or - . ty 2 . I OFT ORNL P 2033 ... --- . cm . EEEEEEEE 11:25 L4 LE > MICROCOPY RESOLUTION TEST CHART NATIONAL BUREAU OF STANDARDS -1963 + . ....:::.... > ORN f 20:33 ..... .. . . i 1965 MASTER . ... ABR 7 . an - -- ... : . .. MULTIPLICATION FACTOR OF URANIUM METAL BY ONE-VELOCITY MONTE CARLO CALCULATIONS* .. mscos John T. Mihalczo Oak Ridge National laboratory Oak Ridge, Tennessee 37831 ......... . . LEGAL NOTICE This report was preparod as an account of Government sponsorod work, Nolthor the United Statos, por the Commission, nor any person acting on behalf of the Commission: A. Makes any warranty or representation, expressod or implied, with respect to the accu- racy, completeness, or usefulness of the information containd in this report, or that the uso of any information, apparatus, method, or pronok dinclosed in this roport may not infringe privately owned righta; or B. Assumes any liabilities with respect to the use of, or for damages resulting from the use of any information, apparatus, method, or pronos diacioned in this.roport.. As used in the abovo, "person Acting on bohalt of the Commission" includes way oma- ployse or contractor of the Commission, or employee of such contractor, to the oxtent that such omployee or contractor of the Commission, or omployee of such contractor proparos, disseminates, or providoo accoss to any information pursuant to his employment or contract with the Commission, or his employment with such contractor. wewe Number of Manuscript Pages : Number of Figures : Number of Tables : *Research sponsored by the U. S. Atomic Energy Commission under contract with the Union Carbide Corporation. . ' nanyiko Moura Anun.io TDATORAMY DISTRIBUTION OF THIS DOCUMENT ES UNCIMITED . ..: VE i. ' ::: ' . AC YA PLN 3 . . . . WI 2 nei .. Running Head: One-Velocity Multiplication Factor Proofs to: John T. Mihalczo Oak Ridge National Laboratory P. 0. Box Y Oak Ridge, Tennessee 37831 . . . ia . . . . . . . 4155 . .. PR ., 1:1 .... . * . ** . . ::-- : MULTIPLICATION FACTOR OF URANIUM METAL BY ONE- VELOCITY MONAVE CARIO CALCULATIONS* :.. J. T. Mihelezo . . . 0 . . . . HRVA Was wolledo Cao ate . ..... ABSTRACT A method is described fox predicting the neutron multiplication factors of geometrically complicated configurations of un: eflected un- moderatad enriched-uranium metal from the results of two delayed-critical experiments in simple geometry, one with a nearly minimum surface-to- volume ratio and the other with a large surface-to-volume ratio. The · method requires two constants characteristic of the metal. These are the total collision cross section (Ed.) and the number of neutrons produced her collision (vp/2_); which are obtained from the two experiments by using So transport theory calculations with isotropic scattering. These factors, together with the assumption of 1sotropic scattering, are then used in 05R Monte Carlo neutron transport calculations to predict the multiplication factors. The method has been tested by predicting the multiplication factors of 21 different delayed-oritical configurations to within a standard deviation of 1.5%. tasca. 1... jamejo ... . Research sponsored by the USADO wder contract with the Maior Carbide . Corporation. NO YP** .. - -- 1 . .. . ...2: . . . Introduction ht - - ..... :. .: ................ . .. .....: . A wide variety of unmoderated and unreflected critical experiments with geometrically complicated configurations of 93.2% 235U-enriched urarium metal (n = 18.7 g/cu>; have been reported. (2-3) Some of these exo perimenta bave been analyzed by a many-velocity Monte Carlo method which provides as detailed a treatment of the neutron energy as the cross : section information will allow.27 This paper shows that if only the multi- plication factors of unreflected homogeneous assemblies such as these are desired, a simpler Monte Carlo treatment of monoenergetic neutions 15 adequate. This "one-velocity" method, summarized in Reference 7, has two advantages over the more detailed one: (1) only two Input constants : characteristia of the material are required and (2) the necessary computer time is reduced by a factor of four to five. It has the disadvantage, of course, that the only meaningful result that can be obtained is the multiplication factor. The method has been tested by calculating the multiplication factors for 21 uranium-metal assemblies that had seen made critical experimentally: ". They included spheres, cylinders, parallelepipeds, and cylindrical annuli, both separately and in certain combinations; arrays of cylinders in lattices; and one combination of cylinders, parallelepipedo, and a hemi- sphere. This paper presents the results of the calculations, which : are given in more detall elsewhere . . : : : Method of Obtaining One-Velocity Constants . . The constants required as input for the Monte Carlo calculations are the collision cross section, Ey, and the number of neutrons produced per 001111100, VED/EL, which stisly the one-velocity Boltzmann transpošt . . : ; 2: es *. . 1 3 : • •.., . . 11 IAM 11: C . equation for two experiments in simple geometry. One experiment should have a nearly minimum surface-to-volum ratio and the other a large surface-to-volume ratio. Although it le preferable that these be delayed- ; critical experiments, since then kopp can be measured more accurately and the proper neutron spectrum exists, the data from two subcritical experia ments will also give the required constants provided kort 18 Smowa ead the spectrum 18 the same as that in a critical system. The solution of the transport equation yields Ex as a fimction of vip/ for each geometry, and the values of Et and velit common to both geometries are characteris- . *tic of the materia.. The experiments used to determine the constants for the calculations ;** · reported here were 37.770-cm- and 38.087-cm-diam cylinders whose dinensions are given in Table I. Since the Boltzmann transport equation cannot be solved exactly in wylindrical geometry, the values of ve, and E. for the two cylinders were obtained from se transport theory calculations using the DDK coad with a 16 x 16 grid of space points describing the geometries and a convergence criteria, e, of/10~4. The results of the calculations are given in Table II. The actual experimental geometries were slightly ..:: under delayed critical, so the values of vi, obtained from the calculations (which iterates Vie until the multiplication constant 18 wity and evalum. ates Alve)/ak] were corrected to those observed experimentally. These corrected values or ve are also given in Table II. Figure 1 shows the corrected values of vip/Et vs Et for the two cylinders from which the values of Ex and VEE common to both cylinders are found to be 0.2385 cm3 and 0.371, respectively. One-velocity sa ulculations were also performed for a cylindrical' uranium-metal annulus with outside and inside 1 : ? • Table I. Measured Dimensions of Uranium-Metal Assemblies . Diameter (cm) Height of Radial Increments of 0-8.89 8.39-11.43 11.43-13-97 13.97-16.51 16.51-19.05 Avexage Uranium Density (g/cm3) Multi. . plication Factor Assembly cm - си cm CM cm . .::::....... 