separation of stable isotopes

Karanam L. Ramakumar 1

Methods for the separation of stable isotopes

Karanam L. RamakumarIndia


Isotopes of an element have very similar chemical properties

e.g. 235U3O8 and 238U3O8 Chemical reactivity is nearly identical

They behave as completely different substances in nuclear reactions

e.g. 235U is a fissile isotope while 238U is not


Many of the stable isotopes find wide spread applications in chemical, industrial, agricultural and clinical research

�Elucidate and understand reaction pathways

�Mechanisms and kinetics

�Effect of trace elements on physico-chemical properties

�Up-take and plant metabolism studies

�Behaviour of trace elements from toxicological and human metabolism point of view


Mass differences result in

Thermodynamic isotopic effects

Shift in equilibrium in reactions

Kinetic isotopic effects

Shift in rate of reactions

Isotopic effects are quite pronounced in light elements

Negligible in heavy elements

“The reasonable man adapts himself to the world, the unreasonable man persists in trying to adapt the world to himself. Therefore all progress depends on the unreasonable man”

George Bernard Shaw ‘The Revolutionist’s Handbook’


Separation Factor in a Typical Enrichment Process

Two types of separation factor

(i) separation factor (αααα) and

(ii) enrichment factor (ε)

y/(1-y)z/(1-z)

α=

y/(1-y)x/(1-x)

ε=

z is the atom % abundance of the desired isotope in the feed. (1-z) is the corresponding quantity of the other isotope in the feed

y and (1-y) refer to the corresponding quantities in the product and

x and (1-x) are defined for tails

Feed

z, (1-z)

Product

y, (1-y)

Tails

x, (1-x)


For material balance:Total U = F = P + W (F = Feed, P = Product, W = Waste, all in Kgs)U-235 = F.xf = P.xp + W.xw (x is atom fraction of U-235)

w pp f

w wf f

x -xx -xF=P W=P

x -x x -x

The ratio of products

flow rate to feed flow rate is called “cut” θθθθ

wF

wP

x -x=

x -x

θ

Cut (θθθθ ) for a given enrichment cascade is optimised

Product flow rate PFFeed flow rate

θ= =

Fraction of desired

component in products

stream is called recovery

“r”y x(1 )r 1z z

θ −θ= = −1 - θθθθ = W/F


Separating Unit, Stage and Cascade

Separating Unit: The smallest element of an isotope separation plant that effects some separation of the process material

Examples of a single separating unit are one gas centrifuge, or one electrolytic cell etc.

No single separating unit can enrich any material to desired value. Throughput is also very very small

To multiply the effects of the enrichment of one unit and to achieve adequate throughput large numbers of units are interconnected in parallel

Stage: A group of parallel-connected separating units, all fed with material of same composition and producing partially separated product streams of the same composition

Cascade: A series-connected group or stages


CascadeStage

UnitZ1

Feed

x1

x1

x1

y1

y1

y1

x2

x2

x3

y2

y2

y3

Concept of Unit, Stage and cascade


FeedWaste

Product

A square cascade has the same flow rates in all stages and therefore the same number of machines per stage. Rarely used because they are not very efficient.Constant flow rate results in constant cut and mixing of concentrations and therefore loss ofseparative work.

Square Cascade


FeedWaste

Product

Simple cascade

Waste

Waste

No attempt is made to reprocess the partially depleted waste streams leaving each stage.

it is impossible to obtain high recovery of desired component because of losses in the waste streams leaving every stage, the recovery falls rapidly as the over all enrichment factor desired is increasing.

A simple cascade has only enrichment section.


FeedWaste

Product

Feed for each stage consists of heads from the next lower stage and wastes from the next higher stage

The most commonly employed cascade

Two sections: the enriching section, consisting of the stages above the point at which the feed enters the cascade and produces material of increased concentration. The stripping section is below the feed point and increases the recovery of the material

In a symmetric counter-current cascade, the waste stream is recycled back to the immediately preceding stage. In an asymmetric counter-current cascade, the waste is recycled more than one stage back.

Counter current or recycle cascade

As (α-l) < < < 1, in most of

the cases, these are also known as close-separation cascades.


