by A. Rist
and J. Chipman
Activityof Carbon
in LiquidIron-CarbonSolutions
INTRODUCTION
of the product [C] . [0 ] . Such experiments may
give information on the activity of carbon if accurate
gas analyses are obtained . In fact , Phragmen
The early physical chemistry of steelmaking was
and Kalling6 did compute an activity coefficient for
content with applying the la "" of mass action in its
Henry 's law from their data which ranged below
original form to solutes in liquid iron . Much was
0.1% carbon . They remarked that the value which
written then on how to express the concentration of
carbon . Was carbon dissolved as atoms or as molecules they found had to increase very fast with concentration
if the solubility limit was to be accounted for .
such as FesC? Precarious phase-diagram and
Marshall
and Chipman7 reached carbon contents as
thermal data could not help to settle the issue.! As
high as 2.0% by operating under pressure. They
metallurgical chemistry was gradually approached
from a more thermodynamical point of view , nonideal found that the activity coefficient of carbon may be
solutions gained recognition , and the necessity
regarded as constant up to I % and that it increases
thereafter
.
Later
, york
, vas not
to confirm
this
to establish activity -concentration relationships was
Vie
, v .
realized . The nature of the solution , no "" kno "" n
In
1953 , l ~ ichardson
and
Dennis8
contributed
to be interstitial in the case of carbon ,2 could be
the first study devoted primarily to the determination
i'gnored for that purpose .
of the carbon activity in liquid iron . Melts
The attention given by metallurgists to the reaction
of carbon and ox )'gen in the open -hearth bath
,vith carbon contents betvveen 0.1 and 1.1% ,vere
equilibrated with control led CO- CO2 mixtures at
greatly delayed the study of the simple binary iron carbon svstem.
The eQuilibrium
of laboratory .
1560, 1660, and 17600 C. The experiments ,vere
"
.L
out , vith
extreme
care , and
the data
are
melts with CO - CO2 mixtures , defining fixed carbon carried
a!id oxygen potentials , was used by a number
very consistent. They point to an appreciable deviation
from Henry 's law dovvn to the lowest carbon
of wol -kers 3, 4, ~. G, 7 to study the equilibrium value
investigated .
The
work
of l ~ ichardson
and Dennis
is authoritative
Based on a thesis submitted in partial fulfillment of the
in
requirements for the degree of Doctor of Science at the Massachusetts and covers most of the range of interest
Institute of Technology . Dr . Chipman is Pr.ofessor
steelmaking . Nevertheless , it seemed desirable , for
of Metallurgy , Massachusetts Institute of Technology . Dr .
the sake of completenessas well as to provide data
Rist is noil "lith the Institut de Recherches de la Siderurgie ,
for ironmaking , to explore the entire liquid field.
Saint-Germain -en-Laye, France.
The present work , although
it met with
limited
The authors wish to thank Professor C. \ \'agner for many
success , , vas undertaken
with
this purpose .
helpful discussions, T . Fuwa for assistancein the equilibrium
Concentrated iron -carbon solutions have already
measurements, and D. L . Guernsey for carbon determinations .
been studied by Esin and Gavrilov9 and by SanFinancial support ,vas received from the lnstitut de Recherches
de la Siderurgie, the Allegheny Ludlum Steel Corporation bongi and Ohtani .l0 These authors built electrochemical
cells of the type :
, and the Office of Naval Research.
ACTIVITYOF
CARBON
IN LIQUID
IRON - CARBON
SOLUTION5
- 3
trol
alloy iron
(sat.)-carbon I Carbide
slag I Liquid
alloy iron -carbon
Liquid
and measured their electromotive forces at various
concentrations of the alloy on the right -hand side.
and
measurement
control
and
analysis
of
In
the
order
,
mixtures
It ,vas proposed to measure the activity of carbon
dissolved in liquid iron as a function of concentr ;ltion and temperature through the study of the
equilibrium :
CO2 (g) + [C] = 2CO (g)
the
melt
by
the
co
Argon
,
drone
,
and
carbon
dioxide
purified
carite
The
,
.
carbon
anhy
at
C
anhydrone
copper
at
at
11000
hydroxide
C
.
