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CONVECTION AND OTHER DISTURBING
EFFECTS IN DIFFUSION EXPERIMENTS IN
LIQUID METALS
T. Persson, P. Eriksson, L. Lindström
To cite this version:
JOURNAL DE PHYSIQUE CoZZoque C8, suppZBment au n08, Tome 41, aoct 1980, page C8-374
CONVECTION AND OTHER DISTURBING EFFECTS IN DIFFUSION EXPERIEENTS IN LIQUID KETALS
T. Persson, P.E. Eriksson and L. Lindstrom
Department of Physics, ChaZmers University of TechnoZogy, GBteborg, Sweden.
1. INTRODUCTION
D i f f u s i o n i n l i q u i d metals has been s t u d i e d f o r more t h a n a hundred years. During t h i s n e r i o d some papers have been devoted t o t h e s u b j e c t o f convec- t i o n as a source o f e r r o r i n d i f f u s i o n experiments. Very few o f these works c o n t a i n i n f o r m a t i o n about t h e o r d e r o f magnitude of t h e t r a n s p o r t o f m a t t e r caused by convection. Davis showed t h a t these e f f e c t s c o u l d be o f considerable importance i n t h e d i f f u s i o n o f s i l v e r i n t o t i n (Ref. 1 ) . Verhoeven
(Ref. 2) t r e a t e d d i f f e r e n t tynes ~f c o n v s c t i o n t h a t
might occur i n d i f f u s i o n experiments i n l i q u i d metals, w i t h s p e c i a l emphasis on ex?eriments n e r - formed by t h e c a p i l l a r y - r e s e r v o i r technique. It i s a very i m p o r t a n t a r t i c l e e s p e c i a l l y f o r e x p e r i - m e n t a l i s t s i n t h i s f i e l d b u t t h e r e a r e s t i l l v e r y few data t o i l l u s t r a t e some o f t h e t h e o r e t i c a l discussions.
The message o f Verhoeven's a r t i c l e must have had some d i f f i c u l t i e s t o reach a l l persons w i t h i n t h e f i e l d as a t l e a s t two new techniques u s i n g horizon- t a l capi 11 a r i es have been developed. (Ref. 3,4)
.
We have made a s t u d y t o g e t i n f o r m a t i o n about t h e amount o f convection t h a t c o u l d occur d u r i n g a d i f f u s i o n experiment on l i q u i d metals and thereby we should g e t a chance t o judge t h e v a l i d i t y o f experiments e a r l i e r made.The
purpose o f t h i s work i s a l s o t o l e a r n more about convection. A thorough knowledge o f convec-t i o n i s an a b s o l u t e n e c e s s i t y (Ref. 5 ) f o r being a b l e t o perform and t o i n t e r p r e t d i f f u s i o n e x p e r i - ments. If e x p e r i m e n t a l i s t s a r e t o c o n t r i b u t e t o t h e understanding o f d i f f u s i o n processes i n l i q u i d s a t a l l they must have a v e r y good and accurate ex- perimental method which t h e y should master com- p l e t e l y . The outcome o f t h i s work w i l l h e l p us i n developing a new experimental technique. As t h e weak p o i n t s o f t h e method a r e known we can a v o i d them i n t h e new technique.
Anoci~er o b j e c t i v e i s t o study t h e convection be- haviour when t h e r e i s a i i o r i z o n t a l d e n s i t y g r a d i - e n t present. T h i s c o n f i g u r a t i o n i s sometimes en- countered i n m e t a l l u r g i c a l a p p l i c a t i o n s on l i q u i d metals,
eg.
s o l i d i f i c a t i o n experimer!ts. I n these cases i t i s i m p o r t a n t t o know what parameters w i l l i n f l u e n c e t h e masstransport as t h e r e i n some cases a r e no p o s s i b i l i t i e s t o change t h e o r i e n t a t i o n o f t h e d e n s i t y g r a d i e n t w i t h regard t o t h e g r a v i t y vector.2'. EXPERIMENTAL
I n t h e a c t u a l s t u d y we have been u s i n g t h e w e l l - known " s e m i - i n f i n i t e - r o d " technique (Ref. 6 ) where t h e c o n c e n t r a t i o n o f t h e t r a c e r i s g i v e n by
where x i s t h e s p a t i a l c o o r d i n a t e i n t h e one dimen- s i o n a l d i f f u s i o n problem, t t h e d i f f u s i o n time, D t h e t r a c e r d i f f u s i o n c o e f f i c i e n t , c t h e concentra-
t i o n o f t h e t r a c e r . c o e f f i c i e n t f o r t r a c e r d i f f u s i o n o f g o l d i n sodium The experimental c e l l s a r e made o f pyrex glass and
t h e geometry o f t h e c e l l s i s shown i n f i g .
