cross section data. The cross sections for 2U2niAm, 2l+2Cm, 2U1*Cra, 2I*5Cin, and 21*6Cm were processed from a preliminary ENDF/B-V library because cross section data for these nuclides were not in ENDF/B-IV. The 218-group cross sections were col-lapsed to six-group sets using weighting spectra for water and brine mixtures.

Critical masses calculated with the computational model using the six-group ENDF/B based cross sections were checked against experimental values and against more detailed calculated values. Critical radius and critical mass curves for several of the test cases are given in Figs. 1—12. These test cases are: 2 3 5U,

239pUj 239pu (0.90) + 2l+0Pu (0.10), 2 3 9Pu (0.80) + 2'4°Pu (0.20) in water, and 2 3 9Pu and Pu02 [ 2 3 8Pu (0.0195) + 2 3 9Pu (0.4979) + 2tt0Pu (0.2138) + 2 U 1Pu (0.1086) + 2J+2Pu (0.0420) + 0 (0.118)] in brine. The calculated critical masses in these test cases were from 30% less to 10% greater than experimental values or more detailed calculated values.

13

10* 10* DENSIT" or ACTMOE COMPOUNDS IN SOLUTION (CM/CC)

Fig. 1. Calculated critical mass plot of 2 3 5U in water.

« — - t - r - i - r J f .-...i..;.-: - ;-ri"ir

t "

—-t— •i—

f-r-frrr-- j—Ui-i-ll l-ii*.

....—..... T---H--H-M f t - r r M t r

j t" •j-rffjf •—{-••-{-••jri' .——j— i . - f i iJ - t i i . i-J-iJ-i-lii

1 i i i i l l

-Li.i-114 " i i i

10 10 10' DENSITY OF ACTINIDE COMPOUNDS IN SOLUTION (CM/CC)

Fig. 10. Calculated critical radius plot of 239Pu in brine.

14

. 3. Calculated critical mass plot of 239Pu in water

10"

10*

>..;-»•;•(•.:..••.-.. L.

: : : : : : :

10- 10" 10' 10-DENSITY Or ACTINI0E COMPOUNOS IN SOLUTION (GM/CC)

Fig. 10. Calculated critical radius plot of 2 3 9Pu in brine.

15

30ML DaG 3 3 3 -

10- 10" 10' DENSITY OF ACTNDE COMPOUNDS IN SOLUTION (GM/CC)

Fig. 5. Calculated critical mass plot of 2,f0Pu + 239Pu in rater.

i—i-i-i-i^:- _ :

- 4 - -

::: 1 i -r Xlm 10- 10" 10* 10'

DENSITY OF ACTINI0E COMPOUNDS IN SOLUTION (GM/CC) « *

Fig. 6. Calculated critical radius plot of 21>0Pu + 2 3 9Pu in water.

16

1G re3SX

t . • .-i - -i- - • : : ; ; - - .. i. — T ' - ' ^ ' M *' r - '

10" W" 10' DENSITY OF ACTMOE COMPOUNDS M SOLUTION (CU/CC)

. 7. Calculated critical mass plot of 2lt0Pu + 239Pu in water.

< il .ti v

v.. • -- : • : f-i-l-!-}-— J "i ' *!•«

- ! - - - -—

OONL-Ouc 78

-r-t-irJ-f s

.J....: : ;

DENSITY OF ACTMDE COMPOUNDS IN SOLUTION (GM/CC)

. 8. Calculated critical radius plot of 2*°Pu + 2 3 9Pu in water.

17

0OM.-EMK *8- 53*8

Fig. 9. Calculated critical mass plot of 239Pu in brine.

Fig. 10. Calculated critical radius plot of 2 3 9Pu in brine.

18

0"M».-D<KO 78-SSAO

10* 10" DENSITY OF ACTNDE COMPOUNOS IN SOLUTION (CM/CC)

Fig. 11. Calculated critical mass plot of Pu02 in brine

onm-soc. -"a F E E E B

10* ' 10' DENSITY OF ACTNDE COMPOUNOS IN SOLUTION (CM/CO)

Fig. 10. Calculated critical radius plot of 239Pu in brine.

19

The primary accuracy limitation of the critical mass calculational model i? the lack of detail in the six-group cross-section structure. The six-group energy boundaries are given in Table 9. To obtain better accuracy a finer group structure is necessary but computational time increases rapidly with number of iroup*.-

Table 9. Six-group neutron energy group structure

Group number Upper energy (ev) Lower energy (ev)

1 2.00 x 107 1-85 V 1 0 6

2 1.85 .«• 106 1.00 A 10s

3 1 . 0 0 • 105 5.5 > 102 U 5.5 x 10 3-05 5 3-05 1.25 10"1 6 1.25 < 10-1 1.00 10-r

Critical masses calculated with these ENDF/B-IV and ENDF/B-V cross sections may differ from critical masses calculated using other cross section sets or previous ENDF/B cross section libraries. This is due to basic differences in the cross section data. Several metal—water mixture calculations were made to compare with critical mass calculational results given in Ref. 9. The results of the calculations are given in Table 10. Critical mass plots for several of the calculations are given in Figs. 13—19. Generally, the agreement between minimum critical masses is within 10% except for 2l4l4Cm, 21+1Am, 237Np, and 21|0Pu. For theses nuclides, the calculated minimum critical masses differ by a factor of 1.5, 1.6, 2.2, and 7.0, respectively. Th^se results indicate basic dif-ferences between the cross section sets used. In all cases, the minimum critical masses calculated with the six-group computational model were less than those of Ref. 9.

CALCULATIONAL RESULTS

Over 400 different cases were calculated in the survey study. Each actinide compound of a specific isotopic composition mixed with a

20

Table 10. Metal-water critical mass calculational results and comparison with values Riven in reference 9

Act inido metal

: -. 7 < 8

? * «

Np

1 • ra

Pu pPu ! P u 'Am 'Am

' -Cm C.ni

? 3 9 P u (80?) + > 3 9 P u (90') +

Densitv of actinide compound in the

moderator for minimum critical mass (g/cm )

Minimum critical mass (kg)

("alcu.ated va 1 ue

Reference va lue

•" 'Pu (2o;j) (10/.)

0.Oft04 20.4 3 19.74 0.0290 19.74 0.0290

11.7 0.00370 O.C- 27

13.5 0.0425 0.0425 0.0135

0.045 20.43 19.ft 0.0 32

19.ft 0.032

11.7 0.005 0.040

13.5 M1.035 M). 035 0.015

Calculated va 1 ue

0.799 29.1 5.79 0.500

21. 3 0.278

ftft.2 0.0201 0.225

14.9 1.18 0.750 0.0409

Reference value

0.820 64.9 5.6 0.330

148.4 0.260

105. 3 0.023 0.213

2 2 . 0 M . 1 5 - U K 7 8 0.042

Note: Reflector and moderator materials were both water, of the reflector was 20 cm.

Thickness

OSNl 53-ir

DENSITY OF ACTINIDE COMPOUNDS IN SOLUTION (GM/CC)

Fig. 13. Calculated critical mass plot of 2 3 7Np in water

21

OPMl OWG 1 0 *

- r i . - r w i i i r - i

1 0 * :

I t x i

: - : i i '- • ^ : : : • i

7 ~ T T T 7 7 T : V : • : i -

. r ~ r- r M ; t-

i : v i M " : • > M •

L J,, r-f-^-r^-r"-

\ ^-.f-j.- .j.^.-l-fV:-- •yt

10 : s i

• ; • _-_> - | *. - ; 1 - -

• c - --t—s—-— i :

v . •:' • }:;•:;

r-r

10 1U 1U DENSITY o r ACTINIDE COMPOUNDS IN SOLUTION (GM/CC)

Fig. 14. Calculated critical mass plot of 2 3 8Pu in water.

ORNL-DWG 78-33-"

10'

V -I..-.-. . . . . . . . . ; . . . . ;

- r v f T v y •

- 4 - ; i - i I -. . . . ; . . . . J . . . . ; .J.J

: i : ; : • : ! \

i E — r . & t : ---J —;—'--V ."*

—f r 1—s—i—;—5—s—— -r i.

- - - - : - <-•• - • - • •

f-j-i-i--'

-i—i—i i i i ; i HJ DENSITY OF ACTINIDE COMPOUNDS IN SOLUTION (GM/CC)

Fig. II. Calculated critical mass plot of 2l,0Pu in water

22

Fig. 16. Calculated critical mass plot of 2 4 lPu in water.

Fig. 17. Calculated critical mass plot of 2<*2mAm in water.

23

Fig. 18. Calculated critical mass plot of 2<>3Cm in water.

ORNl D»6 rs J5«8

DENSITY OF ACTINIDE COMPOUNDS IN SOLUTION (GM/CC)

Fig. 19. Calculated critical mass plot of 2l4l*Cm in water.

24

particular moderator material represented a different case. Output from each case was in the form of tables and plots of critical mass and critical radius versus actinide compound density in the mixture. The minimum critical mass for each case was estimated. For each case from 1 to 15 critical radii search calculations were performed.

Cases were run for waste ages of 10, 100, 1000, and 10,000 years for all actinides. As the 2 3 5U isotopic percentage continues to increase and the total mass of uranium continues to increase beyond 10,000 years due to decay of the heavier elenents to uranium, uranium was looked at also for an age of 100,000 years. Actinide compounds considered were oxides of uranium, neptunium, plutonium, americium, curium, and a mixture of these five. As only one neptunium isotope, 2 3 7Np, is present in abundance, only four neptunium oxide calculations were required; one for each moderator material. (The neptunium isotopic composition does not change with waste type or waste age.) The reflector material was chosen to be identical to the moderator material and four materials were considered: water, brine, granite, and salt. Combinations of these variables result in 4 x 5 x 4 x 5 = 400 cases.

There is a minimum critical mass for each actinide oxide in each geologic material for each waste type of each waste age. The minimum critical masses are given in Tables 11—14 for each geologic material. The concentrations of actinide oxides in the water and brine mixtures at which the minimum critical masses occur are given in Tables 15 and 16. For salt and granite moderator materials, the minimum critical masses occur at the maximum theoretical densities of the oxides. In other words, for granite or salt moderated and reflected cases, the minimum critical mass occurs for a sphere of high-density pure actinide oxide surrounded by a reflector of granite or salt. The maximum theoretical densities of the actinide oxides are given in Table 17.

In Tables 18—21, the maximum number of critical masses per waste container for each of the four moderator materials are presented for each waste type and waste age. These tabulated values were obtained by dividing the masses of actinide oxide per waste container given in Table 7 by the minimum critical masses given in Tables 11—14.

25

l a M . - K - i r . i i . u : . > u J : n i n i n u n i r i t i . a l s , . r

t i n i d t " \ i i i * s n . * } * • r a ~ * a m i r i l 1 . - . t . i ! h - . v a t . r

M : n i n u n t - r i t : . a : T - . a s ^ . - t l

. V t m i d . A e -

< \ « a r - >

i

X a . ! • i r w . i ^ t . T V

'. r . i ^ i a r -

: . i n . n

W i l l i !

5 m i , t ' n n

\

X

X

X

X

X

X

X

X

X

i l 7 . .

i . i

\

X . t> l t i n I u - A : : v . ! . : • m i . 7 u n . M L . 7 - " ' * ' ' . 7

• ' i i i i i -i n n

1 . ' . m i .

l u . l ' . n l

* . > 4 1 7

4 . 1 )

J ! . 1

l i . 1

4 1 . '

1 . 7 "

J . i*

! . ' . . h i

V ' v r i : i

1 . 1 1 " ! ' l . ' . l l D H ; •.)

Z l u . *

n " . i

1 I - ' . *•

I V . 1

; t i i . -

C u r i u r l ' l i ' . %. 7 , ' I H i i . i - . "

I I I " l r . !< " . <>. '1 if*.*- 1 ' l> >

I , ! H I I . " . ( I S ! i i . T i i . I I . ! ' 1 J f , . u n . o ' i

M . l l i X I " J l i i - ' i i i . t i . ( • . t i . " . '

M i x t t i r * t * i v » 111 X I B " 1 ! . . ! • . 4 1

. l i t i n i d v ; 111(1 X 4 _ " i h . ' i 4 t > . « " • | , ' l . 7

i . 1 H M , X J " • ' I I . I

i n . i i i h i X n u n . "> r i f c u . ^

t h a t . r i l t . i l i l : i. i n Hi • t i n , t . ii I t - v . J ; , r .< . 1 1 l . i ! l i . r i .

i 'T n . i N i m r a J v n i ^ i T ^ r „ i : . r i - i l .

l a h l < - I J . I ' a K u l a u - d n i n i r ; u n i r i t i i - i l n i . i ^ ^ f f . u T .1- < i i n i i u , - x i d . s

r t - l t i ' i ' t h v i n

M i n i m u m r r i t i « M l Pj . i**s l o \ i i i -

A t i i d<-A c

( w . i r s i

1

M . i - W a r w . i M v •

i

t .

1 r . m I u r : i n

1 : ' . ' '

! . ( M i l l

M i . , l i i n

X '

X

X

X X

X

X

S

X

H I I : i . ' 1

1

X

X

N V

1 0 1 1 . 0 1 >0 N X 1 U . > i \ t • 0 1 . 1

X ^ p t u t n u n AT>V <>*I s M " . K H 9 . C .

I ' l u t u n i i n i 1 0 . ' 0 . 0 J l . h ! » . 7 •1 7 1 . M l . 7

1 0 0 h H . 1 f J . 7 flh. (i ( i t s . 0 o s . o

1 . 0 0 0 7 7 . J ! "». 4 7 f i . i 1 3 7 . S

I U . 0 U 0 \ S S . 1 l j l i . 1 1 5 7 . h

C u r i t i n i n 1 ' ) . ! > I S . O i . ( S n . (1 3 . 5 h 1 0 0 1 . i s l . S H 0 . ' > 5 1 l . ' • i 0 5 5 ( i

l , o n o n . 4 7 i (1 . i M 0. 0 . 4 6 7

1 0 . 0 0 0 n . i i i 0 . 4 M (1. 4 r , l n . 4 1 0 0 . 4 5 0

M i x t u r e oi t ' i v t - i n N 4 7 M 1 . 5 S 4 J . "i " 0 1 . 1

1 0 0 X M S 1 . 1 i n . 0 s o . q 1 0 8 4 . 0 1 , 0 0 0 N 4 0 7 . 7 i l . h 1 1 * 9 . 6

1 0 . 0 0 0 N i l l f c . 1 ) 7 7 0 . S 1 8 . *

*N means that c r i t U ' a l i t v cannot be achieved for a one-meter r.idius Hph»»rlo«»J b u i s s of maxlnum d e n s i t y m a t e r i a l .

26

..«:»!» • » ,1! i.«t«-o .dim sun »riti«al .»«Ti"ii«V oxtd«*>

<•.*•.«• J 1

\u. i i 5

V1 X X X HH) x X X X

1 .: i< *» % * ; X >15:1.4 X i i),U' >u X X 144. > X

N X 2*1.1 m.i 787.9 4~>. • - >.0 41.0 45.0

• i u? <n Z M U.J 11." IS.h 12.1 17.0 i 21.4 12.4 21.fi i.lilMl 20. J i 19. 1

Id.u'iu 11.1 I 4. 5 11.5 11.8 Air* i i • .» ? Id «>. I 4-...«> ll.i! 4b. 1

UK) 14. 41.9 -9.7 14.1 49.1 i W>. ! nn.h 1S.2 •>7.9 l'J.VHO 7S.9 »>).2 7».9 7».«>

< uriur 10 111. ! 1(1. 1 7.SI 10. J 7.91 lOO •>.19 1.55 •..22 1.5R

1 ,|«K) 1.17 ..17 1.1". l.l» 1.15 1U.IJOO 1.1)4 l.nl i.ni 1.02

Jti.\tur»' ; 'i X 2444.4 21.2 45 7.4 t i v* t i n i d«. s Ht'l X JhiH.i IK >.•> 29.4 149.9

1 .(Kill X 2f.»>9. •* 197.4 11.4 580. : 1U.IHIO X 2204. 4 151.4 41.2 432-4

.\ r.'Mt • r; r i • ; i % cmot *< '-r » «»;**"• u • »<«-. • - in.ir mm . r..»t« r i.i 1.

l.ihK N. i..iU til.itvd minimum <Titi«.i! ruist-s i-t vd in«l rvt'U-ttt-d bv Minimum critii.il n.iss «•: «>xid* (kg)

A. tiniiU 1 j

Xtii U'.ir wast.- t 1 4

ri

1 r.iniiiri I d x-' X X X X loll X X X X X 1 .mil) X X 914..0 X Kl.tMHI X X : j ft4<-.2 X 100,000 X K <•>7.2 1«J.A 2225.7

Xvptuniun •\nv .kftc 7 1.9 7 1. ,9 71.9 71.9 71.9 I'lutoniun 10 -'1.1 JJ. , <> 1J.1 20.9 2 9 . 4

100 -'1.7 Jb, , ? 40.4 21.) 17. 7 I ,000 J i. , 1 JS.2 21. 1 1 3 . 4 10,000 JO. 1 19. . 1 2 9 . 4 1 9 . 9 20. r>

Amoriclum 10 Ml.9 1ft. . 1 MO.O til). 4 79.4 1(10 i7.9 7S. . 1 KS.l 57.7 84.1

1,000 <>3.(1 lf>i. .0 llh.H ( > - . 2 115.2 10,0110 111.1 111. , 1 1 72. J 111.1 1J2.6 Curium 10 17.'] 17. .0 1 1.1 17.(1 1J .2 100 10. J 10. • J >.»>0 10. 1 5.h4

1,000 4.9S 4. 4 . 9 0 4.92 4.91 10,000 4. 7J 4. 4 . 70 4.71 4.70

Mixtur.- of 10 X 4or>r>, 2 h 4 . J 4*5.9 769.1 1'iVf .H I ;nid* '. 100 X 44J7. i2h. 1 >1.3 9 1 9 . 8

1,000 X 4 4 8 1 , ,i 148. H ir>. 1 970.4 10,000 N l«r>7, 264.4 72.9 7 3 0 . 0

'N ta- an 11 .it * rif ii .il itv • -tnnot 1 .i. iii .•v.'d ti>r ,t Hi t. •r r.u! i u-. raass ot cuix»TOiun dens Itv Ruitt'fivtl.

