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Comments on “treatment of diffusion considering changes in atomic volume”
Scripta M E T A L L U R G I C A
Vol. 5, pp. 287-288, 1971 Printed in the U n i t e d States
Pergamon Press,
Inc
COMMENTS ON "TREATMENT OF D I F F U S I O N C O N S I D E R I N G CHANGES IN ATOMIC VOLUME"
F.J.J. van Loo L a b o r a t o r y of P h y s i c a l C h e m i s t r y E i n d h o v e n U n i v e r s i t y of Technology,
In his article Guy
(I) c r i t i c i z e s my paper
Netherlands
(2) on several important points.
I do not agree w i t h this c r i t i c i s m and my o b j e c t i o n s
are both p r a c t i c a l
and theoretical.
(a) R e l a t i o n [ 9 of Guy's article
(that is Eq. [ ~ i n
my paper)
me as the d e f i n i t i o n of the i n t e r d i f f u s i o n c o e f f i c i e n t D paper).
S t a r t i n g f r o m this definition,
expressions
DI, D 2 and D are r e l a t e d to m e a s u r a b l e quantities.
(~
is used by in Guy's
are d e r i v e d in w h i c h Therefore,
values for
these c o e f f i c i e n t s o b t a i n e d from such e x p r e s s i o n s must n e c e s s a r i l y satisfy the r e l a t i o n in question. In a d i f f u s i o n couple with c h a n g i n g total v o l u m e the i n t e r d i f f u s i o n coefficient D is s t r a i g h t f o r w a r d l y r e l a t e d to the flux of c o m p o n e n t i in number 2 of moles per second per cm w h i c h pass through a p a r t i c u l a r i n t e r f a c e with respect to an i m a g i n a r y o b s e r v a t i o n post fixed on the surface of the couple, thus f o l l o w i n g the e x p a n s i o n or c o n t r a c t i o n of the couple. m a t e r i a l constant,
it has a g e n e r a l
significance.
Since D is a
For a p a r t i c u l a r concen-
tration it m u s t be the same c o e f f i c i e n t as the one found in d i f f u s i o n e x p e r i m e n t s w i t h c o n s t a n t total volume.
In some systems it is p o s s i b l e to
verify this by means of a proper choice of the c o m p o s i t i o n of the starting materials.
(b) It is true that e.g. the c o e f f i c i e n t s D I and D 2 in the article of Sauer and Freise
(3) on d i f f u s i o n
in liquid systems do have another s i g n i f i c a n c e
than the i n t r i n s i c d i f f u s i o n coefficients,
m e a s u r e d in solid systems with
respect to inert markers.
However, my article does not allow any m i s u n d e r -
standing on this subject.
The i n t r i n s i c d i f f u s i o n c o e f f i c i e n t s D i, discus-
sed by me,
d e t e r m i n e the flux of c o m p o n e n t i in number of moles per second
per cm 2 p a s s i n g t h r o u g h the m a r k e r i n t e r f a c e to the K i r k e n d a l l
interface)
(in my article r e s t r i c t e d
in a solid d i f f u s i o n couple.
not see why Guy q u e s t i o n s their relevance.
287
Therefore,
I do
288
COMMENTS ON " D I F F U S I O N W I T H CHANGES
(c) The e q u a t i o n s given by Guy
IN ATOMIC VOLUME"
(4) do look simpler,
Vol.
5, No.4
but are in fact m o r e
c o m p l i c a t e d to apply than my methods. (i) The use of v o l u m e f r a c t i o n as a c o n c e n t r a t i o n unit is in m a n y cases unpractical, fraction,
and in some cases impossible.
In order to obtain the v o l u m e
the p a r t i a l m o l a l volumes m u s t be known.
These have to be det-
e r m i n e d by means of the c o n s t r u c t i o n of tangents to the plot of m o l a r v o l u m e v e r s u s mole fraction,
w h i c h is a rather i n a c c u r a t e process.
there are o f t e n not e n o u g h d a t a available, compounds,
e.g.
Moreover,
in m a n y i n t e r m e t a l l i c
since at least two v a l u e s of V m at a d i f f e r e n t c o n c e n t r a t i o n
m u s t be known.
It is even i m p o s s i b l e to d e t e r m i n e the partial m o l a l v o l u m e s
in the i m p o r t a n t case where a "line-compound"
develops
Even the o c c u r r e n c e of only one such l i n e - c o m p o u n d
in a d i f f u s i o n couple.
in the couple rules out
the p o s s i b i l i t y of u s i n g Guy's method. (ii) The c o n v e r s i o n of x
(in cm)
into the new c o o r d i n a t e x' is intricate.
