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The enrichment of radio-active isotopes by thermal diffusion
De Vries, A . E . 1955
Physica X X I 124-126
T H E E N R I C H M E N T OF RADIO-ACTIVE ISOTOPES BY T H E R M A L D I F F U S I O N b y A. E. D E V R I E S Laboratorium voor massaspectrografie, Stichting voor F m l d a m e n t e e l Onderzoek der Materie, Amsterdam, Nederland
Summary A method is suggested to enhance the enrichment of a radio-active isotope in a thermal-diffusion column. The method is of importance when the quantity which has to be enriched, is small compared to the hold-up of the column. In this case a longer column would not give a better enrichment. As an example CO is chosen in which the 14CO has to be concentrated in a small amount of 12C0. The fact t h a t the equilibrium c o n s t a n t k in isotope s e p a r a t i o n processes lies v e r y n e a r u n i t y m a k e s it necessary to a p p l y c o u n t e r c u r r e n t m e t h o d s . Therefore the q u a n t i t y of m a t e r i a l needed for establishing the c o n c e n t r a t i o n gradient in m a n y cases c a n n o t be neglected. In 1949 K. C 1 u s i u s 1) a n n o u n c e d a m e t h o d b y which it was possible to reduce this h o l d - u p in t h e r m a l - d i f f u s i o n columns. T h e m e t h o d consisted of the a d d i t i o n of a t h i r d c o m p o n e n t X which h a d to be c o n c e n t r a t e d b e t w e e n the two original c o m p o n e n t s A a n d B. After equilibrium has been established one can t a k e off the t w o m i x t u r e s A X a n d X B which in t u r n are s e p a r a b l e b y an o r d i n a r y physical or chemical m e t h o d . T h e real action of X is t h a t it reduces the absolute c o n c e n t r a t i o n s of A a n d B in the transition region w i t h o u t h o w e v e r d i s t u r b i n g the relative c o n c e n t r a t i o n s 2). As this area contains b o t h c o m p o n e n t s for 5 0 % in the middle of the column, X will be the m o r e efficient the m o r e it c o n c e n t r a t e s a t this point. F o r molecules which differ only in m a s s therefore the m o s t f a v o u r a b l e m a s s is the a r i t h m e t i c a l m e a n of the masses of A a n d B. T h i s usually not being the case, v e r y little can be said a b o u t the action of X b e f o r e h a n d a n d e x p e r i m e n t s are n e c e s s a r y to find the m o s t efficient gas. In the case of r a d i o - a c t i v e isotopes one is not facing the p r o b l e m of s e p a r a t i n g the two c o m p o n e n t s b u t of enriching one of t h e m , the concent r a t i o n of the r a d i o - a c t i v e isotope increasing e x p o n e n t i a l l y along the column. T h e r e is no t r a n s i t i o n - r a n g e b u t at b o t h sides of the c o l u m n the concent r a t i o n of the stable isotope is v e r y n e a r 100%. T h e chief p a r t of t h e h o l d - u p of the radio-isotope does not occur in the middle of the column b u t at the -
-
124
-
-
THE ENRICHMENT
OF RADIO-ACTIVE ISOTOPES BY THERMAL DIFFUSION
125
side where it is enriched, e.g. for a h e a v y radio-isotope in the l o w e r ' p a r t of the column. B y adding a c o m p o n e n t X which c o n c e n t r a t e s in this lower part, the absolute values of the isotopes will be decreased with a subsequent increase in enrichment. Suppose one enriches 14C in '2C (both as carbon monoxide). As the concent r a t i o n of the 14CO is e x t r e m e l y low, even in strongly enriched material, the increase along the column from top to b o t t o m is purely exponential. The average c o n c e n t r a t i o n of the ~4CO in the column is given b y l / L ~Z=o qz e dl L being the total length of the column expressed in characteristi,~ lengths (the length required to change the c o n c e n t r a t i o n - r a t i o b y a f a c t o r