27

Tib K IT. Concentrations "i .ictir.ide oxid**s 111 v.\r«-r for minimum critical nass

Densiti in water at which minimum critical rnss occurs (g/ca- ) Nuclear waste type

1 3 4 5 Uranium 10 X X X N X

100 s X X X X 1.000 X X X 1.61 X

10 .000 S X ".36 0.347 X 100.01 0 X X 0.347 C -161 0.747

Ne tuniun Anv a f 11.11 11.11 11.11 11.11 11.11 Plutonium 1" 0.053 0.053 11. 46 0.053 11.46

10b 0.053 11.46 11.46 0.053 11-46 1.000 0.053 0.115 11.46 0.053 11.46

10,000 0.053 0.053 0.053 0.053 0.051 Asvrii ium Any ape 11.68 11.68 11.68 11.68 11.68 Curiua 10 0.813 O.Sl'l 0.081 0.813 0.081

100 0.038 0.038 0.018 0.038 0.018 1.000 0.018 0.018 (1.018 0.018 0.01S

10.000 0.012 0.012 0.012 0.012 0.012

Actinide Age (vears)

Mixture of five actinides 10 S 100 X 1.000 S '0.000 X

11.5 l'-5 11.5 11.5 11.5 11-5 11.5 11.5

0.07B 11.5 0.07S 11-5 0.078 11.5 0.115 11.5

TabW \fc. Concent rat ions of .ictinide oxides in brine for minimum critical mass

Density in brine at vhich miniraua critical . mass wcurs (p/cm3) Actinide , AM! . (years) Nuclear waste typo

Uranium 10 s X X X X 100 N N X X X 1 .000 X X s 10. .96 N 10 .000 N X X 1. .61 X 100 ,000 X X i. .61 0. .747 3. .47 Neptunium Any age 11. 11 11. .11 u. .11 11. .11 11. 11 Plutonium 10 0. 362 U. .46 11. .46 0. .362 11. .46 100 11. 46 11. .46 11. .46 11. .46 11. .46 1 ,000 11. 46 11. .46 11. .46 11. .46 11. .46 10 ,000 0. 247 0. .247 0. .362 0. .247 0. . 247 Araericiuni Any age 11. 68 11, .68 11. .68 11. .68 11. .63 Curiam 10 11, 93 11. .93 0. .377 11. .93 0. .377 100 0. 175 0. .175 0. .081 0. .175 0. .081 1 .noo 0. 081 0. .081 0. .081 0. .081 0. .081 10 .000 0. 081 0. .081 0. 081 0. .081 0. .081 Mixture of 10 N 11. .5 n . ,5 11. .5 11. ,5 five act.aides 100 N 11. .5 li. ,5 11. .5 11. ,5 1 .000 N 11. .5 11. 5 11. ,5 11. .5 10 ,000 N 11. .5 li. .s 11. .5 li. .5

28

Tabu- 17. Maximum densities of actinide oxides

Acr iniik' Maximum theoret;'~al oxide densitv ( « / )

Uranium oxide 10. Neptunium oxide 11. .lla Plutonium oxide '1. Amuricium oxiJ-- . 1. Curium oxide 11. • 9Jb

Mixture of five 11 actinide oxides

. . - . . • . F rom . .'*. :: - . .••- .. ; 3 8 t i i edition.

''tsi im.tted based i . i-\t r.ipi. t at ion o: densities of uranium oxide, neptunium .<xide. ). iuton ium oxide, and americiura oxide.

1 Approximate averase density.

Table If*. Maximum number ot ir it ii.il masses per waste container for water moderator and reflector

Nuclear waste type

A S e (vi-ars)

Maximun number of critical masses per container for each actinide oxide

Uranium Neptunium riutinium Americium Curium Mixture of five actinides

1 10 0 0.0027 2.53 0.0046 0.0013 0 1 100 0 0.0035 1.79 0.0097 0.0027 0 1 1,000 0 0.0085 1.90 0.0025 0.0026 0 1 10,000 0 0.0100 2.20 0.0001 0.0012 0 1 100.000 0 » 10 0 0.0121 0.0306 0.0054 0.0059 0.0033 J 100 0 0.0126 0.0072 0.0049 0.0121 0.0031

1,000 0 0.0143 0.0141 0.0021 0.0117 0.0031 •> 10.000 0 0.0149 0.1690 0.0006 0.0055 0.0039 2 100,000 0

3 10 0 0.0046 0.0301 0.0619 4.13 0.0707 3 100 0 0.0072 0.0451 0.0540 4.55 0.0554 3 1,000 0 0.0203 0.0618 0.0260 4.17 0.0522 3 10.000 0 0.0252 1.393 ( 0.0056 1.96 0.0791 3 100,000 0. 23b

4 10 0 0.0254 11.64 0.0201 0.0048 6.84 4 100 0 0.0291 8.25 0.0428 0.0100 2.28

1,000 0 . 0247 0.0509 8.93 0.0109 0.0971 4.33 4 10,000 2. 07 0.0578 10.72 0.0005 0.0045 8.07 4 100,000 II1. 30

5 10 0 0.0097 0.0151 0.0242 1.37 0.0192 5 100 0 0.0108 0.0198 0.0213 1.52 0.0158 5 1,000 0 0.0163 0.0260 0.0100 1.40 0.0151 5 10.000 0 0.0183 0.5891 0.0034 0.657 0.0220 5 100,000 0. 731

29

Table 19. Maximum nutnhv.if critical mas-ii-s per waste container for brin« modvrnt <»r .imi rofl.-otor

Maximun number 1" .riti«al w s s r s o>nt.litier tor •\u-b artinide oxide

raste ypi-

(v»•.lrs Uranium Neptunium Plutonium Anerioium Curium

Mixture of five act ini

1 to 11 0.0027 0. 2Sft 0.U044 (1.0006 0 1 100 0 O.003ft 0. 220 0.009 3 0.00(13 0 1 1,000 0 0.008ft 0.211 (1.0024 I). 000 i 0 1 10.000 0 0.0101 0.227 0.00(11 0.0001 0 1 100,000 0

? 10 0 0.0»22 0.0063 0.0051 0.0027 0.:0i7 100 0 0.0127 0.0062 O.0047 0.0012 0.0025

1 .000 0 0.0145 0.0069 0.0020 0.0013 0.0025 10,000 0 0.0150 0.0175 0.0005 (1.0006 0.0031

i 100,000 0

3 10 0 0.0047 0.0270 O.0568 0.401 0.0620 3 100 0 0.0073 0.0429 0.0501 0.485 0.0494 3 1.000 0 0.0205 0.0515 0.0247 0.464 010462 3 10.000 0 0.0255 0.1417 0.(1053 0.214 0.0655 3 100,000 141

4 10 0 0.0256 ;.32 0.0194 0.0023 0.855 4 100 0 0.0294 1.03 0.0413 0.0010 0.727 4 1.000 0. 001 3 0.0514 0.983 O.0105 0-0011 0.689 4 10,000 0. 104 0.0584 1.07 0.0005 0.0005 0.522 4 100,000 0. 861

5 10 0 0.0098 0.0132 0.0223 0.1332 0.0167 5 100 0 0.0109 0.0183 0.0198 0.1626 0.0138 5 1.000 0 0.0165 0.0231 0.0096 0-1523 0.0132 5 10,000 0 0.0185 0.0596 0.0033 0.0718 0.0183 5 100,000 0. 032

30

TabK- JO. Maximum number of critical masses per wasie container for granite moderator and reflector

Maximum numbei >>f critical masses per container for each actinide oxide Nuclear _

(years.i Mixture t-""><" Uranium Neptunium Plutonium .\raericium Curium of Five

Actinides

1 It) 1 100 1 1 .000 1 10,000 1 100,000

2 10 100

-7 1,000 2 10,000 T 100,000

3 10 3 100 3 1,000 3 10,000 3 100,000

4 10 4 100 4 1,000 4 10,000 4 100,000

5 10 5 too 5 1.000 5 10,000 5 100.000

0 0.0054 0 0.0071 0 0.0171 0 0 . 0 2 0 1 0

0 0.0244 0 0.0253 0 0.0289

; 0 0.0300 0

0 0.0093 0 0.0146 0 0.0409

0.0005 0.0509 (J. 0566

0 0.0511 0 0.0587

0.0024 0.103 0.0541 0.116 0.267

0 0.0195 0 0.0217 0 0.0329 0 0.0369

0 . 0 1 6 6

0.384 0.0087 0.339 0.0185 0.325 0.0047 0.241 0.0002

0.0098 0.0103 0.0100 0.0094 0.0110 0.0040 0.0170 0.0011

0.0459 0.112 0.0799 0.09S6 0.0975 0.0501 0.170 0.0152

1.81 0.0385 1.59 0.0819 1.51 0.0209 1.12 0.0010

0.0217 0.0443 0.0333 0.0395 0.0397 0.0193 0.0803 0.0065

0.0009 0 0.0001 0 0.00004 0 0.00002 0

0.0039 0.(K)54 0.0003 0.0049 0.0002 0.0049 0.0001 0.0059

0.1716 0.1245 0.0752 0.1017 0.0679 0.0954 0.0318 0.1240

0.0033 1.41 0.0003 1.26 0.0002 1.18 0.0001 0.893

0.0599 0.0329 0.0253 0.0273 0.0227 0.0259 0.0107 0.0346

31

Table 21. Maximum nunber ol critical masses per waste container tor moderator and reflector

Xuclo.ir was re-type

'Uxitnura number of critical masses per container for each actinide oxide

Age (years)

Uranium Xeptuniun l'lutoniun Americiunt Curiura Mixture of five actinides

1 1(1 0 (1.0033 0.222 0.00 52 0.0005 0 1 100 0 0.0043 0.195 0.0110 0.00004 0 1 1.000 0 0.0104 0.187 0.0028 0.00003 0 1 10.000 0 0.0122 0.139 0.0001 0.00001 0 1 100,000 0

2 10 0 0.0149 U.0056 0.0060 0.0024 0.0032 2 100 0 0.0154 0.0058 0.0081 0.0002 0.0030

1.000 0 0.0176 0.0063 0.0023 0.0001 0.0029 2 10,000 0 0.0183 0.0099 0.0006 0.0001 0.0036 ••> 100.000 0

3 10 0 0.0057 0.0266 0.0653 0.102 0.0715 3 100 0 0.0089 O.0463 0.0582 0.0477 0.0579 3 1,000 0 0.0249 0.0563 0.0295 0.0437 0.0540 3 10,000 0 0.0310 0.0840 0.0080 0.0205 0.0710 3 100,000 0. 0242

4 10 0 0.0311 1.05 0.0228 0-0020 0.807 4 100 0 0.0357 0.917 0.0487 0.0002 0.721 4 1.000 0. 0014 0.0625 0.872 0.0124 0.0001 0.670 4 10,000 0. 0287 0.0709 0.646 0.0006 0-00005 0.505 4 100,000 0. 1536

5 10 0 0.0119 0.0126 0.0258 0.0359 0.0195 5 100 0 0.0132 0.0193 0.0231 0.0160 0.0163 5 1,000 0 0.0200 0.0229 0.0114 0.0146 0.0155 5 10,000 0 0.0225 0.0462 0.0039 0.0069 0.0205 5 100,030 0. 0059

32

For nuclear waste type 3, plutonium-recycled high level waste, minimum critical masses were calculated for water-water, water-granite, granite-granite, brine-brine, brine-salt, and salt-salt moderator-reflector arrangements. The minimum critical masses for these calcula-tions are given in Table 22. The reflector material has the greatest effect on the calculated critical masses for high concentrations of actinide compounds in moderator. For high concentrations of actinide compounds in moderator, grs..:te or salt reflected spheres generally have lower critical masses than water or brine reflected spheres.

ESTIMATED ACCURACY OF THE CALCULATIONAL RESULTS

The primary limitation on the accuracy of the calculated critical radii and critical nas.ses, neglecting inherent errors that may have existed in the ENDF/B cross section data, was use of six-group cross sections in the computations. Several test cases were run using cross section sets of 42 groups and 218 groups to check the accuracy of the six-group calculations.

In all test cases the minimum critical masses for water, brine, granite, and salt mixtures calculated with the fine-group cross-section sets were from 10% less to 30% greater than the values calculated using the six-group computational model. Based on these results, the minimum critical masses given in this paper are estimated to be not less than 30% smaller and not greater than 10% higher than critical masses obtained using more detailed calculations.

The tabulated critical masses given in Appendix 2 are estimated to be from 30% less to 10% greater than critical mass values obtained using fine-group calculations for water and brine mixtures at all concentrations of actinide compound in moderator. However, for granite and jalt mixtures, as cross section sets were not specifically made for these materials, the calculated critical radii given in the appendix for dilute concentrations of actinide compound in moderator may be a factor of two less than those calculated using fine-group cross sections. For high concentrations of actinide compounds in granite or salt, the calculated critical masses are estimated to be from 30% less to 10% greater than those obtained by more detailed calculations.

Table 22. Calculated critical masses of nuclear waste typi> 3 for various moderator-reflector compositions

Actinide Waste age Minimum critical muss (k>;) oxide (years) Water/water Water/granite Granite/Granite! BrLne/brlne Brine/an It. Salt/Hal

Uranium 10 N N N N. N N 100 N - N N N N N

1,000 N N N N N N 10,000 307.2 282.3 23609.0 N N N

Plutonium 10 28.4 18.6 18.6 31.6 32.1 32.1 100 41.5 23.4 23.4 43.6 40.4 40,4

1,000 32.0 20. 3 20. 3 35.6 35.2 35.2 10,000 1.77 1.49 14.5 17.4 15,6 29.4

Americium 10 84.4 46. A 46.6 92,0 80.0 HO. 0 100 91.7 49.7 49. 7 98.9 85, 1 85. 1

1,000 132.) 68,8 68. 8 ) 39.4 1 16,8 1 16.8 10.000 245.5 90.2 90.2 2 56. 1 172.3 172.3

Cu.-itim 10 0.325 0.456 7.81 3. 1 i V>1 13.1 100 0.0588 0.084 J j. V) 0. 55 I 0.604 5. f 0

1,000 0.0512 0.0724 i. I 5 0.46/ 0.5/0 4.90 10,000 0.0493 0.0697 3.ftl 0. V>1 0,488 6.23

Mixture of 10 2 fi ?. h 151.9 r> i.« JU4.8 264. « 264. 3 five actinides 100 340. B 185.6 185.6 .(HI ,9 m. i 526, |

1,000 361.2 197.4 197.4 4U7.7 148,8 348.8 10,000 237.4 151.4 151. /, JH6. 7 264. 4 264.4

34

DISCUSSION OF THE CALCULATTONAL RESULTS AND CONCLUSIONS

Several general observations on the calculational results are presented in this section.

1. Neptunium oxide and americium oxide have such large minimum critical masses ('-60—90 kg) that they probably do not present a potential criticality problem.

2. The only actinide, disregarding neptunium, in nuclear waste that can form more critical masses at 100,000 years than at iU,UUU years is uranium.

J. The only waste type which does not have at least one critical mass per waste container at any waste age in any geologic material is waste type 2, high level waste from fresh uranium fuel.

' ne following conclusions are related to whether ground water has intruded into the waste repository or whether water already present in the repository has collected in some manner.

1. If water is not present in the repository, the only waste type which has at least one critical mass per waste container for any geologic material is high level waste plus 100% of the plutonium in discharged fuel, type 4 waste.

2. Even if water is present in a salt repository (in the form of brine), again there is only one waste type which has at least one critical mass per container, high level waste plus 100% of the plutonium.

3. If water is present in a granite or shale repository, several waste types have enough heavy-metal oxides to form at least one critical mass per waste container.

ACKNOWLEDGMENTS

The author wishes to express his gratitude to the following people for their assistance with this work: G. H. Jenks of OWI for conceiving the study and supervising the work, E. D. Blakeman and W. E. Thomas for many helpful conversations on neutron cross section processing and compu-tational model development, R. A. Kisner for supplying the nuclear waste

35

decay calculational results, W. E. Ford, III, C. C. Webster, and R. M. Westfall for help v»«-h the cross section processing; D. R. Vondy for help with the in< " -ation factor extrapolation procedure; S. R. McNeany and J. D. Jenkins --viewing the draft report; and Donna Conger and the Reports Offi preparing the fi.-.al report.

REFERENCES

1. G. H. Jenks, Oak Ridge National Laboratory, personal communication to E. J. Allen, Oak Ridge National Laboratory, April 6, 1978.

2. Waste Isolation Facility Description 3edded Salt3 prepared by Parsons Brinckerhoff Quade and Douglas,' Inc., New York, Y/OWI/SUB-76/16506 (September 1976).

3. M. J. Bell, ORIGEN — The OBNL Isotope Generation and Depletion Code3 ORNL-4628 (May 1973).

4. G. H. Jenks, Oak Ridge National Laboratory, personal communication to E. J. Allen, Oak Ridge National Laboratory, Nov. 23, 1977.

5. R. Douglas O'Dell (Ed.), Nuclear Criticality Safety, TID-26286 (1974). 6. N. M. Greene et al., AMPX: A Modular Code System for Generating

Couoled Multiprouv Neutron-Gamma Libraries frorr ENDF/B, ORNL/TM-3706 (March 1976)/

7. W. E. Ford, III, C. C. Webster, and R. M. Westfall, A21S-Group Neutron Cross-Section Library in the Al-lPX Master I-iter face Format for Criticality Safety Studies3 ORNL/CSD/TM-4 (July 1976).

8. ENDF is the Evaluated Nuclear Data File and is the national reference set of evaluated cross section data.

9. E. D. Clayton and S. R. Bierman, "Criticality Problems of Actinide Elements," Actinides Reviews 1, 409-432 (1971).

2011

Appendix 1

CRITICAL MASS COMPUTATIONAL MODEL

The function of the computational model was to calculate and prepare tables and plots of critical mass and critical radius versus actinide compound concentration in moderator material. Several unique approaches and methods were used in the computational model to reduce computer time and data manipulation.

