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Comments on “A thermodynamic analysis of hydrogen in metals in the presence of an applied stress field”
Scripta M E T A L L U R G I C A
COMMENTS
I/ol. 6, pp. 543-546, 1972 Printed in the United States
ON "A T H E R M O D Y N A M I C IN THE PRESENCE
ANALYSIS
OF HYDROGEN
OF AN A P P L I E D
R. Chopra
Pergamon
Press,
Inc
IN METALS
STRESS FIELD"
and J. C. M. Li
D e p a r t m e n t of Metallurgy, Stevens Institute of Technology, Hoboken, N. J. 07030 and D e p a r t m e n t of M e c h a n i c a l and A e r o s p a c e Sciences, U n i v e r s i t y of Rochester, Rochester, N. Y. 14627 (Received In a recent paper of the above sidered
the p r o b l e m of h y d r o g e n
Oriani,
and Darken
erroneous
(2).
February title,
Bockris
Bockris
analysis
sense is also incorrect.
Furthermore,
derivation
w h i c h will
made
complications.
may not be complete we w o u l d
(i) recon-
treated earlier by Li,
and S u b r a m a n y a n
steps and caused many u n n e c e s s a r y
and a simple
and S u b r a m a n y a n
in a stressed metal
However,
that the L i - O r i a n i - D a r k e n comments
18, 1972)
several
Their c o n t e n t i o n
in the t h e r m o d y n a m i c
like to offer
the following
lead to their e x p e c t e d
result
correctly: i.
Bockris
and S u b r a m a n y a n
Eq.
4, p. 1206.
Eq.
372, p.
190.
Inclusion
in all s u b s e q u e n t 1 - (Oh/K) 2.
Eqs.
393-5,
p. 196.
potential
question.
Bockris
After
stress
their Eq.
sum of the terms brackets
~M of the metal
As p o i n t e d
See Gibbs
factors
(3), terms
such as
component
its value depends
and S u b r a m a n y a n
See Gibbs
(2), the
can be defined
on the location
treated This
(3),
in
~M as a bulk
is possible
only
for
situations.
8, Bockris
and S u b r a m a n y a n
claimed
that the
in the first and fourth sets of simple
(parentheses)
to be the case.
in a n o n - h y d r o s t a t i c
out by Li et al.
of an immobile
in all their equations.
hydrostatic 3.
For example,
cannot be easily defined.
only at a s u r f a c e , a n d property
term o~V/2K in their
of this term caused many extra
equations.
potential
situation
chemical
an extra
should all be r e p l a c e d by !.
The chemical stress
included
Such a ter~ should not appear.
reduces
to zero.
This turns out not
If one goes about it carefully
the extra
terms
introduced
their Eq.
9 should read simply
and ignores
due to the one in their Eq.
nMdU M ÷ nHdU H = Vdo h
543
4,
(i)
544
COMMENTS
ON "THERMODYNAMIC
ANALYSIS
OF H IN METALS"
which is nothing but the Gibbs-Duhem temperature
and under hydrostatic
Duhem equation their Eq.
The Gibbsform of
without going through
6, 7 and 8.
The mistake made in their Eq. 9 propagated Eqs.
i0, ii, 15, 17, 18 and 22.
through their
In all t~ese equations,
a quantity whose value depends on a reference these equations situation
5.
invalid.
can be represented
How this comes about escapes
us.
What Bockris
intended
and Subramanyan
the concentration
CH,ch of hydrogen
iron is CH, O.
has to do is to use Eq.
as claimed by by UHs(dnH)eq.
to do was to calculate
in ~-iron under a stress
~h in equilibrium with the hydrogen an unstressed
argument,
by their Eq. 21 can be
by a transfer of hydrogen which,
and Subramanyan,
gas whose
solubility
To solve this problem,
15 of the Li-Oriani-Darken
and the dilute solution behavior
All
This awkward
is finally removed by another erroneous
the chemical work calculated
compensated Bockris
are, therefore,
u H,
state is mixed
up with other terms which have well defined values.
namely,
6, No.
at constant
~h"
from the correct
4 by direct differentiation
their Eqs. 4.
can be obtained
equation
pressure
Vol.
of a stress-free
in
all one paper
(2)
solid:
~H = UH0 + Ch~H oo = UH + RTZnCH,~h
+ ~hVH
00 = u H + RT£nCH, 0 where
~
is the chemical
(2)
potential
of hydrogen
free state of the same concentration chemical
potential
of hydrogen
in the stress-
as CH,Uh and U~°-_ is the
in a stress-free
standard
state.
Hence,
RT£n(CH,ch/CH, O) = -~hVH This equation
differs
first is the sign. ~h is positive solubility
from their Eq. 24 in two respects.
The
If Uh is defined by their Eq. 2, namely,
for compressive
24 is wrong because
(3)
stress,
a compressive
of hydrogen.
the sign in their Eq.
stress should decrease
The other difference
the
is that, upon
differentiating Eq. 3, there will be an extra term ~VH/~Gh which is not included in their Eq. 24.
?
Vol.
6, No.
6.
?
C O M M E N T S ON "THEILMODYNAMIC A N A L Y S I S OF H IN M E T A L S "
In conclusion,
B o c k r i s and S u b r a m a n y a n ' s
simply and c o r r e c t l y by Eqs.
545
p a p e r can be r e p l a c e d
2 and 3 here.
References io
J. O'M.
2.
J. C. M. Li, R. A. Oriani, 271 (1966)
3.
