Atomic Energy for Military Purposes (The Smyth Report)
The Official Report on the Development of the Atomic Bomb Under the Auspices of the United States Government
By Henry De Wolf Smyth
CHAPTER IX. GENERAL DISCUSSION OF THE SEPARATION OF ISOTOPES
9.1. The possibility of producing an atomic bomb of U-235 was recognized before plutonium was discovered. Because it was appreciated at an early date that the separation of the uranium isotopes would be a direct and major step toward making such a bomb, methods of separating uranium isotopes have been under scrutiny for at least six years. Nor was attention confined to uranium since it was realized that the separation of deuterium was also of great importance. In the present chapter the general problems of isotope separation will be discussed; later chapters will take up the specific application of various processes.
FACTORS AFFECTING THE SEPARATION OF ISOTOPES
9.2. By definition, the isotopes of an element differ in mass but not in chemical properties. More precisely, although the nuclear masses and structures differ, the nuclear charges are identical and therefore the external electronic structures are practically identical. For most practical purposes, therefore, the isotopes of an element are separable only by processes depending on the nuclear mass.
9.3. It is well known that the molecules of a gas or liquid arc- in continual motion and that their average kinetic energy depends only on the temperature, not on the chemical properties of the molecules. Thus in a gas made up of a mixture of two isotopes the average kinetic energy of the light molecules and of the heavy ones is the same. Since the kinetic energy of a molecule is (1/2)mv2, where m is the mass and v the speed of the molecule, it is apparent that on the average the speed of a lighter molecule must be greater than that of a heavier molecule. Therefore, at least in principle any process depending on the average speed of molecules can be used to separate isotopes. Unfortunately, the average speed is inversely proportional to the *square* root of the mass so that the difference is very small for the gaseous compounds of the uranium isotopes. Also, although the *average* speeds differ, the ranges of speed show considerable overlap. In the case of the gas uranium hexafluoride, for example, over 49 per cent of the light molecules have speeds as low as those of 50 per cent of the heavy molecules.
9.4. Obviously there is no feasible way of applying mechanical forces directly to molecules individually; they cannot be poked with a stick or pulled with a string. But they are subject to gravitational fields and, if ionized, may be affected by electric and magnetic fields. Gravitational forces are, of course, proportional to the mass. In a very high vacuum U-235 atoms and U-238 atoms would fall with the same acceleration, but just as a feather and a stone fall at very different rates in air where there are frictional forces resisting motion, there may be conditions under which a combination of gravitational and opposing intermolecular forces will tend to move heavy atoms differently from light ones. Electric and magnetic fields are more easily controlled than gravitational fields or "pseudogravitational" fields (i.e., centrifugal-force fields) and are very effective in separating ions of differing masses.
9.5. Besides gravitational or electromagnetic forces, there are, of course, interatomic and intermolecular forces. These forces govern the interaction of molecules and thus affect the rates of chemical reactions, evaporation processes, etc. In general, such forces will depend on the outer electrons of the molecules and not on the nuclear masses. However, whenever the forces between separated atoms or molecules lead to the formation of new molecules, a mass effect (usually very small) does appear. In accordance with quantum-mechanical laws, the energy levels of the molecules are slightly altered, and differently for each isotope. Such effects do slightly alter the behavior of two isotopes in certain chemical reactions, as we shall see, although the difference in behavior is far smaller than the familiar differences of chemical behavior between one element and another.
9.6. These, then, are the principal factors that may have to be considered in devising a separation process: equality of average thermal kinetic energy of molecules at a given temperature, gravitational or centrifugal effects proportional to the molecular masses, electric or magnetic forces affecting ionized molecules, and interatomic or intermolecular forces. In some isotope- separation processes only one of these effects is involved and the overall rate of separation can be predicted. In other isotope- separation processes a number of these effects occur simultaneously so that prediction becomes difficult.
CRITERIA FOR APPRAISING A SEPARATION PROCESS
9.7. Before discussing particular processes suitable for isotope separation, we should know what is wanted. The major criteria to be used in judging an isotope-separation process are as follows.
9.8. The separation factor, sometimes known as the enrichment or fractionating factor of a process, is the ratio of the relative concentration of the desired isotope after processing to its relative concentration before processing. Defined more precisely: if, before the processing, the numbers of atoms of the isotopes of mass number m1 and m2 are n1 and n2 respectively (per gram of the isotope mixture) and if, after the processing, the corresponding numbers are n1' and n2', then the separation factor is:
This definition may be applied to one stage of a separation plant or to an entire plant consisting of many stages. We are usually interested either in the "single stage" separation factor or in the "overall" separation factor of the whole process. If r is only slightly greater than unity, as is often the case for a single stage, the number r-1 is sometimes more useful than r. The quantity r-1 is called the enrichment factor. In natural uranium m1 = 235, m2 = 238, and n1/n2 = 1/140 approximately, but in 90 per cent U-235, n1/n2 = 9/1. Consequently in a process producing 90 percent U-235 from natural uranium the overall value of r must be about 1,260.