The computational model performs progressive radial search calcu-lations until a curve of critical mass versus actinide compound concen-tration in mixture is generated. The calculations start at the maximum theoretical density of actinide compound. A search for the critical radius is made. Then the concentration of actinide compound is reduced by a factor of (O.l)1^3 and the remaining volume is replaced by the moderator material. The critical radius for the new composition is calculated. These steps continue until criticality is not achieved or the critical radius exceeds one meter. Then, the smallest critical mass is determined and about this point two more concentrations are selected and critical radii are calculated. The results are then output in the form of tables and plots. In all critical mass calculations the mixture of actinide compound and moderator material are surrounded by a reflector of 0.20 meters thickness.

The computational model had to be accurate from very high actinide compound concentrations to very low concentrations ('bO.Ol g/cm3). To satisfy this requirement, a discrete—ordinates neutron-transport method was selected to compute the multiplication factors for each spherical radius. The discrete-ordinates method selected uses a diamond-difference* scheme and treats four angles (S4) and second-order scattering (P2).

Critical radii searches for each concentration are made in the fol-lowing manner. A starting radius to begin calculations is estimated. This starting radius is selected to be the critical radius of the previous concentration of actinide compound in moderator or 7.5 cm for the first

*George I. Bell and Samuel Glasstone, Nuclear' Reactor Theory3 VanNostrand Reinhold, New York, 1970.

38

concentration (maximum theoretical density). Multiplication factors axe calculated for radii of 0.67 and 1.5 times the starting radius. These multiplication factors and radii are then used in the equation

1/k = a + b/R2

to estimate a and b. In this equation, k is the multiplication factor and R is the spherical radius. This equation fairly accurately describes the curve of multiplication factor versus spherical radius. The third radius is calculated using this equation by setting k = 1.0. A multi-plication factor for this third radius is next calculated and the parame-ters a and b are again calculated using the additional information from the third radius. A fourth radius and multiplication factor are then calculated. At this point the search is normally completed. However, if for some reason the multiplication factor differs from unity by more than 2%, the search calculati ns continue. Usually, the multiplication factor for the fourth radius is within 0.5% of unity. If during tne search the radius exceeds one meter, the multiplication factor for a sphere of one meter radius is calculate-3 If this multiplication factor is less than unity, the search calculations are terminated.

The multiplication factors for each radius are calculated using the following procedure. The angular neutron flux calculations are allowed to proceed without interruption for 25 outer iterations. For each outer iteration, two inner iterations are made for groups 1—4 and four inner iterations are made for the two lower energy groups. After the 25 outer iterations are performed, if the current multiplication factor differs by less than 0.01% from the proceeding multiplication factor, convergence is assumed and the current multiplication factor is taken as the true multiplication factor. If convergence is not satisfied, single-mode extrapolation on the multiplication factor is perforF°d if the require-ments for extrapolation are satisfied. If extrapolation criteria are not satisfied, outer iterations continue until convergence, extrapolation, or the maximum number (65) of outer iterations is reached. In all test cases the maximum number of outer iterations was never reached. Extra-polation or convergence generally occurred between 25 and 35 outer iterations.

39

Single-mode extrapolation on the multiplication factor is carried out using the following procedure. Consider the equation:

k - k = c(k - k ) n n-1 t n

where

and

k = multiplication factor for nth outer iterations, n

kt = the multiplication factor at the infinite outer iteration,

c = a constant.

This equation assumes that the difference between successive multiplication factors decreases as the calculated multiplication factor approaches the true multiplication factor. From this equation the true multiplication factor can be estimated:

e t n n n-1 where

kg = extrapolated multiplication factor,

and

u = (k - k ,)/<k . - k ) « 1/(1 + c) . n n—1 n—1 n—i

The value of u must be constant, less than unity, and greater than zero. Extrapolation is allowed (after a minimum of 25 outer iterations) if p is less than 0.99 but greater than zero and successive y's differ by less than 2%.

The cross section handling by the computational model is straight-forward. Cross section resonances were treated for various metal-to-hydrogen ratios for each actinide and tables of absorption and fission cross sections were prepared. For each concentration of actinide compound in moderator, the tabulated cross sections are interpolated depending on the ratio of actinide to hydrogen concentration. Therefore, a unique cross section set is used for each concentration of actinide compound in the moderator.

40

Input other than cross section information which is the same for every case consists of the following seven cards:

CARD 1 Title card of all calculations Format(20A4) CARD 2 NCALC,NPLOT,NRADP Format(24I3)

NCALC = Number of calculations NPLOT = 0 No plots requested

1 Plots requested NRADP = 1 Plot both critical radius and critical mass

2 Plot critical mass but not critical radius The following cards are input NCALC times in the order shown for each of the NCALC calculations.

CARD 3 Title card of current calculation Format(8A4) C.*RD 4 Number of nuclides in the reflector, density of the reflector

in grams per cubic centimeter, number of nuclides in the moderator, density of the moderator, number of nuclides in the actinide compounds, maximum density of the actinide compounds Format(6(13,E9.3))

CARD 5 Cross section identifier for first nuclide in the reflector, mass fraction of first nuclide in the reflector, cross section identifier for second nuclide in the reflector, . . . continue until all nuclides in the reflector are described Format (6(I3,E9.3)>

CARD 6 Same as Card 5 but for the moderator CARD 7 Same as Card 5 but for the actinide compounds

Output for each calculation consists of several tables and plots if requested. The first table summarizes input information, such as moderator, and actinide compound compositions. The next table gives concentrations of actinide compound in the moderator, critical radii at these concen-trations, critical masses, and calculated multiplication factors. The table continues until the actinide compound concentration is so low that criticality cannot be achieved for a radius of one meter. If plots are requested, critical radius and critical mass are plotted against actinide compound concentration in the moderator.

41

Running time and storage requirements on the IBM 360-91 computer are low. To do a calculation of 15 critical radii searches and plotting these points requires approximately two minutes computer time and less than 270,000 bytes of computer memory.

2017

Appendix 2

PLOTS AND TABLES OF CALCULATED CRITICAL MASSES

Many plots and tables of critical mass versus concentration of actinide oxide in moderator were generated. In this appendix, the calcu-lated critical masses are tabulated for nearly all the water, brine, granite, and salt mixtures studied. Critical mass plots are given for nearly all the water and brine mixtures studied. Each plot or table has a unique identification which is explained below.

Identification for cach case is:

CASE HLW,PWR-WW,XXXXXX,Y,Y,Z—0

where

WW = SF = Type 1 waste (spent fuel) = UR = Type 2 waste (fresh uranium) = PU = Type 3 waste (recycled plutonium) = PP = Type 4 waste (plus plutonium) = UP = Type 5 waste (Mixture of Type 2 and Type 3 waste)

XXXXXX = waste age in years Y,Y = W,W = water moderated and reflected

= B,B = brine moderated and reflected = G,G •» granite moderated and reflected = S,S = salt moderated and reflected

Z-0 = U,N,P,A,C = oxide of uranium, neptunium, plutonium, americium, or curium, respectively

= UNPAC-0 = mixture of all five actinide oxides

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«l> |«.|«> ft|TK»l ; 0 . 0 1 «UrGU*«S

crw fimT; t.. e*"t LI fr«v lf.»/(CI

r •too.*.* -r riiTirit «. »r.io* « r«i •u im UHlct <u<n

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rrn;iTv nF •tTINi.if trw runns t* «rtcti»K to«/cri ii if * tr.ih* lr«| C»1I|«U hk^ ««r.l

o.it<iw c r. "st'F C 1 a . rt IHUK n t 0.->«!T«t Ot at o.»<ti>f at Ot 01 o.t«t«lF ol c.ti^or ol C.*«« It f 01 O. 'tA* lit CI o.<(vFl» at oc ( , > > « ) < Cl a. »c»«f oc c»it«*et or r,* t ft ot (i.itr>f ac 01 o. « - o i O.i*T>>«r -Jl «.»t?«if CI J.ST«t»F -Ot 0.f*i| lr-01 (.»»HJlt ot q.*IVT-OI 0. 11 <.70' -01 e? c.t?t c? t.f?!7«-{' C.l"»«» o o.»<iT«o»r-ol Till! -Of C.f-tljof a; 0)

«t« ttot trttic» ««ftr*

c. loon* et o.toatfr ot 0.MMW 01 c.taoa*r al btMIMT 01 n.iaaaz* ei n. tooar* ot 0.UTM' oo a.ioottr ot oo o.mot** ci 0.1UIW CI talMD* CI

00 cei il«t *•««« 1.5 o.'i'in-nii lKCtw,

K'lMP-t A " / ( ( 1

Ct tT» r«_ o j f K t lltfl ICaVlt.* *

Cl OI CI .1. 1X.1 K f 1 <. 1 ct ..a c. 1 Xko«r ct C.U-.-3* Ct CI I-1 c.s1-**** oc CI .»_ 1 ; ar f.4 D. ii>i»a«» Cl f. " )(1 c.. ? is *r c» I.'taol- r l C.UfJ1 on r ,»M j i-C I J.1 • » » Ot .. f r» "" -CI CI ol O. -P"-*. .« aa a.•''--> n . l-uo ri w.l.'7I'-OI Cl - oi U. 1. CC O.I1H4--C1 0 1 »»»- -al 1 . t JOt 7. •it C.11 C r O. r" -i. 1 >*. 111 0." r-02 r.iM j; a. -fi« - - o i f . bO 3.f = TOJ.-4? r. .«!•>.)-•• c? 0. lo.io 4.1 * 1*. !<•.)« rLfTKKi : l«

O t N S I l T o r K T 1 K I K coweiMos IN ax.«<t«< C N M I C N . «»OI« ( C " L

«tkl««M C"ITtC«t- wSS IS e.»t2«IE 01 «tl00ms

ic»/tc 1 o.tt«eac cs a. ro«03C Ot 4.l»TSf a? as o.uiox ot !l.«7*«lt "1 l .«««t 00 o.2«e«aE ot S.12193E 92 a. i 'e i f Jtf a.ioom 01 O.H4MC Ot S.I49W 02 J.I«.TSUF 02 a.tooobe OI e.ui«K ao 02 1.II44W 0? 4.IOOC7F 01 O.M««t OO 92 OI 3 .1 OOOOC 01 0.114MT OO S.714 7* 02 ).«7S7«( 01 :.ioa tor C4 «.7ft77I-»l 9.2J74W W 91 Olt 0.2»««2E 02 J.4U4IF 01 1.10312' 01 C.9M4M.CI •52 ).i<i«n<c of oo C. MMH- Ot O. M*tt1F »2 01 oo

OCSSITV or ACTtMIOC (•XWCUNBS IN SOLUTIC"" IOWCCI C.IMMC «>S]I«X t>«M«K O . I I W 4 C 0.5JK* o.M««a o.tt«e«E

CaiTICM. DDOIUJ <C«I catTIcat. «»ss l«CI

«|K|»UK CDIIICM. •«» IS 0.21 )0«E 02 «ltO<M»S

MUT-titn. <C«TIO»> r » c i w

cs 9.K27M at S.1I3ME 32 o.tooooe Ot •t a.ii>*4C 02 il.lttMC 02 O.IOOOIC 01 Cl S.1MMC 02 J.42HM! J»2 0.»>N«4f oo or 0.20IOIF 02 02 4.III0 04F OI oo 0.20A2IE 02 0.420 Wf 02 cc oo 0.33272E 02 a.Mo«4t 02 3.100 0 IC ot oo 0.*36«TE O* 02 0.<»<»<» ViE oo

case tv«.»wt-un. taao.o.o.P-o ocuti* or aCTtMIOC CIWWMK IN 9HUTION I sm /ct I

«.U«M( M «.UIU( 01 C.MMOE OI «.u*««t « «.sn«x oo «.»«•« 00 « . L * H L T OO 0.1 loot oo C.TM771-01 «.Sil4X-M

C K I T U T L > « ) I U S «c«> •.mi«€ ot o.itarte 02 a. H»3« 02 I.IH1W 09 0.2I5TTT M «.«*••*€ »> 02 0.2MME M a.3*sno€ 02 t.tMMC 02

OltlCH «SS l«C» .I.IV^.SE a? i.ltl'J'E 02

Of 1.2MM «? 0.2£3M*e 02 9. IS IWK « I t>tll*lt 02 9>IUIM 02 d . l M W »» ».»tji«e 02

•uLiin. ic »i iuh Foctan

o.ioooac oi a.«««OTC oo 3.9904TC ao a.toooac ot 0.100021? 01 o.ioootc et 00 ,, o.iooooe oi \\ o.t oaa?f oi | o.toovE at " ••ItotMU* CKtfltM. IS O.lill*: 02 «liO«4«i

CASE N.I.Nain^tMtfatKP-O OCNClVt OP OCTINlOe CO«n«MS IX SOLUtlOH ««M/CC I

0.11460E 02 o.s»*x ot C<«M«K 01 O.U4&OC 01 O.SJIUC CO C.I14MC OO

01 OI CtH««K<

COITICM. MSIW «««»

« . < > M 1 X 0 1 o.«2«r*c ot 0 . 1 1 4 I K 0 2 0.lJ020e02 OatMtK OS ••tMIW OX «.MMt( 02 t«MIMi 02 o.t rt we 02

02 0.26172? 02

cniricai. <*«ss me) O.IMOTE 02 t . ireix 02 4.IS]«W 02 4.IM«t 02 «.*9!IIK at 9.MMIE Ot ».l»«»»t 01 t>t»iwe ot «.ti2ire ot J.IMtX 01 l l t l M t X O I

MUktlPLtCATlON rtcn*

0.TO93K 00 O.OOOOOE 00 O.IOOORE Ot O.IOOOOF ttt a.ioooic ot O.tOOOOE Ot O . I O O O O E o t o.mnc oo oo o.toocse ot o.toooie ot

M U M I * C R I T K M . M A S S t s 0 . H 2 1 re o t « H . O « R A « S

96

c»« «.«.»— u».ia•».».»-n O C M S I T T C F K C T I A I K cx TICM. M O I U S cwiricaL m m icoiraK racTDi

T O I » A * « I N S O L U T I O N « O < I « M I IOUCCI c - 1 I « N F AT * . U M X A ; I , W I M E M

CBITItM. I S ».«Mttl as < N . O O T M S

oc»sir» or ACTtMioe C O W Q I M K IN VH.WTIOM lowtci

(.ntsai « • IMiw O I I T K U . M A S S is

caw ti cat. HaMin (Cat D.I2I?« U

i v ai utiootra

oiltica. wass

a?

LftPLIMTIM Faciei

case w.*."— i)».<aa«.».«.*-o oensitt or KttNiac

COM»OUMOS IN SOLUTION «*«;c » r.ilMCC W

C H I T I C U . aass is

can T I C M . naotus • C N I

a.max «i • . i m t e OJ «n.ecRftfas

CMiriCM. <*«ss tKCt a.uaait oi

W L I I X . I C A T I O M ractc*

a.aaaiac M

ease m».toooo.».«.A-o «N5IH OF M TINIOC tOTOUNOS IN SOLUTION (OWCCI

O.I1MOE R MINIMUM caimu. vass IS

c m T I C M . M O I U S toil o. i«5)K at

« . i « u a « a n a o c M i K

GKiticaa. "ass «K«> a.HOJtt os

W L N N . I C I T I O I I Facte*

o.9«i roe oo

- U N . 1 0 . « . « . C - A

cm TICM. amis «CN» OCMSItT OP aCtlNIM awrauMis IN SOLUTION ««Mttl C.UIMC « 0.MIM1 oa C . I W H E OI 0.1I030C •« • . tunc oo t . t n n i oo a,3rme oo O.ZSTOX OO

minimum CMITICM. »aass is o.os2rx oi kilocrams

a.SMMC oi o.aooue ot j.iauae oz o.tisose o* 9.1MIM o* a.iasioe u o. iot««e os a.iMtat ox

ottrtCM. Mass m i

s.uanc M t . i u w u 1.I IMH M g.maac ot 0.MS73F ot 1.raa*ac oi g.«t]«K ot j . iaaw ot

MULTIPLICATION FACTUM

o.iooiee ot O.I MOM 01 o.iettac ct c.ioooce oi a.wttx M O.IOOOSF OI O.OOOTTr OO O.INOtt «

ease N.atNDMM.iM.a.atC^ oeMi -TT or a c T i N i n e C0HFCVM IN tOLUTtW ICMSCO

«.nojoe at a.(UT«t OI C.tMOX Ot 0. IIOMC OI O.C9S7SC OO a.t97ax oo O.IIUM OO c.otnoe-ot • .sint 'Oi C.29TCX-01 0.II0S0C-01

cat TICK. U O I V S I C M I

o.«otoae oi 9.W1IH Ot o.«tsa«e at a . M t m ot « . m « K ot o . n o M e oi t . m » n oi t.NtTW 01 o.nsaoe oi o.tooare 02 o. 11 asae « o.2ta«TC n

CMiriCM. «aass tatel a.«o«T«e 01 il.tttIK 01 3.tUMt at o.tsxroe 01 o.Tovoac os o.iatMC oa a.saizac 00 O.UTWE 09 A . T O A S S E 0 0 o.ltait oo O . I W K oo T A S M U T 0 0

M M . T I N L I C A V I O N ractcn

o.iooax ot o.tootx 01 a.iNiit ot o.iooooe 01 » .M « «K eo I . I M I X OT o.ioaoae 01 t . m a i F 00 0.1001M 01 « . i « o m 01 0»aaBtaF 00 • . M m 00