This t i m e - c o n s u m i n g task m u s t be f o l l o w e d for each d i f f u s i o n couple again, since this c o n v e r s i o n d e p e n d s on the c o m p o s i t i o n of the starting m a t e r i a l s .
(d) The r e l a t i o n b e t w e e n the i n t e r f a c e at x = 0 and the two "Matano interfaces"
(one for each component)
in the c o o r d i n a t e system used by me is
s u f f i c i e n t l y d i s c u s s e d in my paper
(2). Guy claims that one of the advant-
ages of his m e t h o d is the c o i c i d e n c e of his "Matano interface" initial plane of joining of the two halves of the couple However,
it can be shown g r a p h i c a l l y that this is g e n e r a l l y not the case.
(e) T h e o r e t i c a l o b j e c t i o n s by Guy
and the
(4, p.318).
(4, p.319)
into cm2/sec.
can be raised against the p r o c e d u r e f o l l o w e d
w h e n he converts the units of his d i f f u s i o n c o e f f i c i e n t
In fact,
(i) this is not n e c e s s a r y for the sake of dimensions,
(ii) the m u l t i p l i c a t i o n
factor seems to be rather arbitrary,
and
(iii) the
s i g n i f i c a n c e of the r e s u l t i n g d i f f u s i o n c o e f f i c i e n t is not clear.
In conclusion,
the e q u a t i o n s d i s c u s s e d by me are f u n d a m e n t a l l y d i f f e r e n t
from those given by Guy and give d i f f e r e n t results for the several d i f f u s i o n coefficients.
I have the strong feeling that the d i s c r e p a n c y
b e t w e e n both m e t h o d s o r i g i n a t e s
from an u n j u s t i f i e d use of Fick's second law
by Guy. For both p r a c t i c a l and t h e o r e t i c a l reasons his t r e a t m e n t seems to be less adequate. I. A.G. Guy,
REFERENCES
S c r i p t a Met.,
This Issue.
2. F.J.J. van Loo, A c t a Met. 3. F. Sauer, V. Freise,
18, 1107
Z. Elektrochem.
4. A.G. Guy et al., A S M Trans.
61, 314
(1970). 66, 353 (1968).
(1962).
Vol. 5, pp. 287-288, 1971 Printed in the U n i t e d States
Pergamon Press,
Inc
COMMENTS ON "TREATMENT OF D I F F U S I O N C O N S I D E R I N G CHANGES IN ATOMIC VOLUME"
F.J.J. van Loo L a b o r a t o r y of P h y s i c a l C h e m i s t r y E i n d h o v e n U n i v e r s i t y of Technology,
In his article Guy
(I) c r i t i c i z e s my paper
Netherlands
(2) on several important points.
I do not agree w i t h this c r i t i c i s m and my o b j e c t i o n s
are both p r a c t i c a l
and theoretical.
(a) R e l a t i o n [ 9 of Guy's article
(that is Eq. [ ~ i n
my paper)
me as the d e f i n i t i o n of the i n t e r d i f f u s i o n c o e f f i c i e n t D paper).
S t a r t i n g f r o m this definition,
expressions
DI, D 2 and D are r e l a t e d to m e a s u r a b l e quantities.
(~
is used by in Guy's
are d e r i v e d in w h i c h Therefore,
values for
these c o e f f i c i e n t s o b t a i n e d from such e x p r e s s i o n s must n e c e s s a r i l y satisfy the r e l a t i o n in question. In a d i f f u s i o n couple with c h a n g i n g total v o l u m e the i n t e r d i f f u s i o n coefficient D is s t r a i g h t f o r w a r d l y r e l a t e d to the flux of c o m p o n e n t i in number 2 of moles per second per cm w h i c h pass through a p a r t i c u l a r i n t e r f a c e with respect to an i m a g i n a r y o b s e r v a t i o n post fixed on the surface of the couple, thus f o l l o w i n g the e x p a n s i o n or c o n t r a c t i o n of the couple. m a t e r i a l constant,
it has a g e n e r a l
significance.
Since D is a
For a p a r t i c u l a r concen-
tration it m u s t be the same c o e f f i c i e n t as the one found in d i f f u s i o n e x p e r i m e n t s w i t h c o n s t a n t total volume.
In some systems it is p o s s i b l e to
verify this by means of a proper choice of the c o m p o s i t i o n of the starting materials.
