'B -1 s L -D o c tA nl e IA -s Awe - cc DocKr -tort DE _LPS FIED pcE 88b3y2A st l'1 HC___ -2 HS DECLASSIFIED IV $I 2C 1 By r-1 H C'_ R CF TF CRT TO TEE PRFSID7'T IATICNAL ACADP 4Y OF SCIMTC S by the Academy Committee on Uranium r ovember 6 1941 UtdTtD ST Your committee appointed to advise with regard to uranium fission begs to submit the following supplement to its reports of ay 17 and Tuly 11 1941 The special objective of the present report is to consider the possibilities of an explosive fission reaction with T5235 The importance of this investigation lies in the possibility few years the use of explosive fission may that withi become the pr dominant factor in military action Since our last report the progress toward separation of the isotopes of uranium has been such as to make urgent a consideration of 1 the probability of success in the attampt to produce a fission bomb 2 the destructive effect to be expected from such a bomb 3 the anticipated time before its development can be completed and production under way and 4 a preliminary estimate of the costs involved 1 Conditions for a fission bomb fission bomb of superlatively destructive power will result from bringing quickly together a sufficient mass of element U235 This seems to be as sure as any untried prediction based upon theory and experiment can be - L- 1 oc Ar-Ae VN4S Av v- ricolh boc- L4r gn DErins'SIFIED poE 3go32A C- eS r' NS DECEASSMED M m' 1 H r $1201$ _NA Cur calculations Appendix A indicate further that the required masses can be brought together quickly enough for the reaction to become effidient The destructive effect of the resulting fission explosion should be equivalent to that of vastly larger masses of chemical explosives Appendix B 2 Destructive effect of fission bombs a Mass of the bomb Appendix A The mass of U235 required to produce explosive fission under appropriate conditions can hardly be less than 2 kg nor greater than 100 kg These wide limits reflect chiefly the experimental uncertainty in the capture cross-section of U235 for fast neutrons it is difficult to improve these data until considerable quantities of the separated or enriched isotope are available Because of the greater de- structiveness of the larger bomb however the question of size between these limits is not one of major importance b Energy released by explosive fission Appendix A Calculations for the case of masses properly located at the initial instant indicate that between 1 and 5 per cent of the fission energy of the uranium should be released at a fission explosion This means from 2 to 10 x 108 kilocalories per kg of uranium The available explosive energy per kg of uranium is thus equivalent to about 300 tons of TNT Doc ArHe lA4 wGrica Doc co w ev oEC AS REW fly pcE 8%b32A Rs U ' MS DECLASSIFIED 5120ig Bf %- y Yti1 H C Destructiveness of a fission explosion Appendix B c The destruction caused by a bomb will depend upon the magnitude of the pressure wave produced in the outer part of the devastated region For an explosion of so short 11 duration as a fission reaction a considerable part of the energy will be dissipated as heat Taking this into account we estimate roughly that the destructiveness of a fission explosion in air liberating the energy estimated above should be equivalent to about 30 tons of TNT per kg of U235 would note that this conclusion differs from a reported conclusion drawn by G I Taylor in England which gave the destructiveness of the uranium as equal to that of the TNT delivering the same energy Not having seen his calculation we are unable to judge its reliability and experimental data on such super-energy explosions are entirely lacking It is known from experiment however that very all masses are less effective than slower explosions of the same energy involving larger fast explosions involving Certain calculations footnote 2 Appendix B would suggest a much smaller effectivness for the fission explosion masses 'rte thus favor the more conservative estimate made above It is possible that the destructive effects on life caused by the intense radioactivity of the products of the explosion may be as important as those of the explosion itself - 4 s L -D o c u l e vN DECVS F1W BI -ncE 38b3 q2Afz v rican Doce tmert HS DECLASSIFIED $ a 0 $ Ytii H G By Ln C 3 Time required for development and necessary a hin pr oduction of the Amount of uranium needed Appendix B Since the destructiveness of present bombs is already an important factor in warfare it is evident that if the destructiveness of the bombs is thus increased 10 000-fold they should become of decisive importance The amount of uranium required will nevertheless be large If the estimate is correct that 500 000 tons of TNT bombs would be required to devastate Germany's military and industrial objectives from 1'to 10 tons of U235 will be required to do the same job b Separation of U235 ppendia C The separation of the isotopes of uranium can be done in the necessary amounts Several methods are under develop- ment at least two of which seem definitely adequate and are approaching the stage of practical test These are the me- thods of the centrifuge and of diffusion through porous barriers Other methods are being investigated or need study which may ultimately prove superior but are now farther from the engineering stage c Time required for production of fission bombs engineerAn estimate of time required for development only very ing and production of fission bombs can be made roughly at this time - 4s OGtArif h#S t DECLFSf'FIED -pcE 990 B 01 HC AwtericaN DocetwterI HS Y DECLASSIFIED $I 20 f$ - C RA_ If all possible effort is spent on the program one might however expect fission bombs to be available in sig- nificant quantity within three or four years 4 Rough estimate of costs Appendix C The separation process will probably be the most ex- pensive and time consuming part of the work required to produce fission bombs The estimates in Appendix C indicate that unless some new method should appear a cost of the order of 350 000 000 to $100 000 000 for building the separation plant For its operation large quantities of electric power will also be required should be envisaged The other costs in connection with producing the bombs will probably be smaller of the order of $30 000 000 It will be understood that these figures represent only the roughest estimates since the scientific and engineering data needed to make them more precise are not available Immediate 3equirements Though eventually the funds needed for carrying through this program to its military use are thus large the immediate requirements are relatively moderate before any large sums can be spent at least the following work must be done 1 Building and testing of trial units of the cen- trifugal separator and the diffusion separator S T o 4s A rv% e v Ae er ca % Doc Kmt % DECLSSS FlED WE 88b3qq2A - M S Bi 01 HH_ IRS C11_ DECLASSIFIED Sr2or8 re 2 Securing by the most immediate method of separated TJ235 for physical tests of samples on spontaneous fission in U235 and on the capture cross-section of TJ235 for neutrons 3 Certain direct physical tests including a ex- periments on inelastic collision of neutrons in U238 and b measurement of the energy range of fast neutrons for fission of U238 4 in the meantime groundwork on the engineering of the isotope separation plants should be started so that the plans can be ready when the requirements are more exactly known This program part of which is already in hand should have available now some millions of dollars the exact amount of which can-be estimated better by the working committee on uranium under Dr Briggs Looking toward maximum speed and efficiency in carrying through such a program we would note that the isotope paration has reached the development stage and should be placed under the direction or a competent aevelopment enEinaer This development program must be coordinated with an intensiF 1 4S ' 1J O L LC 1 e V% AvytriCarl boc- Lkr tn DECL Ar'flED ToE YtiIHG _I 4S C211721 t1ECLASSIflED 88b442A-S B7 8rzor8 -S1 01 H I -PA Pet- Sa For best research progress we would strongly recom- mend the selection of certain key research men of proven ability and integrity to whom would be assigned certain major research tasks and adequate funds to be used for these tasks according to their best judgment For satisfactory coordination of the research and development a reorganization of the entire uranium program may be called for Such reorganization should be given prompt and careful attention by the appropriate administration officers Conclusion The possibility must be seriously considered that with- in a few years the use of bombs such as described here or somethin similar using uranium fission tary superiority Adequate care may determine mili- for our national defense seems to demand urgent development of this program Respectfully submitted with the unanimous approval of 0 E Buckley 1 Chubb Coolidge Kistiakowsky Lawrence W K Lewis D G B E 0 a S Mulliken J C J H Slater Van Vleck Arthur H Compton Chairman