18.759 Cylinder 1 Cylinder 2 Annulus 17.770 38.087 38.090 OD 22.865 ID 2.626 7.635 - 7.790 7 0.9986 7.795 14.938 .640 15.131 .7.630 · 15.341 18.705 28.705 0.9982 :: I. .DC 1101 ::.16...::::"ibri a. The mits available for the construction of the assemblies included 8.89-cm-diam cylinders and 2.54-cm-vide cylindrical annuli having inside radii of 8.89, 11.43, 13.97, and 16.51 m, all in a variety of thicknesses. The over-all height of the assembled units varied slightly from section. to section. Based on Bere = 0.0068. - . ii: . :. . ..... . Hehe... BL613! I! . . . . . . 1 . 1 Trutnya:- -: 1 . 35... .. .... > Table H. Et and ve, from One-Velocity sc, Calculations för Cylinders and Annuli weise . . . e.com A. VE (cm23b . Corrected vee (cm ) En 17.770-cm- . 38.087-cm- 17.770-cm-: 38.087-cm- . Diam Dian Diam diam Cylinder Cylinder Annulus: :. Cylinder - Cylinder Annulus 0.050 0.128024 0.114513 0.117892 0.128002 · 0.114354 0.117681 0.128028d .100 0.115082 0.106532 . 0.108446 "0.115061 0.106382 0.108419 0.150 0.104165 0.099472 0.100530 0:204146 0.099334 0.100351 0.200 0.0948820.093268 0.093754 . 0:094873 0.093042 0.093586 0.0948948 .. 0.225 0.0907790.090272 0.090734 . 0.090762 - 0.090140 0.090571 0.250 0.086966 0.087519 0.087910 0.086950" 0.087394 0.067753. 10.300 0.0802.37 : 0.024270 0.082772" 0.080122 :0.082314 0.082623 0.01303262 0.350 0.6774215 0.077840 0.078225. 0.074202 0.077689. 0.078085 0.400 0.069016, 0.073678. 0:074183 0.069034 0.073577.' 0.074050 0.069053 0.600 0.053727 0:060487 -0.061554 0.053727 0.060409 0.061447 0.800 0.043784 ; 0.051098 0.052663 0.043775 0.051034 0.052567 1.000 0.036864'' 0.036858 . - i. - 1.200 0.031803 0.038753 0.040920 0.031797 0.038703 0.040839 2 * . ...... .... ... .. ... .. .. . :, ,Doli • . a. 16 x 16 grid, e : 10-4, DDK calculations ; b. ' These values are for the assemblies of Table I having kopp i. C. These values are for the assemblies of Table I having the experi- mentally observed values of koe They were obtained from the values of ver given in the preceding three columns, the calculated factor : A(2)/ak, and the values of Bopp reported in Ref. 1. a. Values determined from 8,6 calculations. .............................................................................. *:::.. - me.. . Ó, ORNL-DWG 65-539R4 0 17.770-cm-diam SOLID CYLINDER --- o 38.087-cm-diam SOLID CYLINDER A 38.090-cm-09, 22.865-cm-ID - ANNULUS * URANIUM SPHERE 100 · 31:34 : -- 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 by (cm') ..... : .. - too.. . . .. • S ;'-,,niin ... ...; ... : . e rn diameters of 38.090 and 22.865 cm, respectively. The aimensions of the annulus and the results of the calculations are also given in Tables I and II and in Fig. 1. They show that values of Et and vac/Et common to the 17.78-cm-diam cylinder and the annulus, 0.2292 cm2 and 0.393, are almost identical to those obtained from the two cylinders and indicate their in- sensitivity to the shape of the assembly. If one of the constants is already known, the value of the other constant can be determined from a single experiment. To demonstrate this, a value of v_// = 0.4, calculated: by Carlson and Be11 ***. for a critical sphere having a radius of 1.9854 mean free paths, was used to determine for the 8.718-cm-diam uranium-metal sphere (Godiva I) of LASL.? Since the 235v enrichment of Godiva (93.8 wt% 235y) and its uranium density (18.75 g/cm3) are slightly different from those of the materials for which these calculations are being made (93.2% and 18.7 g/cm3), small corrections to the constants obtained were necessary. The collision cross section was reduced by multiplying it by the ratio of the uranium densities, and the value of Vap/, was' reduced by multiplying it by the ratio of the enrichments. The latter correction assumes that negligible 2500 fissions occur in these assemblies. The corrected values of