Car
passing
C
dioxide
.
and
4500
by
-
5900
-
dry
and
then
over
a
solution
con
and
-
as
-
.
The
flow
trolled
rates
by
flow
flow
of
adjusting
meters
rates
GLOBAR
FURNACE
'CO2
TANK
Fig. 1. Diagram of gas system
.
4- S0LUTES
IN LIQUIDIRONOR STEEL
.
lines
containing
over
carbon
benefit
rate
turnings
graphite
argon
to
vapor
columns
over
potassium
and
gas
water
dried
residual
,
three
manufactured
over
from
centrated
the
in
was
CO
flow
the
magnesium
oxygen
steps
between
order
total
clearly
was
from
,
in
increased
and
monoxide
CO2
from
dioxide
purified
lary
,
,
PROCEDURE
of
oxygen
-
fact
deposition
reactions
added
shows
in
Mixtures
purified
ascarite
Carbon
an
I
was
dioxide
bon
.
,
.
Gas
being
of
Fig
com
( and
side
-
carbon
which
difficult
favored
mixtures
argon
effects
of
and
con
with
to
in
carbon
,
the
gas
,
the
carbon
EXPERIMENTAL
of
sketch
where p's represent partial pressures in the gas
phase and ac is the activity of carbon in solution .
Temperature and the " gas ratio " (Pco)2IPco are
taken as the two independent variables. Th ~ activity is proportional to the gas ratio , the proportionality factor IlK ! being determined at each temperature by the choice of a standard state for carbon. In the experiments, gas ratio and temperature are maintained constant, and the metal which
is exposedto the flowing gasadjusts its composition
to the carbon activity imposed by the gas phase.
The study is thus designed to )Iield the activity composition relationship .
The main experimental problems are: the con-
AND
used
the
and
attained
respect
is
when
are
high
arises
gas
slow
crucible
Ternary
,
,
be
with
the
is
Preparation
of
thereby
in
APPARATUS
composition
must
dilute
situation
reaction
and
range
ratios
impossible
) ,
were
K 1 = ~ .Q2l:
PCO2
. GO
gas
control
becomes
in
the
high
A
position
(1)
"" here [C] representscarbon dissolvedin liquid iron .
The equilibrium constant for the reaction at temperature T is
.
gas
temperature
.
cover
extremely
'dioxide
the
of
metal
to
centration
STATEMENTOF THE PROBLEMAND METHOD
of
measurement
.
of
the
component
the
pressure
Through
CO
most
and
gases
drops
argon
of
were
were
across
the
experiments
kept
con
capil
constant
-
-
and each equal to about 300 ml / min while the
flow rate of CO2 was varied to obtain the required
gas ratios . The entire range of gas ratios ( 100 to
4300) was covered with CO2 flow rates ranging
roughly from 2 to 0.03 ml / min .
WATER OUT +
. WATER
E
=
IN
:
:
GAS
IN...
A
Gas Analysis
The apparatus was equipped with facilities for
the gravimetric analysis of CO2 by absorption on
ascarite and of CO by conversion to CO2 in a cupric
-oxide furnace followed by absorption on ascarite
. Analysis was used to establish or check the
calibration of the capillary flow meters . In the case
of argon , a volumetric method was used.
The anal )!sis of CO2 required special care in view
of the small quantities involved . Over 4 hr were
necessary to collect about 15 mg at the lowest flow
rate . T ,vo ascarite bulbs were put in series, the
first one being capable of absorbing over 99% of the
incoming CO2. Argon had first been used as a
flushing gas; later , hydrogen was substituted for it
to minimize the ,veight fluctuations of the enclosed
gas, and a dummy bulb was used to suppress buoyancy
corrections .
B
A -
PYREX
B -
RUBBER
CONNECTIONS
HEAD
C -
PYREX
r;
GROUND
JOINT
D -
D
E
!
