The absorption spectrum of UF6 is far more complex even than that of uranium metal, because the spectrum of the UF6 molecule involves transitions between many vibrational and rotational states that are absent in the uranium atom. Absorption bands of the 235UF6 molecule overlap those of 238UF6, so that highly selective absorption by one isotope is seldom found. This is illustrated by Fig. 14.43, which shows the absorption by 235UF6 and 238UF6 at four different pressures at room temperature at an infrared wavelength around 16 /tan at which the difference between the spectra of the two compounds is greatest. The peak in the 23SUF6 absorption band is displaced 0.55 cm-1 from the peak in the 238UF6 band at a wave number (reciprocal wavelength) of 625 cm’1, about 1 part in 1000. However, the absorption by 238UF6 at the peak absorption by 235UF6 is so great as to preclude selective absorption under these conditions.

It has been predicted theoretically by Sinha et al. [S5] and observed experimentally by Jensen and Robinson [J4, R2] that if UF6 is cooled to 55 К and its absorption spectra measured with high resolution, wavelengths can be found at which selective absorption by 235UF6 takes place with relatively little absorption by 238UF6. The reason for this is as follows.

Uranium in the UF6 molecule is at the center of an octahedron, with the six fluorine atoms equally spaced at the comers. Such a molecule can vibrate in six different modes, of which the uranium atom moves in only two, the only ones with an isotopic shift. In the v3 mode to which Fig. 14.43 is attributed, the uranium and two opposite fluorine atoms move up and down together out of the plane of the other four fluorine atoms. The absorptions of Fig. 14.43 are caused by transitions in which the vibrational quantum number increases by unity, while the rotational quantum numbers change by plus or minus unity. If all transitions were

Table 14.27. Estimated characteristics of uranium metal laser isotope separation plants Source of estimate Osaki et al. [03] Janes et al. [J2] Capacity, million kg SWU/yr 8.75 3 Specific electric power, kW/(kg SWU/yr) 0.20 0.02 Unit investment cost, $/(kg SWU/yr) 36 195

from the lowest vibrational level, the fine structure of the absorption bands would be as shown qualitatively in Fig. 14.44, where the individual peaks are due to transitions from different rotational levels. Under such conditions, a 23SUF6 absorption maximum might be found that occurred at a 238UF6 absorption minimum, as shown in the figure. Then a tuned laser beam with a frequency spread narrower than the line spacing of 0.1 cm-1 might be able to excite 235UF6 to the first vibrational level without exciting 238UF6.

Such selective absorption is not possible at room temperature. There, only about 1 percent of the UF6 molecules are in their lowest vibrational state, so that the observed absorption spectrum is a composite of vibrational transitions from the ground state and many excited states, in each case to the next higher vibrational quantum number. These excited-state absorption frequencies are displaced somewhat from the ground state, so that 238UF6 lines from an excited state overlap 23SUF6 lines from the ground state, thus destroying selectivity.

There is another difficulty with working at room temperature. In the photochemical method, a second light beam would be used to dissociate vibrationally excited 23SUF6 molecules into a physically separable, nonvolatile lower fluoride and fluorine, while leaving unexcited 238 UF6 molecules with too little energy to be dissociated. However, because most of the 238 UF6 molecules at room temperature are already in excited states, many of these would necessarily also be dissociated.

For these two reasons, two-step photochemical dissociation of UF6 at room temperature would yield only very partial separation and would make very inefficient use of laser energy. At very low temperatures, the fraction of UF6 in the lowest vibrational state increases, reaching 69 percent at 77 К and 85 percent at 55 K. However, the vapor pressure of UF6 at 77 K, extrapolated from measurements at higher temperature, is only 5 X 10-25 Torr.

Jensen and Robinson [J4] have described an experiment at Los Alamos in which a dilute mixture of UF6 in hydrogen was cooled to ЗО К by expansion to high speed through a hypersonic nozzle. In this experiment, subcooled UF6 molecules remained uncondensed long enough to assume the low-temperature energy distribution and display an absorption spectrum in which 235UF6 lines and 238UF6 lines were separate and did not overlap.

In the proposed separation process, this high-speed, subcooled gas mixture would be irradiated first by 16-/ли light of a frequency absorbed by 23SUF6 and not by 238UF6 and then by additional light of sufficient energy to dissociate the excited 23SUF6, but insufficient to dissociate the unexcited 238UF6. The dissociated lower fluoride of 23SU and undissociated 238UF6 would then be separated in one of several possible ways. If condensation of subcooled UF6 could be delayed long enough, the solid lower fluoride of 23SU might be separated mechanically from the still gaseous 238UF6. Or both might be condensed and the 238UF6 leached with water from the insoluble lower fluoride of 23SU. In either method, transfer of a fluorine atom from undissociated 238UF6 to the possibly unstable lower fluoride of 23SU would impair selectivity. Because of classification, information is not available on how successful this postirradiation separation step has been.