Separation of heavy isotopes

e.g. 235U from 238U


Concept of Separative Power, Separative capacity andSeparative Work Unit

In conventional industries, where the level of separation is almost 100%, throughput parameter is sufficient to indicate the capacity of the separating plant

e.g. a heavy water production plant, where the grade is fixed for reactor use.Petroleum refineries

In the case of uranium enrichment, two parameters namely extent of enrichment and total quantity of enriched isotope decide the plant’s capacity

e.g. 3% for LWRs to 90% & above for weapon grade

To compare the capacities of two different plants, only throughput may not be sufficient to gauge the size of an enrichment plant, particularly when enrichment levels at which the plants are operating are different


Separative power or Separative capacity

A combined function of quality & quantity of separation performed by a separating element or a plantIt is independent of the level of concentration of feed material

Separative power: A change in the Value effected by a separating element, i.e. the increase in the value of output over the value of input. A quantity called value function is defined as a function of the concentration, x, of the desired isotope by the relation:

The work WSWU (separative work per unit time) necessary to separate a mass F of feed of assay xf into a mass P of product assay xp, and tails of mass T and assay xt:

xV(x)=(2x-1)ln1-x

p tSWU fW P.V(x ) T.V(x )-F.V(x )= +


For material balance:Total U = F = P + W (F = Feed, P = Product, W = Waste all in Kgs)U-235 = F.xf = P.xp + W.xw (x is atom fraction of U-235)

w pp f

w wf f

x -xx -xF=P W=P

x -x x -x

p w fwpSWU f

wp f

xx xW =P(2x -1)ln +W(2x -1)ln -F(2x -1)ln

1-x 1-x 1-x

pSWU w fwp f

wp f

W xx xW F=(2x -1)ln + (2x -1)ln - (2x -1)ln1-x P 1-x 1-x

P P

wF

wP

x -x=

x -x

θCut P F

wP

x -xx -x

(1-θ) =


Let us calculate the amount of feed (F in kg) required to produce 1 kg of product and the number of SWUs needed for this operation in two cases:

193218Case 2: Xf = 0.00711,

Xp = 0.9, Xw = 0.003

229176Case 1: Xf = 0.00711,

Xp = 0.9, Xw = 0.002

SWUF(kg)Case #

Feed and SWUs operate in opposite direction. If the availability of feed is no problem, one can save on energy consumption by allowing larger fraction of desired isotope in the waste streams.


1/22 1

[M /M]α=

The gaseous diffusion process makes use of the phenomenon of molecular effusion to effect separation. If a gas is allowed to pass through a porous membrane with pore sizes equal to the at molecular dimensions, the relative frequency with which molecules of different species pass through the pores is inversely proportional to the square root of their molecular weights. For a mixture of two masses M1 and M2 (MI < M2), this ratio, called separation factor, αααα, is given by

Gaseous Diffusion Process


Gaseous diffusion process

Feed Product

z, M1, p1 y

1-z, M2, p2 (1-y)

Porous membrane

Rate of diffusion (D) αDensity

1

No. of molecules crossing the barrier α pressure x diffusion rate

J α P.D (p α z)

y = J1 α . z. (1-y) =J2 α (1-z)

Mass1

(D) α

/M

1 21

1/

M1 22

1

yy

MzMz

2

11 1

=− −

M

M2

1

α =


Separation of U-235 from U-238 by gaseous diffusion

Feed : UF6 M1 = 235UF6 = 349 M2 = 238UF6 = 352

Separation factor M

My/( y)z/( z)

2

1

11

− α−

.352 1 00429349

=

Separation factor is very close to 1!!

Back-diffusion brings it down further.

For useful degree of enrichment, many stages in series

(Cascade) are employed.

Lower elements have better separation factor

20Ne-22Ne = 1.0488 36Ar-40Ar = 1.0541 D-H2 = 1.414


Natural uranium U-235 : 0.00711%

Product U-235 : 0.03%

Tails U-235 : 0.002%

No. of stages required (n): 1275

UF6 is highly reactive, powerful fluorinating reagent

B.Pt. = 56.40C Vapour pressure at 250C = 111.9 mm (Hg)

Gaseous diffusion of UF6 : a technological challenge

Materials compatible with UF6

Lubricants

Seals and gaskets

Diffusion cells

Diffusion membranes

Compressor materials

Complete elimination of air

leakage inside the process

system!!

wp

w p

x ( x )n ln

x ( x )

−=

α− −

121 1


Materials used in diffusion plants

Fluorocarbons and chlorocarbons as lubricants and gasket valves

Alumina or Nickel vessel protected by chemisorbed Nickel fluoride layer

Alumina or Aluminium protected by alumina for construction of plant

Diffusion membrane : Chemically resistant, even sized and shaped pores of radius ≤ 10 nm