National Academy of Sciences Committee on Uranium s Docir1e n -S 4o zriCah boGkY n DECLASSIFIED 88b Bf Yti1 H G y2A- HS I Cal V DECLASSIFIED $1201$ 4s 5OC-L tr'-le v% rS vHGr CC V% 1 0 C_ -L r e 1 DEILPS°'FlED T cE M8 3 y2A-HS DECLASSIFIED Conditions and Effioienc Van eo an 1 of Fission Explosion Comp on Critical Size a The condition for a chain fission reaction is that the number of neutrons emitted by fissions resulting from capture of the initial neutrons shall exceed the number captured and lost If the captured neutrons all produce fis- sion and the loss is due wholly to escape from the mass of as is presumably the case for U25 there is a critical size of the mass above which the probable gain of neuuranium trons exceeds the probable loss If the uranium forms a sphere its critical radius is of the order of magnitude of the average distance from the point of origin of a neutron to the point of its capture Independent approximate calcula- tions by various physicists give results in good agreement cf Footnote 1 and which are o_' substantially the form R - k'flt lf ere 3 is the critioal radius 1 k is a quantity of the order unity involving the average number n of neutrons emitted per neutron captured It and if are the mean free paths between collisions and before capture respectively calculations is that of Fermi who obtains k - 1 82 In n Typical of these 2 sL hoc- LAmf vN Avv%erica v% bocKw en - DEMLSS'FIED -poE 88b3 y2A- MS By Yh HC ' 4S Ca _ DECLASSIFIED 8120 18 i r m r4 -Kvs' - 3KY -2- If the uranium sphere is surrounded by a shield of material which scatters the neutrons that escape so that there is good chance of their return the critical radius is thus reduced by approximately a factor of 2 and by a greater ratio if a surrounding medium of higher scattering power can be used of Footnote 2 b The greatest uncertainty in the value of a arises from the uncertainty of the mean free paths These paths are usually described in terms of the cross-sectional areas of the nuclei of the uranium atoms with the following relation between the cross-section and the mean free path 3 c t - 1 hat and C-f - 1 Nlf Here 6t is the total cross-section for collision with a neutron jf is that for capture of the neutron resulting in fission and N is the number of uranium atoms per cm 3 Simi larly we use the scattering cross-section S3 which refers to the deflections of a neutron without capture Thus Tt 6s 6f- 4 Determination of Fission Cross-Section f is pure U235 is not available at present fission cross-sections can only be measured in commercial uranium containing 238 and 235 about in the ration 140 1 Since 238 decomposes only for fast neutrons the fission observed for 4s1 Mor t rye vN4-5 Y e %r' of o o K rv o DECIASSIFIED DoF 882A-HS of Y11 H C DECLASSIFIED 21201$ RS Cz' must be attributed entirely to 235 The corresponding fis- sion cross-section is 4 x 10-22 om2 the relevant This is however not for a superbomb of pure 235 as the quantity neutrons coming from the fission of 235 have energies of the order 106 volts and usually will escape before being slowed to the thermal for neutrons region of the so what is needed is the cross-section order 105 to 106 volts Experimental data are available on the cross-sections of ordinary uranium for fast neutrons of approximately known energy produced by gamma rays from disintegrating beryllium The fission crosssections of ordinary uranium for neutrons of energy 4 6 8 and 5 million volts are respectively about 017 011 014 and 4 x l0-24 cm2 that the fission It is reasonably certain theoretically cross-section of 235 is at that of 238 and tends to decrease Thus 4 x l0-24 5 x 10- 2-4 with increasing velocity can be regarded as a lower section for the fast least as high as neutrons in U235 with to the crossan estimate of limit as a rough average over the range of energies of A higher estimate of 'rf is obtained by assuming that the observed fission in the range 2 to 8 million volts is due mainly to 235 i e that the effect of 238 has practically disappeared when the neutron'energy has sunk much below 106 s L b o c- Lc M e n J-s rieriCat r' DoLtotMLrt DECL4S'IFIED 6 2A' M$ -poE sgb ¢4 1 h H G_ as c OECLASSIFlEO $1201$ By volts 1 t L kF I 2 If all the capture is due to 235 values of 6f 235 are thus obtained between 2 4 and 4 x 10-24 cm2 for the range of energies tested leading to an average value of about 3 x 10-24 for fission neutrons In favor of this higher value of O'f is a reasonable but not well verified theory that there is a share threshold of neutron energies below which impacts on U238 will not cause fission and above which the probability of fission increases linearly with the neutron energy Tests have been made Westinghouse reported by Breit which seem to show such a linear increase for neutron energies greater than some 2 x 106 volts This rc uld indicate a threshold for U238 at about this energy Since the tests have not however been made with neutrons of definite energies the significance of the results is open to question It will be noted that on the former interpretation U238 is subject to fission from capture of the fast neutrons with a cross-section for 106 volt neutrons of between 01 and On the latter interpretation the capture cross-section of 238 for these neutrons is negligible 02 x 10-24 cm2 Determination of the Scattering Cross-Section o The uncertainties in s are much less serious than those in cTf For the normal mixture of uranium isotopes 6t has been s t b0c- rrte s DECLfSS'FIED -noE 3903 y2A Awercoah b0C i4rnert NS DECLASSIFIED $f 2018 measured as about 12 x 10-24 cm2 A very small part of this corresponds to CT-f but perhaps half is due to small angle scattering that has little effect upon the range of the neutrons Thus the effective value of the scattering cross- section for normal uranium is about 6 x 10-24 cm2 All evidenee indicates that 6s should be nearly the same for U235 This value may therefore be used for the scatter- and U238 ing cross-section of either isotope It should be noted that an error of a factor of as much as 2 in the value of 6s 235 would not be important since a smaller value of las could be compensated by using a surrcund- ing shield of larger 9 as indicated in paragraph la c Until further experiments are therefore performed we must consider two possibilities witch may be summarized thus TABLE Al CjOSS SECTIONS 'CH U_j DIIU 1 Units zf Definite high threshold c_s Case a U235 U238 Case b Uz35 U238 6 6 10 -24 6 2 t for U28 3 0 6 No definite high threshold for 6 cm 0 5 0 015 6 6 U238 -k4st T octtr- e v% DECL'SSTIED ggo3 B Y11HC -I as Aw%e riaaA 'D oc-K'vie rl IA NS DECL0 SSIFlED C iNr s 8f 20 1$ NA I -3 -6From present information it seems that alternative a is the more probable A choice between the two cases can be made experimentally by present technique if a sufficient quantity perhaps ol g of U235 can be isolated Using improved technique in more nearly homogeneous high energy neu- trons a more definite indication should also be possible without separating the isotopes Substituting the values of ITf and 0-t given above assuming a sphere of metallic U235 density 18 6 which gives N ' 4 8 x 1022 cm-3 and using Ferai s value if It 7 cm 2 3 cm 42 cm 3 5 cm d bare 7 cm 27 cm R shi of k the criti- ded bass bare 3 5 cm 10 5 cm 26 720 kg 49 The critical sizes for the shielded bombs are calculated for large thicknesses of material with the same scattering crosssection as the U235 a condition which should be attainable Thus the final column represents a reasonable expectation for the two cases The experimental errors might make the criti- cal masses uncertain by a factor of perhaps 2 for each case in question As mentioned above however we cannot now say whether case a or b will prove correct Doc-t cr ie 5 A w%e rl Cc% 1 D o A w a n DE°LfSS'FlED -DoE B DECLASSIFIED 88b32A-MS IRS 't'_ $12018 e B1 ii hf 2 Possible Explosive Fission with U238 Unless he energy of the fission neutrons A zl' is rapidly reduced by inelastic collisions in the uranium explosive fission should occur with U238 as well as with U235 The critical radius calculated as above for the shielded sphere of U238 is 70 cm or a mass of 27 000 kg There is some evi- dence that inelastic collisions occur which will slow down the neutrons until a non-fission type of capture occurs preventing the chain reaction but this t first sight it might is not certain appear to be of advantage to dilute the U235 with U238 in order to obtain additional energy from the latter isotope Calculation does not however sup- port this suggestion Thus if equal quantities of U235 and U238 are mixed because of the much higher capture cross- section of the lighter isotope at any instant after the chain reaction has started the ration of U235 fissions to U238 fissions will be Cf 235 cf 238 which is of the order of That is the U238 will add but little to the energy of the reaction while it will considerably increase the size 30 1 of the bomb required In case a the presence of U238 as far as can be seen at present would act merely as a