Eand ven/Er are 0.2271 cm -and 0.3974, respectively. The results of further transport theory calculations, reported in Table III, show the multiplication factor to depend only slightly on the values of the constants within the range established by the above geometric combinations. Transport theory was used for determining the constants in preference to the Monte Carlo method because of the large statistical error, 1% for reasonable machine time, associated with the latter. *** .. - . ..::. ... I m . im NAL . .: L ATES: 28.8 . :. .. ble HI. Dependence of Calculated Multiplication :: :: Factors on the One-Velocity Constants insa Calculated Multiplication Factors for Critical Geometriesa 17.770-cm-diam Cylinder Annulus Source of Constants : (cm ) VER/ ......... 0.3974 : 0.9977 :: 0.9973 z Uranium Sphere : 0.2272 17.770- and 38.087-cm-diam : Cylinders 0.2385 0.371 0.9991 : 0.9936 17.770-cm-diam Cylinder and Annulus 0.2292 0.393 0.990 0.9980 . . T ::.. San, € = 21-4, 16 x 16 grid. See Table I for dimensions and experi- mental mul iplication factors of the assemblies. . :: .. - ccm:. 1 . .:: . 1 : . .. . ' ... . .' 1: 0 . lo The determination of the one-velocity constants by the solution of the Boltzmann neutron transport equation for two delayed critical geometries has the advantage that knowledge of the fuel-material properties is not required. It is not necessary to go through the cumbersome tasks of averaging the cross sections (which may not be well known) for the material over a neutron energy spectrum (which also may not be well known) and of correcting for the effects of assuming isotropic scattering. . A . .. Monte Carlo Calculations of Delayed Critical Assemblies Method. The calculations which used the constants from the S2 80- lutions were performed with the 05R Monte Carlo code which has a geometry routine that divides space into parallelepipeds and describes the material. boundaries within the parallelepipeds by quadratic functions. Independent functions can be used within each parallelepiped. The 05R code calculates the spatial Assion distribution from a batch of source neutrons put into the system on some assumed initial distribution. This resulting fission distribution is then assigned to the succeeding batch of neutrons and a : new fission distribution is obtained. This process is repeated until the spatial effects of the assumed distribution disappear and the desired statistics are obtained. Since, due to statistical fluctuations in the spatial distribution of neutrons in each batch, it is difficult to deter- mine convergence by examination of the fluctuating source distribution, the so-called matrix method is used to determine spatial convergence. If Fly is the probability that a neutron born in region i produces a neutron in region j, a matrix le formed whose elements are Fus. The batches with the nonconverged source distribution provide useful information for the , ..:: :: :: : 1 - , ---- ---- , LAZA - . • A . . :.: . . * . CLASSESTION . . . 13.10 . . 1 ".. . 1 . . ..:-- - - ., - • , - - calculation of F., if the system is divided into a sufficient number of regions. The source distribution obtained from the first batch is iter- ated with this matrix until a converged source distribution is obtained. The nwaber of iterations required for a converged source distribution 18 the average number of batches that need to be calculated before spatial convergence is obtained. The desired statistical accuracy of the results determines the number of additional batches needed. Since for unrellected uranium-metal assemblies the average number of collisions before leakage is about two, the initial source distribution