Large porosity : 109 / cm2

Small thickness and sufficient mechanical strength

Diffusion membrane is Key to the process

Method of manufacture and performance characteristics remain classified


Diffusion membrane materials

Metals : Au, Ag, Ni, Al, Cu

Oxides : Al2O3

Fluorides : CaF2

Fluorocarbons : Teflon

Film type membranes : Pores are bored through an initially non-porous membrane

Alloy of Ag(66) + Zn(34) HCl leaching of Zn

Au(40) + Ag(60) HNO3 leaching of Ag

Al sheet anodically oxidised by 5% H2SO4

Aggregate type membranes : Pores are the voids left when fine particles are agglomerated under pressure or sintered at convenient temperature

Sintered Al or Ni powders

Teflon granules pored into a grid


~~

~~

~~

~~~

~

~~

TailsWt.Fr. U-235 = 0.002

Natural U feed

Wt.Fr. U-235 =0.00711

ProductWt. Fr. U-235 = 0.03

Stage 594

Cooler

CompressorStage 1

Controlvalve

0.007095

0.007125

Stage 1275

Ideal Gas Diffusion Cascade

A

A

A


Centrifugal Methods

M1 and M2 are the masses of the lighter and heavier isotopesω is the peripheral velocity of the moleculesa is the radius of the centrifuge r is the radius at any given location in the centrifuge R is the molar gas constant T is the absolute temperature

αααα increases with the length of the rotor, the peripheral speed and also with the radius.αααα depends on the difference between the massesBetter separation possible, of the 235U and 238U isotopes of uranium than of the isotopes of hydrogen with masses 1 and 2 Since the difference in the atomic masses is always same for a given element, the efficiency is independent of the molecular weight of the compound whose vapour is being centrifuged

2 2 2122

(M -M )ω a rα=exp (1- )a2RT

Separation factor α


2 2 2122

(M -M )ω a r=exp (1- )a2RT

α

When a gas or vapour flows into a rapidly rotating centrifuge, the force acting on the molecules will produce an increased concentration of the heavier isotope at the walls, while the lighter isotope tends to collect nearer the axis of rotation. If the centrifuge is vertical, a current of vapour can be made to flow down near the axis and up near the wall. It should then be possible to draw off a product richer in the lighter isotope at the bottom of the apparatus, near the centre, whereas the heavier species would be removed at the top near the periphery. The separation factor α for centrifugal method along the radius is given by


Pressure gradient of the gas

Ph = P0 exp (-Mgh/RT)

For two masses M1 and M2 (M1 < M2)

h o

P Pexp[ (M M )gh/RT]

P P1 1

2 2

1 2

= − −

Pressure gradient between the axis and the wall

Pa <<<<< Pw

Lighter isotope accumulates near the axis

Heavier isotope accumulates near the wall

Separation factor

depends on mass

difference

Separation factor

same for same

mass difference

(light and heavy

elements!!)


For a given mass difference between the isotopes, the stage separation factor is more than in gaseous diffusion plant.

To get 3 % enriched uranium, 13 stages are needed in centrifuge as compared to about 1300 stages required in the gaseous diffusion plant.

This advantage is partly off set by a lower yield per stage compared to the process of gaseous diffusion.

Large number of centrifuges need to he operated in parallel to multiply the net yield

With current technology, a single gas centrifuge is capable of about 5 separative work units [SWU] annually, while advanced gas centrifuge machines can operate at a level of up to perhaps 40 SWUs annually. About 120,000 SWU is required to enrich the annual fuel loading for a typical 1000 MWe light water reactor.


Separation factor does depend on the angular velocity (peripheral

speed of the rotor)

3.3 x 10141.329700

4.5 x 10101.233600

2.5 x 1071.156500

5.5 x 1041.0975400

Pressure ratio between axis

and wall

Separation factorPeripheral speed

m/s

Maximum velocity is limited by tensile strength of the rotor T.S. >

ρω2r2

Aluminium alloys

Titanium alloys

High tensile steels

Polyamides


Advantages of gas centrifuge over gas diffusion processes of enrichment

Higher separation factor hence requires less number of stages.