dilutant enlarging the critical value of the radius and not affecting the fission reaction D0C-LA Y - e s A c r ca oLKrneL DECL S F1ED npb y2A- I4S DEClASSMED 812018 By M HC_ 3 KA' zi Percentage of Available Energy Released at Explosion If the bomb has a larger mass than that corresponding to the critical radius it will initially be highly explosive However because of the heat produced it will start to expand This expansion lengthens the mean free paths which increase inversely as the density The critical radius 3 increases at the same rate i e it is proportional to r3 where r is the actual radius of the sphere The chain reaction will develop in intensity until ' r beyond which value the number of neutrons produced will be less than those that are absorbed and escape so that the reaction will decline in intensity The question arises as to what fraction of the total available energy of fission is released when the expansion is complete The appropriate mathematical problem has been studied by Pryce Secret 3ritish ms P1 and in this country independently but with rougher approximations by Fermi Oppenheimer and Compton see Footnore 3 The results of Fermi and Compton are in good agreement with Pryce's calculations Oppenheimer probably through neglect of some factor considered by the others-details of his calculation have not been submitted finds efficiencies about 10 times larger -' 44s 1 -D o c LA r- e v -s DECI 'F1ED NS peg 88b3 y2A cN Y11 HC as DECIASSifED e M m r4C 8izoi8 HA El- The results of Pryce for a sphere of 1T235 enclosed in a container of about half the mass of the uranium and of 2 times the critical mass give an efficiency of 3 5 per cent Compton for a bare sphere finds 1 4 per cent and a somewhat higher value for the shielded sphere Fermi es- timates roughly within a factor of 10 1 per cent A value of 2 ppr_ cent can hardly be in error by more than a factor If the mass is n times the critical value the efficiency is proportional to n2 If the explosion occurs before the parts are placed together the efficiency will be reduced by a factor lying between I a-l ao-l J o and L a-l ao-l 2 where a is the actual effective multiplication factor and ao is the value of thefactor when the parts are brought together In the case of partial approach the efficiency will thus be reduced by a factor estimated roughly as a-1 ao-l In the cases considered below where the reaction is triggered by a neutron at the instant of critical approach this ratio is about 25 per cent This would reduce the efficiency of the explosion to about 5 per cent 4 Avoidance of Predetonation In order to have a superbomb one puts two or more parts together such that combined they exceed the critical volume but separately they do not The possibility must be examined that stray neutrons may trigger off a reaction before the s L Doc- r e n4-s Ao eri «n b0CKw cn OECl1SS'FIED c 88b32 i2A NS OECIASSIFlEO $f 201$ parts are thoroughly put together so that the bomb fizzles instead of explodes Uranium has some spontaneous fission which will tend to introduce this effect Measurements can -be made at present only on commercial uranium which has about 5 spontaneous fissions per kg per second The question is how much of this is to be apportioned to U235 The theoreti- cally favored viewpoint is that all the observed spontaneous fission is to be attributed to U235 7 kg bomb about 2 x 10-4 On this basis for a seconds and for a 150 kg bomb about 1 x 10-5 seconds would be available to bring the parts of the bomb together In the opinion of some competent theoretical physicists however there is no conclusive theoretical reason why the observed spontaneous fission of uranium should come entirely from 235 or even why the spontaneous fission of 235 should be pronouncedly larger than that of 238 If the probability of spontaneous fission is the same for 235 and 238 the available times are increased by a factor of 140 and the detonation difficulties to a large extent disappear The development interval of the chain fission reaction is also long enough to be significant fter the introduc- tion of the first neutron the time interval until the explo10-6 sion is complete varies from about 3 x according to the initial conditions to 10-4 second For a sphere above the critical mass the interval after the first fission until N fissions have occurred is t -2-e 1n N 4 r s 1 L o L c r % e n Ao ri can Doc_K e- DECLWVF1ED -DoE 88o Bl Ytil H L y2A NS ' CK c' _ DECLRSSIFlED $1201$ 4 BiL nAS cz where j- is the time required for a multiplication by a factor e This is in turn calculable from the relation re -T ln a 5 where -C' is the mean time spent by each neutron in the uranium and a is the average number of neutrons produced a is less than per initial neutron the multiplication factor n used in section 1 above because of the probability of escape of neutrons without fission capture of twice the critical mass a - ca For a sphere 1 4 and for a shielded U235 sphere of radius 4 4 cm 'C- ca 2xl0-8 sec Thus 10-8 T'e - 6 x sec Using in equation 4 the value N - 3 x 1025 10 per O ent of the total number of atoms - we obtain t - ca 3 x 10-6 sec Now consider the initial condition of two hemispheres each having the critical mass approaching each other with a velocity v When the parts reach a certain critical dis- tance from each other the value of a will rise to unity and an explosion becomes possible If at this-instant a neutron is present the rate of increase is given by the equation dN _ a 1 N dt 6 where a is increasing according to roughly a - 1 Avt 7 v 4 sl- ToctA rf v% 4'S cav% DocKr e- h DECLAS _'FIED DoE 88D2A 4S cr Bf MS DECLASSIFIED S1 20 f$ b Q'L Of rr He - hkas oe a F1GuRE Substituting in sq 6 and solving t2 X- In N 8 The value of A will depend upon the geometry but for the smaller size bomb case a could probably be made as great as 0 1 per cm Assuming v - 105 om sec and Viand N as given During this interval the hemispheres will have approached close enough to raise a-1 to some 30 per cent of its maximum value and the efficiency of the explosion may be expected to be roughly the same fraction of that from the bomb in its spherical form For the large sized bomb case b and base sphere the appropriate values of the constants are t - 6 x 10-6 sec N i 4 a 1026 A - 0 02 and v - 5 x 105 cm sec Using these values the development interval for the sphere of twice the critical mass is by eq 4 Z- 1 x 10-5 second For the ap- proaching hemispheres triggered at the instant of critical separation equation 8 gives case b t - 1 1 10-4 sec 'gam 5L- 'Doctkrne 4s A tricaP D0C_ Kwien DEL LJSS'FRED HS DoE 8863 y2AL I DECLASSIFlED 4N 6_ L_ 2-018 SA' Lrt This interval is long enough for a-1 to grow to about 25 per cent of its value for the completed sphere so that the explosion will be of high energy The total interval available to bring the parts of the bomb together is the sum of the probable interval between fissions and of the development interval ing all spontaneous fissions to occur in U235 Consider- most unfavor- able case these total intervals are case a 2 x 10-4 seconds case 1 x b 10-4 seconds These times should be reliable within a factor of 2 For the lighter bomb the interval is long enough to bring the parts to their optimum positions For the heavier bomb as noted above though the interval is too short for optimum placing it is nevertheless sufficient to ensure a high energy reaction Footnote Al A H Compton Mathematical calculations of the critical radius The only pertinent published paper is a preliminary calculation of Peierls Camb Phil Soc Froc 610 1939 Van Vleck sets up a differential equation equivalent to Ncf h-r P where o is the neutron density and D is the diffusion coefficient given by 1 - c4s k b o c L-c rn a x -s Av ericc v Dncztwn en DECLASS' FIED ti -DoE Y21 H C DECLASSIFIED 8g03jq2A-HS $12018 as r -14N is the number of atoms per cm3 a- f and trt the fission and total cross sections n the number of neutrons emitted per fission capture and ft the neutron's mean free path betweencollisions The left hand side of 1 when multiplied by dV represents the loss due to diffusion from a small vol- ume dV while the right side wren similarly multiplied gives the rate of neutron birth in V The spherically symmetric solutions of 1 finite at the origin are tid-11' ' 2 The proper boundary condition is one which states that at the boundary of the sphere the neutrods diffuse into free space The requisite analysis for this condition has been made by Hopf for an analogous astrophysical problem Cambridge Tracts 1To 31 1934 eq 174 we must have '71POf The result is that at r a R 14 o Combining this with eq 2 gives the transcendental equation xRUt KR for determining t 71 4 Following apparently a similar prccedure his calcula- tions have not been available to us Peierls is said to ob- 4s o c t c rvt e v% Av ericotv% DocL4men DECLFS-'FIED 1 NS of 88b3asyzAc°t DECLASSIFIED $ 20 I$ Yh HG i A H L HRPS C-e a It is not clear to us whether this result is for a shielded or an unshielded sphere Fermi using a different procedure