is not important. ' li * * -- + - - --- The multiplication factor is computed by two methods: the batch method and the matrix method. The first calculates the ratio of the number of neutrons produced to the number of source neutrons in each batch and averages them over all the batches using the matrix of Fry to determine when the effects of the assumed Initial source distribution have disappeared. Only subsequent batches are used in computing the average batch multiplication factors. The second, or matrix, method di- vides the assembly into a number of regions, computes the probability that a neutron born in any region will produce a neutron in any other region, forms a matrix of these probabilities, and calculates the multi- plication factor;; Whir ) is the largest eigenvalue of this matrix. The multiplication factor computed by the matrix nethod was always within the standard deviation of that computed by the batch method. The multiplication factor as a function of batch number for a de- layed critical uranium sphere, Godiva I, 18 given in Fig. 2 assuming a - . . .- . --- -- ten . ; ORNL-DWG 65-5863R SOURCE DISTRIBUTION: UNIFORM MULTIPLICATION FACTOR: A MATRIX METHOD: 0.9955 BATCH METHOD: 1.0005 + 0.009 (FROM BATCHES 5-30) MULTIPLICATION FACTOR colº 0 0 0 . 0 5 .: 10 .15... 20 BATCH OR ITERATION NUMBER 25: 30 . . . . - 2 WC . . SCHE*7:01 . 1 1 ...:: 12 - - - Us . $700 ... uniform Initial distribution in space. Also plotted in this figure 1s the multiplication factor for the different iterations of the matrix of Fig. The matrix iteration Indiçates that the effects of the assumed source distribution on the multiplication factor disappear after iteration five and that the source distribution converges after about seven batches Results. Since, as observed in Table III, the variations in the three pairs of one-velocity constants do not significantly affect the multiplication factor, the values used in the calculations of the critical ... experiments were Et = 0.2271 cm+ and vp/ER = 0.3974. Some of the ex- periments' calculated are 1llustrated in Figs. 3-5, and the others are : described in Table IV. This table also gives the multiplication factor calculated by the batch method and, for most of the experiments, by the . matrix method also. The values of the multiplication factors of the 21 experiments calculated by the batch method are between 0.971 to 1.028, with an average of 1.002 + 0.014, and with the statistical errors of in- dividual values (standard deviations ) ranging from + 0.009 to + 0.014. The average of the multiplication factor for 16 experiments calculated by the matrix method is 1.001 + 0.015. : The differences between the calculated and experimental multipli- ·cation factors are either statistical or result from errors introduced by differences in the spectra of the various assemblies. The close agree- :ment of the calculated and experimental values implies strongly that the differences are statistical. . . . . . .. - - 1.1 .. 」. : [ " . i i. . .1中 ​·書 ​·1、 在 ​. 114 T ry H : i 7 . i ni 、 ; w 在本 ​i. . . . 年三 ​ - - 1F 售出 ​: “ 中 ​|) 再 ​; * .* * , * i . ... more more........... TE: M : . : : . دم "مه . و ا .. ودون: ا .. . . . . ... .. .و به .. .. عدم . ,..*,.د .... - - - - - - - - - - - - - . د سه۱. مبتس مه ده .همه م امی - - با سر و .دک سكسسكمصمم می ... .محم... 16 .... Table IV. One-Velocity Multiplication factors for Vranium-Metal Geometries . : 1.0 1.022 • Multiplication Bactori Datoh Matrix Geometry Methodb Method Uranium Sphere Dimension 1.005 2.013 1.003 0.995 1.015 Cylinder, 38.10 cm diam x 7.65 cm high 1.028 Two Coaxial Cylinders · Dach 38.10 cm diam x 6.04.cm high, flat faces separated 12.27 cm 1.002 . Each 17.78 cm diam x 7.31 cm high, flat faces separated 0.86 cm 0.986 Cylindrical Annulus, * 38.10 cm OD, 22.86 cm ID, 14.98 cm high. 1.020 1.014 ::. Parallelepiped, 12.70 x 12.70 x 23.19 cm 0.996 i 6.994, Iwo Parallelepipeds8 Each 20.32 x 25.40 x 7.94 cm, large faces separated 12.45 cm 1.014 1.008S!