Absence of inter-stage gas compressors in centrifuge plant allows it to be squared off more towards ideality. Whereas in case of gas diffusion plant use of compressors makes it necessary to go for bigger squaring off (more off from ideality) in order to avoid use of large number of compressors of different capacities. This makes the centrifuge cascades more efficient.

Gas centrifuge being modular in construction, capacity addition can be done more easily. The plant can initially be constructed for lower capacity and can subsequently be expanded without much penalty.


Gas diffusion plants must be of large capacity to be economical due to requirement of large number of supporting systems like captive power plants etc. Whereas the gas centrifuge plants can be economical in smaller capacities.

Higher material inventory in gas diffusion plant makes it more difficult to switch over from one level of enrichment to another in an operating plant without a sufficient lead-time. This reduces flexibility of the plant in catering to different users requiring different enrichment levels in short delivery periods. In G.C. plants this problem does not arise due to much lower material inventories.

It has low equilibrium time, which reduces time between start up of the plant and start of withdrawal of product. Gas centrifuge process is considered superior above nozzle process also because of low separation factor (compared to gas centrifuge) and very high-energy consumption of nozzle process.


Feed

Product

Tails

Aerodynamic methods Nozzle separation process

S = 0.03 mm

A = 0.1 mm

95% H2 + 5% UF6 feed

α = 1.01 to 1.05

Processes in which isotopic composition changes are produced when a flowing gas mixture experiences large linear or centrifugal acceleration are termed aerodynamic processes.


Mixture of about 95% H2 and 5% UF6 at a pressure of about 1 atm. is allowed to expand through a narrow nozzle (0.01 mm wide) in to a curved (0.1 mm radius) wall.

The high speed gas experiences forces 160 million times the gravitational force in the curved nozzle.

The gas stream coming out of the nozzle is divided into lighter and heavier fractions by a very sharp skimmer knife.

Separation factor depends on the configuration of the nozzle, type of diluent gas and its abundance in relation to UF6, the inlet's absolute pressure and expansion ratio of the heavy fraction.

About 740 stages are required to produce 3% enriched uranium.

Jet nozzle process


Dilution of UF6 with hydrogen has two beneficial effects:

It helps to increase the speed of flow

It delays the establishment of a hypsometric distribution of Uf6 density. This delay reduces the re-mingling by diffusion of the isotopes of uranium already separated by the centrifugal forces.

Aerodynamic methods Nozzle separation process


Thermal diffusion methods

When heat flows through a mixture initially of uniform composition, small diffusion currents are set up, with one component transported in the direction of heat flow, and the other in opposite direction. This is known as thermal diffusion effect. The effect is generally small. For example when a mixture of 50% hydrogen and 50 % nitrogen is held in temperature gradient between 260 and 10°C the difference in composition at steady state is only 5%. In isotopic mixtures the effect is even smaller.


Thermal diffusion methods

Separation of molecules of different masses by radial diffusion in cylindrical columns due to temperature gradient across cylinder walls

Vertical separation due to temperature-induced convection currents

One of the methods first adopted in Manhattan project

Uranium was enriched to about 1% which was taken to electromagnetic separation for further enrichment

Solutions can also be enriched

Separation factor ~2

High energy incentive!!

SS

Cu

Ni

15 meters heightInner tube (Ni) at 2860COuter tube (SS) at 640CGap between Ni and Cu tubes ~ 1mmMaterial passes through this gapEquilibration time ~ weeks


Electromagnetic separation methods

Mass spectrometric principle

Mono-energetic ion beams are deflected by magnetic fields to

different m/e charge ratios

M H re V

2 2

2=

Requirements

Ion source

Acceleration field

Magnetic field analyser

Suitable collectors

Efficient pumping system


Very large separation factors possible