obtains for an unshielded sphere t 73f f f n 3 Oppenheimer for unshielded sphere gives approximately R A 3 t T'f Approaching from two different limiting cases Compton finds It is possible that Peierl's value of refers to a shielded sphere which would then be in line with the other calculations in light of footnote 2 In te text we have used Fermi's value of k 1 73 Very possibly a value of 1 which is the largest of all would be nearer the truth This would reduce the critical radii by the factor 4 8 and the critical masses by the factor 0 5 The sizes calculated in the text should thus be considered as upper limits c s -oc1 tMe vx -S Avve ricav% Doc- Lt vne1 DEC Lam' FIED UoE 8gb3qy2ABy f MS DECLASSIFIED $1201$ HC_ 4S Ca By Ys'1 Fl ' _ _kAl L'L1 -16- Footnote A2 effect of surrounding shield Cppenheimer has cal- culated the effect of surrounding the uranium with a shield of material that will scatter the neutrons thus increasing the chance of their absorption in the uranium If if and It are the capture and total mean free paths respectively and L is the scattering mean free path in the surrounding shield Oppenheimer obtains -lSr fir L n-1 and For comparison the equivalent though less for the accurate formula bare uranium is Thus for L s lt the shield reduces the critical mass by a factor of 8 It is probable that a substance can be used for which L lt in which case the reduction in size will be even greater It will be noted that the addition of the shield also increases the efficiency of the explosion cf footnote 3 highly dense shield is to be preferred - stn -DoclArne v -S Awl- cati'bocw evt DECLA C RED 81 DoE 88 b3342A MS Y2 HC DECLASSIFIED $120 $ ''4S C Footnote A3 B1 M t4c fW-' Dzt- A H Compton Calculation of Efficiency of Explosion A good approximation to the rate of expansion of the U235 results from assuming that as it becomes hot all portions of the sphere will expand at the same rate If r is the radius of the sphere at any instant its density and v the radial velocity of its outer surface its kinetic energy can be shown to be The rate of increase of this kinetic energy can be equated to the rate at which work is done by the outward pressure of the high energy uranium It is to be noted that no import- ant part of the motion occurs until the temperature is over 105 deg C or 10 volts and that after this temperature is reached the uranium may be treated as a perfect gas Below 103 volts where the pressure is due to molecular and elec- tronic motions the pressure is equal to 67 x the energy density Above 104 volts the radiation pressure is predominant and eq'sls 33 x the energy density Consider first only the molecular pressure -p ' e have LV 4 7T or since dr dt - v P 1 P' - 2 s1 I OGL Me A DECL4S FLED s o 8%b y2A-MS L RS ' DECLASSIFIED $ a0 g Yl HG of M 14C- 'IoR Ue -18a The rate of fission energy increase is however given by - _ cot- E J 3 where E is the energy per cm3 'Z'is the mean life of a neutron and a is the multiplication factor i e the ration of the number of neutrons in the second generation the first ' Vriting eq 3 becomes Substituting in eq 2 we have Ct9td _ 1ti jV Note that if the class is twice the critical value the initial value ro of the radius is 21 3 Ro Because of the lowered density however the critical radius at a later instant is a The critical condition is reached when r has expanded to the b AvnG-icah Dockr itr DECL1 SflFlED of 890 3 of I'f1 H C - zA - e DECLASSIFIED S $1 2-C Bf tti1 NC_ NAIS 2 IM -19- Thus in 7 r and hence also eq o change only slightly during the critical part of the expansion and a sufficient approximation is obtained by ascribing to them a constant average value of iq 7 may then be written e ta t 3d or integrating 601 Since e 1 e °o and v vo this U_pB o_ 77 3 r_ ll C° s becomes A AB P 8 to a good approximation - - 9 The critical radius is however reached when r has reached ro 12ro i e whe or by eq l 9 IrJ t - 12 o or again since e 1 Eat- 2 v and For the unshielded sphere of case a 4 1 2 1 Ro 8 r r For the value of a it can be shown that for n 3 and ro - 21 3 Ro under the initial conditions so - ca 1 4 At the critical radius a - 1 Since the efficiency is proportional to a-1 2 and since the value of t will be A v-icah boc_kw en DECLASSIFIED D of 3 y2A- MS DECLASSIFIED 8120 $ 1 Bf tti 1 RC_ NAI 'j' Sa determined chiefly by the forces in the first part of the expansion where a - 1 is large the larger values of a - 1 sho ii d be heavily weighted in taking the average 77e shall use Thus ' _ 77 - 85 aa - 1 34 ' 108 seconds X 0PA_6_ For evaluating B we have at once 18 6 g ca 3 ro - 8 8 cm If we consider the zero instant to be when the pressure is Fo 1012 dynes cm 2 corresponding to a temperature of 10 But corresponding to the initial pressure of 1012 dynes cm 2 the energy per U235 atom is 20 ev As in has reached its maximum rate of energy production ' e may expect the energy developed after the maximum to be roughly the same as that before Thus the total should be 2E 4e note also that at the higher stages of temperature the pres- sure being due to radiation is t only half our estimated DocLA rleY4S E ggb32A DfCLAS 'FlED Q vnG r i c a P% D o c t t r 1 e rti fS value DECLaSSIREP Srzoia This leaves a longer time for the growth of energy Pryce estimates this effect as introducing about an additional factor of 2 which appears to us without however any good calculation as reasonable Thus finally for the bare sphere the efficiency will be about 4 z 6 a 1 T a 1 4 per cent It is not impossible that the higher value of 3 4 per cent calculated by Pryce may result from the shield which he assumes surrounding the sphere this shield should slow down the for energy development The inertia of expansion giving more time r- 5 L1 aE O1 H L o c L4 Pi le v 4 A v caP 1 oc- tw # DECLASSIFIED DECLASSIFIED HSb3y2A- MS $f 20 f$ as Ca Mm1f KARS E21 % 4s oc- vv rS Doc t Aw e ricot DECLLS°'FIED pcE S%b3 1A- NS DECLASSIFIED $1 201 By I-i la APPENDIX B The Probable Destruc HC de ort on ve Action of Uranium Fission Bombs B s a owa The following is an attempt to evaluate the effects of the use of atomic fission for military purposes The in- formation given to the writer is that a bomb containing 20 kg of uranium may be expected to release some 20% of its nuclear fission energy within a time interval of one microsecond willl$e Although these figures are admittedly uncertain they taken as a basis for the following considerations in absence of more positive information Taking the energy per atomic fission as 175 m ev Henderson hys dev 56 703 1939 we obtain 3 4 x 109 kilocalories total available energy from the above-mentioned bomb This is approximately the same energy as contained in 4000 tons of TNT1 The simplest asof a bomb sumption is to suppose that the destructive action released energy and hence that the 20 is proportional to the action as a kg uranium bomb will have the same destructive bomb containing 4000 tons of TNT This quantity of TNT is of has ever been course very much greater than anything that used in a single bomb However some unintentional detonations detonations of of explosives magazines and some deliberate land mines in the last war approximate the conditions Cf 1Cn the basis of data available November 6 1941 Total efficiency fission energy per kg U235 1 7 x 1010 kg cal kg 1 2 x 106 of bomb - 2 per cent Explosion energy of TNT explosion kg cal ton This gives energy released in fission of 20 kg U235 bomb o energy released in explosion of 6000 tons AHC -- 'fist boGtAn1e v 's DE LS _''FlED DcF Bga32p Awe rica % Doc- gjarti NS DECtAS51RED $r2 C ii P%ittC _ 4 _z the former the case occasionally cited in the Halifax Explosion of a munitions ship during the last vi r The damage there extended to a radius of much more than a mile but in the opinion of the wri ai'4his is not a fair case to consider because the conditions for large da aage were unusually favorable in that the exploded ship was in the middle of the harbor and the city forms a sort of a natural amphitheatre with no barriers to reduce the effects of the blast The land mines detonated in the last war on the other hand are very unfavor- able cases because the detonations occurred at a great death underground and their effect was ma'_nly to produce large craters rather than to spread the damage over a large area Consequently for instance the opinion found in many articles in Zeitschrift fur das all emeine Schiess- and Sprengstoffwasen on the effect of land mines of the last war is rather deprecatory and the radius of action from a charge of several hundred or even a thousand tons of explosives in a mine was found to be rather limited In this war the British have gathered very extended information on the effect of German aerial bombs dropped over 3n7lish cities It is- noteworthy that the destructive effects were found to vary from one bomb to another in a very striking manner depending on the exact relation of the point of detonation to the 5 LOGt Ar eh-s Awerca bobLr- DECLASSIFIED sr DoE ggp3- C t' y2A-14S DECLASSIFIED 1812018 Y1 HL of Yl Hr- HARC