9.9. In nearly every process a high separation factor means a low yield, a fact that calls for continual compromise. Unless indication is given to the contrary, we shall state yields in terms of U-235. Thus a separation device with a separation factor of 2 - that is, n'1/n2'= 1/70 - and a yield of one gram a day is one that, starting from natural uranium, produces, in one day, material consisting of 1 gram of U-235 mixed with 70 grams of U-238.
9.10. The total amount of material tied up in a separation plant is called the "hold-up." The hold-up may be very large in a plant consisting of many stages.
9.11. In a separation plant having large hold-up, a long time perhaps weeks or months is needed for steady operating conditions to be attained. In estimating time schedules this "startup" or "equilibrium" time must be added to the time of construction of the plant.
9.12. If a certain quantity of raw material is fed into a separation plant, some of the material will be enriched, some impoverished, some unchanged. Parts of each of these three fractions will be lost and parts recovered. The importance of highly efficient recovery of the enriched material is obvious. In certain processes the amount of unchanged material is negligible, but in others, notably in the electromanetic method to be described below it is the largest fraction and consequently the efficiency with which it can be recovered for recycling is very important. The importance of recovery of impoverished material varies widely, depending very much on the degree of impoverishment. Thus in general there are many different efficiencies to be considered.
9.13. As in all parts of the uranium project, cost in time was more important than cost in money. Consequently a number of large-scale separation plants for U-235 and deuterium were built at costs greater than would have been required if construction could have been delayed for several months or years until more ideal processes were worked out.
SOME SEPARATION PROCESSES
9.14. As long ago as 1896 Lord Rayleigh showed that a mixture of two gases of different atomic weight could be partly separated by allowing some of it to diffuse through a porous barrier into an evacuated space. Because of their higher average speed the molecules of the light gas diffuse through the barrier faster so that the gas which has passed through the barrier (i.e., the "diffusate") is enriched in the lighter constituent and the residual gas which has not passed through the barrier is impoverished in the lighter constituent. The gas most highly enriched in the lighter constituent is the so-called "instantaneous diffusate"; it is the part that diffuses before the impoverishment of the residue has become appreciable. If the diffusion process is continued until nearly all the gas has passed through the barrier, the average enrichment of the diffusate naturally diminishes. In the next chapter we shall consider these phenomena more fully. Here we shall merely point out that, on the assumption that the diffusion rates are inversely proportional to the square roots of the molecular weights the separation factor for the instantaneous diffusate, called the "ideal separation factor", is given by
α = Sqrt[M2/M1]
where M1 is the molecular weight of the lighter gas and M2 that of the heavier. Applying this formula to the case of uranium will illustrate the magnitude of the separation problem. Since uranium itself is not a gas, some gaseous compound of uranium must be used. The only one obviously suitable is uranium hexafluoride, UF6, which has a vapor pressure of one atmosphere at a temperature of 56 deg C. Since fluorine has only one isotope, the two important uranium hexafluorides are U235F6 and U238F6; their molecular weights are 349 and 352. Thus, if a small fraction of a quantity of uranium hexafluoride is allowed to diffuse through a porous barrier, the diffusate will be enriched in U235F6 by a factor
α = Sqrt[352/349] = 1.0043
which is a long way from the 1,260 required (see paragraph 9.8.)
9.15. Such calculations might make it seem hopeless to separate isotopes (except, perhaps, the isotopes of hydrogen) by diffusion processes. Actually, however, such methods may be used successfully - even for uranium. It was the gaseous diffusion method that F. W. Aston used in the first partial separation of isotopes (actually the isotopes of neon). Later G. Hertz and others, by operating multi-stage recycling diffusion units, were able to get practically complete separation of the neon isotopes. Since the multiple-stage recycling system is necessary for nearly all separation methods, it will be described in some detail immediately following introductory remarks on the various methods to which it is pertinent.
9.16. The separation of compounds of different boiling points, i .e., different vapor pressures, by distillation is a familiar industrial process. The separation of alcohol and water (between which the difference in boiling point is in the neighborhood of 20 deg C.) is commonly carried out in a simple still using but a single evaporator and condenser. The condensed material (condensate) may be collected and redistilled a number of times if necessary. For the separation of compounds of very nearly the same boiling point it would be too laborious to carry out the necessary number of successive evaporations and condensations as separate operations. Instead, a continuous separation is carried out in a fractionating tower. Essentially the purpose of a fractionating tower is to produce an upward-directed stream of vapor and a downward-directed stream of liquid, the two streams being in intimate contact and constantly exchanging molecules. The molecules of the fraction having the lower boiling point have a relatively greater tendency to get into the vapor stream and vice versa. Such counter-current distillation methods can be applied to the separation of light and heavy water, which differ in boiling point by 1.4 deg C.
GENERAL APPLICATION OF COUNTERCURRENT FLOW
9.17. The method of countercurrent flow is useful not only in two-phase (liquid-gas) distillation processes, but also in other separation processes such as those involving diffusion resulting from temperature variations (gradients) within one-phase systems or from centrifugal forces. The countercurrents may consist of two gases, two liquids, or one gas and one liquid.