MINIMUM CNITICAL MASS IS O.IM27C 00 KILOCCAMS

97

WMin OF tCtlNIM ,tMo.*.w.c-n

COITICW. M O M S (CM* cotnci « « »6> W . T I 1 I C « T | O K R « C R C

a.tt«ME «z • . m m at i.MraK at • . S S J M C a a a»«sa*ac aa a.22n't at • . M I X a a at >. i«iw at •.tttMi aa O.M9MC at J . I N N C a a • . isi ix aa at J . « A « M C a a r.Kitit aa • . T T J N C at aa T . I N W a a •.MJtK at t.iwnE aa «.SS3T5E-at S.ri2*ac 01 C.2SWI-M •.MMSE Ot 0.1T3I te-aa a.aaarae at l.SIMIE-tl o.uusE-ei 3 . I I 1 S F ax • . U N T C - A I C.8I1ME-K •.I1ISK a* a.«t t«2E-«t • . I V I X ax C.KNX-K ax t.ius«c at

a.u * . I « » N E • > I . I H M E O I 9 . I O M K AT • • iN«t at o.taaose at t.iMMf at » . « T « T a c O . I M S K a t <«tt»t>c aa I . I H M F O I * * * * * * * * * S V L M S M . C O 1 . I M M E a t

i CMIKU t;s »«t a-s»aiE~ai U I O O W K

. • . • .C-O MMtin OP •CTtHiae

CO—tu»ai | N S O L U T I O N I C W C C I

COf TIC*. • C R I T I C A L M S S «>CI •W.n«lKMIO« ritTOt

•.iiuoc ox 0.3T04VF 01 o.xsaise at a.taaaae at «.»:JT« 01 at « •» • •« at t.lMMC at t.H>ex oi a*9asaac at t . i M W at 9.t*MK at c.tavsac at KSMMC at a.atsvae aa a.taaatF at «.?am aa «.M)HE at aa g>iMgft 0 1 ' . J ? > C K a a 1 . U M X ot « . » T 3 * a a a. too ex ot O . I I « M C a a at a.t«*«x aa a.taaax at 0.«S3T9E-ai O . ra««H ot j.aixo*E-oa 1.1MHE •t o.Mnx-oi a.aasstr at VIMUC at < .miK-« a.aTTaae aa • • m m aa t . i m n at 9.9M7X at a.taatse at o.aixaoc o> a.taasee ox e.saasae-aa a.taaoac at a.isiaic ox ii.aonjw-at a. testae •t O . M T O C - U «.«I*MC ax J . R T R N T a a oa

KTHUM C M I T I C M . Mass I S e.aaoaTE-ai «tt .OCMAMS

CASE .i»»«»»iwm-B cat ricaL moius O T M M OR O C T I M I O C

O M M M A M I N S O L U T I O N :««/tc»

c.ttscoc C2 i.«>inr 02 •iwiaiaa caittcM. uss is o. Mltze a* (ILOOIUJ

can ICAL MSS IK6I •ULTIH. ICATION FACTv.*

o.iaaaac •<

ease »<*.»w»-u*.ioo.e.e.uNFAC-o DENSITY or ACTINIOC rawouwi IN mviiax (autc 1

O.II9MC 0» •INTNUN at I TICM. MASS IS

cn riCM. Maaius «c*t I.MJMt 0*

«.«n»ll KILOGRAMS

caiTicM. u u t««l C.«IHtt M a.i aooac ot

case n.«,nM-uii.uH.>.«.uNMC4 CWTICAL amius (cat OCNSITT OP ACTtNtO* CUNNOUNUS IN SOLUTION •Ol'CCt

Q.1ISOOC 0> O.MtM U m o M K CMTKtL M t s IS O.tHin «* IIUMMMS

OITICAL ««SS

o.«x«xre o«

MULTIPLICATION **CTCM

a.tooooc 01

case -ua.ioooo.«»«.uNPAc-o OCMSITV OP ACTINIOC COHPOUMO* IN SOLUTION (CMSCCt

O.tl! MINIMUM CMIftCAL MISS I S

cat TI COL PAOtUS tCNI O . « I Z * T C at

0.JINM OO I I L O B M N S

C R I T I C A L M A S S

I .UHK 1«

MULTIPLICATION P AC Tea

h I N N I oi

98

< -.« 11. X. <_• l» I K .

" - l »11 » - » »

.... i;.- C ".i -T >J>-~ 1 '1 •-JlklVl CI " .t I » Jt%W- •» » 1J ct " .1 * i - ; • "* i r -r ?.t r : .

CMIICM. MMIS acnntac M W W B t MMICN ; U M C C I

O. IMMC OC O.IIMF M s . M d i m t . i i n f t »a M J M X CX I . I M I 3 C a a e. itwtf at t.i*n*c * i O.IWXC M k I M H E M *•!«>» »* •.IMIK M •••Mate n

iinhim mncM. « » is s.»«Ttt oi <n.aai

0.23BIX «.IM*1C O.IC

« I T K « . M A S S KCI D.U1IK 03 OaiWK as

M N N t at » . T | 1 « W J L

L T T * u u n w N C I

. r M I H I * X H ' l M .

I > -.««»«- f. •.?»r ." ct

H .«•»«.« | . 

O IT |C ». U i S Hit •VLiloiirtllin Facto*

• » id % r : : * n j . r t ' t :i

c a s r H I • . N N - R N J O ;

OtNSItT i» KtlxIM a>»iHM«s IK smtTint leasee I ».MI«3f 0? •Jl

CBITICM. «MH<» K«) r . tv i i t 01 Muitc at

M I N I M U M c«tIICAI t.*l**)t li MtawMs

CM ll tea. «»s> «ct

i .avrrse M

•ILTIFlICattOM FACTUM

t.lMIK

ii l . I lT 'T OCtlMIUt I fr tCl

- « L T I C at. H A M U S «CM» : .«»i«.r at :.j»FM u

• Id-«.« CH'IUL 1«'.S IS -.Mi;lit. •lt'KN«S

CNittcaL

3. M

• U . I I P I I C A T I O M » K I N

i . i i tcx et o.aoTOJe M —

Last Mi.*>»a»N,i gcy-,«,t.iM> U C N S I T T OR ACTINItft

c e w a u w ! I N S O l l t t C N ICM4CC*

; . m « f et s.ttaaoE st e . t ! i < K r c C.lmt'.Cr CC )<ti«<tt :c ;.»ie»t-si

C«STIC«L oaotilf ICM* ».M»«t at tt.t >i«Jl M «.l{Mtf 99 4.IWIK U o. ititour M «.!»»]( 02 t.tTUM tt « P.I «HM M 0.MSO9E U C.JWOt 5?

ct-trtcAk «ass

M U M V 5.IHTW «* 3.MTIK 3< ) . l l t ( « CI o.a«roa£ at S » M 9 t •>* 5. IH11* 91 SIMtlt «l a.aoosje ct

t . t t i w 00 e.taeeae st kitenc ei k lMIt t si 8.19 COX 01 .too c ot I.VKMF 00 I.IIKIC Ot

MtNtMUN CMtTtCM. Mats IS C.tTttrtat St «U9V*<n

99

» » T LL"*L JT « . N I K < L M M A C - I M C * . < « U L T | T > L L C 4 F I J K » T > > » 0 U O 5 L \ S P H . N I > : ( C H T < • « ! )(•«( I

v t.ii'WF li «•»•»»* •?.«••»»»»£ d u t i c t . « s s i s . - > « « I « c . a U L I » M S

- . l u r ? • i - . i ** .* c - i t i i v « . i :

IxltlCO. 4101 J!. 'ItK*. m i K i n u i a k f * c r r w

M S I ?• ).«.a»A-0 UPlSllt xrn KTIUM

tlHWIWWli |<l Su t l l l ' - **

lumti " M I « M T I M I 1 K M . « S S I S

i a r n « L -MMIIS «C"I

9* : . I « « » F ) I « M I W » « s

•It. Hot l< ><I(M r«C*ON

w

C A S S P » . 1 0 C * 0 « » . W

OCMsITT OF AC Timor cwpnwws IM Munct I V M C C I

. .u t ta ci K N I K W M L T J C U M A S S I S

CMIKM. • «t»t •-a IDS S I

5 . M S S H U «!«.««•»

COITtC*. «vs net 9.MSMI Q*

MVL T M . K * T I M

•Ci«ec*i aa

A C K I I T I I U F X I I N I K C M I K « . *wi«s W I I K * . « S I MULri«ttc«Tiant r«c«aw I L I » / C C I

SI - 1 CJ : . 3 : ; i « £ ?t - 1 • > - . l - C t i t 3 . « » t * 31 S . i M K t : i : t l . l ' C M f j . t t . ; c t -.1 t . » M U t c» 3 . i r t « u 0 . 1 J ' i l C •<1 S . t t l W C «c J.WSFT ? t C J •.I.1VW t .^ i ' j r c; 31 3- ~ t c . i t w r * f t r.aooate M : • i i t u t j . t : e * . t •M C . i t i s t v - l l ( . M M M : i f . W I M J . S t J J S d ' t l r. I i«ut » oa

M t t t U l.tMth. " . I - " « f . l W J I F » ' • H i k l X M M J I t

• I N I « H M :»t«t«.«c M A S S is * . I M M I « T T ( N * W S

off Htt^MhMrfw.n.trf-a • M M OR K T I I I X

C M P O U M I | M S O L U T I O N

< C * K C I

t.llfMI C* «•»!»« ei »«n>UF at a . n o * ti O . S S J T S T c c (rfitcx eo e.nsjac ce « . * 5 T » J E - S I 9 > M I K - C I , eaiutr-t i o.ai*aar-q* >.95J»Sr-e*

C M T I C M . M A D I U S ICMI C . J N M C 91 I.SIIMC 91 I.MfHC at 0.aetart »i 01 CtlMSK 01 < . N | I K CI Muncc 01 1.*IMM SI ( • i cw i ot t. IJMTI » o . i r a w c S2

C * | T I C * . < M S S (Ul

:.<«>»it si i . i m n a* 0 < * I S M I 0 3 .SOStSE 30 8.JTTTAC a.1S4TAC so l.Wt'M-OI 9.*]S««e-91

O . I S I M K oe

M U . T M . T C « T T W » P AC T O T

MWtlE 31 O.lOClal Ot • . I K 9 K 0 | o.iooctc oi • . W W oo I . I I M H OT •.IMIII «l o.ioootr ot O . I O C O J C a i

• . K M X 0 1

MINIMUM CHIttCAt. »«W IS 5.1«T*Jt-3l MIOCDMS

100

•>£»sm v* aCllvIO) C»|TI(H«MJS ciric*. MSS aiLllKICOKM r*C«M civwo; IN unitm icat ««• «4»<t> -.n-ij'-- :<• C. J'J»t 31 lit ~i c.ii«ur it 31 >.<t*Nt Ct M;CMF -1 i.saii.'tf ri : . i» i i» ri 3.IMI3 31 J^'JK as C.1MHE ~— -t I I i .w ' i ^ t : n -V 31 3 .A? t X. K t . n x * %wJW " 1 }.I«S*V: 35 C. l»Oiit -.-12V* Cl i 9 . I W 3 W Cl rt l.lZCtX T* Ifc-'l 31 C . F M I * « *.M«JSt-»l ! • " . « • € SI M 1 . I M M E ot l.lMlW M ».WWE 00 '.IMIiE c.««r?je oc

«-t>i"n,» <--iiK»-_ is *if-ji on.icn—&

i.u»MUi,; IK IS"»ttl U«1 C-IT«C«- ««s. « t t t M K * l l d H f a c i w

C .JMSit : i rt ' .^•IM 31 it SI l.t«stlF :.u»j» -i c .wi i r - I -ditftar 30 • « 31 - . » » • -ft 31 *.j m -3 f.nn.'t : i -.1 • 3" :i - it o.imu-ai c.watt ct NII«I«C eg —i

- •S.tSlOT" : .wi«f - - i * . * U 1 1 1 i t

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110

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C A S E H I I.n«-uii .1 O O M .a.a.i>-O DENSITY OF AC1INIOC COVOWOS IN SOLlttO* I CM/CC I

CRITICAL RWXJS « C M |

C M I T I C A . M A S S I K G I

M U L T I P L I C A T I O N F A C T O R

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s O.MtStE CI 0.23613E OI C.ieSOTE 01 0.I72SAE Ol

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CRITIC*. MASS (ICS)

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COMPOUNDS I N I I N U R I O N I C N > < . (G«/CCI O.H«-3t 0? >.<i»T)Hf Jt j . 'TUV . • . "I O.iilJj; el 3. 1 • «"»<»F 02 J..MM: J' 03 C.2»fQ0«r 01 J. 'OJfcTF 0? J.«f73»0-" OJ J . C O C.llAr-0. ri 3. ItioTOt zr C1 CO

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з.ld0l«c "I и.«VI0li 00

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CASE 10 «B.»-0 flfusitt ••» WTMIOE

C O N P C U N O S N S O L U N M ICHrtC 1 0.1I»40F O?

MINIMUM CRITICAL «t«S IS

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CASE ML».P««-SF.13S*.C.G.P-0 H K S M * A C T I N I O *

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MINIMIS! CRITICAL MASS IS C.I2499E 02 KILOGRAMS

CASE ML«.P«(R-UA,l30.e.G.P-O DENSITY OP ACTINIOE C3NR01MO5 IN SOLUTION (GM/CC1

t l « e 0 E 92 S 3 I 9 3 E OT

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<« IN I RUM CRITICAL MASS IS C.IS390E 02 KILOGRAMS

124

CASE M.a.n«Mia.i«M.c.c.»-a .IF KTINIOE CRtttCM. MD1U? (OltlCM. >««SS MUL'IFVtt»'10» Fact CM CIWOMS im <oLUin> IC«I osi IC»/{C »

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C . H ^ V - 1 O . t K M t 0 2 0 » 2 3 » — C • O . W U E

O I T K U « * 5 S I ! M I S M C 3 3 (IUKM«

r a * « . n < a K c t 1 c m . m o i u s c » i t icv. • t t . T m . i o i i M «:?»• t l » W » S In SKIiflOk ICM nsl t« / t t t M I S T * 22 c.i»ee» 0 2 o.iwnf 03 tuwuc oc ;.«!•»» :i r.JMiOf » c.MTVf 03 f .wsn oc

Cl C . M J 3 U 3 ? 0 . 7 I 2 0 M E oa h « M I « OO

• I M W C » | t | C « t « « ! S l « I S ( I I O M M 6

• H S I M OR >C TIMIOC IN snuflON iw tc t s.itscof ; . « I T « c i c.x«*Tae at i-nsa": : i e. S3JT* 33

. 1 3 330 . « > C . l i » K -Q C « t T t C * L « t o i m I t *

*.l«M4t 32 9 . M M C 3 2 C . « ^ T 3 E 02 a.»»xioe 32 «.1Hie 32

otnick. u » t*s» 1 . 1 V W E 0 3 « . « « * • « « O S S . I H M E OM «.MM« «> O . W M K 0 3

<u.Tm.it«nM n e w

MIMli 00 o. m m 00 c.mtir oa M M W 01 O. IOOIOS 0 1

<l>t«» c a i T i c a i a»« i? o . i s i t : ^ 73 K I L O O M S

(«5* tlt.»l>w,] J30.C.C.>1-1 K«!in i» xtikine

«C»/TC »

C>K<rK 32 • » » ! • • * . • c m t i c a t

catuci). i«5iiis IC«I

l.snwt 9* •IICCCKK 00

case j oaoj.c. nfn«i» 1* inmtN

C W I W I I N WLUMCfc t « * / C C I

C . l t W « 0 2 t . w n f o» r.»3(i* -1 (.inr«E 01 I.SW1E 00 t.?•»•»«* CO t.ssi* «e Mtt»*. -r Mitpit re

C»1 T I C M . a a n i u s ( C « l

« 0 2 o.«*«t«e 02 •.•WOOF 02 ].M*Mt C2 0 . C S I 0 0 C 0 2 a . » i a a * F 0 2 S.'WK 12 02

C 4 K 1 C M . l « C >

0* < t . « I H K 0 1 4.lO%<3« o* J . ) 4 » I * E »

0 5 J . M W 0 J J.1MM* Cl 31

< H « . t l » l K H | < » » « « { •

a.i«Mx 01 t . m n t r a . m i « c« • .wmc ao c.i«3t«r si 0.1 at car ct i.iM«n «t 0 . I M H E O I t . m m ai

« l » l « t K CTMT|Ca«. " K M IS l . W H M 03 • t l . W t a S

case I M M « ( > « 4 H I

MMIT» or actio 10c c o w n u w s IM SOLUTION leasee 1

I . I M M C 0 2 l.n*IK ot M N I X (•l«MT «l ••feint oa : « { » I X r e c.tasear oa

C R I T I C A L AAOIUS ( C « L

I . I W W ox OaXtOOOK OX HSXiii II a. r»«ai? a* a.st112c ax O.OOOMC OX

O I T I C M . I 1 S I

a.iitoac as OaXXMOC 0 3 oajoaoxe « « . N * I X 0 9 a.tixxte #3

0 3 * . I I S M ' a s

At <M.ri«i icartga »»cw»

A T * M M * C R I T I C A L M**S as o a i i a x o c ai A T U

OalOMOS C*

\J

130

CASE MLJ.H5-PP.13, •C.P-0 DFX SI 1Y OF ACTINIDE COMPOUND? IN SOLUTICK ( C«/CC I

o.u*foe C . « ! f > 3 E O. 2A«-90E C.lt«tOE 0. !3193E C . J l * ' - ^ rr c.satojE-ci

o? "l oi ci 00 00

CRITICAL UOIIK «c«o

0.6 31 tag Ot 0.1344SE 52 o.irooae 02 0.26921E 92 0.37132E 02 o . J O A O T E 0 2 3..76156 - 2 0.t>3607E 02 3.7793SE 02

CR tTICAL >ASS « K C I

J.U3TOC 02 J.257S2E 02 3.S19S3E 02 3.Q366AS 02 O.UAO E 03 9.3S964E 02 >.51*?3E 02 02 J.48900E 02

MULTIPLICATION FACTCR

o . t o o t o e oi 9 . « M U C o o « . « M M E OO 0 . 1 0 0 C 1 E O t o . o o o a o c oo 0 . 9 9 2 9 1 E 0 0 0 . 1 0 0 C 9 E O t 0 . 1 0 1 3 2 E C l

MINIMUM CWITIC4L »»i« IS 0.12070E 02 KILOGRAMS

<"»V. Ht,..F«!<-t-a.lO'}.r»,C.»-C *cu»'iv CJITICH ooiin CRITICAL MASS iuiLTiPLir.«Tiak F«CTCR c.«( rui- r. rrLcttfN icn KCI t CSCC 1