zt location of nearby buildings the type of construction of these buildings the type of fuse used instantaneous or de- lay nature of the soil etc It is possible therefore to draw only very rough estimates of the average effect of In that sense only therefore one can say that a destructive action from a one-ton bomb extends over large German bombs a radius of about 100 meters being naturally more intense near the origin and decreasing roughly linearly with the distance Cver this radius however the damage is quite serious in most instances unless the structures are of reinforced concrete construction The British have also established on the basis of a large amount of experimental material a dimensional law which says that if all distances are expressed in terms of charge diameters the effects of all' detonations 15 times the diameter of a one-ton bomb it may therefore be expected that the damage from a bomb of this size would ex- tend to 1500 meters varying of course very greatly from one bomb to another It is now necessary to consider whether there is any justification to the assumption made above that the section of the uranium bomb will be similar to that of a M'T bomb releasing the same amount of energy Unfortunately there is no way of proving this contention theoretically and only some plausible arguments in its favor can be made r% sk DOC_L4e e n A ver ca % b0c_Krti- p DECIASS'FlED DcE 8gb Br y2A-MS r j HG_I'45 Cz' DECUSSIFlED $1201$ p B NR' S Cet _ As mentioned above a one-ton TNT bomb causes serious damage over an area of 100 meters radius Yaw the weight of air in a sphere of this radius is 5000 tons and we see that the weight of the explosive relative to the mass of air which is blown about within the effective volume is very insignificant Hence it would seem to be reasonable to believe that the weight of the explosive itself is unessential for the effects produced and thus that nearly the same effect will be produced by a lighter but more powerful explosive The British report that HDX bombs have about 10% greater radius of action than TNT bombs of the same weight hence about 30 greater action volume The energy content of 3DX bombs is some 30% greater than that of TNT bombs which agrees well with the above fig- ure for increased action No quantitative data are available on the increased effectiveness in air of mixed explosives containing aluminum but the British informed the writer that the effects of such bombs are greater than those of pure TNT bombs This qualitatively at least is again in agreement with the increased energy content Stronger experimental evi- dence has been obtained by the British to show that in under- water explosions the effectiveness is to a large extent determined by the energy content of the explosive These con- clusions however cannot be extended to cover the case of uranium which is so far beyond the range of available ex- plosives even with the aid of the now available mathematical theory of shook waves for theory of shock waves see b s k b o c- rrt e vJ-S Aw d cot -N Doc Kvnev% DECUUS FIED MS peE 8gb3gy2A R' rN ni He _ D£CLASSIFlED c B M -E $ 0 $ 0 Oe - 2 for instance reports of Division B NDRC by a B Kistiakowsky and B Wilson cr and also by Tohn von Neumann only certain qualitative arguments can be here presented the shock wave is an irreversible phenomenon and its passage through air and through water but to a very much lesser extent is ac- companied by an increase of entropy of the medium that is by an irreversible conversion of mechanical into heat energy The fraction of energy thus dissipated cannot be calculated quantitatively because of the is-o'ompleteness of the theory but qualitatively one knows that the greater the intensity of the wave that is the greater the deviation from infinitesimal acoustic waves the more proportionately is this dissipation Therefore in the immediate vicinity of the uranium bomb where the shock wave will be thousands of times more intense than in the vicinity of a larger TNT bomb of the same total energy content greater fraction of mechanical energy will be converted into heat and hence will be lost as potential source of damage In water because of its low com- pressibility shock waves with a maximum pressure of as much as 2 tons sq inch behave as infinitesimal acoustic waves and it has been found that as much as 40 of the total explosive energy is transferred into the shock wave in water In air on the other hand a very much smaller fraction of the total l- s Doc 1e_v -s Aw er cav% Doc Kren DECL1S iFIED Tp OF 88b q 2A- H5 By I H C DECLfSSMED $J2dr$ By Y1 h i Cz ' 4s c' energy is transferred to the shock wave because of higher compressibility and shock waves with a maximum pressure of 2 tons per square inch are already very different from acoustical waves i e much faster and are accompanied by a considerable not known wuantitatively dissipation of energy Because of the absence of a quantitative theory of shock waves even of such intensity as caused by ordinary explosives and because of additional difficulties of extrapolation into regions which correspond more closely to conditions in the interior of the stars than anything met with on Earth no calculations can be now made The opinion of the writer is that uranium bombs detonated deep under water will have a destructive action which is very nearly the same as that of TNT of the same energy content In regard to uranium bombs detonated in air or on the ground the writer is not convinced of their equivalence with TNT bombs and rather be- lieves that they destructive action will be proportionately 2 less perhaps by as much as a factor of ten Some words now on a subject which is perhaps outside of the scope of this report but which is nonetheless of interest to the writer This is the question of the economics of uranium bombs If one takes as the basis of comparison the cost of TNT per pound some fifteen cents then evidently 'g sL I oc nie r -s cE A Me r ca % Doc-qy% e DE'LkS 'nED DECIASSMED 3903 Ly2A-9S $f 201$ By m r I t -' w _ -6s2 Note added November 6 1541 The following calcu ation qualitatively supports this lower effectiveness of U235 for the same energy but suggests a much greater reduction factor It we assume that it is the outward momentum of the explosion which produces the destructive air wave we have pr - my e 2mW 1 where m is the effective mass of the bomb and 7I is the energy released For equivalent explosion therefore 2 mfWf - 2 mc7Ic where mf and me are the effective masses of the exploding materials for the fission and chemical explosions respectively and Nf and are the corresponding energies Thus Wf 2 me 7c- mf Under optimum conditions of surrounding shield we may roughly assume mc ° 1 5 m and mf ° 10 m235 7'f ' c - m235 T235 mnTT JTNT' per unit mass where j is the energy released Lq 2 then becomes m'I IT - 2 6 T 235 JT I t 3 mz35 Using footnote 1 J235 JTNT - 3 x 105 we thus obtain mTNT - 1400 m235 This would mean that 20 kg of U235 would be equivalent to about 30 tons of TNT a reduction factor of 2000 as compared with the estimate based on equivalent energies From the evidence presented by Kistiakowsky it would appear that the reduction factor of 10 is much more probable Yet in our present state of inexperience with such superexplosions more theoretical attention should be given to this point AHC s % -D CC- rw a vJ-S AY ericar voCLtmeti DECLLSS'FIED e 88b3 y2A- HS DECLASSIFIED 8r 20 91 L3 k4 r a TPTT bomb of 4000 tons costing $1 200 000 is'incomparably cheaper than a uranium bomb in terms which in the last analysis represent man hours of work and hence the strain on the national economy It seems however that this is not a fair basis of comparison i ather one should include in the cost estimates the auxiliary costs such as those of aircraft crews flying fields etc Although the writer is not in possession of exact figures on these matters the following is probably not too far from the truth to be unworthy of consideration The cost of a heavy bomber will be taken as 350 G3C ane the cost of training its crew as 150 000 50 of all bombers will be assumed lost in each operational flight which means that each flight costs $25 000 To this must be added the cost of maintaining ground crews flying fields service on the bombers etc which will probably double the figure giving $50 000 per flight in which 4 tons of explosives will be assumed to be dropped There- fore the cost of dropping 4000 tons of TITT bombs which were assumed to be the equivalent to one uranium bomb is 450 000 000 This is then a sum which in all fairness should be compared with the cost of uranium bombs except that the actual figures must be treated as subiect to revision in light of more exact information which is undoubtedly available to the proper authorities r-5L T c- Lk roe V S DECLASC F1ED CF 8%b3_ 42A NS H h HL DECIASSiFlED SI 20 $ Rs k 1'x'1 4j ----'id's Cr'e There are further tactical considerations writer will not attempt to assess -2 which the They are the greater facility of getting to the objective one bomber r