-
~
GRADED
JOINT
( PYREX
TO
VYCOR
WATER
VYCOR
)
JACKET
F -
JET
PRODUCI
NG
SWIRLING
E
t
F
-----fffl
I
I
A
Furnace
The
and
was
Design
metal
Fig. 3. Furnacehead mountedwith watercooled
Vycortube.
was
contained
in
alumina
crucibles
and stirred by high-frequency in -
heated
A
A - PRISM
B - SIGHT GLASS
C- PYREX HEAD
8
G
I
D -
EXTENSION
E -
GASKETS
F -
CLA ~.1PING
DEVICE
GLAZED
SILICA
TUBE
( 24 IN . LDNG . 2 . 5 IN . O . D . I
H -
ALUNDUM
1-
INLET
INDUCTION
( 29
,
G
PUSHER
RUBBER
G C
E
F
HOUSING
( SILICONE
TUBE
COIL
TURNS
J -
RADIATION
( ALUNDUM
K -
GRAPHITE
L -
ALUMINA
)
SHIELD
)
SUSCEPTOR
CRUCIBLE
M -
LIQUID
N -
CRUCIBLE
STAND
( ALUNDUM
)
METAL
0 -
STAINLESS
P -
SUPPORTING
Q -
BRASS
R -
LOCKING
S -
QUENCHING
STEEL
TUBE
COLLAR
BOTTOM
NUT
TUBE
)
duction . The furnace , as first designed and
mounted , is shown in Fig . 2. An Alundum tube ,
13 mm i .d ., led the gas flow do,vnward to the melt
surface . The crucible was surrounded by an annular
graphite susceptor in order to delay cooling
of the gases as they left and thereby to delay carbon
deposition . The furnace enclosure was a glazed
silica tube equipped with a sight glass and prism at
the top to permit optical temperature readings .
The above version of the furnace failed at gas
ratios higher than 1150 when carbon deposition
began to appear in the Alundum inlet tube . A
new inlet tube was installed , made of Vycor and
water -cooled all the way down to its mouth above
the melt (see Fig . 3). That second version , which
was successful in preventing carbon deposition at
the lower temperatures used ( 1360 and 12600 C)
introduced other errors to be discussed later .
p
( NOT USED
PROCEDURE
IN
)
STANDARD
0
Temperature
Measurement
Temperature was measured with a disappearing ~
filament p)'rometer . Previous work ! ! gave information
on the emissivity of pure iron and its variation
with temperature , thus permit ting calibration of
the instrument at the melting point of iron and
providing
an optical temperature scale over a
range of temperatures . The validity of the calibration
has been extended to iron -carbon alloys at
E
- - 0
R
I
Fig . 2 .
Furnace
arrangement
.
lower temperatures by using the eutectic point
(11530 C) as a reference in conjunction with a
ACTIVITY OF CARBON IN LIQUID IRON-CARBON SOLUTIONS- 5
linear extrapolation
of the emissivity curve for
pure iron . Agreement was found vvithin t'vvo degrees
by observing the solidification of alloys of
slightly hypoeutectic composition .
3 . 2
1360
::
log K(
....:-:: ~~ 1360
0
2 .6
Running
SeriA
Ser
.8
...
Procedure
2 .4
C
-i >
.
0
...
<r -
Corburizo
C 0 -(>.. . . . "' 4. !....." ' "
1260
C
..."""0 /
tion
<r -
No net re.octi ? n
Decorburlzotlon
- I- Saturation
points
Eutectic
- i- 1153 C
For each run a temperature and a gas ratio were
2 .2
0
1.0
2 .0
3.0
4 .0
5 .0
selected. A 30-gram charge ,vas prepared from
Weight
Percentage
Carbon
electrolytic iron and a very pure grade of graphite .
Fig. 4. Experimental data ; K1' = p2CO
/ (PCO2. % C). The solid
Air was flushed out of the furnace with argon , and
lines represent equilibrium ; broken line at 13600 represents series B,
the charge was heated under argon . Melting was
known to be Subject to errors of thermal diffusion and incomplete
completed under the ternary gas mixture to avoid
equilibrium .
excessive reaction between metal and crucible , and
temperature was stabilized at the assigned value
in Table 1 and plotted in Fig . 4. In the fifth column
after 15 min of heating .
of Table 1, the " initial % C" of a heat was
The heat was held at temperature for times
which varied between a few minutes in recovery
Tab !e 1. Experimental Results, Series A
runs and a maximum of 31 hr (s~e Tables 1 and 2).
Temperature was control led manually through the
Tcmper Heat
ature ,
Gas
Time ,
0/(. C
~o C
power output of the high -frequency converter unit .
Ko .