e), qt the e n r i c h m e n t factor at a point at a distance 1 from the top and e the concent r a t i o n of ~4C0 at the top after equilibrium has been established. Now (l/L) f L 0 q, ~ dt = ( e / L ) / L 0 e' dZ = (e/L) (eL -- 1) A column with a q of l04 will have a v o l u m e of the order of some litres. Assuming 2 litres and a b o t t o m v o l u m e of 100 cm 3 in which one wants to c o n c e n t r a t e the 14C, the hold-up would be a b o u t 650/0 . A longer column would not be of a n y help, the increase in volume of the column just compensating the decrease of the average 14C concentration. We now add a c o m p o n e n t X which c o n c e n t r a t e s in the lower part of the column. The c o n c e n t r a t i o n of the ~2CO at a place 1 from the top is given b y )J = ½ [1 -- t a n h {(L -- L0) ] 3) L 0 b e i n g the point where )~ = ½ (50% 12CO and 50% X). The total 14C0 c o n t e n t at this place is found b y multiplying this value with the fraction of the 14CO in t h e 12C0, which is the same as w i t h o u t X (theorem of the " i n d e p e n d e n t s e p a r a t i o n " ) . Therefore the average c o n c e n t r a t i o n of ~4CO in the column is g = (e/L) ftL=o e y' 7 d l =
(e/2L) .fi=o L ey, [1 -- t a n h ½(/-- L0) ] d l
in which L is the length of the column (in characteristic lengths) for the t2CO -- X , and y L for the ~2C0 -- 14CO separation. We find g = ( e / L y ) f ~ o (e t-Lo + 1) - l d d ~ If we assume y = ½ this becomes g = (2elL) e ~Lo [bg tg e ~/L-L"I -- bg tg e -~Lo] W i t h a b o t t o m volume of 10 l, containing 1c}~, of tzCO, the total a m o u n t of ~2C0 will be 100 cm a, t h a t is the same as in the case without X. W i t h the same q = 1 0 4 for ~2C0 -- 14C0 the q for the separation of ~2C0 -- X is 108 in this case of y = ½, so L = In 108 = 18.4.
126
THE
ENRICHMENT
OF RADIO-ACTIVE
ISOTOPES
BY THERMAL
DIFFUSION
The length over which the concentration ratio ~2CO/X changes from the b o t t o m value 1/100 to 50/50 is In 100 -= 4.6 = ¼L so L 0 = ~L = 13.8. Thus the total amount of 14C is 2 × g ~ 324 e, while the total amount of 14C in the reservoir is 0.1 x 104 e ---- 1000 e so the hold-up is less than 25% . As in the former case 35% from the total amount of 14C0 was concentrated in the b o t t o m and in the latter case about 75%, both in the same q u a n t i t y of 12C0, the specific activity in the latter case will be more than twice as large. Here, as well as in the case without X, the formulae only hold exactly where isotopic mixtures are concerned. Experiments, therefore, are carried out in our laboratory with different added components. NI4N 15would be very valuable when added to CO, but as it is difficult to obtain and very expensive it has to be replaced. Ethylene which concentrates in the lower part of the column (0,5 < y < 1) in respect to the radio-isotope t4CO looks very promising. It is emphasized t hat the method is not restricted to small samples. Even if the sample is infinite it is of much value for a given column because in the end situation the column contains a great part of the radio-isotope. By closing the column and replacing part of the CO in the upper reservoir by X the enrichment is also increased in the same way: only the ratio of the column and bottom volumes is of importance. This work is part of the research program of the "Stichting voor Fundamenteel Onderzoek der Materie" and is made possible by financial support from the "Nederlandse Organisatie voor Zuiver Wetenschappelijk Onderzoek". R e c e i v e d 23- 12-54. R E F E I~.ENCES I) C l u s i u s , K., H e i r . p h y s . A c t a 2 2 (1949) 473. 2) S c h u h m a e h e r , E., H e i r . c h i m . A c t a 3 6 (1953) 955. 3) S c h u h m a c h e r, E., Q u a n t i t a t i v e T r e n n u n g polym'/irer G a s g e n f i s c h e d u r c h T h e r m o d i f f u s i o n , diss. 1951, Ziirich.