ith a uranium bomb as contrasted with 1 000 bombers carrying 4000 tons of TNT but on the other hand there is the advantage of a greater area of moderate damage caused by say 4000 one-ton TNT bombs dropped at random as contrasted with the intense and concentrated damage by one uranium bomb in regard to the problem of starting the rapid fission reaction in the bomb two methods appear possible at present although others are decidedly worthy of further consideration The two methods are 1 The firing of two halves of the bcmb towards each other until on close approach the fission reaction sets in initiated by an artificial source of neutrons or spontaneously it seems entirely feasible to bring together the two pieces of uranium weighing some ten or even hundred kg each with a speed of several thousand feet per second One alternative is to use a double gun with the uranium pieces acting as projectiles and facing each other the other is to adopt the principle of the fragment gun developed by the Eritish for this purpose The second alternative has the advantage that the weight of the auxiliary parts of the bomb will be greatly r ed the length of the acceleration period also reduced and yet the terminal velocity maintained Of course consider- able development work must be done on both devices before they r e v' 4s 4s -T o DECL S'FlES Bi DcE 88_b3 yy H C ac Iricot n boclnGn 2A- MS DECLASSIFIED S1 20 _ $ ' 81 Wl 1- hL ne can be considered as practical 2 The second method is to have a barrier between the two halves of the bomb which is impenetrable to neutrons and which is shot out in the instant before fission is to occur This is alto entirely feasible as one might use a mixture of metallic boron for instance and TNT which may be made to give any degree of brisance i e speed of explosion depending on the composition particle size etc If this mixture is not too brisant the damage to the uranium hemispheres between which the explosive is placed as a layer of proper thickness will be minimized and yet the detonation will progress through the explosive layer at a speed of several thousand meters per second and the products of the detonation will be ejected at a speed of about 1000 meters per second During this time interval the motion of the uranium hemispheres because of their large mass will be quite small and may be reduced still further by backing them up with larger masses of properly dimensioned inert metal The details of the procedure must again be worked out by experimentation but a priori the method appears to be feasible 0C-LAr 1Q v W%G fiCAV1 1 0 Gr 10 DECLASSIFIED o asb3 za-Hs M Yti1 HC DECLASSIFIED $1201$ cr 6v m N FIAR F vV%O- frtCA D0C_gVV1en DEIAS FIED cE 8gb3 y2A HS DECLASSIFIED ei Y1 H G $ 12 0 1 $ Summary and Conclusions There are several separation methods which show pro- mise for large-scale production using the hexafluoride Three of these are in a more or less advanced stage of development 1 ' e cannot adequately judge the promise of the English method for molecular diffusion of vapor at low pressures on the basis of information now available in about two weeks we should have a first-hand report For 1 kg day production of metal the estimated diffusion area is 70 000 sq meters and plant cost 50 000 000 2 The atmospheric-pressure vapor diffusion method looks feasible but may be slow in development For 1 kg day production the estimated diffusion area is 10 000 sq meters plant cost 327 000 000 and power consumption 72 000 kw For 10 kg day production the esti- mated plant cost is 380 000 000 A study of this method from engineering viewpoints should be begun at once 3 The vapor-centrifuging methods look feasible and their engineer- ing and certain other aspects are farther advanced than for the vapor diffusion method For 1 kg day production the present estimate is that 22 000 separately-drives 3-foot centrifuge units would be needed at a cost of 344 000 000 The centrifuge method also looks promising for relatively prompt small-scale production of material for experimental work The study of the centrifugal method on both experi- mental and engineering scales should be pushed 4 Work r k sL b0C-_ r-f yrs A f cQ$A Dock men DECL'SS'FIED _ CE 88b3g2A DEC1ASSIf7ED 8f 2018 M HC _' RS E now in progress on the possibility of separation by elec- trolysis and by other methods should be continued and a study of certain recently proposed new methods should be undertaken in particular methods involving the use_of positive rays At the moment the use of positive rays in the mass spectrograph furnishes the only means of obtaining large concentrations of the rare isotope although only in extremely small quantities the use of this method to obtain samples for experimental work should be pushed 5 The feasibility of molecular evaporation at low pressures from a solvent including engineering aspects should be studied If a suitable solvent can be found this method appears to involve fewer new experimental and engineering problems than the diffusion methods 6 Study of the pos- sibility of separation by ordinary fractional distillation should be pushed in collaboration with chemical engineers ' ' 'bile at the moment the method looks relatively unpromising it may if feasible offer the minimum of expense and of new problems to be solved The development of certain compounds which promise to be suitable as lubricants resistant to and as solvents of the fluoride should be strongly pushed As lubricants these compounds are important or possibly essential for the success of methods 1 - 3 or as solvents essential for 5 Search for possible liquid uranium compounds of v sk oc r e v% -S ot IN DocKrnCn DECLASPfl D y2A- IBS cF 88b3 I IR rz1_ DECLASSIFIED 81201$ YF1 HG e MHr -No a A moderate volatility should be intensified since if a suitable compound could be found the relatively quick and inexpensive evaporation method could be used In general to accelerate progress 1 closer contact or unification should be effected between projects located at different institutions but closely related in their objectives 2 increased support including added personnel should be brought to some of the work now going on and provision should further be made for developing certain additional phases of the whole problem particularly along engineering lines 3 in view of the crucial importance of the time element the principle of parallel development should be very extensively applied a in the simultaneous study of all methods of separation which have any promise at least until one or more methods have conclusively outdistanced the others b in simultaneous study of successive stages of de- velopment of a given separation process e g laboratory and engineering stages and in each stage simultaneous study of different phases when possible General Considerations In -emeral any system of separation is based on the coordinated operation of a large number of individual separation units arranged in a number of stages In the operation of each unit the ratio cl a of the concentrations of the light and heavy isotopes is changed in the light fraction to s D0C_ ur e n1-5 Aw Grcah Doaq en DEC LASSIE ED gr o g8b32y2A- S 4Jg2 Kt DECLASSIFIED $I 2D 1$ RS Ce By MHC a value of ci 22 c being the enrichment ration for a-single unit In our raw material 21 22 - 1 139 let us call this 11 i2 i It is desired to secure a final product with a relatively large terminal value say ei 22 t of c1 a2 At_ the other end of the apparatus waste heavy fraction must be discharged in which c2 has been decreased to a value cl E2 w perhaps half as large as cl c2 i Let For a type of unit in which the separating process is molecular diffusion operating at theoretical maximum efficiency dif where 72 2'l in C C-1 1 1 00426 for otir compound the cut C is so defined that 1 1 is that fraction of the material entering the unit which undergoes diffusion ri simple and convenient pro- cedure is to divide the entering material into two equal fractions C - 2 3q 1 then gives C dif - 1 0 00295 In practice efficiency must be sacrificed more or less to speed and of becomes of dif - 1 - 0 00426 E in C C-1 2 where C is the effic-fancy Df the unit In order to operate the process with an over-all factor G we must send the material through a number n of successive 4 o c t c i 1 e N -5 DECLASSTFlFD -DoE 8803 y2A- A - cah Dockr cM MS DECLASSIFIED er M Hr stages of enrichment such thatP n - G n - in G lnc $1201$ RV cr r Or In G a -1 3 For the diffusion process Just considered assuming _ - 0 7 which seems feasible for rapid operation and G - 27 800 we find n w 4950 in operation the inflow into a light fraction which goes into the heavy fraction which goes to the Fig l each stage divides into next stage next stage forward and a backward see in the rectifying stages 21 02 21 22 i there is a net excess stages c1 c2 of forward flow the transport T in the stripping ci -E2 i a net excess of backward flow The inflow into each stage has a maximum at the input or feed stage and tapers off toward both outflow ends see e g Fig 2 which corresponds approximately