* Each 20.32 x 25.40 x 5.08 cm, large faces separated 0.97 cm 0.997 .. 0.994 1X1W! Cylinder and Cylindrical Annulush i 1.007 :0.999 .... z PAA:Till - - - - - - Annulus: 38.1 cm OD, 27.94 cm ID Cylinder: 17.78 cm diam Each: 10.11 cm Kigh · Cylindrical Annulus and Parallelepiped ia . 1.01 . . Annulus: 38.10 cm OD, 27.94 cm ID Parallelepiped: 12.70.cm square Each: 12.98 cm high Cylindrical Annulus and Two Parallelepipedol Annulus (two sections combined): 38.10 cm OD, 27.94 cm ID, 12.98 cm high ' - 14.. in · Upper Section Parallelepipeds: 12:70 cm square No. 1, 7.62 cm high; No. 2, 11.18 cm . sh T!! .•'.. Lower Section 094%!!!ATION. .. . , 1 ". ... . .. ..... . . .... : 70!!!*;... ...:.:.:./in... 17:18: noriniai: .. .. VC Dable IV. (Continued) . : . Multiplication Factora Batch Matrix Methodb Method : . - ; Array :: 0.975 1.0.997 1.004 :..; - 0.966 : 0.993 1.001: ::: 0.993 11.51 : 5.38 21.48 16.77 ... 0.995 - . 3.95 10.5 :.. . ! Geometry Three-Dimensional Arrays of Cylindrical Units? Unit Unit ... Surface Unit Diameter Height Separations Mass . (cm) (cm) : (cm (kg U) : 2 x 2 x 2 11.49 8.08 15.7 .. . 11.51 10.77 21.9 3 x3 x 3 10.5 . 6.36 : 20.9 4.4 4 11.51 ...5.38 x1 12.49 10.77 1.52 20.9 . 2 11.49 20.77 20.9 2 X 2 X Each unit a 11.45-cm-diam x .. 5.38-cm-high cylinder between z two 9.16-cm-diam x 4.32-cm- • high cylinders 2 x 2 Each unit a 9.12-cm-diam x '; 4.32-cm-high cylinder between two 11.49-cm-diam x 2.69-cm- high cylinders Eight units of various shapes arranged in a circle around an irregularly shaped centerpiece. 484 26 ADIN 0.988 0.971 0.993 0.997 1.010 3.89 NN 15.7 UR 0.977 . 1.022 1.017 0.9971 . .. 1 . a. 12,000 neutron histories in 30 batches; Et = 0.2271 cm ; vel = 0.3974. Uniform initial neutron source distribution except where noted. The experimental values of the multiplication factors varied between 0.998 and 1.002. . b. Statistical errors of individual values (standard deviations) vary from t 0.009 to $ 0.014; the average of the batch multiplication factors for all the different geometries is 1.002 to 0.014; the average of the matrix multiplication factors is 1.001 – 0.015. The overall average 16 2.001" + 0.015.. . • Point source. Cosine source. See Ref. 2. IRepeat of calculation with different initial random number. "mig. See Ref. 3. h. See Ref. 6. See Ref. 5. j. Equal in three dimensions : k. See Fig. 3. duo . See Fig. 4.. m. See Fig. 5. d. e. ở ở 6 6 6s is si .. . . ..... . :..... . .. . . - . -- --- :18 . . 2.1. .. ..in ' . 3 Conclusions: The one-velocity Monte Carlo method of calculation has been shown to yield multiplication factors which agree with the experimental values por delayed-critical unmoderated and unreflected enriched-uranium metal. in complicated geometries to within a standard deviation of about 1.5%. Considering this accurecy, the method should be useful for predicting the multiplication factors of complicated configurations of unmoderated and unreflected uranium metal of any enrichment, of unmoderated and un- reflected plutonium metal, or of homogeneous uranium solutions. The simplicity of the method lies in the fact that the two input constants required can be obtained from two delayed-critical experiments in simple geometry provided that the neutron energy spectrum is the same in all cases, or from two subcritical assemblies if the multiplication factors have been accurately determined and the neutron energy spectrum is the same as that in a critical assembly. : : .. 