Physica X X I 124-126
T H E E N R I C H M E N T OF RADIO-ACTIVE ISOTOPES BY T H E R M A L D I F F U S I O N b y A. E. D E V R I E S Laboratorium voor massaspectrografie, Stichting voor F m l d a m e n t e e l Onderzoek der Materie, Amsterdam, Nederland
Summary A method is suggested to enhance the enrichment of a radio-active isotope in a thermal-diffusion column. The method is of importance when the quantity which has to be enriched, is small compared to the hold-up of the column. In this case a longer column would not give a better enrichment. As an example CO is chosen in which the 14CO has to be concentrated in a small amount of 12C0. The fact t h a t the equilibrium c o n s t a n t k in isotope s e p a r a t i o n processes lies v e r y n e a r u n i t y m a k e s it necessary to a p p l y c o u n t e r c u r r e n t m e t h o d s . Therefore the q u a n t i t y of m a t e r i a l needed for establishing the c o n c e n t r a t i o n gradient in m a n y cases c a n n o t be neglected. In 1949 K. C 1 u s i u s 1) a n n o u n c e d a m e t h o d b y which it was possible to reduce this h o l d - u p in t h e r m a l - d i f f u s i o n columns. T h e m e t h o d consisted of the a d d i t i o n of a t h i r d c o m p o n e n t X which h a d to be c o n c e n t r a t e d b e t w e e n the two original c o m p o n e n t s A a n d B. After equilibrium has been established one can t a k e off the t w o m i x t u r e s A X a n d X B which in t u r n are s e p a r a b l e b y an o r d i n a r y physical or chemical m e t h o d . T h e real action of X is t h a t it reduces the absolute c o n c e n t r a t i o n s of A a n d B in the transition region w i t h o u t h o w e v e r d i s t u r b i n g the relative c o n c e n t r a t i o n s 2). As this area contains b o t h c o m p o n e n t s for 5 0 % in the middle of the column, X will be the m o r e efficient the m o r e it c o n c e n t r a t e s a t this point. F o r molecules which differ only in m a s s therefore the m o s t f a v o u r a b l e m a s s is the a r i t h m e t i c a l m e a n of the masses of A a n d B. T h i s usually not being the case, v e r y little can be said a b o u t the action of X b e f o r e h a n d a n d e x p e r i m e n t s are n e c e s s a r y to find the m o s t efficient gas. In the case of r a d i o - a c t i v e isotopes one is not facing the p r o b l e m of s e p a r a t i n g the two c o m p o n e n t s b u t of enriching one of t h e m , the concent r a t i o n of the r a d i o - a c t i v e isotope increasing e x p o n e n t i a l l y along the column. T h e r e is no t r a n s i t i o n - r a n g e b u t at b o t h sides of the c o l u m n the concent r a t i o n of the stable isotope is v e r y n e a r 100%. T h e chief p a r t of t h e h o l d - u p of the radio-isotope does not occur in the middle of the column b u t at the -
-
124
-
-
THE ENRICHMENT
OF RADIO-ACTIVE ISOTOPES BY THERMAL DIFFUSION
125
side where it is enriched, e.g. for a h e a v y radio-isotope in the l o w e r ' p a r t of the column. B y adding a c o m p o n e n t X which c o n c e n t r a t e s in this lower part, the absolute values of the isotopes will be decreased with a subsequent increase in enrichment. Suppose one enriches 14C in '2C (both as carbon monoxide). As the concent r a t i o n of the 14CO is e x t r e m e l y low, even in strongly enriched material, the increase along the column from top to b o t t o m is purely exponential. The average c o n c e n t r a t i o n of the ~4CO in the column is given b y l / L ~Z=o qz e dl L being the total length of the column expressed in characteristi,~ lengths (the length required to change the c o n c e n t r a t i o n - r a t i o b y a f a c t o r e), qt the e n r i c h m e n t factor at a point at a distance 1 from