to the operating conditions of stage its flow capacity must be varied proportionally or a proportional the previous paragraph If there is one unit per number of units of uniform capacity may be connected in paralle The total required capacity A of the installation is proportional to the area under a curve such as that in Fig 2 Since both the ordinate and the abscissa are propor- tional to n of Eq 3 the area is proportional to is found that A is given by n2 It where T is the output rate and F is the rate of flow per unit of operating capacity For a diffusion system A is the r 4st boc- - ever Avv% r cav% bocKw en DECLeSS'fIED HS DoE 88b3as yzA' r2 DECIASSIf1ED $12171$ total diffusion area in square the rate of diffusion T is in kg day meters and a - 21 if F is in kg per square meter per day and If a centrifuging system is used A may represent the number of units if r' is the inflow per unit It is important to notice that the final stages of enrichment require relatively small flow capacity In fact just as much capacity is required to change c1 2_2 from 1 139 to 1 25 as from 1 25 to 1 An important feature of any installation is the holdup H equal to the total amount of light isotope present in the installation at any moment The larger the holdup the longer it will take to build up the necessary steady state which must be produced before the installation will begin to deliver an output approximating the desired composition F is evidently proportional to A and to a depth factor i e hold-up per unit of diffusion area or per centri uge unit depending on the design of the units and their pumping connections Vapor-Diffusion and Centrifugal ethods In general the following problems must be faced in connection with all the proposed separation methods which are being most actively pushed at present vapor-diffusion and centrifugal methods cient single 1 design and testing of a rapid effi- unit 2 pumping system to transport material -4 5 k T ocLArv f v s Aw cric DocKr e n DE'IAS FlED H pE 880 C VhH y2A MS 4q Cr' - DECLASSIFIED $1201$ b from one unit or stage to the next 3 provision for automatic control of the flow and for cutting out and replacing defective units Common to all of these is the question of obtaining resistant materials for walls pipes membranes and so forth and the question of a lubricant which is not attacked too rapidly If the vapor is kept free from moisture a suitable getter is available for removing the products produced by moisture there are metals which seem not to be attacked thus probably answering the first question For a lubricant an oil is known which is attacked only slowly and may prove usable on the other hand a program is under way toward the synthesis of lubricants which are not attached at all In case this program should be unsuccessful it may be necessary to turn to labyrinth glands these are now being studied The matter of a pumping system and that of automatic controls are engineering problems whose solution may be difficult and time-consuming There are at present the following four more or less promising types of single unit in various stages of development 1 The low-pressure vapor diffusion unit pressure 2 mm on the high-pressure side with molecular diffusion through very thin membranes with fine holes Eq 2 applies 2 The high-pressure vapor diffusion unit upper pressure about 1 at ap here with diffusion through thin submicroscopically porous membranes Eq 2 may be used although s -s 'D o c-4c r 1 e r AvtiCriCav1 DoLkv er DEC LASS I FIED Br VaF_ 88642A-HS as r DECLASSIFIED $ 201$ HL possibly the nature of the diffusion process is saaewhat centrifuge unit in which altered 3 The flow-through vapor flows through a fairly large metallic cylinder rotating heavier fraction at perhaps 550 r p s and is divided into a taken out nearer taken out near the periphery and a lighter one fractional distillation or the center 4 n unit in which takes place in a cena related type of counter-current flow trifuge to give a multiplied separation The type 1 or Lnglish unit of which preliminary serves at the sketches are available includes a rotor which theoretical calculations same time as pump and according to 0 4 or pershould give good efficiency at high speed haps 0 5 C - 2 in 3q 2 n of 2q 4 perhaps 70 000 square tests are meters for 1 kg day output Preliminary practical This unit encouraging but e do not yet have full details 1 a membrane which seems to have the fcllowin0 advantages sufficiently rugged seems to is highly permeable and probably de- testing and engineering be available 2 the preliminary It is not clear sign are probably fairly well advanced repair can readily be arwhether automatic control and easy lubrication problem is being solved ranged nor how the The pumping work cause of the low and frictional losses should be large befor pressures used The cost of a plant $50 000 000 with a 1 kg day of metal output is estimated as construction is complete time-lag of only 5-12 days after to build up the steady state 4sr Doc-LAr evN-S Avvv-%- c - DocKr en DECYSPFIED I f -pct 883 c' ZA-HS DECLASSIFIED 8i zo i8 c The type 2 unit might consist of flat diffusion screens on grills or of say fifty diffusion tubes between two headers with a very thin laminar feed box at the input header into which the input vapor is forced in a thin sheet with turbulent flow at 1 atmosphere pressure by a centrifugal pump Encouraging progress has been made Columbia experi- branes resistant to the gas and suitably porous tests with other gases indicate that 3 70 per cent or better can be secured at F ° 7000 kg per square meter per day but direct tests for our vapor have not yet been finished be A 5-stage pilot plant is about to set up to test the performance of these membranes in the separation of carbon isotopes in CO2 The data now available indicate that a total diffusion area of 10 000 square meters should give an output of 1 kg day Determination of the best type of membrane and its indus- trial fabrication remain to be worked out Assuming that this problem can be solved it is estimated that a plant to produce 1 kg day of metal can be built for 27 000 000 Of this estimate more than half is for pumps For operation a power requirement of 72 000 kw is estimated or 33 000 000 per year at 1 2 cent per kw hr For a plant of 10 kg day capacity the estimated cost of construction is about $80 000 000 and the power consumption 700 000 kw It should be noted that these cost estimates are preliminary no detailed engineering rj 4S k TDom rOAe vN rS AYNA6 Ck V-% DocLt VI-Ien DECLASS R D H -pcE 2 c3 ZA ' as c MS $1aC18 P HH By lay-out has yet been made E'- -21 The problems of automatic control and replacement of defective units remain to be worked out The hold-up tends to be high but it is hoped that it can be kept dowzsa-4 tons-of total UF6 for 1 kg day output The time required to reach the steady operating state barring accidents is estimated as 100 days Although prediction is uncertain it seems very unlikely that such a plant could be set up ready to operate in less than two years The type 3 and 4 units appear promising for prompt results in that the mechanical problems of materials and operation appear to have been solved difficulties as already noted Lubrication may present rin experimental type 3 unit in actual operation may be ready within two weeks The general theory for this type of unit can be counted on and has been tested for other gases and other related types of units several tests just reported for our substance indicate that it separates in accordance with the theory n enrichment ratio D of 1 04 in each unit as ccanpared with 1 003 in the diffusion units appears practical still larger values could be obtained if the peripheral speed could be increased but theoretical calculations indicate that for large-scale operation this ad- vantage must be partially sacrificed c being cut to about 1 01 in order to obtain speed ticcording to these calcula- tions the best procedure vc uld call for a large number of separate units each a cylindrical tube of 6 or 8 inches r SL T oGmile- e 4S A e_riGA 1 DoC-M rvie n DECU'Sc11ED -poE 88b3 y2A-MS DECLASS i FIED 812018 Of m t4 C_ _NAr- cEt a diameter and 1 to 3 meters length For a production of it is estimated that 58 000 units of 1 kg day of metal 3-foot length would be needed and that 60 days would be required to reach the steady state needed for production The type 4 unit shows theoretical possibilities of using much greater enrichment in a single unit of values as large as 4 0 may be feasible although only for a low rate of flow per unit This looks promising for the prompt pro- duction of relatively small amounts of material for experimental work since a relatively small number of units arranged in relatively few stages would suffice However the calcu- lations indicate that the use of large values and slow flow would require units of excessive length also a somewhat larger installation for a given rate of production than the use of values near 1 2 with more rapid flow Thus the latter appears