I.IIOFJ: c-- at J. 12 "« »= •J' o.9?jf at CO C.f't-.-" Cl 3.I06«tr 02 OS 00 -J 3.17422c C2 •J! 0.999e0 CO C.ll.. 0"= 01 02 0. t«200C 03 0.100CIE Cl O.HIJi- CO j . j<si7re 32 J.1J594C "3 •I C.^I'-'O" ro 0. 3««« 0? 0» 0.»<i««r CO c . l l ~ * . i : r o o. a? J.->t5»f= 3? J.9s22-i'r 00 C.M 1 "1 :.=S12PF t j .ol l1"'!r - i -.TJSS""-: CO

rciUCil IS O.UJl'f 03 K1L0CVAMS

JF»-<ITY OP C<1<<PCUND5 IN CASE

• C t l N I O E SOLUTION

HLM.FVR-PP. 1000.O.C. P-0 CRITICAL RADIUS CCM» CRITICAL MASS l t d MULTIFLICATIOH FACTCB

(C-«/fC > C.U460E 0? 0. 6 3S31E Ot 0.12310E OS 0.999A6E 00 e.saiwE ft 0. I0612E 02 9.26613E 02 0*99999C 00 C.24C90E Ol 0.17362E 02 0.SA126E 02 9 . 9 9 9 6 7 E 00 C.11AC0E Cl 0. 27S77E 02 il. 10060E 03 0 . 9 9 9 S 4 E 0 0 C . 5 3 l ? 3 e e « 0.38198E 02 4.12419E 03 0 . 9 9 9 S 2 E 0 0 o . s « e < i o = oc 0 . 3 9 3 6 3 E 0 2 0 . 6 3 S 7 9 E OS o«iooo?e Ot C.11*601- 00 3.5Q217E 02 J.61794E 02 0.98672E 0 0 C.<219?E-01 0.64689E 02 0.60320E 02 0.98079E CO C.24M0E-01 0.77571E 02 3.48A64E 02 0 . 9 9 9 6 0 E 0 0

MINIMUM CRITICAL MASS *S 0.1231OE 02 KILOGRAMS

CASE HL«.*OI»-PP.10000.6.G.P-0 DENSITY OF ACTINIOE CRITICAL RADIUS CRITICAL MASS MULTIPLICATION FACTCR COMPOUNDS IN SDLUTICN «CM» <K«» (CM/CC 1

C.Il*enF. 02 0.&21H1E Ot 3.US42E 02 0.I00C9E Ct 0.SJ193E Ol 0.103SBE 02 0.2A762E 02 0.9996OE O O C.24«-a?E 01 0.1688BE 02 Q.A9816E 02 0.9997AE 00 C.llteOE 01 0.267656 02 0.92045E 02 0 . 9 9 9 9 0 E 0 0 C.-2J93E 00 0.3734SE 02 3.1163SE 33 O . I O O O O E ot C.24FQ0E OO 0.J4140E 02 0.62017E O S o . i o o t c e o t C.lt«*0E OO 0.48964E 02 3.S3321E 02 Q.9C7I3E 0 0 *. 531*5 JE--"1 -.619266 52 3.32916E 02 0.99627E 0 0 C.?4» 90*-0» U.7J78BE 02 0.41551F 0? 0.993S2E 0 0

MINIMUM CRITICAL MASS IS 3.11542E )2 KILOGRAMS

CASE H-M.PMR-PP.IO.G.G.A-O OEMS! TV OF A C T I N t O E

COMPOUNDS I N SOLUTION ( G M / C C I

c . n e s o E 0.S42I4F C . 2 8 1 6 4 E c . n e s o E

02 01 01 OI

CRITICAL RADIUS <CM> 0.90138E Ot 0. 1MA3E 02 0.30438E 02 0.69909E 02

CRIT EC AL MASS (K«> 0.358J2I? 02 0.955296 OS 0.297266 03 0.16717F OA

MINIMUM CRITICAL MASS IS 0.J5832E 02 KILOGKAMS

M U L T I P L I C A T I O N FACTCR

0 . 1 0 0 0 S E 0 1 O.OOOS2E CO

^ 0 . 9 9 7 4 0 E 0 0 0 . 9 9 0 6 0 1 - 0 0 »

131

CASE I j > . . • ; . < • . % - r

I t> UF tciiHinr c i . w r v w s I N s p l u t i c n

( < « / C C I

c . i i r a O E o ? C . ? « ; I » F c i c . ; ; i b « E 0 1 C . 1 I M 0 F 0 1

C I T i c « l k X I U i I C M I

— »I ,1 0? o > « L o r -

• • U U T I P L I C A T I ' I K c « c t w

.J- IT »T • I V " ->-» j lit?*-* of

a • o »

J . l U O C t 0 1 ).M««f 03 J . 9 « 7 4 I < CC d»o«M2i 00

c a s e H.a,w-pv.iooo.t,c,*-a O E N S I 1 T OF A C T I N t O E

COMPCUNOS m S O L U T I O N I C » / t C 1

o . u e a c E C . S A 2 1 A E 0 . 2 E I C A E C . I I » K

02 ei 01 01

C R I T I C M . C A O I U S ( C D )

0 . 1 2 0 S 6 E 0 1 9 . l » 5 Z « 9 2 O . H 3 S 3 E 0 2 3 . 7 A 9 3 3 E 0 2

C R I I 1 C U . MASS (K6t J . W J O ' E 9 3 0 . 1 C 2 9 6 * 0 9 0 . 3 2 A 9 0 E 0 2 0 . 2 0 6 0 3 E OA

« U . T < R . I C « I O » F A C T C R

1 . 1 M C 7 E « 1 « . 9 « I « X OO «>wr«K oo o.wwr oo

N I K I««U« C R I T I C A L MASS I S 0 . 3 9 2 0 T E 0 3 K I L 9 C M 1 1

CASE rf-M.PMR-P«*. 1 0 0 0 0 . C . G . A - O

O F S S 1 T V OF A C T I N I O F CtlMFCUNOS I N S O L U T I O N

( C » / C C I

o . l o ? C . < 4 ? t « P C l C . 2 S l f A ? 0 1

C R I T I C A L R A O I U S «CN»

0 . 1 1 T 2 9 E 0 2 0 . 2 1 9 0 2 E 0 2 0 . A 7 9 9 7 E 0 2

C R I T I C A L MASS

J.'iWHE 02 9 . 2 3 8 6 0 E 0 3 O . H 6 S S E OA

M U L T I P L I C A T I O N P A C T C R

o.ioocas ci o.ioocie ai I . 9 9 M I E OO

M I N I P U P C R I T I C A L MASS I S 0 . 7 8 9 3 A E 0 2 K ILOGRAMS

CASE f L M . r n R - F B . l a . G . G . C - O

• ' E N S f l V • * A C T t N t O b O M F C L N O S I N SOLUTtCN IC/CC)

C . l l ' " * ' V f o ? C.S* . *TA«" 0 1

t . l l ' «a? oi c.???»te oo c . r * 7 o v c o

• I M » l « r - I H C A L M « « JS

C R I T I C A L BAOIUS «e«j o .s *>oo( . : : o i U.102«« OS 0 . I 7 7 A A E 3 2 0 . 3 0 2 9 I T 0 2 0 . 3 7 2 0 S E 0 2 9 . 0 ?

KtLCC-'-AMS

C R I T I C A L NASS ( K G !

l . I W C 01 i . »«mie o? 4.U1«7£ 02 t . l l a O O E 0 3 ) . I t « A a C 3 3 ' I . I M 1 W 0 !

M U L T I P L I C A T I O N PACTCR

O . I O O C S C O l O.Wa7SE 00 I. I1U4' 00 0 . 9 9 9 2 9 E 0 0 3 . 1 9 0 A S E C l 9 . 1 0 0 1 % O l

CASE I00.G.C.C-C " F N 5 I T * .IF ACTLNLDF

c o » p r u « i i r n m i U T I O N

c . u < i - - r » C . ' t v « f oi C . f J ' 0 3 £ 0 1 *•! !«•«-€ "I C.««T«* CO C.S»TJ3 CO C.ll' tO!" 00 C.»f.-7* "-C1 :.s«7- w.'i

C R I T I C A L RADIUS I C * I

J . 4 R 9 2 I E 3 1 0 . 9 1 4 T 6 E 0 1 O . 1 J 5 8 2 E U2 O.20<>b0S 9 2 o.2«siPr a? O.JMM^ *a J . W i 7 " i S 0 2 O . A 2 3'»9F ) i 3 . I ? ' * : * ' - 3 2

C R I T I C A L NASS <KGI

J.l 37,-76 o? l» .2«S97A« 0 2 0 . A * O I « E 0 2 3 . S 3 7 9 9 F 0 2 S J « « « 1 « 9 2 J.2A-J0T-; 0' 1.tli'i'-. J . L L L J I T o?

M U L T I P L I C A T I O N FACTCR

0 . 9 9 9 0 7 " OO 0 . 9 9 9 2 A C 0 0 0 . 9 9 9 T D E C I 0 . 9 S 9 S B E 0 " O . I O O O O F € 1 9 . « 9 9 « 6 P 9 0 0 . 1 0 0 1 9 C 0 1 0 . 9 9 9 2 A r CO 0 . 9 « 1 2 V 0 0

I S j . 3 > 1 7 2 E 01 M L C O I A N S

CASE M L R . F V R - P P . 1 0 0 0 . G . G . C - 0

O E N S I T V OF A C T I N I O F C R I T I C A L RAOIUS C R I T I C A L NASS MULT I P L I C A T I O N FACTCR COMPOUNDS I N SOLUTION ICRI ( K G I

1 C l / C C t

C . 1 1 9 3 0 E C2 0 . 1 9 8 2 3 E O t i t . J I S O O E 9 1 0 . 1 0 0 2 2 E 0 1 C . S S 3 7 A E C l 3 . 6 6 A 3 2 E C l J . 6 0 0 0 6 E 0 1 0 . 9 9 9 2 S C 0 0 0 . 2 S T 0 3 E 0 1 0 . I 0 5 7 7 E 0 2 0 . 1 2 7 A I E 0 2 0 . 9 9 9 C S F 0 0 0 . I I 9 3 O E 01 o . i o o a n E 0 2 0 . 2 . 7 2 3 E 9 2 0 . 1 3 3 C 3 E 9 1 Q . S S 3 7 S E 0 0 9 . 2 2 T 9 0 F 0 2 4 . 2 7 3 4 S E 0 2 0 . 9 9 9 e i « 0 0 0 . 2 9 7 0 3 E 0 0 0 . 2 7 9 S 0 F 0 2 0 . 2 3 S S S E 9 2 9 . 1 0 0 0 A E 0 1 C . I 1 9 J C E Cf 5 . 2 7 6 2 3 6 f 2 3 . 1 3 6 3 4 6 1 2 4 . 1 0 0 1 1 * 0 1 C . & E J 7 9 C - 0 I 0 . 3 3 3 9 1 E 0 2 0 . » e 3 T « E 0 1 0 . 9 0 8 C 9 C 0 0 B . 2 S 7 0 3 E - 0 1 0 . A 0 2 8 8 E 0 2 < I . 7 0 A 0 6 E 0 1 0 . 1 0 I C 3 E : i M l t J X ' C I 0 . A 7 I A I E 0 2 J . S 2 3 9 3 E 0 1 0 . 9 9 9 2 S F 0 0 0 . S S 2 7 S E - 0 2 0 . 9 7 1 2 9 F 0 2 9 . A 3 S S 0 E o t a.tooire 0 1

M I N I M U M C R I T I C A L MASS I S O . J I M O E 0 1 KILOGRAMS

132

c o » t i i * j « i n s f L u t u i « c » i » « • . » « C » / « C 1

. 1 »« ;« ' - - 2 J . W i T J t Ot O t O . t 9 0 2 S X ot o . ; ; s v o i 0 . 6 S 5 1 N C O l 3 . 6 S 2 1 W O l 0 . 0 0 0 0 7 ^ oo c.«?7o;e oi - 2 3 . < 2 2 3 t € 3 2 cc C.IIUOE Ot 0. ISMS' 0 2 J . I < H » F 0 2 O.tOOCOF ct C . * « ; J S E o o 0 . 2 2 S 1 M F 0 2 0 2 o . < m n r o o C . J ! T : « CC -.27SS3F ~ 2 0 . 2 1 2 6 9 E 0 2 O . t O O O ^ F - 0 1 0 . 1 1 0 3 0 E OO 0 . 2 7 7 9 3 6 0 2 a.lOMl1 o» o . t o o o a s ot 0 . ? S 3 7 « I E - 0 1 O . 3 2 S 3 2 E 0 2 3 . T 9 S 6 2 E 3 1 ~ —

C . I ; T C 3 E - C I 0 . M 0 0 3 3 E 0 2 T L . » « S T K Ol o . o o a T a ® o o C . L L « 3 0 C - 0 1 0 . a " M 3 S E 0 2 0 . S 2 4 0 1 E 0 1 O.OOOOOF o o C . I S 3 7 S E - 3 2 0 . 9 A 3 2 7 C <•2 J . V . 7 9 M 9 1 0 . 9 0 0 0 3 F oo

« | N L > U A C R I T I C A L M ! S I S « . M 9 > N OL « K O O > « « S

CASE

C « L T I C A L M U 3 I U S 1CM1

W k : i l « OF A C T I N I O C COMPCUNOS I N S O L U T I O N

K a / C C I

a. 11 ;ooe 02 C . 5 3 3 7 0 6 0 1 C . 2 A 7 7 0 E C l C . 1 1 S O O C 0 1 C . S 3 3 7 9 E OO C . 2 « 7 ? K CC c.ii"00e oo

M I N I M U M C R I T I C A L MASS I S 0 . 2 A I S 3 E 0 2 K I L O G R A M S

C - M T I C A L M A S S

Ol 0.261SK: 02 0.100C2F ot 02 J.S7223C 02 0.009C3E oo P2 J.12133E 33 o.oooeoe oo 02 0 . 2 1 7 0 0 * Ol O.l oooo*" ot 02 O.tOOOAF S9 0 . 1 0 0 C 9 F 0 1 02 I I . I 9 8 9 9 E Ol ! . « « » « oo 02 3. IMW 01 O . I O O K E ot C-2 3 . 1 I 7 6 3 E : i i.i :JTI« Cl

CasF H.«.Fm.n>.n3iC,G>UNPnc-n H f * C T I N | p t - "

C I 'NPCUKOS I N S O L U T I O N I v K / C C l

' . 1 1 S O O C 0 2 C . « ; 3 ' K 0 1 C . ? 4 7 7 « € C l C . I 1 « 0 0 E O l c.suToe co : . i « l T I E M C . l l - O O E o o

c«lTlcai cuius < C » )

o.aasose 01 0 . W 1 T 3 E 0 2 9 . 2 « M l f 3 2 0 . 3 9 S 2 3 E 0 2 0 . S 0 4 7 1 E 0 2 0.«MTE 02 0 . 0 1 4 S 1 E 0 2

C R I T I C A L N A S S lucl 0 . 2 0 3 0 1 E 0 2 0 . 0 0 3 0 9 E 0 2 J . 1 4 9 7 2 C 0 3 a . M T t t l 0 3 0 . 2 9 4 3 T E 0 1 o . i o a j t c 0 3 0.260ja* 0?

M U L T I M L I C a T I O N « « C T C »

0 . I 0 0 0 2 E 0 1 0 . 9 9 0 9 0 E CO : . < M « M c OO 0 . 0 0 9 I 4 F CO O . I O O O I E 0 1 O .OOOSSF 0 0 0 . 1 0 0 S 2 E 0 1

M I N I M U M C R I T I C A L MASS I S 0 . 2 O 3 0 1 E 0 2 K I L O C R A M S

c a s e H L a . p « t t - p p , i o o o . 6 . c a u M > a c - o

O E N S I T V OF A C T I N I O E C N I T I C A L R A D I U S C M I T I C A L MASS M U L T I P L I C A T I O N F A C T C * COMPOUNOS I N f t i L U l I ON 1CMI ( « C I

( C M / C C I

0 . I 1 1 0 OE 0 2 0 . 9 S 6 M O F O l d . 3 1 J S 2 F t 2 3 . 1 : i : J r C l C . S 3 3 7 0 E 0 1 O . t A S O O E 0 2 0 . 7 0 9 4 0 ® " 0 2 0 . 0 0 4 4 0 E a o c . 2 * 7 7 e e o i 0 . 2 4 7 a I E 0 2 0 . 1 S 7 1 9 F 0 1 0 . 9 9 9 e i ' a o c . i t « : s e * i 9 . I O A 2 4 E " 2 3 . 2 0 5 1 9 ? i ; 0 . 9 9 9 S 9 F e o O . S 3 3 T O C OO o . a a t o s E 0 2 0 . 2 b 2 « 4 e 0 • O . I O O O O E 0 1 C . 2 4 7 7 M o o 0 . 9 1 S 0 7 F 0 2 3 . 1 4 1 9 1 C 0 1 0 < 9 K M € r - . I I « ? ; E T d . 7 2 a O O E 0 2 i.10902° 0 1 0 . 1 OOTS* e i C . S 3 J T O E - 0 1 0 . 0 7 4 0 0 * 0 2 J . l a « 3 1 ? 0 1 o . o a i OSE e c

M I N I M U M C R I T I C A L MASS t s 0 . J I 3 H 2 E 02 K I L O G R A M S

CASS • e a . F M M - P P . I O O O O . C . ' i . U N P A C - C

O C N S I T V OF A C T I N I D F C'tMPCUMOS I N S O L U T I O N

C O V / C C I

o . i i e u o c C . S -2370E C . 2 4 7 7 6 E C . l l S C O C C . I 3 3 7 9 E 0 . 2 4 7 7 & C

02 Cl 01 •1 oo 00

C R I T I C A L « AO I US ICMI O.OAOOOE O l 0 . 1 6 0 4 0 F 0 2 0*209IOE 02 9 . A I S 2 9 E 0 2 O . A 7 | o 3 F 0 2 0 . 9 2 3 1 1 * 0 2 1 . T I U H 0 2