9.18. We have pointed out that gravitational separation of two isotopes might occur since the gravitational forces tending to move the molecules downward are proportional to the molecular weights, and the intermolecular forces tending to resist the downward motion depend on the electronic configuration, not on the molecular weights. Since the centrifuge is essentially a method of applying pseudogravitational forces of large magnitude, it was early considered as a method for separating isotopes. However, the first experiments with centrifuges failed. Later development of the high speed centrifuge by J. W. Beams and others led to success. H. C. Urey suggested the use of tall cylindrical centrifuges with countercurrent flow; such centrifuges have been developed successfully.
9.19. In such a countercurrent centrifuge there is a downward flow of vapor in the outer part of the rotating cylinder and an upward flow of vapor in the central or axial region. Across the interface region between the two currents there is a constant diffusion of both types of molecules from one current to the other, but the radial force field of the centrifuge acts more strongly on the heavy molecules than on the light ones so that the concentration of heavy ones increases in the peripheral region and decreases in the axial region, and vice versa for the lighter molecules.
9.20. The great appeal of the centrifuge in the separation of heavy isotopes like uranium is that the separation factor depends on the difference between the masses of the two isotopes, not on the square root of the ratio of the masses as in diffusion methods.
THERMAL DIFFUSION METHOD
9.21. The kinetic theory of gases predicts the extent of the differences in the rates of diffusion of gases of different molecular weights. The possibility of accomplishing practical separation of isotopes by thermal diffusion was first suggested by theoretical studies of the details of molecular collisions and of the forces between molecules. Such studies made by Enskog and by Chapman before 1920 suggested that if there were a temperature gradient in a mixed gas there would be a tendency for one type of molecule to concentrate in the cold region and the other in the hot region. This tendency depends not only on the molecular weights but also on the forces between the molecules. If the gas is a mixture of two isotopes, the heavier isotope may accumulate at the hot region or the cold region or not at all, depending on the nature of the intermolecular forces. In fact, the direction of separation may reverse as the temperature or relative concentration is changed.
9.22. Such thermal diffusion effects were first used to separate isotopes by H. Clusius and G. Dickel in Germany in 1938. They built a vertical tube containing a heated wire stretched along the axis of the tube and producing a temperature difference of about 600 deg C. between the axis and the periphery. The effect was twofold. In the first place, the heavy isotopes (in the substances they studied) became concentrated near the cool outer wall, and in the second place, the cool gas on the outside tended to sink while the hot gas at the axis tended to rise. Thus thermal convection set up a countercurrent flow, and thermal diffusion caused the preferential flow of the heavy molecules outward across the interface between the two currents.
9.23. The theory of thermal diffusion in gases is intricate enough; that of thermal diffusion in liquids is practically impossible. A separation effect does exist, however, and has been used successfully to separate the light and heavy uranium hexafluorides
CHEMICAL EXCHANGE METHOD
9.24. In the introduction to this chapter we pointed out that there was some reason to hope that isotope separation might be accomplished by ordinary chemical reactions. It has in fact been found that in simple exchange reactions between compounds of two different isotopes the so-called equilibrium constant is not exactly one, and thus that in reactions of this type separation can occur. For example, in the catalytic exchange of hydrogen atoms between hydrogen gas and water, the water contains between three and four times as great a concentration of deuterium as the hydrogen gas in equilibrium with it. With hydrogen and water vapor the effect is of the same general type but equilibrium is more rapidly established. It is possible to adapt this method to a continuous countercurrent flow arrangement like that used in distillation, and such arrangements are actually in use for production of heavy water. The general method is well understood, and the separation effects are known to decrease in general with increasing molecular weight, so that there is but a small chance of applying this method successfully to heavy isotopes like uranium.
9.25. The electrolysis method of separating isotopes resulted from the discovery that the water contained in electrolytic cells used in the regular commercial production of hydrogen and oxygen has an increased concentration of heavy water molecules A full explanation of the effect has not yet been worked out. Before the war practically the entire production of heavy hydrogen was by the electrolysis method. By far the greatest production was in Norway, but enough for many experimental purposes had boen made in the United States.
STATISTICAL METHODS IN GENERAL
9.26. The six methods of isotope separation we have described so far (diffusion, distillation, centrifugation, thermal diffusion, exchange reactions, and electrolysis) have all been tried with some degree of success on either uranium or hydrogen or both. Each of these methods depends on small differences in the *average* behavior of the molecules of different isotopes. Because an average is by definition a statistical matter, all such methods depending basically on average behavior are called statistical methods.
9.27. With respect to the criteria set up for judging separation processes the six statistical methods are rather similar. In every case the separation factor is small so that many successive stages of separation are required. In most cases relatively large quantities of material can be handled in plants of moderate size. The hold- up and starting-time values vary considerably but are usually high. The similarity of the six methods renders it inadvisable to make final choice of method without first studying in detail the particular isotope, production rate, etc., wanted. Exchange reaction and electrolysis methods are probably unsuitable in the case of uranium, and no distillation scheme for uranium has survived. AIl of the other three methods have been developed with varying degrees of success for uranium, but are not used for hydrogen.