to be preferable for large-scale production Using an arrangement of the latter type it is estimated that 22 000 3-foot units would separate 1 kg dey ar d that 20 days or less would suffice to set up the operating steady state engineering plans have already to a considerable extent been worked out for a system using either type 3 or 4 units The cost of construction is estimated as about 2 000 - -sL 1 oc-LAr-f r I VV%0-riC01 1 Dockrn Y% DECLM1SSl1ED -pcE 88o ofG_ qr''iA- MS f DECIASSR ED 4 Si Wt r C N per unit or about $44 000 000 for the type 4 system producing 1 kg day The cost per unit includes about w1 000 for building the unit $250 for the electrical drive a separate 7 F P motor for each unit and the remainder for accessories It may be possible to reduce t _e costs by increasing the length and a lterinl the metal used in construc- tine the units The problems of control and certain other items of equipment may also be simplified if the type 4 unit is successful Two varieties of the type 4 unit have been proposed one with liquid and recently one with vapor reflux to latter appears to be the more nromisinc for successful operation n preliminary experimental unit using liquid reflux is already bein _7 tested and one using vapor reflux should be ready within three months The diffusion and centrifugal methods both appear suf- ficiently promising that the experimental and engineering developments should be pushed as fast as possible This would be a safeguard against unexpected difficulties with either method ' oreover it has been suggested that one method perhaps the diffusion method might prove to-be better adapted to the earlier or quantity stages of enrichment and the centrifugal method to the later or quality stages Evaporation and Distillation 1'ethods If a liquid compound having moderate or small vapor pressure at room temperature were available a very simple 4 s L -D o c LA DECYSSIFlED 88 b3ggzA-14 S 01 H __1 DECLASSIFIED 81201$ - type of unit could be used in which the active process is irreversible evaporation at low pressure The theory is similar to that for diffusion and a is given by the sane formula Such units could easily be combined into a frac- tionating scheme requiring only heating and cooling and practically no mechanical power The absence of moving parts and the probable ease of automatic control indicate that the method which has been tested in the laboratory with mercury and works excellently mi ht be the simplest and most rapid to put into operation if a suitable liquid compound could be found Although no satisfactory compound has yet been pre- pared progress has been made and efforts in this direction should be intensified If a suitable solvent can be found our compound dis- solved in this could be evaporated at low temperatures perhaps 00 or -20001 very much as if it were itself a liquid although the complexities of the method would be greater It is estimated that the evaporation area needed would be comparable to the diffusion area needed in the high-pressure diffusion methods Pumping equipment would be needed but the problem would be far easier than that of pumping gas as in the diffusion methods It seems probable that a stable solvent of sufficiently low vapor pressure can be made although considerable time might be required to produce this in adequate quantities However it would seem that efforts in this r 4 5t T DC_ utrri2N-% AwcricavA DocKw en DE'LAVIFIED Di cE 88b312A-S 'i HC DECLMIrIED $1 201$ rz KAI' nzt of ti'1 F4C'_ direction should be pushed Sa especially since the same or related compounds may be valuable as resistant lubricants This latter use is the basis of a research project Just being organized on the preparation of such compounds It is possible that the liquid metal itself sub 'ected to separation by an evaporation process might be although the high temperatures needed make it questionable that this would be feasible nstead of differential evaporation differential condensation also offers possibilities Simplest and least expensive of all to put into opera- tion would be fractional distillation if it would work has been estimated from theoretical considerations that It -1 for distillation is only 5-7 per cent as large as for diffuEven with this handicap the method probably would be successful if it were not for the relatively enormous hold-up sion which it is estimated would entail a delay of years before the steady state necessary to begin production would be reached even using a very efficient column packing evertheless in view of the remarkable achievements in the oil industry in cutting down hold-up in fractionating columns the method seems wort' examining as soon as possible in collaboration with chemical engineers 'xperiments already made in our compound using a 30-foot 100-plate column were negative but the work is being continued with a 200-plate column and improved technique 44 s 'I o c 4c r1 e v1 S L' A ricav1 DocKv 0n DECLAS 'f1ED _ 8gb32 2A MS of 1 HG 4S C DECLASSIFIED - $f 201$ Bf ti1 HC_ to _r z b Y other Diffusion Methods Thermal diffusion of the vapor of our compound has been tried with negative results in three different laboratories In general thermal diffusion in vapor is a rather effective method but the theory is complicated and the results depend on molecular parameters of the particular compound If dif- ferent temperature conditions or a different volatile compound could be used there might be a possibility of success Theremal diffusion of some compound in solution liquid thermal diffusion is another possibility Some trials made recently with a solution using this method in an ingenious laboratory apparatus showed an astonishing rate and degree of Diffusion of the vapor through a streaming gas a method which offers considerable promise is being tried Unfortu- nately the obtaining of a high efficiency is dependent on diffusion through an inert gas of high molecular weight Compounds of the same class as the hoped-for lubricants and solvents mentioned above may be of value here Electrolytic 'ethods Experiments on certain salt solutions indicate it to be probable that isotopic ions differ in mobility If this is confirmed extremely great enrichment ratios may be secured by keeping the ions on a sort of electrolytic tread-mill for 44sI Toc r %e v% Qv eriCaN DocK e n DECLAS FIED -DOE 93 a I'f1 H L DECLASSIFIED 32 f2A-MS ' 2oi8 $9 as -16- some days Tests are now being made in suitable compounds This method may even if successful and valuable for obtaining small samples prove to be too expensive cost of electric power for large-scale production but calculations on this should be rechecked 'Partial separation in the process of electro-deposition or electro-solution is a remote possibility Cther Methods 'ethods of separation depending on differences in chemi- cal equilibria such as have proved successful for lighter laments do not look promising Photochemical methods although possible in principle are unpromising n method using differential adsorption of uranyl ions from acid solution was proposed at the committee meeting on Cctober 21 This deserves further examination A method using dialysis was also proposed and seems worthy of attention Counter-current extraction of uranyl ions between water and ether has been tried with negative results The possibilities of the positive ray method giving large separations but very small samples are well known but should be re-examined with respect to large-scale operation The use of this method for obtaining small quantities 'g -rk4 s L- -D o c- - cE e f$ Aw er cot v% 'C o K - e DECLASS' FLED Sgb32A-MS DECLASSIFIED 81 20 $ By M f C_ _IiAR r'z' of separated material much needed for experimental purposes should in any event be pushed Two attractive positive-ray methods for completly separating the isotopes in considerable quantities in a single operation were proposed at the meeting of the committee 1though the difficulty of getting enough positive rays and the electrical power cost might be prohibitive for large-scale production these methods deserve investigation The foregoing report is based on a series of interviews and consultations curing a period of about three weeks with members of the uranium committee and others working on its projects and with members of the present committee It em- bodies information and ideas from all these sources although it cannot be expected that the re-ort is entirely complete or accurate the riter believes that it presents a roughly correct view of the situation U235 SEPARATION PANT 235 990 0 Key RECTIFYING STAGFF No 4540 High Low A Pressure Pressure V LIGHT FRACTION HEAVY FRACTION A l1 FF UMPI S - -1 '-'L 110 EN E N 32 i 2 0 400 800 1200 Serial Number of Stage 2000 2400 1600 Scale SKetch 2800 of Apparatus 3200 3600 4000 4400 U235 SEPARATION PLANT U235 99% Key RECTIFYING STAGE No 4540 7 High T - Low Pressure' Pressure LIGHT FRACTION E 0 HEAVY FRACTION RECTIFYING STAGE No 2 RECTIFYING STAGE No I FEED U2350 7% STRIPPING STAGE No I PUM STRIPPING STAGE No 2 4 e STRIPPING STAGE No 329 Waste 1235r A5