C H I T I C A L MASS ( K C 1

O . A H S O E 0 2 0 . 4 2 4 2 0 E 0 2 0 . 2 0 2 2 9 C 0 3 3 . 3 A S 3 A F 7 3 0 . 2 3 4 * 0 * 0 1 J . 1 S 0 2 S E O J J . I 7 7 0 2 E 0 3

M U L T I P L I CA T I O A F A C t r a

3 . 9 0 9 0 T ? CO 0 . 9 9 9 7 I E OO 0 . 9 9 9 6 1 E 0 0 3 . « « « C 0 E 0 0 0 . 9 M 4 * OO 0 . 4 O S S 4 F CO 0 . 1 0 0 2 S E 0 1

M I N I M U M C R I T I C A L N A « « I S 0 . 4 1 I S 6 E 0 2 K I L O G R A M S

133

case M.*«wiMiP>i«nM>c>c«uM] O C t S I T V OP A C T I N I O E

O I W C I M S 1M SOLUTION I t » < C I

C R I T I C A L M O I I K (CM1

CRITICAL MASS Oi l

« I H » W i C R I T I C A L WIS IS O.rsmaE 01 HILCCAMS

M U L T I P L I C A T I O N «»cir»

C - I t t M F • 2 0 . J 0 9 A 3 C 0 2 a . t M A l t OA • . S H J E t l 0 . S 0 1 9 2 F 9 2 j . A W V o » I . I N O T f O l

C I O . S 4 3 2 1 F 0 2 . » . 1 S 8 S S F OA O . I O O O K e i o . i e c e t r O l 9 . » 9 2 « 7 F Z? • • 1 . 9 < S 9 e v - c -o . i c s e o E 0 1 0 2 a . 7 S 7 « M E o ? 0 . 9 9 S S 9 F o o c.i«ercE o o o . o s e s - * e 0 ? as t . W V 0 0 C . S C E T 2 E 2 . T S 2 A 1 E T2 J . M 7 W Ol a . i w t r 9 1

C A S F ^ . " W - u a . K - . I . C . t - J

OfcNSlTY OF ACTIMIOF CRITICAL M.'Uf. CRITICAL MASS MULTIPLICATION *ACTCR cwnfwm IM «nLUTI|-N ICMJ UCI IGPSCC 1 C . 1 1 A > 9 C g j 9. »97I»i. 01 J . l ^ t h f a ? co e . ' j i u s c i I . I I U " 9 ? J* "»Mt 9* O.WW o o C.?«fCC? "I ..IHJ»S

3® 0 . 9 9 9 S A F CO C . U A f O * 0 1 J . J 1 9 A T S OJ « * CO C . « 2 1 S 3 = OO 9 2 3 3 0 . 9 9 9 7 M S c ?

J ? •J . T 9 ® O . W S " a o o . H A e a ^ o o 3 . . 9 3 6 1 = J 1 3 . 1 < « l »-. 0 1 0 . 9 9 7 9 V 1 c a t . t i l ' I K - C I -i i.i*«»®r - i ;.O<J® J I -

IUR CRITICAL MA«« IS O.lil'tf O? KlLrCNAMS

CASE .•FNSITY IT «CT|MI(M-f"«Br«M>i IN SOLUTION (W/CC1

C R I T I C A L t M I l " . «CM»

C R I T I C A L MASS I ' C I

M U L T I P L I C A T I O N F A C T C R

0 2 3 . 7 o J M f 3 1 . 1 . 11 7<J T- 0 2 3 . T S 9 V 0 3 C l O . U 1 9 * ar> I . M i l V 3 2 3 . 9 4 4 2 9 E 0 1 9 . 2 2 9 2 9 E 9 2 < i . i ? a o 3 E 0 » 0.<J<J<J2<SE CO 0 1 9 . 1 9 0 0 9 6 a ? OB 0 0 - p 3 . V 4 3 7 3 * C 2 0 3 0 0 0 0 9 . ® I 7 t 7 = 0 2 0 . M ? J 1 « O ' 0 . 1 0 0 7 3 ® 9 1

»IM»L» O-IIICM. MA«« ' . ' 1 7 - f t 0 2 « I L C C A M S

CASE MLR.PHR-UP.1930.G.G.P-O O E N S I T Y OF A C T I N I O E

COMPOUNDS I N S O L U T t C N ( C M / C C I

C.1IA6CE "2 0.S2I93E 01 0.2AC90E 01 0.1I460E 01 0 . S 3 1 S 3 E 0 0 e . 2 A e « 9 E o e 0 . 1 1 4 6 0 E 0 0

C R I T I C A L HAOIUS too O . ' J T M E 0 1 0 . 1 2 9 3 2 E 0 2 0 . 2 1 2 1 3 E 0 2 0 . 3 4 S 2 A E 0 2 0 . 4 7 4 4 6 E 9 2 0 . S 9 9 8 3 E 9 2 0 . 8 4 3 1 0 E 0 2

C R I T I C A L MASS m e i


01 9 . 1 9 2 7 2 E 0 2 O . I O O O O E 0 . 4 J 0 9 S E OS ( . M I M E 3 . 9 R 7 3 4 E 0 2 0 . 9 9 9 A 9 C 0 . 2 0 2 B 9 E 0 3 0 . 9 9 9 3 1 E 0 . 2 T 7 9 9 E 0 3 0 . 9 9 9 I Q E 0 . I 3 7 O C C OS 0 » 9 0 9 1 1 E 0 . 2 S 7 7 0 E 0 3 O . I O O O T E

00 00 99 01 MINIMUM CRI I S 0 . 1 9 2 7 2 E 0 2 KILCGQAMS

CASE HLM.FRQ-UP.lOODO.C.G.P-O DENSITY OP ACTINIOF CQMPCUNOS IN SPLUTITN C R I T I C A L R A D I U S

( C M » c r i t i c a l m a s s

I G M / C C )

' . 1 1 4 6 C E : ? 0 . 6 2 7 1 R E 0 1 0 * 1 1 8 4 J E 0 2 C . S 3 1 9 3 E 0 1 0 . 1 0 A S 2 E 0 2 0 . 2 S A 4 4 E OS C . 2 4 « 9 0 E 0 1 0 . 1 7 9 6 4 E 0 2 0 . S 1 3 9 3 E 9 2 0 . 1 1 A 6 0 E 0 1 0 . 2 7 0 S 3 E 0 2 0 . 9 S 3 6 9 E 0 2 0 . S 2 I 9 3 E CO 0 . 3 7 7 3 3 E 0 2 0 . 1 1 9 7 3 E 0 3 C . 2 A C 9 C E CC 9 . 3 9 3 1 HE 0 2 9 . 0 2 O 6 S E a e O . l l A i - O E 0 0 0 . A 9 1 B 1 E 0 2 0 . 5 7 1 0 9 E 0 2 C . f 2 I = 3 = - 0 1 0 . 4 3 4 0 3 E 0 2 0 . 5 6 7 9 4 E 0 2 C . P A f O O f c - 0 1 0 . 7 7 5 6 7 E 0 2 0 . A 8 2 6 8 E 0 2


0.10009E 01 0.999605 00 0.999S2E 00 0.9«9«5e 00 0.10001E 01 o.iooeie at 0.9S971E 00 0.999S2C CO 0.100C7E Ot M I N I M L M C R I T I C A L MASS I S 0 . 1 1 8 A 3 E 9 2 K I L O G R A M S

134

CASE K.«.nm-UO.IJ,T.T,»-a DENSITY NR ACTINIDE c n w n w IN SOLUTION leucci

C.lKHF u €.M»«e ot c.ni«E ai C.1KME Ot •mm.* CPitK«L «•?«

CRITICAL <UOtUS «C*» 9.941ME Ot 0.40020E OS

IS 0.«*31« Cg «ILOC»W

CRITICAL «*ss t«c> ».««3tac as O.IMUC •] o»3«saae 03 0.2S470E 0+

LTt»*.tCaTtO»> r«ewi

NCSFIN . * W T I N I K C.NimiLB* IN •auitc« ic»/rc» cr c.^wm at -.rsit* *i Ull««* €1

••••in1* C*ITI«-*L * > ;

CP1TICAL caPIIK tCMl

•». ioaisc 02 a.a*a7er 32 «.W>«Jt 02 0.»l«iX 02 O?

cai>ic«. "MUSS («tl ).«>•>w 92 4.13*12? 03 0.«*2»*<i OT a.i»j««F o*

L W U C L T M R«CTCW

o.gurr aa •»«nsK 00 C.WTIW 00

tiwrcwnn »N <xiuTt(M <G» CC I c. lle*ag M ei -.2«te*s -1

C«1TIC«L

a. iti-je j.' a? g<«?'Mf 02

C4ITICAL 1*61

OT 03

•uiriK K«'li» F-OCTC*

00 i.wi«t ti «.<«(« aa «l> CUITICAL M!< IS O.OT442- 02 «tltKSU<K

C»SE N.».F»1-UP,I]300,C.G.»-0 13EKSJTV OF ACTtNIOE CnWFCUNOS IN SOLUTION ICK/CC)

t.l»"K OP 0.!«7l«t 01 t.l!IF«E Cl

CRITICAL CUIUS foil O.UTIOE 02 0.21900E 02 1.V1HE 02

T*ITLC»L « « S ( K M

i.T v-o? a2 4.IM2M OS 0.IISM* 0*

«ULll>LICMIO» rntics

o.i«m 00 o.ioaxss o« o.oooooe 00 MINIMUM CRITICAL MASS IS 0>7SS»0E 02 KILOCttAMS

CASE M-«iW<l-UP.l«.C,C.C-r OENSITY -JF ACTtNIPE CTMPCUNOE IN SOLUT1PN €CM/CC >

C.I1C10T 02 C.S?JT*E " I O.SSTOX 01 C.11V30E 01 C.JtJIS CO C.2STCTE OO •.1ICJTE f ' C.*iJTi»-Cl

CMITICAL BA9IU-. (CM!

01 O.aiTAIS 01 O.mtsf 02 3«X3tO'F J2 0« MMlt 02 0. 31 02 0.»PIT?« 02

CRITICAL MASS t«c» a.Taioi: 31

112 J.3»2S*= 0» 3.MTA34E 02 *t«»«« 02 «.J1I«K OP il.Pl^K 02 3.2*059* 02

MULTIPLICATION FACTCM

lalMCK Cl 0 . W I 1 " 00 1.MMX CO «*lMCtC Ct •.t««m 00 s.mnt co a.<>«3*sr 00 o.«PM3*r to

MINIMLM CMITICAL MA5? IS O.TalaiE OI K1LOGMAPS

CASP HLM.FM-L-UP.IOJ.G.C.C-C OFNSIIV or ALTINIO«

CO»ORUN0-I in TILUTTRS (r»/cc > CaH-^C* 02 0.TSS"»A- 01 C.I«?OJ- 01 C. I I " ' 05 01 •.'••JS6 ** 0.2TTCTE CO t«ll"*iir 0v> C.««J»!^-C1 C.f«»J!t-(ll MJMfE-:i

CRITICAL t«nir TCM>

Jttl1lfr 01 O. It340? o? 3.if>»A-t a* )< 'Jotir 9? J« !»J7SS J? J.MI1" •>> 3. »1 10«»F 02 3>«M*E 03

OITICAL MASS

oi >1 4.IHF1E 02 j«<ytic 02 3.*i»T?*E 0» 01 >.»»*•: »l ?» J.'illtC 41 i.'tnis ai <1 3.»'»3*2= 01

MULTIW-ICATION FACTCM

0ol09l*t Ct :.«M«I' CC O.aMW CC «.IM(K 01 • . m m 00 a.mn* ot li 0.1 coin* ot «.«niw co •>«HiJr 00 0.I021E' 01 INIML« CRITICAL MAJ? IS ( . «ILCJ&.AMS

135

f f M l l t t » «CT I« |KC I • «ll>« l: II n\ottr» « T » / C C I

UIU'J: « ;.»«•»•* -» M co (•tlfix oa

I M ' I F m i n e a t is a. st«-«-

c o n t u M c i m it»i

s= Tt « . M t W Ot a? M - O H * or-J.Ji'W.t 03 02 fc!T>kt «.» O-*

o?

at *n.oo>«K

OtTtcat. nass uei

-.ttaOTc It ll.o»«»C Ot i.titmc 02 02 O . f ' P W 02

i l . t o Z J I E a t 1.7:214= st O* at

auLTIPLIOTiak Ftctca

01 eo o . m « t . co O.lOOOlE 01 O.OOOOOE 00 "».t«or*e et o.toot«E ct o . w t r co j.101 iM; ct o.oeoase oo S.M4CTE CC

f » K x. a . r»» •<»». i .c. c. c—i •»»«»« w ttmlOE e *» 't»xf la st «rtc» M»/rci

C. 1 l rMC 02 (.MJMf Ol f.«T:jr "t C.IWME 01 t.«*iWE CO U J ' T W dO co

MMMT-tt

mrictt cuiw «c*i

j. o« ot Ot h l M M C OS 9.IMHF 02 0.3XS03F OO OS 9.ZTMK 0> 2 0.r»22tc 02 O . M M * 02 a.ntM: 02

citticv. Mass « t i

11 J . 9 M W ? Ot l.tvll' »> J . l W t ' 02 i.jolMt ?» 02 J.t 02 i.ljioj" 02 Ot j.uwrt ot Ot

KULTiaLlCttiok F A C T C M

«>I««KC Cl eo CO «>IMCIC 01 ).<99tt° :c «.1MCK 01 o.ioocic 01 t . w w cc 4.W»Wf CO C.WT34; c» o.oaoee*- 00 «IM««I« C'ltKH a»«« 01 >n.ceu^

ease K t . n a U M O ^ . C « M O I C - O

r£«ll* W aCTIMlOC c r w e w e s i« jnurncn I C » / C C 1

Cat 19 e.«

O W T I C A C « A O I U S I C M T

0.21I7SF 02 O. "

C « l T 1 C M - « a s s ItCl « . « 5 » ! T { 0 3 a . u M t t o«

MULTIPLICATION FACT CM

0.100C1€ 01 j . w w e co ataMjH 01 I T teat, w i t N o.osnoc oa K I L O G R A M S

C A S T H . « . R M ^ N > T I 9 A . C , C , U W « C - O

« A s m « ActtMtor piwcutirs n swrtw. I CM/CC I C . 1 1 - OQR 0 2 C . 9 S S T 0 P CL

C»lTICAL caotus f CMJ 0.2251 Tt 02 g.«M2«K 02

 ckiticat. MAts as a.3«**ac 01 titcmas

COtT ICAL MA*s ««G» «.na«SAF 0 9 oa

MULTIOLICATIna e « T f »

«.9«OC«E CC CO

c » « * 4 . A . F M A - U O . I J D 0 . 6 . C . U M > A C - < L

« * M » * '» aCtiMtoe e w o o o s II SOLUTION tc/cct c.11--?«-C . I M W £ 01

CM1 TICaL KBOIUS «e-Mi

).u«fic ct 0»«HI20fc OS "WHia c«tt»eAt. M n s « m u ( ca >n.c«i»t

C R I T I C A L M A S S <«CI

i.jtn*" 33 «.»•«»« 0»

MULTIPLICATION FACTCR

J.MtW 00 o.oonaaF 00

ease M . » . C M 4 - U * » . I O O O O . G . G . U N I > A C - O

0*N«IT» «r ACTtNlOC natcuos In 9ULUTICK «C"/CC» C.IIMt* a? c.t;."« ci C.M1HC et

C R I T I C A L M O l i n (CHI

l>M'*Mt 02 a.mix 02 9.5048TE 02

O U T I C A L M A S S ( « 6 l

J.*tt«J~. Ot J . l « « 1 « . 04

04

MULTIPLICATIOK FACtCM

0>9«0S2S CO 0.90000? CO 4|4ln» CMTIC4L MAS« IS 0.«32«0c CI KILO«WAMS

136

<€K;IIT JT Mii^iy c*«PttM>i IN ULUitOk

tG-/«"C » *s> 01 O.UAbOE ct O.^ilW oo «IM»l« C'lIIOt •«««

CMTICIL M»llf. «c««

>1 i. i«g*«. >.»IW C2 U ' M M ' 1 *

silica. »«K (Nit

m i u ^ a s o» t 5»€ -» ««

LTI<H.IC*T|q« r«CTt"

Ot OO i . m t v oo M«ttClc t-00 I S ,

« ,13? .S.S.P-C *\«l»* nr KIIMOT C.I«rCuMlS IN <o.unck « c»/rt l

o,n>-»; u ex e.i«<«c -t :.II4mc at co

CI*I TICM. HOIW IC«1

3.KIMC *2 M a.>n»r ox

MRICn. OSI M

J..M4IE OS ) . U * I « M

e.teect- OI I . M M I C OO OO co

- 1 v i r o i T i r a i «4«« i s a. ax m i a e i t i s

CAS* H».MO-!iF,l«M.S.S.P4 nEOSIll OP KTIHIKF. COWOUMBS IK SOLUTION lOWCCt

C.IUMF OX t.!M«3E Ct o.x«c4ee ot •.I1MSF OI C.S-'LL* OO

( • I T I U L PAOT«FS ICM1 4.HWC at 0*14122E OX OAXSSOXE ax t.T4T««t- ax

CDITUM. «S5 IMI « . I » « K ax « . * M I E ox e. iax««c os 4.MIH* OS «.IM»X o»

