mL × VL2 = mH × VH2 ,
while the average speed of light molecules is higher than that of heavy ones:
VL = VH × (mH/mL)1/2.
An ideal separation factor, a0, for a mixture of two gases diffusing through a porous partition, is:
a0 =(mH/mL)1/2 » 1 + Dm/2mL.
For uranium hexafluorides 235UF6 and 238UF6 (mL = 349, mH = 352), the separation factor a0 is equal to the enrichment factor e0:
a0 = 1,0043; e0 = a0 – 1 = 0,0043.
The free path of molecules should be larger than the typical size of pores, so that such molecules could interact mostly with pores in a partition, rather than with one another. The free path of molecules is inversely related to pressure. For UF6, the free path at 1 atm. is 1 mm, and at 1 mm Hg makes 700 mm. Fabrication of partitions with pores measured in microns is a fairly complicated task, which requires a low operation pressure.
Partitions should be:
·thin (fractions of millimeter);
·strong (to withstand a pressure drop of ~ 0.3 atm.);
·corrosion-resistant in the atmosphere of UF6. Partitions with micron-sized pores are made of:
·sintered aluminum and nickel oxide powder;
·sintered nickel powder;
·aluminum with pores produced by electric etching;
·teflon.
The uranium GD–enrichment factor at one stage is sm all (1.0043), wherefore the gas flow has to be repeatedly passed through many enrichment stages. A series of GD stages forms a cascade.
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2. Uranium enrichment in gas centrifuges (GC)
It is assumed that a tube rotating at an angular speed of w contains a mixture of gases with molecular weights of М1 and М2. Their molecules are exposed to centrifugal forces proportional to the mass and radius:
F1,2 = M1,2 × w2 × r.
Gas pressure rises steeply from the center to the periphery:
P1,2 = P0 × exp(M1,2×w2×r2/2RT) ~ exp(a × V 2).
The heavy fraction subjected to the higher pressure is driven to the GC periphery, while the light fraction collects in its central part.
The separation factor in a GC is:
a = exp(DM×w2×r02/2RT) = exp(DM × V(r0)2/2RT); e = a – 1 » DM × V(r0)2/2RT.
Calculations suggest that the following enrichment factors can be provided by gas centrifugation as a function of rotation speed:
e= 0.068 at V = 330 m/s;
e= 0.098 at V = 400 m/s;
e= 0,152 at V = 500 m/s.
Centrifuges are manufactured from the following materials:
·aluminum alloys (for speeds V £ 350 m/s);
·titanium alloys (for speeds V £ 450 m/s);
·alloyed steels (for speeds V £ 500 m/s);
·graphite-reinforced fiber-glass plastics (for V = 500–700 m/s).
3. Separating nozzle
This method essentially relies on different behavior of uranium isotopes in a centrifugal force field. Uranium hexafluoride is fed into a highly curved nozzle where centrifugal forces cause spatial separation of light and heavy isotopes.
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The advantage of this method over GC lies in the absence of rotating components, but the small size of separation slots (a fraction of a millimeter) calls for precision assembly. The uranium enrichment factor for the separating nozzle is e¢ = 0.025.
4. Laser methods
Laser methods of uranium separation are based on the difference in the arrangement of excited energy levels of electrons in atoms of 238U and 235U, which is made possible by use of a monochromatic laser. Excitation of electron shells leads to selective intensification of physical or chemical processes (intensified ionization of excited atoms or intensified dissociation of excited molecules). The conditions for laser-based enrichment include:
1.Presence of an excited electron level unique to one isotope. This level should be sufficiently far removed from other spectrum lines and from lines of other isotopes.
2.Availability of a laser tuned to an appropriate radiation frequency.
3.Existence of processes separating excited atoms and molecules.
Laser-based enrichment of uranium vapors. This enrichment method consists of the following stages:
·evaporation of U atoms in vacuum (an electron beam knocks out U vapors from the U–Re alloy);
·irradiation by a xenon laser with ensuing selective excitation of 235U atoms;
·irradiation by a krypton laser with ensuing selective ionization of excited 235U atoms;
·collection of ionized 235U atoms on a charged plate.
Laser-based enrichment of UF6 molecules. This process has three stages:
·cooling of the UF6 + H2 mixture to 30 К for the UF6 molecules to be mostly in an unexcited state;
·irradiation by an infrared laser with ensuing selective excitation of 235UF6 molecules;
·irradiation by an ultraviolet laser with ensuing selective dissociation of excited molecules:
2 × 235UF6 * ® 2 × 235UF5 + F2.
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White powder of 235UF5 (“laser snow”) precipitates from the gas mixture.
The enrichment factor of laser methods is as high as 3 to 15. They offer a possibility to use the waste of GD plants (containing 0.2–0,3 % of U) for recovery of uranium suitable for light water power reactors.
5. Chemical enrichment methods
Chemical methods depend on different stability of isotopes in compounds. A contact between chemical compounds of one element with different valences leads to isotope exchange. Thus, boron can be enriched in isotope 10B via an isotope exchange reaction:
BF3 + BF3O(CH3)2 ® 11BF3 + 10BF3O(CH3)2 ,
in which 10B builds up in the organic phase.
Heavy water generation results from an isotope exchange reaction between light water and hydrogen sulfide:
H2O + HDS ® HDO + H2S,
with deuterium accumulating in the water phase.
The USA and Japan are developing a uranium enrichment process involving UF6 and NOUF6 as contacting compounds. This is essentially oxidation–reduction chromatography achieved by alte rnation of oxidation reactions (addition of oxygen gas) and reduction reactions (addition of
hydrogen gas). In this case it is possible to separate compounds including ions of UO2++(with 6-valent 235U) and U4+(with 4-valent 238U). The
experimentally obtained separation factors reached 1.08 and power consumption proved to be up to 150 KWh/SWU.
6. Plasma method
This method is based on the effect of ion cyclotron resonance.
Charged particles (ions) moving about in a magnetostatic field experience the action of a force
F = q × [V × B],
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causing them to spiral about magnetic field lines. The orbital radius is found from the following equation:
F = q × V × B = mV 2/R ;
R = m× V /(q × B) = (2m × E)1/2/(q × B),
while the rotation frequency w = V/R = q × B/m is the ion cyclotron frequency (ICF).
If a variable electric field is applied, with its frequency equal to the ICF of a specific isotope, this will be the only isotope to take up the field energy. A higher energy of ions of a certain isotope will increase the radius of its rotation about magnetic field lines. It is then possible to separate ions of different isotopes and to accumulate ions of 235U and 238U selectively on appropriately arranged collectors.
Uranium enrichment technologies viewed in the context of non-proliferation of nuclear weapons
Gas diffusion:
a)technically sophisticated process;
b)high power requirements (2300–2600 kWh/SWU); one GD facility in the USA consumes about 5 GWe;
c)relatively low enrichment factor (e¢ = 0.0043);
d)unlikely secret construction of a GD facility.
Gas centrifugation:
a)technically sophisticated process;
b)low power requirements (100–300 kWh/SWU) and hig h enrichment
factor (e¢= 0.2–0.3) make this technology hazardous from the viewpoint of non-proliferation.
Separating nozzle:
a)less sophisticated than GD and GC processes;
b)low enrichment factor (e¢ = 0.025) and high power requirements (3000 kWh/SWU) make this method a lesser proliferation hazard as compared with GD and GC processes.
Laser methods:
a)the highest enrichment factor (e¢ = 3–15) and the lowest energy requirements (10–50 kWh/SWU);
b)the most sophisticated process; the most promising enrichment technology and the most hazardous process from the non-proliferation point of view.
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