Production of large ion currents (space charge effects)

Strong stable magnetic fields

Suitable material for collectors (proper cooling)

Suitable for producing small amounts of isotopes

60 stable isotopes have been enriched

One of the first methods employed in Manhattan project in conjunction with thermal diffusion method


Laser separation methods

Electronic levels of atoms and vibrational levels molecules differ marginally depending on the isotopic mass

e.g. Hydrogen spectrumR

n n2 21 2

1 1

υ = −

Rydberg constant R ech

= π µ2 43

2 µ = reduced mass =MM

M M+1 2

1 2

HH

H

mM

M mµ =

+D

DD

mM

M mµ =

+

For a given transition n1→→→→n2

H

D

H H

DD

R

R

µ= = µ

υυ For D, λλλλD - λλλλH = 0.1785 nm


In the case of molecules, the fundamental frequency of a

diatomic moleculekυ= µπ

12

For different isotopes µ is different.

∆µ for lighter isotopes is large and for heavier isotopes small

By selecting a suitable wavelength it is possible to selectively

excite and ionise isotopic atoms

Uranium enrichment by lasers

Still at development stage

AVLIS: Atomic Vapour Laser Isotope Separation

MLIS: Molecular Laser Isotope Separation


AVLIS Process

Reservoir of uranium atoms by heating U metal

U atoms vapour pressure: a few torr

First U-235 atoms are selectively excited and then ionised by

another laser.

Ions are collected by electric or magnetic fields

235U*

Ground state

235U+

591.94 nm

210 - 310 nm

Xenon laser

Copper laser

Nitrogen laser

Dye laser

Nd-Yag laser

MLIS Process

235UF6 molecules are

selectively excited

with IR-laser.

Excited species are

irradiated with UV-

laser.

235UF6 →→→→ 235UF5 + F235UF5 is solid and is condensed


151133MLIS

170110AVLIS

350014001.012Nozzle

210671.25Gas centrifuge

210039201.00429Gas diffusion

Energy kwh/SWUStagesSeparation factorProcess

Performance of different processes for uranium enrichment

Feed: U-235 = 0.00711

Product U-235 = 0.9

Tails: U-235 = 0.002


Ion exchange enrichment of uranium isotopes

238UO2+2 + 235U(IV) � 235UO2

+2 + 238U(IV)

K = 1.0015

Ion exchange resin

Uranium loaded on column in H2SO4 medium

Repetitive oxidation, reduction carried out on the column

U(VI) is strongly absorbed

Many process conditions are classified

20 days of continuous operation yielded ~ 3% U-235


Separation of light isotopes

e.g. Deuterium from Hydrogen


Mass differences result in small but significant differences

in physico-chemical properties

1.106 g/cc0.991 g/cc------Density at 200C

201842Molecular weight

276.8K273K18.65K13.95KFreezing point

374.4K373K23.67K20.39KBoiling point

D2OH2OD2H2Property

Differences in the behaviour of isotopes due to mass

difference:

Diffusion

Evaporation

Mobility

Reactivity


Separation factors from vapour pressure ratios at boiling point

1.038-245.920Ne/22Ne

1.0046100H216O/H2

18O

1.004-195.8

1.029100

1.026100

1.036-33.6

1.81-252.9Ortho-H2/HD

αααα At boiling pointBoiling point (0C)Compounds

NH /ND33 3

H O/D O2 2

H O/T O2 2

N / N14 152 2

Conversion from ortho to para form should be minimised (large

power consumption!!!!)

No paramagnetic or ferromagnetic materials for construction!!


Distillation methods

Small differences in vapour pressure (boiling point) between the species

containing different isotopes

Separation factor x/( x)y/( y)

−α =−

11

x = atom fraction of desired isotope in liquid phase

y = atom fraction of desired isotope in vapour phase

AAB

B

πα = π

H2O + D2O ⇌⇌⇌⇌ 2HDO K = 4

H2O, D2O, HDO species in liquid phase

HDO D O H O HDO*

H O HDO HDO D O

x x y y

x x y y

+ +α =

+ +2 2

2 2

2 2

2 2x

HDO H O D Oy x x .x

Pπ

= =2 2

H O H

DD O

π π

π π2 2

22


P

Hydrogen rich gas,

depleted in D to ammonia

plant

Hydrogen

from

ammonia

plant

Recycle

compresso

r

First

coolin

g

refrigeratio

n

Secon

d

coolin

g

Feed

compresso

r

refrigeratio

n

First

cooling

and

water

removal

Second

cooling

and

nitrogen

removal

Joule-Thomson

coolingNormally

closed

Depleted liquid hydrogen

flux

Primary distillation tower

Generalised flow sheet for hydrogen distillation heavy water plants


⊗⊗⊗

HD-Free

hydrogen

low pressure

Secondary

towers

Exchange reactor

2HD ⇄ H2 + D2

Pure D2

Heat exchanger

HD

HD + H2