1 .. . . Acknowledgment The author wishes to acknowledge the assistance of J. Knight and E. Whitesides of the Central Data Processing Facility at Oak Ridge in , performing the transport theory calculations and to G. W. Morrison, also. of the CDPF, in carrying out the required programming for the Monte Carlo calculations. The advice of D. Irving of Oak Ridge National laboratory in explaining the OSR Code was invaluable. menonton .. :- :: :: Ki ... : .. ::-1::: angin . - References: within 2 min med samma t j 1. G. E. Hansen, "physics of Fast and Intermediate Reactors," Proc. of a Seminar, 1;:453 TAEA Austria (1962). John T. Mihalczo, "Prompt-Neutron Mfetime in Critical Enriched- Uranium Metal Cylinders and Annul1," Nucl. Sci. Eng., 20, 60 (1964). 3. John T. Mihalczo, "Prompt-Neutron Decay in a Two-Component Enriched Uranium-Metal Critical Assembly," Trans. Am. Nucl. Soc., 6, 60 (1963). 4. John T. Mihalczo, 'Neutron Phys. Div. Ann. Progr. Rept. for Period. Ending Aug. 1, 1963, ORNL-3499, vol. I, p. 64, Oak Ridge National laboratory (1963). 5. J. T. Thomas, "Critical Three-Dimensional Arrays of Neutron-Interacting Units, Part II. U(93.2) Metal,". ORNL IM-868, Oak Ridge National Laboratory (July 1964); J. T. Thomas, Trans. Amer. Nucl. Soc., 6, 169 (1963). J. T. Mihalczo and D. C. Irving, "Monte Carlo Calculations for Enriched Uranium Metal Assemblies;" Trans . Amer. Nucl. Soc., 1, 287 (1964). 7. J. T. Mihalczo, "One-Velocity Monte Carlo Calculations of Uranium-Metal :: Critical Geometries," Trans. Amer. Nucl. Soc., 8, 201 (1965). 8. J. T. Mihalczo, "Multiplication Factor of Uranium Metal by One-Velocity Monte Carlo Calculations," ORNL-IM-1220, Oak Ridge National laboratory (1965). 9. W. J. Worlton and B. G. Carlson, personal communication. 10. B. G. Carlson and G. I. Bell, Proc. Internal. Conf. Peaceful Uses of Atomic Energy, 2nd Geneva, 1958, 16, 535 (1959): 11. D. C. Irving, R. M. Freestone, Jr., and F. B. K. Kam, "05R, A General Purpose Monte Carlo Neutron Transport Coåe," ORNL-3622, Dak Ridge National laboratory (February 1965). . .m" norimissima.... na iniciatia doamnare' . ..:-.' Fore.. . Ato . . .: 204 10 Figure Captions ... : Fig. 1. VER/Et vs Et for Several Enriched Uranium Metal Configurations. Fig. 2. Multiplication Factor vs Batch Number of Iteration Number for a :: Delayed Critical Uraniim Sphere (Godiva I). Fig: :3. Three-Dimensional Array (4 x 4 x 4) of 10.5-kg Cylinders of Uranium Metal. iii.... . Fig. 4. Three-Dimensional Array (2 x 2 x 2) of 15.7-kg Units of Uranium Metal. Each unit consists of a 11.45-cm-diam x 5.38-cm-high cylinder between two 9.16-cm-diam x 4.32-cm-high cylinders.. Fig. 5. Critical 93.2% 235U-Enriched Uranium-Metal Assembly with Hight- Unit Upper Section Around an Irregularly. Shaped Centerpiece (Inset). The unit at the top of the photograph is an approximate parallelepiped whose base 18 12.70 by 12.70 cm and whose height varies in three steps (13.05, 13.44, and 11.15 cm, front to back); the opposite unit is a parallelepiped with a 7.65 by 12.70 cm . base and a 8.91 cm height topped by a 9.14.cm-diam by 4.32-cm-high cylinder; the four small cylinders are 8.36 cm in diameter and . 12.98 cm high; and the two large cylinders are 10.48 cm in di- ameter and 12.35 cm high. The centerpiece, which penetrated the hole in the support diaphragm, consists of a 20.48 cm diam by 2.59 cm cylinder topped by a 5.71-cm-high parallelepiped having 12.70 by 12.70 cm. base and in turn by a hemisphere with a 6.07 , cm radius. ; ..... ........... " " . .-*. marec-wow- END re we DATE FILMED 1 / 18 / 68 .