(b) It is true that e.g. the c o e f f i c i e n t s D I and D 2 in the article of Sauer and Freise
(3) on d i f f u s i o n
in liquid systems do have another s i g n i f i c a n c e
than the i n t r i n s i c d i f f u s i o n coefficients,
m e a s u r e d in solid systems with
respect to inert markers.
However, my article does not allow any m i s u n d e r -
standing on this subject.
The i n t r i n s i c d i f f u s i o n c o e f f i c i e n t s D i, discus-
sed by me,
d e t e r m i n e the flux of c o m p o n e n t i in number of moles per second
per cm 2 p a s s i n g t h r o u g h the m a r k e r i n t e r f a c e to the K i r k e n d a l l
interface)
(in my article r e s t r i c t e d
in a solid d i f f u s i o n couple.
not see why Guy q u e s t i o n s their relevance.
287
Therefore,
I do
288
COMMENTS ON " D I F F U S I O N W I T H CHANGES
(c) The e q u a t i o n s given by Guy
IN ATOMIC VOLUME"
(4) do look simpler,
Vol.
5, No.4
but are in fact m o r e
c o m p l i c a t e d to apply than my methods. (i) The use of v o l u m e f r a c t i o n as a c o n c e n t r a t i o n unit is in m a n y cases unpractical, fraction,
and in some cases impossible.
In order to obtain the v o l u m e
the p a r t i a l m o l a l volumes m u s t be known.
These have to be det-
e r m i n e d by means of the c o n s t r u c t i o n of tangents to the plot of m o l a r v o l u m e v e r s u s mole fraction,
w h i c h is a rather i n a c c u r a t e process.
there are o f t e n not e n o u g h d a t a available, compounds,
e.g.
Moreover,
in m a n y i n t e r m e t a l l i c
since at least two v a l u e s of V m at a d i f f e r e n t c o n c e n t r a t i o n
m u s t be known.
It is even i m p o s s i b l e to d e t e r m i n e the partial m o l a l v o l u m e s
in the i m p o r t a n t case where a "line-compound"
develops
Even the o c c u r r e n c e of only one such l i n e - c o m p o u n d
in a d i f f u s i o n couple.
in the couple rules out
the p o s s i b i l i t y of u s i n g Guy's method. (ii) The c o n v e r s i o n of x
(in cm)
into the new c o o r d i n a t e x' is intricate.
This t i m e - c o n s u m i n g task m u s t be f o l l o w e d for each d i f f u s i o n couple again, since this c o n v e r s i o n d e p e n d s on the c o m p o s i t i o n of the starting m a t e r i a l s .
(d) The r e l a t i o n b e t w e e n the i n t e r f a c e at x = 0 and the two "Matano interfaces"
(one for each component)
in the c o o r d i n a t e system used by me is
s u f f i c i e n t l y d i s c u s s e d in my paper
(2). Guy claims that one of the advant-
ages of his m e t h o d is the c o i c i d e n c e of his "Matano interface" initial plane of joining of the two halves of the couple However,
it can be shown g r a p h i c a l l y that this is g e n e r a l l y not the case.
(e) T h e o r e t i c a l o b j e c t i o n s by Guy
and the
(4, p.318).
(4, p.319)
into cm2/sec.
can be raised against the p r o c e d u r e f o l l o w e d
w h e n he converts the units of his d i f f u s i o n c o e f f i c i e n t
In fact,
(i) this is not n e c e s s a r y for the sake of dimensions,
(ii) the m u l t i p l i c a t i o n
factor seems to be rather arbitrary,
and
(iii) the
s i g n i f i c a n c e of the r e s u l t i n g d i f f u s i o n c o e f f i c i e n t is not clear.
In conclusion,
the e q u a t i o n s d i s c u s s e d by me are f u n d a m e n t a l l y d i f f e r e n t
from those given by Guy and give d i f f e r e n t results for the several d i f f u s i o n coefficients.
I have the strong feeling that the d i s c r e p a n c y
b e t w e e n both m e t h o d s o r i g i n a t e s
from an u n j u s t i f i e d use of Fick's second law
by Guy. For both p r a c t i c a l and t h e o r e t i c a l reasons his t r e a t m e n t seems to be less adequate. I. A.G. Guy,
REFERENCES
S c r i p t a Met.,
This Issue.
2. F.J.J. van Loo, A c t a Met. 3. F. Sauer, V. Freise,
18, 1107
Z. Elektrochem.
4. A.G. Guy et al., A S M Trans.
61, 314
(1970). 66, 353 (1968).
(1962).