LTIPLKATION. FOCTC*

»I»!»U" CHITICNL ««S IS 92 «I11(»«S

•A. M • SF . 1 533 3 »S .S. HK«lt« if »CTiNt v: CCXKUM3 IN STLUttro (C"/CCI

c n TL CM. M«L« Idl C4ITI CM. «1W (N«t

»INI»«N C-<l TIC»L !S ».?»«"£ a? • tl!1C««S

"ULTIBL IC«TION r«CTia

• . l l » » * •2 1. •«*#* ai a»2oo»-F ax a.toac«r 01 e . u i « x Ot 3.I1TOM 02 4.SOHW as o.a«s*i« 00 h l W W OI 3* SAsSAL NT J . W I t ' * • C.IINOOC 01 a. »si m 02 • 4JKMN a^ I . 9 M I C CO C.«3I«1E CO 3. » » » » ' 02 at •.••ear*" CO

c » w OFHSITT «V ACT|N|DC COMPOUNUS IN SULOTICN I CM/CC I

O.LLTMJF OX O.!«JI«E at 0.»lt« 01 C.iih* :i

.I0.S.S.A-) CMt TICM. ««1II« IC«I

a. i»»wc ax o«xoaiac ox ». W M « ox :.»«rr 32

CM I TICM. « • « (nil

il.HMt OJ d.asaroE ot

MULTIPLICATION FACTC*

i.tMw ee I > « H I « * oa a.TMWE 00 a.MwsTsr oo

MINIMUM CRITICAL MAIS IS I.MHK 02 «tLCC»»MS

CAS* *.M.Paa-SF.|}3.S.S.A-C •TFMSITV OF ACTINITFC COMPCUNOS IN SOLUTION I C«/CC I

0.tl**0£ 02 O.SOX1AE Ot '.PtltAt "1 o. i i t>oe ot

CRITICAL NAOIVS (CM» A.I0STPC 92 0.XOX2IC ox iiinw 62 1.WtK «2

MINIMUM CRITICAL MASS IS 3.W1I 92 MlLCCRAMS

CMIIICM. MASS «K«I «.*TOOA* ox «.iniK oi a.21* we oa

MULTIPL ICATION FACTC*

<!.«««(>( O0 t.H17ff O0 S8 0*«0M«C 00

137

case H.>.M.sF.i<tts.s.s.*-i '•rusrn <"» actinic.r c»i »ic«c saoius «inc«. »«ss •u.im.K*ni% c cwruws IM sntutick (o D. low* a? oo Tt 3..£139b£ 32 3 .2132 IF 3.9M0SE OC c.2St»*E <it o.«astiE 02 J.tqw^ oi o.ooseoc OO C. 11 * "or Cl O.OOOS2E 02 OA f? (VIT IOL ««a;s is o.t>w»ss o? mtocnts

C«Sf N.aiW)-SF.lMM>S<S<>4 *«iSH* I* »CT|i«|Ot CNI1IUL MAOtUS IxlIICAL Mass NULTIPL TCATtON FACTC® COMPOUNDS IV SOLUTION (C*l (Ktl

-.1!»(«-? 3.IK6IE C2 0.13314? JJ «.9«i«e oo C<:«<1«E Ot 0.271SIE 02 OS O.OQM72E oo Ol O.SaTOSE 02 <J«I1M!< o« C . W M E CO «i«rw« onttrn *a«s is «.nii«c 03 >ko«m <1

case N.«<P*M.SF,19<l<5.C-a DENSITY OP ACTIMIOF COMPOUNDS IN SOLUTION

t CM/CC 1 C. 11 t w 02 C.«S3>aE SI a-i:T03E 01 O.U°NC Ol O.SS3TSE OO

CRITICAL naoius ICMT

O.OOQ29F 01 0. 131 TIC 02 •.Mint 02 o.astooe 02 0. 30IE 02

CHITICAL N»ss i«ei d.lTti*; o> 4.SMMF o» <1.15790€ 03 J.»»>TI5»T 33 d.lMHE oa

MULTIPLICATION FACTCM

00 O.OOOTSE O.VU19E 0.00500® co 3.00023E CO «.«»>* OO MINIMUM CRITICAL <«« IS 3.1T319E 32 KILOOTAMS

CAS- ta.M.CMO-sF.10 J.s.s.c-r 3FNSH* I» ACTINtft* COMPOUNDS IN SOLUTION IGMSCCI

M 0.!!3»E Ol 0.2-T03F Ol C.1I930E Ol O.HJTK OO

COlTtCaL Rantus CCMI *.S91«3T Ot 9.I09S1C 02 3.IV7VTE 92 0.3079FE 02 0.61244C 02

CttTICM. «»« l«Gl J? J.DM1IK 02 J.»3: 12 O.2044NE 9? K.IJiW 03

MULTIMLICaTEON FACTCM

0.100C9E 01 0.49322E OO a.oooesp cr O.OOOA2* 00 0.00024E OO MUM CRITICAL ««!S IS 0.102.NE 0»

CAST •a.M.p»a-sF.iooo.s>s.c-n DENSITY nr ACTINIOE COM FOUNDS 11 SOLUTION (cm/CC i

C.I1030F 02 0. !«374E Ol C.(-T03E Ol C.U930E Ol c.ss?*se eo 0«2fT03C OO

cniTtcaL aaotus ICM) U.40297E 01 0.8S39CE 91 0.131TAF 02 0.2M09E 02 0.4UI«f 02 O.T1874E 0?

CRITICAL NkSS IKOI o.avaoaF 01 3.1MWS )1 t.iralM 02 H.MT1IE 02 (t.H7J« OJ 0.34099C 03

MULTIPLICATION FACT CM

0.100CIF 01 0.003S6C ec «.«mtt oo O.OOOCIF 00 O.OOOOOC 00 0.990S2C CO MINIMUM CRITICAL MASS IS I .11H4E Ol MLCCOAMS

CAS" tia.nM-W.UMIiSiS.C-O »TNSIT* or ACTtNtn* C 3MP0UN0S 1*1 SOLU1ICN ICM/CCI

C.II1JK 0> O.St3Tae oi f.«r« ;t c.ns3oe oi 0.teaisp oo 1.CTUE CO

«IN|ML« CRITICAL MAF IS

CMITICac RADIUS I CM | J . a s s s j f o i 0.4AO73E Ol 0.1413V 02 0.2S406E 02 0.42436E 02 0.70416E 02

.«72t7£ 31 RILCCOAMS

CRITICAL MASS |l«l iiaaliirc oi D.I371K 02 o.ssorte 02 O.M937E 02 j . i m « 93 <3.37992E 03

MULTIPLICATION FACTCO

Oat0007* Ct 9.49KK OO ••win* co l.lMtlf 00 3.000S7* cc 0.994sac 00

138

CASE -<€il«IIT OP * C H « I X C T C W I : I I SOLUTION tcwcci

CillXC u;n»s ax a -t ae

CHTIOL »M>IUS tCMt 1.ITTMF et O . H M X 02 •»*S1«3F 02 1.IMI23F 02

O d I I C « W«l

J . i t m * * a s t.*oiM as j.nuir M

Ln«-KMim. ractai

O.tMOlC «| •.a "" O.VMSAE co

n>ti«v* 0 nit«i »»•« ts o» «aoiww«

CASE •«.«.« OEM SIT* OF ACTIMIOE cammos n SOLUTION w c t i

OtiiMOE ae a.ui«x ct C.2ACROE at c.itw«r at ce

.100.S.S.O-C OttTtca*. CAOiu-IC«I

a.K>m at a.tsezas 02 0.2T443E 02 S.«t»IC 92 3.WTSE 92

OUT IC«. MASS «««* 12 t.TWE «2 «.2I««K OS J.5WME SI l.ltt J»t M

LTIPLICATION FaCTC*

O.IMOJF at o.ns«x tc

C«- IT K«T MASS IS 0.2MM3E (2 «ILOC»»«I

CASt m>.MiH«.l3<S>S>Iil OOSIIT OF ACTIMItM UIMIWS !•> SOLLTICN t CM/CC I

T.UAKS: 92 : . S ! I U 5T C%I»«C; 91 ".U«6X "1 C.SIlUr CO

CHIT tCAL MAOIJS «CMl 3.RN»«E 91 3. IUAW 92 : .«S»]E 92 : .itime

LMIttCa. MASS net NtlSTJt 92 3 . U T W E U 3>m»Tt SA 1.M1IJE 3) a.nwit o«

•Na.tim.iCATia* •-Mttcfc

0* 19501 A. It e.tv»tt •.wikit ac C.CTWH C3 bfTM* CC MINIMUM C«l TIC At. MASS IS r n l E 92 KILOCBAMS

CAST O DENSITY OF ACtlNIOff COWOUS1 IN SCLLTtCN IO/CCI

0.1IA0CE 02 O.E31«3t 91 0.SACME 01 O.tlAME 01 o.jiiw aa

CRITICAL MOMS tCMt 3.U223IC 31 = .1S220E 92 9.2TA«4C it C.MISIE 92 1.««>T1E 92

CB1T1CA. MASS

».<M«Jc 92 M 4.1UW1 93 C.STOOJE «j 3.1A124C OA

HULTIPLICA1IQN FACTE

C.1IMX 41 I . W 4 M OC

o.mnc oo NININtm CM 1 TIC At. NASS IS C .2tX>«3 fc 32 Ktl JOANS

its ~i».t-«»-tiM.i;: 3 .s.i.v-u •LNSI1V OF AC TikiTM UWIUAL IN SCLLTICN TCA/CCI

CWITICAL *»AOIJ> ICN1 L4IIILA. «AS» t«61

CRITICAL MAUS IS " A IL >«*AM»

HIA.T1M.IC.AHQN FACTCM

'•IltMt » 31 :. i3i: IF :i 91 •. I 12 0.VRS41L : : 11 : liuni. 32 93 O.vwraJt r.ilaee; Ct 92 l.MMA : i (.«MI CO %SSIW -o : •-i<>M«f 32 '.IMSK 94 c. vwsw 30

CASI Mcn.f-MR-uM.ic is.s.t»-o JTNSITT RM ACTIMOF CON»UU«OS IN SOLLTICN ISMsCCI

:.ti <»ci :.«>» 9.24t«3e 3.11*45* 32 :i at ci 00

CHITICN. MAOIJS I CM*

3.T3ST3E 91 32 r.2»21it 32 • .«2l*'E C 2 3.7*»3Sfc 32

CHIT1C4. *ASS t««> 3.141 IBT <JT 3.SSSHL *.I»>boc :i L.MIME 91 M W i f t 9 3

MtA.IIMI.ICAl I CN F AC TON

1.MCWK s: 0.««SA«E l>WWt ct fcwmi «t MINIMUM CRITICAL MASS IS C.I4IUE 32 NtCJWANS

139

XkMTr r tcnuK I* SOL ITT CM ««M(CI

"M

ir-i.s.«~u UMIK«. •USUS

( C M *

r.tucv x : ..HJll 32 }<»1MK St 3J*S*U » :.iiH*r • INIMLM CKinCM. IS «tL.16B«MS

CilTK*.

>.?MVf OA -1 l.llHIt 9*

•tt.iin.ic»to> »a*.vo>

O'VlUK 0-MttUC Of

CASfc. ML>. CH1HA. K M

oe»stT» tm «n<4Bt. CMMOUO; |k SELL TIC* l«»iCCt 3.IUM at ti -J«u» oi i.utrt ci

•MIH» CMITICA4. MASS tS r.'AIITF U Ml

J.IIM*r 32 :<>;Mk 32 : . M U M .

OIIIU. 4 (<«l LtiM.K*n«k r*cna

e.HilK z< ).29<IE Z1 *««HMC 9C c i w a 3C

cast. HLm.»woe.i3ro».s.*-o OAMSII* UP tcitmsi

C A M U O ! IM SO.UICK COB4CC* CMITIC4L MMJS (CM*

M :.IM«lt 32 3 U W M I ot ->ret 32 MINIMUM C4|tl(M. oast IS 9.I944IE Cl MUK4WS

CUniCA. 44U

MAO* :i 3.I2VMI OA

LllMICAlUk FaCTOM

e.soAoac ::

CASK Jntllf UF AtTIMIO*

OIMPJAWOI IM K t c n o . K*4KI Miutcr e.i«it«t ca

Ckltltt MAOIrfS

:.I]HI<: 32 st

LMITICAL MASS IS '.IlilU It KILU3H4MS

C4IIICA. 4 4 »

:.llllk ;t !.«•*«* : J I.1T444C.

•WkllM-ICillCk FA*.TOM

SI S.MMIC J:

LA* MCM.MM«-UM. I -a R*1»L»» OF *CTLMW U«tHNM |M SCLLTIC* («*/CCI

MllJfe W C . S U H t ' I :i :<ituo 31

LMlTICA*. MAot*» l« .M|

:.«**(K »» ;>umt 3t ?.<«4»«t >t "A

A|kl*w> CMiticAL MASS ts :.irou( 3t 4ureM

?.9t3M»: a • m u c oi i«mnt n i.ium cc

CMITIC4L * M M t ion :>WM*K 31 :.imu 32 :a«nf( ct :.himf ot

CAITICA. «UT (K«l M M H t W l>UtMt Ot e j

C3

MUL TIPL1C4 tlOA rtCIC*

« . I M M Ct faWIIK M « 1 CO

MINIMUM CRITICAL MASS t* .1 S44AC 32 KILOeAAMS

140

•tensar* <r o c n w uo»s a» smuio. lOiCCI C.IIW r.sssiw :i u n rc rc Haw canic**. "O'.i n

( t i T i c * waaus tea* :» M

: .i>i»»f : . ai)Wi«

KltKA. uei

).t«»2tc is 1 . 3 W A 31

a.i::ai a 0.«*JS«k. K ss a.«cac jt

CASE •SIT* «F KtlMDt »s ik siunck ICMCI

I . I I U K s x o.-sjut ca auaitx aa O.IISJOE «a 1 ec c ec

Gnat teat. < low 3.»uut aa g^Msm aa 3.IMXM. M

•MAA%A C'LLKH WSS IS C - .'MIM 3*

,»rUTC 3 a ULOBMb

i IT ica. aass

3* 3 . I M J E W I.XHTtt W >«u>i ax i.iniK u l.IKMl. as

Lll«ucaltck racxa

a.i«9c*E aa

east m.» rfWH* .w» ac-o j w s m tw acriMoc c<i«uua; i». igunc*

I C * < « I

c.»»;ccr a ALNIBW* CHI IICW. MASS IS

ouiica. aaaotjs loa :.»na>t 3*

:.aotu»2e H atLJsa

cairic*. aass

3»

L r i K i c a n a K r a

a.«m% Jt

cast. o».t3r drtumMCo J » i l U » HIINIDt COWQwaii IK XUIIO IC»XCI

cwltl(.ac •«)I3I te«t i.HS'* IX

«iM«t» eaincaa. : 124 F 32

ass IS 3a aU.n>t«

I - IIICA. MS> u«l Lti*uc*iiOk raci

3.13CSCE SI

Its M.a.Fah-wi(l3>]i».i>ilWM:-<> octasitv <* aciiMioa CilOMtW! Ik SOLlTtt* IkXCCI

-.Itt'e* 3X alklaw cat IK«l MASS IS

caitiiaa. aaokn ICN»

C .«M11L >a «H(M>t«

c« ll ica. «US t«c» l.Mlllt

>u.Tin.lC«llCk Fat Tea

8.WMH X

•ifkilit OF octtartur UMOOIMt Ik WkVtltN (Ca«CC > u>li ICA4. *AOIM IC«I

r.ittr* a :.wi*tc » « W I W C*I«ICA*. <MM U AA MUMMAN*

C « I T I C A . 4 A S S tut i.jas'tt. 3*

•NLllKICMitk FACToa

hlMtll 91

CAW •«.•*• W I W OF A C T I M I D C

J S O M I T I O F T IIWCCI C. 10 _ o.so*fxe ct blNIX OI

»-0Va10000*aS«SaW-n cat Ticac B A O I U S «ca»

OVXOXOOF ox a.asaoae ox

aikltu* taitltH m » ts :.«*i« is atiMUiK

catTlCat MOSS l««l a.•»-.»!at >,» A a.%«Ttw: a*

MULT I Ft. ICATIRM FACT'*

oo •.twin oo

141

cast n.».rw •t*sm * K i m * >?>|ttCM. HMIIS Otitic*. •MLIIX.k«io« •«»»» ;R»FIWR IN <>T.<mci> IC«I K M I C J t C 1

c.n^te M •? ti C.5JIUS at W a.AT«« a? J.HJiJ1 ca at k as «.w«t« w - . I W -» J . i l M K J . » J » > V n 1 . W N F c%

«I«»t"C" K U K * . IS fctiUtf W «H*»*$

•**SItt <J» KtlHIBF en—•mwos^tg^ suTisk V

( . t ^ l V X « « . » • » * «

cm vtct. MMW I C M »

j.Mim at l.l>bME « •.ui^e J»>»I«|F 5®

•Ultll ICATtnv r«cm

kiNtlc at f ci

»t»-t-u« C'llKN. IS » »IIM»«S

•» KtMnt timnas n an. am OK ••nwy et ».;ii« M rt U l t a M t M

.1 jaa.s.s«»-r> Ttcac WIU5 (CM! S.MITM at ).urasc M

M

oatic* (•St j a n i i f as J.ltblT »j J. W*V>C II ).«tj**c at

««.>l>L I C » T I « k >tcit*

0.t 1.raK 9.

et

-ATWIMW* CRITICAL «ass is H •AACWT

ease Ml «.t«rl—|eaji M l i i t m «tr K t K I K

U N W W I N SOLUTION IPMTCI C.lt«<«F (i at r.2at«ct :i •.ll*HC « a.s*i*9e am

"IM^V" CvltKH «aas«

C a t T I C a t . a a a t u t ««l J.HWM! Ot •fctlSISSa its hiMIW »? a. assart a?