A possible simplification of the photochemistry of this process is afforded by the discoveries of multistep photon absorption by Lyman et al. [L5] and by Ambartzumian et al. [A3]. An intense laser beam of the frequency absorbed by 235UF6 will deliver a sufficient number of photons successively to a 235UF6 molecule to dissociate it, while hopefully leaving 238UF6 unaffected. This would permit a single laser to do the job.

parameter Av = 0.002 cm Figure 14.44 Schematic representation of unresolved structure of absorption spectra of,3SUF6 and 238UF6.

[1]In this text each nuclide, such as uranium-235, is referred to by its chemical symbol, in this case 235U.

*The mass of the electrons is not included in this calculation because the electrons emitted from the nucleus in radioactive decay ultimately return as orbital electrons surrounding the nucleus of a neutral atom.

t Ratio based on 235U thermal fission for 4 years, no depletion, typical spectrum for light-water reactor.

Source’. American Nuclear Society Standards Committee Working Group ANS-5.1, “American National Standard for Decay Heat Power in Light Water Reactors,” Standard ANSI/ANS-5.1, American Nuclear Society, La Grange Park, 111., 1979. With permission of the publisher, the American Nuclear Society.

and by continuous processing. Examples of continuous-processing removal are the vaporization of one or more gaseous elements from a solid or liquid at high temperature or the continuous separation of one or more chemical elements from a well-stirred fluid mixture. Nuclides within the chain under consideration are linked by radioactive decay or neutron reactions. In the present analysis for batch operation we assume that there is a finite initial amount of only the first member of the chain, that there is no source for continuous formation of this first member, and that there is no source of any other member of the chain other than its precursor in the chain itself.

First we assume a chain in which adjacent members are linked by radioactive decay. The

*Calculated for the neutron spectrum of a typical pressurized-water reactor.

[4] Bennett [ВЗ].

[5]In reality, the neutron flux varies spatially throughout the reactor. The method of calculating effective xenon poisoning for spatially varying flux is developed in texts on reactor theory, such as Weinberg and Wigner [W3].

[6] Requires information from cycle 4.

Requires information from cycle 5. ® Requires information from lot 5.

10.027 weight fraction 235 U in U. ^ In spaces between assemblies.

[8] 53.9 kg Cm 949 8 kg FP

Figure 3.32 Fuel-cycle flow sheet for 1000-MWe LWR fueled with natural uranium, recycle plutonium, and plutonium recovered from reactor fueled with enriched uranium. Basis: 1 year, 80 percent capacity factor.

[9] і = Dixi

[10]Data from American National Standard for Nuclear Criticality

Safety in Operations with Fissionable Materials Outside Reactors [A2] and J. T. Thomas [Tl].

* The fissile material is subcritical if any one of the listed conditions is met, with no other fissile species present.

[13] Provided the nitrogen-to-plutonium atom ratio is equal to or greater than 4.0.

“Height of mixer-settler limited to 7.6 cm. Not amenable to efficient neutron poisoning for criticality control.

* Built of stainless steel containing a neutron poison such as gadolinium or boron.

“Sieve plates or packing constructed of “poisoned” stainless steel, thus allowing large-diameter columns.

[15]With variable-speed drive and replaceable impellers.

“With variable-speed drive.

Source: Adapted from M. W. Davis and A. S. Jennings, “Equipment for Processing by Solvent Extraction,” in Chemical Processing of Reactor Fuels, J. F. Flagg (ed.), Academic, New York, 1961, by permission.

[16] Ores containing tetravalent uranium

Uraninite (pitchblende) U3 О 8

Uranothorite Th! _жих8Ю4

Coffinite U(Si04 )i _j.(OH)4j

[17] Hydrated ores containing hexavalent uranium

Gummite U03"nH20

Camotite K20’2U03,V205’3H20

Tyuyamunite CaO-2U03 •V205’8H20

Autunite CaO*2U03,P2Os‘8H20

Torbernite Cu0*2U03 •P205 "8^0

Uranophane Ca0’2U03’2Si02‘6H20

[18] Refractory minerals containing tetravalent uranium

Davidite UFe5 Ti8 Ом

Brannerite (U, Th, Ca2 ,Fe2 )Ti2 06

Pyrochlore (Na4 ,Ca2 ,U, Th)(Nb, Ta)4 012

a 1 M SO4; pH = 1; ~1 g metal/liter; 0.1 M amine in kerosine; 1:1 phase ratio. b Trialkylmethylamine, homologous mixture, 18-24 carbons.

"Mixed Си alkyls from tetrapropylene by oxo process. dDodecenyl-trialkylmethylamine, homologous mixture, 24-27 carbons.

"Trialkylamine with mixed п-octyl and n-decyl radicals.

■^Kerosine diluent modified with 3 v/o (volume percent) tridecanol.

[20] Mixed Cg alkyls from oxo process.

Source: D. J. Crouse and К. B. Brown, “Recovery of Thorium, Uranium, and Rare Earths from Monazite Sulfate Leach Liquors by the Amine Extraction (Amex) Process,” Report ORNL-2720, July 16, 1959.

* 1000-MWe reactor, 80% capacity factor.