H2 + HD + D2

Pure D2HD-free hydrogen

high pressure

Primary

tower

Cold natural

hydrogen

0.028%HD

5.14%HD

Final concentration of deuterium by distillation of liquid hydrogen


≈≈≈≈

Electrolysis

Once-through process

≈≈≈≈≈≈≈≈

≈≈≈≈≈≈≈≈

Feed water

Partially enriched water

Counter-current process


F

E1 E2 E3

T1

600CT2 T3

BB

T

P

C1C2

C3C4

C5 C6

C7 C8

C9 C10

Three-stage cascade of electrolytic cells and exchange towers

T1, T2, T3 Exchange

towers

E1, E2, E3 Electrolytic

cells

F Feed water 10000

moles, 0.0148% D

T 9999 moles of

depleted water 0.005# D

B Burners

P 0.982 moles of Product

99.8% D

C1 0.0598% D, C2 0.0501% D, C3 2.013% D, C4 1.818% D, C5 98.89% D, C6 98.81%

D C7 491.92 moles of 0.101% D, C8 13.818 moles of 3.618% D, C9 492.9 moles of

0.300% D, C10 14.80 moles of 10.0% D


Chemical exchange methodsHD + H2O(l) � H2 + HDO(l) Catalyst Pt or Ni

K = 3.78 at 250C (Separation factor)

HDS(g) + H2O(l) � H2S(g) + HDO(l)

K = 2.32 at 320C

HD(g) + NH3(l) � H2(g) + NH2D(l) Catalyst KNH2 in NH3

K = 3.60 at 250C (ammonia plant needed!!!)

Water-hydrogen exchange reaction needs catalyst. Finely

divided Pt or Ni

Wetting of catalyst inhibits catalytic exchange

Water has to be in vapour form

Alternatively hydrophobic catalysts may be used.


Depleted water Waste

SulphurAir

Sulphur

recovery

unit

H2S + ½ O2 →H2O + S

H2S

320C

α = 2.32

Water

Heavy water

product

D2S

generator

Al2S3

producer

2Al + 3S → Al2S3

3D2O + 2Al2S3 → 3D2S + Al2O3

Al2O3 Al

Mono-thermal water – H2S

exchange

G.S. Process


Feed:Natural water

Cold towerT = 320Cα = 2.32

Hot towerT = 1280Cα = 1.80

D2S flow

D2O flowProduct

Recycle D2S

Depleted water

Blower

Dual temperature Water – H2S ExchangeGirdler – Spevack Process (GS Process)

Heat exchangers

Dual temperature exchange or bi-thermal exchange processAvoids reconverting the products into initial reactants to achieve the multiplication effect in the separation factor. Basis: Temperature dependent property of the equilibrium constant for the exchange reaction.

H2O(l) + HD(g) < = = > HDO(I) + H2(g)Keq = 3.78 at 25

0C and 2.60 at 800C

H2O(l) + HDS(g) < = = > HDO(l) + H2S(g), Keq = 2.32 at 32°C and 1.30 at 138°C.


Ion Migration

Slight differences in velocities of isotopic ions in solution under an electric field

These small differences are due to the different sizes and masses of the ions.Contributions due to differences in the degree of dissociation and in complex formation also to be considered.Ion migration can occur not only in aqueous media where the ions are invariably hydrated but also in fused salt media where the ions are relatively more free from solvation effects.

Advantage of the fused salt medium: Absence of ion solvation resulting in larger mass effects in the

migration of isotopic ions.

Separation factor αααα ∆∆∆∆v/v ∆∆∆∆v is difference in velocities between the isotopes and v is the mean velocity


v/v-m/m

∆µ =∆

The extent of separation effect between the two isotopes can also be expressed in terms of relative mass effect given as

where m is the mass of the ion. Thus the actual enrichment factor is somewhat less than expected when only velocities are considered. More over, whileelectromigration builds up a concentration gradient along the field direction, the reverse flow of the electrolyte due to diffusion tends to neutralise the effect partially.

In a typical example, 39K and 41K were separated by theelectromigration of potassium chloride solution in a U-shaped tube using platinum gauge electrodes,


1. K. Cohen, The theory of isotope separation, Mc Graw Hill, New York (1951)

2. M. Benedict and T.H. Pigford, Nuclear chemical engineering, Mc Graw Hill, New York (1965)

3. H. London, Separation of isotopes, George Newnes, London (1961)

4. S. Villani, Isotope separation, Amer. Nucl. Soc., Hinsdale, (1976)

5. H.J. Arnikar, Isotopes in atomic age, Wiley Eastern, New Delhi, (1989)

6. J. Koch(Ed.), Electromagnetic isotope separators and applications of magnetically enriched isotopes, Interscience, New York (1958)

7. G.M. Murphy(Ed.), Production of heavy water, Mc GrawHill, New York (1955)

separation of stable isotopes

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