CMiTtcaL Mass toe » 9®

J . 7»*»-. '*£ J i J a l < * i « ' O I J.t^l" (1 >.l't>M»- 3*

avLtlUKmoo racTca

».IMC Cl cm oe re

ras* H.«^yi-aM.i«.I.I.Mt CTIlltM. aaoius <(W l»«5ltT FLT A C T I M I O C

C U R * C U M O S IM S O L U T I O N I P » « X I

mi»»*; -a at c.KiNt at at NIH»»V C N I T N < * « T< H R M N « *ILOCM«S

J.MWK » at •.tiMx as

otitic* aass ( * « t

J.TM4M 91 A > M « N OJ «<Wt(«t oi <».itaoK •*

M U L T I P L I C A T I O N - A C T C M

».«iHif aa «>«Niit aa >•«««« « la«tMlf ca

W V •La.fH^i.iM.t.f.*^' fHlt» « tctiaioc CONRTUMO* IW SOLUTION

I CM/CC I C .M*~*F AT O . ! « I * I ai tea* at C . I I M W a*

C»l TICM. cant us (C«l 1.IWW ».• M 0 . a a « x a « a x

CRITICAL oass 1(61

>.4i**«t a? 4.I»IHI O*

ML'I*icattoa racTca

i.M»r» eo >«*>*MI * *

W W R OlIICaL attl IS 0.1'<l>tc 32 «tLCti»*«S

142

• W I N E» actiwt CM TICK. * M D « OUT tea*. a« .FM. IC*TM ««CN» CIWOMS N S U N N ton m i »w#ct> i.UMW v «.I]«MF a? (.naTK «i »«T»TBc C.;MI«E at fcamr ax i . m M ! co C.MMC «( t.tMMi M «.!»««' Oa ».«tM*£ CO

r«w K a . r x - N h i N N ^ . ' - l "*««m a* KiiaiH H auniok icwtci

.:<ii«( M

c m T i c a » . s a n i u s teat a. IVIW «

a n i w . a«« ts t.it»*f n •>

•j t i i tcaa. «aass ( a c t

4 . | T ; M C « » a.9aa«c at j.iaaiK a*

L I M . K A T L L

J.T1W*

c a v K a a u r « « , | i , $ , t l t > 9 « « « 1 » » O r a c t i a a i o c Ix AtfT|» l*»*CC»

C . K W F ai C. It CMC Ot

cat TTcat AMIFC «Cxa

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Cast MU*. * m » » nr aCTixior roues ix snartoa «o*«cc»

CtKiMt «.«»•* %IW«» C.9S39SC

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xixtxwa C R I T I C at. at;: is o.M9*oe ot auncMm

LTIHKMNa ractc*

T2 OaOOMO* et 3.940*4* Ol OatOOC2> Ol Ol OaOOOatC ot a.laJTIC o< 0.09309C OO Ol t.m*w 02 J.»20aac 02 (•Him CO Ol o.2T|iar 02 o.oaosoc ot O.000cog ao oo •.ansae 02 J.ltlMt o? o. *ooaac oo oo 3.TOI4SF C2 4.«rSMt cs OaOOOOOS oc

casr O C M S * t* «ir aCTixinr

C M M M O S ix n.imn Oatt**OK. if biUMr ot C.2STOSS ot CallWXC Ct C.HJT* OO C«I»TOI oo

x|k|Mva C > I T | ( U xa«« is

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o»aotsoc oi OaOStSTe OS O.I SI Me 02 j.ntiat ••mix 02

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9 . * 4 * O S C C C O a O M O K O O o.ooraor oo

a n s m acsitm* m m tx mniok U M R I c.tiaiar w C.tiltM st C.2STOSC Ot c.iiosae «

.s.s.c-a CMticat. daiw tcxi

a . w w ot O. IVMIt os patoiooe » t&ss&u

c*ttic«. »•« too* ' t^irw* ot «.i*t*n «* O^ITSM 0> 3.010120 02 3:SH3 3!

M T T T L I I E U N K M C T M

oa toons ct

atai»vi co IT teat, xats is «,*tt««l ot «nMM«t

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Jl

M I K*TIV>

n s n.».nii ro.ioo«s.s«wae-c MIS IN V KTIHIDC c»T TIC*. U B I « OUIKIL WS^ • • H . ' I I R A « t e » eewcvas 11 soiwirx ic«> w*» «ca#cet

(.II ' IM^ OE *.L«>LFF W »• J.IMCI; CL -» j.imie w M a w s » c.7*Tf«E a *.nuir « a* M

OI^mi* niiicot. •»«« is *.]MX tawnwi

CaSF . I M . 1 3 ."• . S . S . U W C - q

» « « ! » l i r t n i n w C»« TIC*. MSIlB O.IT KM. •W.rMICltW c IM snLKTiOM text u t i lt»/CCI "v % n m t !» i.jx"*' mi i»IMCI' ci BM.'^E EI >.HH«TC K ^.LU^K •* ( .T IK I * OS o.7»»Ht at « *.«»a«se <m <r?

«I1I»«" C-'ITICM. * « « IS O* «ICQ«B»<»5

CAST M.»<MKW<IMN>S>S.INMC-« •I"NSI»» >JR ACTUM*** CMITIC*. wi«S exit tew. mimiCktnw r«cm CVMFTWNOS I I M.«N«M ICMI i<tt •W/CCI

C.I IMS* « M t l W *t t.ftkin M M M C K at a.!um ot ».iMM «t ai >.*«k#> c ( . M m at t.«ny u n aa c» IT teat. * « is a.jwi't as aitowtn

CASE )«: .s.s.u-o * i m w » acnwioM cainiM. twins ctiricA «»ss antmicanaN ntiii UAMWAS IN snLincN (cat «««» ISMMXI

t.i-*«e :.tH3ic 9* 9.»ias9t a* minimum mtiCH * » is m u m : h (Ilomwi

case mt.m>.ia.n»«*attrtwi »atin urn ACTINIBC cat TICAL atoms CM|TICA MASS MATtHtcattON FACfOa cowcotros t> «•«.»!« ON tea* l«U «CM#CC»

:.ir>at* 3.* ".wine os a-aaat*- at %t««* et {•suTM ct c.tttMi u a« c.nmi oc t.iuiji ei r.aaajTt » a.aaatnr oa a. iwwt OC •INI'o" ratticAt. «ats is n « IUN*m(

CMC IA».WI W.M*TT .M^NA •TONSIR* or tenant CRITICAL.AAM*I CMITIC*. MASS MULTIPLICATION *acm» IW aOLWTION «c» tut n u K i

t&ZZSl lll'SrZlX & S S S 3 S S S Z i i

MINIMUM cot TICAL MOSS ts 3.tat??t » aiLOowans •

144

rit.t.cw-.ie.n .S.S.P-O JthSITy OF *CT|KlOc ClVOtNO'i IN SlllbTIC*. «t«/CC I

:.IMC:'. -» :.'.<H3v Tl -i

nor. :: M- |<u« rmuoi »»5«J

C R I T I C A L l A O t U S (C*l •.'VMF 3 1 :.II9i>E 02 U.24M3E C2 ?.«M3tE 32 ".745ME 32

•:itl- 32 <ILOC»««

CRITICAL "ASS (KGI 3.238>>1F 02 0.6360TE 02 9.16062E 03 3.3980«E 03 C.99782E 03


S . t t l M E OO 0.99SS0E 00 9.997S1E 00 0.99873S OO <:.naa« cc

LAS* NL»«P»«-PP.l33 .S.S.P-O 3FNSIT* OF ACTINIOt CPITICAL RADIUS CRITICAL MASS MULTIPLICATION FACTOR CWI'0*.TS IN SOLUTION (CM) (KC) CiN/CCl

7. II .j *.7»AOOE 31 9.21*65? 02 e.iccciE 01 C.S310TT *1 0.1A10AE 02 0.62ST1E 02 0. 995*1 S 00 "1 -7.2S2BSE 02 0.16720E 03 C.«97T*E cc C.llAhOE CI «.»**3BE 02 3.A212SE 03 0.9906A: 00 C.S3193F C? C.7A7A0E 92 0.1087BE OA o.scaaoE OC »IM»U" CRITICAL ««SS IS 32 KILOGRAMS

CASi ML».OMR-»P.I933 .S.S.P-O OINSITr lie ACTINIOE C3MPOUNOS IN SOLUTION I GM/CC I

C.11A6CF C3 C.*>)|03F OI C.2«fc<J0E CI c.u*e9c ;i

COITICAL RADIUS (CM| ;.T(,32SF 31 <J. IA0S1E 92 3.25221E 92 C.AA247E 02 3.'M«2E 02

CRITICAL MASS IKGI 3.213A5E 92 3.62210E 02 0.16S92E 93 9.A1700E 03 3.1071AE OA


0.99992E OC 0.995ASE 00 0.99T70E 00 0.99670E 00 0.99e6IIE 00 »1N1*U" CRITICAL MASS II 32 KILOGRAMS

CASE HL».PMQ-PD,13953.S.S.P-O 11N5ITT of ACTINIDE CPITICAL KAOIUS CRITIC*. MASS MULTIPLICATION FACTOR COMPOUNDS IN SllLCTICN (CM> IKGI (l.M/CC 1

r. i i«f>:- C.TAS'SE 01 0.19919 F 92 C.10009E 91 c. i jigjc si C.IT7*6E 32 0.S7877E 02 0.993*3: 00 C.2Aft«j; ti 9.2*S7BE 02 3.IS3SSE 93 9. 99778E 00 ti <>.*2973E 02 3.3S090E 03 0.99881E OC C.S Jt<>3= z * 0."'5*26E 92 3.9S6IAE 93 0. 99896E 90 <INIMi|N CRITICAL "ASS li 3.19413E 32 KILOGRAMS

CASC HL»,».<-no,|3,?,5,«.o ir».SITY OF ACTINIOL

C J L W O J V O S I N S O L L T I C N C'-.M/CC 1 :.II-e*E ".'>».'' 1 AF Cl C.J114AC Jl h m ^ :i

IIMW CRITICAL MA'S IS

CRITICAL RADIUS I CM! :.i3*2it ?? s 0.23S51E OP " C.IOA6AC 3 i t.'TBASF C 2

32 KILOGPAMS

CRITICAL MASS • KGI :.«O40«it o? 3.I9?32E 0 3 3.E.ATAAE 0 3 3.21091E OA


o. S. 99A015 o.ssA8e>= o. 9<;se»-oc OC nc cc

CASE ML».P»"-OP .1 3; .S.S.A-0 JLNSI TV (IF AC Tl NI DC C IMPOUNDS IN SOLUTION t GM/CC I

c. l l raf lcr 32 0. 3A2I*E 31 C.::IC«E si C.llMJC* Cl

CRITICAL RADIUS C CM! 3. 1356AE 32 0.232AAE 32 9.34R26E 02 0.'6399E 32

CRITICAL MASS (KGI MULTIPLICATION FACTOR

9.5T63C6 32 0.IS8A3E 03 0.61696E 03 9.21818F OA C.9S98*: SO 3.99383= 00 0.SSA55S OC 5.99S6S: OC

MINIMUM CRITICAL MASS IS O.S'ftBOE 32 KILOGRAMS

145

1 .«/(C I -I'lCU -IMIUf IC«"I C « I T I C * . « « 5 3 «St • a T i s L i c a t t i N F a c T o t

"i fillet I-

:.jiii3t C . » J - » ' l f 2 2

3 3 3 . W 1 «E 3 S

3a

c . OC 0.4M9K 09 O . t t U H OC

OC

|T« IF « II •»! DC I' :'|1»1. -.All r. '1ITK*. ««S'i aULTIPtlOIIDN FACT1M »' I-. • . 1% SlLLtlCS IC«) <<<.1 « > -• -.i*«..i. '.iiiiu c:

-„ tl * • •J.afiA F. -3 « l.qwyt cr :i j.niDf DA 3C •I'.f.'JM r-i tlf ' - I« 1 ! !1 1 ?»

<"AV_ .LA.. 2 .S.S.C-O i'M«lt» 1C till >' fJlltCH J»L>1US CUItlC*. MASS «»ULtI«»LICATtl3»» FACTOR KI1"1 l-» •_UII.TII:N IC"»» »"C6» i i.—jzc t

I 1 - 3 - _ " * 1 - . A 3 1 : t : . I T C 2 A F 3 2 9 . « 9 < 9 7 S S 3 C .1 C I : . 1 u 7 » t 0 ? 3 - S . 1 C T A t 0 2 C O

- 1 C •3 J O . S O S a t E 9 C i i ' - ' : . - 1 r2 3 0 • » : : - . ->» ' • 3 - l t 3 . i s a s a e • * A C O

C VMI' tt ' I* "•.'-» .iLitMlHS

•>FNS1 I* »C M >1 r • i s I *. hi l\ I : i -I T 1 C At. U4IU1IS 1<-«| CUITICAL " A S S <« r. i aui TIOCICATI3N FAT TOO

-. U < - 3 . i 3 )•>: F ICCC1E n r « - s « ~ I - . 1 •">•* TF 3. lOOATf 32 oc - ' "* . r Cl 32 a.ssfee-jE OC 1 1 <• J?" "1 *.21tASf 33 o.wi'; CC " . ' ' ' - ; - i C 3«3AC I 3 3.4SBJH oe

1 M - a i ' i '

IV IF « T1 M 1 ' I T t d l W A J l U S CRITIC*, aass «a ti»LirA"Ti IN FA; 1*. MIL 1.11 <.«. <C«1 1KGI 1'.« /c r 1 - 11 • c 1 3 .A<)?2 .1 31 <•. 1: - c»-- 1 - • i "1 • . • » . < * . » ; ' • : 1 3.1 a36M 02 SC r « ' • i." 01 - . 1 i l S O f : ? 3 . I T a a i f 52 33 11=3: •>.'•> a a j F 32 0 .AF.2S01-32 ".flucT": — r £ < ~ . « 3 1 A J . ;.» 1 . 1 t * 6 2 A f 03 it ?.-12f 32 3. 1WT37I-3 * 3'. oc

• !•-1 « ' - M l ! H :i «iiu(.»-»«s

CAS-- HU ».OAW-pi'.! 7:30 .5 .s .c-u 3FNSITV OF ACTISI"' CUITICAL RADIOS '.U I T 1 C MASS «L«. T |T»L I C A T 1 T » C TO" CIWLWOS IH SHLOTI CN IC'I IO.I I 0"/cc1

r. 11 n r r? 1.ASi3iF } J 1.«'C9lt 31 C. 1C3W - J Cl '•.HJOSSt 31 1 .13TaJt C 2 O.OSAlTi e-; :i 1AQ2IE 02 3.JS7«JF 0? 0. KTSft-00 C.1|oj«e M C . 2 S A a 3 F 32 3 .-122-UF 32 0. <9C0C<)F 30 r. siTsr oc 3 . a 2 T 6 JE 32 3.1*6*0E 03 CO C.2S7C3t cn 0. "*331 7 E 02 3.37ajaE 33 cc • • - 1 1 - 31 KILOGRAMS

146

C A « ^ H I . « . T > » J - L > O ,T 1 , S . U 1 P A C - 0

UNitTY nr c >«uc*r.«s i s n n i . n o > ( W/CC I

t.iiaoc: r.-C.-i-JJJW 01 rt C.11533? c»

4IM|«V> C ® » » I C«l «**s t;

<«ITICX. RUIIIS K«l • • • •HMt 31 :.J»9Mf 32 sa

CRITIC*.

3.IIS1H 93 3.4DSA2E C3

MULTIR"|_ICATL IN F»:TL»

0 . 9 M 5 I " CC C . 9 4 » C = I T c.ss-sae a-; cc

MI.CW»«S

ttNStTY a« (CttMOC CMTICU. o«5IJ>. tin ICV. «U.TI>tKtlln FA1TOR r )»U(1JS-)S IN SXOII CK (CM1 KGI c r i :.r;ui cc ri 3.i-i02 03 a.9<j6C»- rj •. UTJf fj •.••iilf *».«2a6«»t 33 0.«"S= ce ;» c.6?-T3t 32 a.n«i«r o* oc

-1--1. y- ' - I n i l J ; - 1 ~ ? m i

CASE J53,S,S,UNP«f-r 1FNSIH OF »CIIMOS

C I M O U M U S IN s r a . N I T I . I(.«/CC I C.IIS:OF C2 St C.2«7-7ec Cl t . n s o o r 01

canicti »»;i

CRITICAL RA3IUS <c«> -.ICAS-F 52 J.IMJ5E 32 3.TS3S3£ 32 3.-.A29TE 32

32 KILOCbAMS

CRITICAL ««SS KCI

3.SSC3' 3? T.IMKst 33 J.12S3St 3*


0. cc C.99619E OO 0. dE 00 c.nuK oc

< L » . « • . • . - < • € » . | IC 3 3 , S . I . O N P A C - O

JtNSlTY IF arriM'i: C R I T I C A L A T A I J I ruiTtCUL MASS C O . J U J M 1 S I N " U A U ' K K «CM| <*G» 1 U*SCC 1

C . U 1 - : : ' " •>.ll«Hlt 32 3. s -i - . / I T 1 2 T 3 2 1.>17J7E 3 3 r. .•«-•*<- ri 3. "Mill 32 3.M3A1F 33 -i 32 • l i t ^ j i r m i i a i 1 « - . T I I 3.*» KILObVIAIA

0. sscsw: C. QOftSTf C.SSTetE C. <398263

or OC 00 CC

C A S E KLV.BMQ-UP. 100000.S.S.U-O lENEIT* OF ACTINIOE CRITICAL UStUS CRITICAL "ASS NULTIPl ICATtON • ACT'R COMPOUNDS IN SOLUTION «CM» <«CI (G»SCCI

0.1CC60E 02 1.36*6IE C2 » .1 . ' 01 C. CFT2F 01 0.73A37B 02 0.OA }«'':: 0* 0."<«*l>- 00 MINIMUM CRITICAL MASS IS ".222S7E OA KILOGRAMS

Mf.SITY 3F «CTIM3t (<IIK«t OADUs CWHICAL MASS MUL T IPL It A M UN FACTOR C IWiimuS IN UILUTICN IC«I <«&> I <.«/C' I 1 l«t.V » 31 l.iDISf 3? 0.IC5W Cl M i! c.is'Ase 32 3.dhB90t 52 3.99435= CC Z1 3.2-JSASt :2 3.2A0SQC 33 ;c r. il*t3-*i '.'.Ulif 3 .6S2*>0( 33 0. <5981 IE oc 32 3.1V2«i*>F OA C.SSAfctt 30

lIM'tu" ClTIOL ««A!i I? *ll.nt.u»i*i

C«sr ML».P«o-UP.l 3 3 .S.S .P-0 I T N S I T V W T C T I M O E ClVOC'JNtlS I N S O L L T I C N (r.M/cr 1

:.i !»»•:- :2 -.3M9V ci t.-HtlQ* -1 Mt»Mt Cl

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