the top and e the concent r a t i o n of ~4C0 at the top after equilibrium has been established. Now (l/L) f L 0 q, ~ dt = ( e / L ) / L 0 e' dZ = (e/L) (eL -- 1) A column with a q of l04 will have a v o l u m e of the order of some litres. Assuming 2 litres and a b o t t o m v o l u m e of 100 cm 3 in which one wants to c o n c e n t r a t e the 14C, the hold-up would be a b o u t 650/0 . A longer column would not be of a n y help, the increase in volume of the column just compensating the decrease of the average 14C concentration. We now add a c o m p o n e n t X which c o n c e n t r a t e s in the lower part of the column. The c o n c e n t r a t i o n of the ~2CO at a place 1 from the top is given b y )J = ½ [1 -- t a n h {(L -- L0) ] 3) L 0 b e i n g the point where )~ = ½ (50% 12CO and 50% X). The total 14C0 c o n t e n t at this place is found b y multiplying this value with the fraction of the 14CO in t h e 12C0, which is the same as w i t h o u t X (theorem of the " i n d e p e n d e n t s e p a r a t i o n " ) . Therefore the average c o n c e n t r a t i o n of ~4CO in the column is g = (e/L) ftL=o e y' 7 d l =
(e/2L) .fi=o L ey, [1 -- t a n h ½(/-- L0) ] d l
in which L is the length of the column (in characteristic lengths) for the t2CO -- X , and y L for the ~2C0 -- 14CO separation. We find g = ( e / L y ) f ~ o (e t-Lo + 1) - l d d ~ If we assume y = ½ this becomes g = (2elL) e ~Lo [bg tg e ~/L-L"I -- bg tg e -~Lo] W i t h a b o t t o m volume of 10 l, containing 1c}~, of tzCO, the total a m o u n t of ~2C0 will be 100 cm a, t h a t is the same as in the case without X. W i t h the same q = 1 0 4 for ~2C0 -- 14C0 the q for the separation of ~2C0 -- X is 108 in this case of y = ½, so L = In 108 = 18.4.
126
THE
ENRICHMENT
OF RADIO-ACTIVE
ISOTOPES
BY THERMAL
DIFFUSION
The length over which the concentration ratio ~2CO/X changes from the b o t t o m value 1/100 to 50/50 is In 100 -= 4.6 = ¼L so L 0 = ~L = 13.8. Thus the total amount of 14C is 2 × g ~ 324 e, while the total amount of 14C in the reservoir is 0.1 x 104 e ---- 1000 e so the hold-up is less than 25% . As in the former case 35% from the total amount of 14C0 was concentrated in the b o t t o m and in the latter case about 75%, both in the same q u a n t i t y of 12C0, the specific activity in the latter case will be more than twice as large. Here, as well as in the case without X, the formulae only hold exactly where isotopic mixtures are concerned. Experiments, therefore, are carried out in our laboratory with different added components. NI4N 15would be very valuable when added to CO, but as it is difficult to obtain and very expensive it has to be replaced. Ethylene which concentrates in the lower part of the column (0,5 < y < 1) in respect to the radio-isotope t4CO looks very promising. It is emphasized t hat the method is not restricted to small samples. Even if the sample is infinite it is of much value for a given column because in the end situation the column contains a great part of the radio-isotope. By closing the column and replacing part of the CO in the upper reservoir by X the enrichment is also increased in the same way: only the ratio of the column and bottom volumes is of importance. This work is part of the research program of the "Stichting voor Fundamenteel Onderzoek der Materie" and is made possible by financial support from the "Nederlandse Organisatie voor Zuiver Wetenschappelijk Onderzoek". R e c e i v e d 23- 12-54. R E F E I~.ENCES I) C l u s i u s , K., H e i r . p h y s . A c t a 2 2 (1949) 473. 2) S c h u h m a e h e r , E., H e i r . c h i m . A c t a 3 6 (1953) 955. 3) S c h u h m a c h e r, E., Q u a n t i t a t i v e T r e n n u n g polym'/irer G a s g e n f i s c h e d u r c h T h e r m o d i f f u s i o n , diss. 1951, Ziirich.