I .
k
(The capi 1 la r y d i a -meter w i l l be
locrn symbolized by "d"
Fig. 1. D i f f u s i o n c e l l s
A small amount o f t r a c e r i n m e t a l l i c form i s placed a t the b u t t end o f t h e c a p i l l a r y and a f t e r evacua- t i o n and h e a t i n g t o t h e ?redetermined d i f f u s i o n temperature the l i q u i d metal i s pushed o n t o t h e t r a c e r by means o f argon gas. The sample i s k e p t i n an o i l bath, which i s o u r heat r e s e r v o i r , f o r a time t and then t h e sample i s taken o u t o f t h e o i l bath and allowed t o cool t o room t e y e r a t u r e . A f t e r t h a t t h e c a p i l l a r y i s c u t i n t o anproximately 12 pieces and t h e c o n c e n t r a t i o n o f t h e t r a c e r i s determined by means o f a NaI ( T I ) c r y s t a l and standard e l e c t r o n i c s i n c l u d i n g p r e a m p l i f i e r , ampli- f i e r and a s t a b i l i z e d s i n g l e channel analyser. I n t h i s i n v e s t i g a t i o n we have been concerned w i t h t h e i n f l u e n c e on t h e measured o r apparent d i f f u s i o n c o e f f i c i e n t when some parameters 1 i ke t h e o r i e n t a - t i o n and t h e i n n e r diameter o f t h e c a p i l l a r y , t h e temnerature and t h e d i f f e r e n c e i n d e n s i t y between t r a c e r and m a t r i x have been varied. We have a l s o b r i e f l y touched upon t h e e f f e c t s o f dead-time losses i n e v a l u a t i o n o f c o n c e n t r a t i o n p r o f i l e s and d i f f u s i o n c o e f f i c i e n t s .
I n these measurements we have been u s i n g lg8au as t r a c e r t o determine t h e apparent t r a c e r d i f f u s i o n c o e f f i c i e n t i n sodium, ' l 4 3 n i n Ga and 6 7 ~ a f o r s e l f d i f f u s i o n s t u d i e s . The apparent d i f f u s i o n as a f u n c t i o n o f o r i e n t a t i o n and temperature i s g i v e n i n f i g . 2. F i g . 2. "0" vs T f o r h o r i z o n t a l and v e r t i c a l cap. As can be seen t h e r e i s a nronounced c o n t r i b u t i o n of convection as t h e c a p i l l a r i e s a r e k e p t i n a h o r i - z o n t a l n o s i t i o n . We do n o t c l a i m t h a t o u r data are of s u p e r i o r accuracy b u t t h e d e v i a t i o n s a r e s t i l l s i g n i f i c a n t . The v e r t i c a l c a p i l l a r i e s almost a l - ways gave l e s s spreading and s m a l l e r e r r o r bars than t h e h o r i z o n t a l ones. Therc i s 2
a r ~ c i
3 i :re-JOURNAL DE PHYSIQUE C8-376
-
100 Zoo2,
F i q . 3. 'ID" vs T f o r d i f f u s i o n o f I n i n t o Ga d = 0,7 mm I n h o r i z o n t a l c a p i l l a r i e s t h e amount o f convection a l s o seemed t o bea
f u n c t i o n o f t h e c a n i l l a r y d i a - meter i n t h e case o f l g 8 ~ u as t r a c e r i n Na. This e f f e c t which i s q r a p h i c a l l y represented i n f i g . 4 was a l s o expected.(Only some data p o i n t s a r e i n - dicated.)
,
rr
roo m 303 '
Fig. 4. "DM vs T f o r h o r i z o n t a l cap.
From f i q u r e 2 i t looks as i f t h e r e i s a diameter dependent d i f f u s i v i t y even f o r t h e v e r t i c a l cap- i l l a r i e s , b u t t h i s d e v i a t i o n i s n o t s i g n i f i c a n t . We must a l s o p o i n t o u t t h a t t h e r e i s a g r e a t s c a t t e r between t h e i n d i v i d u a l p o i n t s f o r t h e h o r i z o n t a l c a p i l l a r i e s . The l i n e s given i n t h i s qraph merely show t h e trends.
As expected t h e convection i s most pronounced i n t h e beginning o f a d i f f u s i o n r u n when t h e d e n s i t y g r a d i e n t i s very stee?. A number o f h o r i z o n t a l c e l l s were prepared i n e x a c t l y t h e same way and annealed a t t h e same temperature b u t they were k e o t i n t h e heat r e s e r v o i r f o r d i f f e r e n t times. The r e s u l t s a r e shown i n f i g . 5 where t h e appa- r e n t d i f f u s i o n c o e f f i c i e n t f o r l g 8 ~ u i n Na i s
p l o t t e d as a f u n c t i o n o f annealing time.