$33 MWd/kg, 32.5% thermal efficiency, calculated for 150 days after discharge, equilibrium fuel cycle.

§ Core: 67.6 MWd/kg, 41.8% thermal efficiency, calculated for 60 days after discharge, equi­librium fuel cycle. Residence time of radial blanket = 2120 days.

[22] The decay of 8.05-day 1311 avoids troublesome quantities of gaseous and dissolved radioiodine in fuel reprocessing.

[23] The decay of 6.75-day 237U eliminates the need for remote handling of the purified

uranium recovered by fuel reprocessing. Also, presence of high activities of 237 U would

interfere with monitoring for fission-product decontamination of the recovered uranium.

^Each light-element concentration is calculated on the basis of no other light elements present,

[27] Includes 232 U daughters present after 100 days of postprocessing storage.

*From references [B4, G1, N2, N3, R2].

[29] Gaseous state.

® Sublimes.

to chlorinate any Pu02 impurity. Fresh РиСІз containing as much as 15 percent Pu02 is added continuously, with the molten plutonium product drawn off continuously at the cathode at demonstrated rates of 300 to 400 g/h. Another process demonstrated on a laboratory scale in­volves PuCl3 in a mixture of 28 percent BaClj and 42 percent KC1 at 800°C, also in a MgO-TiOj crucible [C2].

Electrodeposition as a means of reducing plutonium to the metal has been limited by the corrosiveness of the chlorine and fused chloride environment. It also provides relatively little separation from impurities, except for those elements that form volatile chlorides [C2].

^SF, spontaneous fission. *’24201 Am.

I = = 0.1475; *Йі0 = 0.01; 4,0 = 4u, o = 0.

[31] Given concentrations.

[32] Fissile nuclide (23SU, 233 U, or 239 Pu)

[33] Proportion of fertile nuclide (238U, 232 Th, or 240 Pu) diluting fissile nuclide

[34] Mass of fissile nuclide

[35] Geometry (shape and dimensions) of region holding fissile material

[36] Volume of region holding fissile material

[37] Concentration of fissile material

[38] Nature and concentration of moderators

[39] Nature and thickness of reflectors surrounding fissile material

[40] Nature and concentration of neutron-absorbing poisons, such as nitrate ion or gadolinium nitrate

[41] Homogeneity or heterogeneity of fuel-moderator-poison mixture

[42] Degree of interaction between two or more regions containing fissile material

[43]From California University Cyclotron.

*See, for example, papers presented by Dr. E. W. Becker and his associates at the International Conference on Uranium Isotope Separation of the British Nuclear Energy Society, London, March 1975.

[44]For consistency with the original references, conditions in U. S. heavy-water plants have been expressed in English units. Conversion tables to SI units are given in App. B.

[45] The deuterium content ym at and above which hydrogen is burned and recycled

[46] The increase in deuterium content taken per stage

[47] The stage separation factor a

[48] The heads flow rate M

[49] The stage separative capacity Д

[50] The compressor volumetric capacity V

[51] The stage barrier area A

[52] The stage power requirement Q

[53] The initial cost of the stage Co

[54] The annual cost charged to the stage C

[55] The unit cost of separative work cs = Cl A

The objectives of this section are as follows:

1. To develop equations for the dependence of these stage characteristics on the independent variables

2. To show how the stage design may be optimized for various criteria

3. To work out the stage design conditions that lead to minimum unit cost of separative work for a specific barrier type

[56] The flow pattern efficiency decreases from 0.56 at va = 400 m/s to 0.19 at 700 m/s. When combined with the v% in the first factor of Eq. (14.226), the overall effect is to cause the separative capacity per unit length to vary as vl’02 over this range of ua, instead of as v%.

and 700 m/s. These parameters have been cast in the present dimensionless form from numerical integrations carried out by May [M6].

As this table shows, concentration of counterflow near the outer wall of the centrifuge in the Berman-Olander profile has these principal effects compared with the optimum uniform mass velocity distribution:

[58] In the circulation efficiency, Eq. (14.228), the factor [/(rj/a)]2/4/3, which has the value unity for the uniform mass velocity profile, increases rapidly with va, thus reducing the circulation efficiency.

[59] The radial separation factor, expressed as a — 1, is nearly independent of va over this range, instead of varying as vl as would be the case for a uniform mass velocity profile, and is much smaller than the local separation factor between the center and outer radius of the centrifuge, given in Table 14.13.

Overall separation performance. To evaluate the overall separative performance of a gas centri­fuge from the preceding results for the local separative performance at particular height z and composition y, it is necessary to integrate the differential enrichment equations (14.181) for the enriching section and (14.182) for the stripping section. Because the parameters Cj and Cs are functions of the circulation rate N for a given axial velocity profile, it is necessary to know how N varies with z before these integrations can be carried out. A qualitative description can be given of the dependence of N on z for the principal means used to drive the circulation.

Scoop and baffle. With an unbaffled scoop at one end and a rotating baffle at the other, such as shown in Figs. 14.10 and 14.15, the circulation rate will decrease exponentially from the