J. W. Gibbs, "The C o l l e c t e d Works" Conn. 1948) p. 184.
Bockris
and P. K. S u b r a m a n y a n ,
A c t a Met.
and L. S. Darken,
19 1205
Z. Phys.
(1971)
Chem. New Folge
(Yale U n i v e r s i t y Press, New Haven,
49
COMMENTS
I/ol. 6, pp. 543-546, 1972 Printed in the United States
ON "A T H E R M O D Y N A M I C IN THE PRESENCE
ANALYSIS
OF HYDROGEN
OF AN A P P L I E D
R. Chopra
Pergamon
Press,
Inc
IN METALS
STRESS FIELD"
and J. C. M. Li
D e p a r t m e n t of Metallurgy, Stevens Institute of Technology, Hoboken, N. J. 07030 and D e p a r t m e n t of M e c h a n i c a l and A e r o s p a c e Sciences, U n i v e r s i t y of Rochester, Rochester, N. Y. 14627 (Received In a recent paper of the above sidered
the p r o b l e m of h y d r o g e n
Oriani,
and Darken
erroneous
(2).
February title,
Bockris
Bockris
analysis
sense is also incorrect.
Furthermore,
derivation
w h i c h will
made
complications.
may not be complete we w o u l d
(i) recon-
treated earlier by Li,
and S u b r a m a n y a n
steps and caused many u n n e c e s s a r y
and a simple
and S u b r a m a n y a n
in a stressed metal
However,
that the L i - O r i a n i - D a r k e n comments
18, 1972)
several
Their c o n t e n t i o n
in the t h e r m o d y n a m i c
like to offer
the following
lead to their e x p e c t e d
result
correctly: i.
Bockris
and S u b r a m a n y a n
Eq.
4, p. 1206.
Eq.
372, p.
190.
Inclusion
in all s u b s e q u e n t 1 - (Oh/K) 2.
Eqs.
393-5,
p. 196.
potential
question.
Bockris
After
stress
their Eq.
sum of the terms brackets
~M of the metal
As p o i n t e d
See Gibbs
factors
(3), terms
such as
component
its value depends
and S u b r a m a n y a n
See Gibbs
(2), the
can be defined
on the location
treated This
(3),
in
~M as a bulk
is possible
only
for
situations.
8, Bockris
and S u b r a m a n y a n
claimed
that the
in the first and fourth sets of simple
(parentheses)
to be the case.
in a n o n - h y d r o s t a t i c
out by Li et al.
of an immobile
in all their equations.
hydrostatic 3.
For example,
cannot be easily defined.
only at a s u r f a c e , a n d property
term o~V/2K in their
of this term caused many extra
equations.
potential
situation
chemical
an extra
should all be r e p l a c e d by !.
The chemical stress
included
Such a ter~ should not appear.
reduces
to zero.
This turns out not
If one goes about it carefully
the extra
terms
introduced
their Eq.
9 should read simply
and ignores
due to the one in their Eq.
nMdU M ÷ nHdU H = Vdo h
543
4,
(i)
544
COMMENTS
ON "THERMODYNAMIC
ANALYSIS
OF H IN METALS"
which is nothing but the Gibbs-Duhem temperature
and under hydrostatic
Duhem equation their Eq.
The Gibbsform of
without going through
6, 7 and 8.
The mistake made in their Eq. 9 propagated Eqs.
i0, ii, 15, 17, 18 and 22.
through their
In all t~ese equations,
a quantity whose value depends on a reference these equations situation
5.
invalid.
can be represented
How this comes about escapes
us.
What Bockris
intended
and Subramanyan
the concentration
CH,ch of hydrogen
iron is CH, O.
has to do is to use Eq.
as claimed by by UHs(dnH)eq.
to do was to calculate
in ~-iron under a stress
~h in equilibrium with the hydrogen an unstressed
argument,
by their Eq. 21 can be
by a transfer of hydrogen which,
and Subramanyan,
gas whose
solubility
To solve this problem,
15 of the Li-Oriani-Darken
and the dilute solution behavior
All
This awkward
is finally removed by another erroneous
the chemical work calculated
compensated Bockris
are, therefore,
u H,
state is mixed
up with other terms which have well defined values.
namely,
6, No.
at constant
~h"
from the correct
4 by direct differentiation
their Eqs. 4.
can be obtained
equation
pressure
Vol.
of a stress-free
in
all one paper
(2)
solid:
~H = UH0 + Ch~H oo = UH + RTZnCH,~h
+ ~hVH
00 = u H + RT£nCH, 0 where
~
is the chemical
(2)
potential
of hydrogen
free state of the same concentration chemical
potential
of hydrogen
in the stress-
as CH,Uh and U~°-_ is the
in a stress-free
standard
state.
Hence,
RT£n(CH,ch/CH, O) = -~hVH This equation
differs
first is the sign. ~h is positive solubility
from their Eq. 24 in two respects.
The
If Uh is defined by their Eq. 2, namely,
for compressive
24 is wrong because
(3)
stress,
a compressive
of hydrogen.
the sign in their Eq.
stress should decrease
The other difference
the
is that, upon
differentiating Eq. 3, there will be an extra term ~VH/~Gh which is not included in their Eq. 24.
?
Vol.
6, No.
6.
?
C O M M E N T S ON "THEILMODYNAMIC A N A L Y S I S OF H IN M E T A L S "
In conclusion,
B o c k r i s and S u b r a m a n y a n ' s
simply and c o r r e c t l y by Eqs.
545
p a p e r can be r e p l a c e d
2 and 3 here.
References io
J. O'M.
2.
J. C. M. Li, R. A. Oriani, 271 (1966)
3.
J. W. Gibbs, "The C o l l e c t e d Works" Conn. 1948) p. 184.
Bockris
and P. K. S u b r a m a n y a n ,
A c t a Met.
and L. S. Darken,
19 1205
Z. Phys.
(1971)
Chem. New Folge
(Yale U n i v e r s i t y Press, New Haven,
49