F i g . 5. "D" vs d i f f u s i o n time, t
From t h e c o n c e n t r a t i o n p r o f i l e s we determined t h e apparent d i f f u s i o n c o e f f i c i e n t s i n t h e same way as i f t h e c o n c e n t r a t i o n p r o f i l e had been caused by d i f f u s i o n . As i s obvious from t h i s p i c t u r e convec- t i o n dominates over d i f f u s i o n a t s h o r t annealino times and t h i s means t h a t i t i s n o t c o r r e c t t o ex- t r a c t a d i f f u s i o n c o e f f i c i e n t from t h e concentra- t i o n curve as i f i t had been ~ r o d u c e d by a pure d i f f u s i o n orocess, b u t we made these exoeriments t o show t h e r a p i d and pronounced convection a t t h e s t a r t o f t h e experiments. There i s a l s o a l a r g e s c a t t e r between i n d i v i d u a l ? o i n t s e s p e c i a l l y f o r s h o r t times and t h e p o i n t s i n t h i s graph merely rep-
r e s e n t t h e t r e n d i n these experiments.
Some c e l l s were f i l l e d when t h e c a p i l l a r i e s were t i l t e d a t an angle o f 45' t o t h e normal and then t r a n s f e r r e d t o t h e h o r i z o n t a l p o s i t i o n i n a smooth way. Others were f i l l e d when t h e c a p i l l a r i e s were a l r e a d y placed i n a h o r i z o n t a l p o s j t i o n . We c o u l d n o t see any s i g n i f i c a n t d i f f e r e n c e so v i b r a t i o n s a r e probably o f minor importance i n generating con- v e c t i o n compared t o t h e d i f f e r e n c e i n d e n s i t y i n - s i d e t h e sample.
tion determination. This means t h a t the concentra- ways be v e r t i c a l l y oriented. Furthermore r e ~ e a t e d tion p r o f i l e seemed t o be more f l a t than the real
s i t u a t i o n . The apparent diffusion coefficients determined from these concentration p r o f i l e s gave a larger value than f o r those evaluated from con- centration p r o f i l e s determined without dead time losses. In f i g . 6 the apparent diffusion coeffi- c i e n t s a r e shown as a function of the time elapsed since the f i r s t determination of the concentration p r o f i l e .
Fig. 6.
"D" vs time elapsed a f t e r diffusion run
V e r t i c a l c a p . d = 1 , 5 m mAs the r a d i o a c t i v i t y i s decreasing the apparent diffusion coefficients a r e approaching a real d i f f u - sion c o e f f i c i e n t . We made t h i s check t o find out about the order of t h e magnitude of the e r r o r s caused by dead time losses as we think t h a t t h i s e f f e c t might have been ~ r e s e n t i n some e a r l i e r published data on the diffusion in l i q u i d s .
3. CONCLUSIONS
In t h i s study we have shown t h a t convection e f f e c t s a r e considerable in diffusion experiments in liquids i f the necessary precautions a r e not taken. The obvious conclusion t o be drawn from the present work i s t h a t i t i s extremely important always to
have the density gradient a n t i - p a r a l l e l t o t h e vec- t o r of gravity. Even i f density differences do not seem t o be present the diffusion path should a l -
concentration measurements must be made i f radio- a c t i v e t r a c e r s a r e used t o check the "dead-time" e f f e c t . I t should a l s o be stressed t h a t a gaussian shaped concentration n r o f i l e i s not necessari1,y a proof of convectionless exneriments. In f i g . 7 we show a concentration p r o f i l e from an experiment where t h e amount of convection i s a t l e a s t 30 % of t h e apparent diffusion c o e f f i c i e n t .
I
>O ;O O; 0 20 'im51
Fig. 7. Concentration p r o f i l e a f t e r diffusion
r u n
Horizontal cap. d = 0,8
mm
T = 210 OCFull curve represent Gaussian d i s t r .
4. REFERENCES
1. Davis
K
G 1970, Can. Hetall. Q u a r t .2
4P91
2. Verhoeven J
D 1968, Trans. Metall. Soc. AIME
242 1937.
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3 . Larsson S , Broman
L ,
Roxbergh C , LoddingA
1970, Z. Naturforsch.
5
a 14724. Keita
M ,
Steinemann S , KUnzi H U 1976, Ber.~ u n s e n ~ e s . Phys. Chem.
80
7225. Rigney
D
P
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