C
Ratio
hr
Initial
Final
d % C
log K' *
Fluctuations in temperature ", ere normally less
than :!: 1o degrees.
53
1560
104
4 .0
0 . 16
0 . 19
+ 0 .03
2 .750
53
1560
103
6 .8
0 . 31
0 . 20
- 0 . 11
2 . 710
At the end of the run , argon '''-'as substituted for
54
1560
102
3 .0
0 . 20
0 . 19
- 0 . 01
2 . 725
58
1560
336
4 .0
0 .55
v .57
+ 0 .02
2 .770
the gas mixture , the power turned off , and the melt
59
1560
325
6 .0
0 .64
0 . 62
- 0 . 02
2 . 720
cooled under argon . The heats containing less
61
1560
325
6 .0
0 . 59
0 . 56
- 0 . 03
2 . 765
72
1560
1045
6
.0
1
.12
1
.
14
+
0
.02
2
.965
than 2. % carbon were killed with aluminum .
68
1560
1030
5 .0
1 . 17
1 . 17
0 . 00
2 . 945
Quenching had been planned originally and was
63
1560
990
6 .0
1 . 18
1 . 19
+ 0 .01
2 .920
1560
1030
5 . 25
1 . 29
1 . 27
- 0 . 02
2 . 910
to be effected between two helium jets at the bottom 6665
1560
1035
6 .0
1 . 23
1 . 22
- 0 . 01
2 . 930
of the furnace . It was abandoned , however , to
75
1560
1150
6 .0
1.28
1 .29
+ 0 .01
2 .950
suppress opportunities for scraping or shaking loose
any carbon deposited on the exit path of the gas.
133
81
82
83
.
~,
K
=
taken
from
milling
analysis
was
was
present
grey
or
fully
.
present
screened
out
amounts
of
po
solidification
equal
The
,
chips
were
The
As
experiments
and
series
a rule
approach
Series
inlet
the
to
equilibrium
A .
tubes
recognized
with
gas
6 -
S0LUTES
The
,
and
ratios
IN
to
the
heats
, vere
are
, vere
error
to
LIQUID
care
for
2 . 810
2 .930
2 .995
2 .9' JO
.
-
all
carbon
carbon
1150
IRON
OR
series
used
the
closest
with
obtained
The
into
.
.
made
1560
data
STEEL
Alundum
free
Table 2 .
levels
setup
to
listed
at
.
divided
heats 81, 82, and 83 is also given later .
Series B . The heats were made ,vith the Vycor
each
duplicate
furnace
corresponding
results
up
taken
at
heats
systematic
, vas
proportional
of
are
according
, only
graphite
It
RESULTS
reported
B
+ 0 .02
+ 0 .03
+ 0 .01
and gas ratios 1vhich could be investigated \vere
limited by the occurrence of carbon deposition,
which is discussedlater. justification for quoting
if
produced
.
EXPERIMENTAL
A
.
and
spread
of
The
segregation
of
chips
weighed
carbon
- half
.
had
constant
: 1: 0 . 01 %
were
one
amount
the
and
was
to
0 . 00
3 .21
3 .81
4 .38
calculated after
runs sho\ving that over
99% of the carbon
was recovered . In the
seventh column , il % C is the difference betvveen
Jltures
final and initial % C. The range
- ~I of tern -per C
conventional
mixed
to
certain
, vith
determination
an ,d
, a
and
the
samples
representing
insensitive
.
- gram
thoroughly
made
, vder
sample
by
One
When
iron
was
analytical
.
and
thus
mottled
powder
performed
chips
ingot
any
1 . 76
3 . 19
3 .78
4 .31
(('
was
method
solidified
1 . 76
6 .0
6 .0
6 .0
Cl( ) ' Po
~(
analysis
combustion
the
6 .0
2750
3705
4290
pC ~ . <;,;, C
of
and
14600
are
recorded
any
~-~ ~_
; .: ~ 0--I~II ."0oc3
I '~ ?.z..
metal
1140
1360
1360
1360
( 'JCO ) 2
. r ,-- ' "
Metal Analysis
The
1460
Results, Series B
d % C
195
194
196
201*
188
204
187
203
186
182
. In
C
Experimental
1360
1360
1360
1360
1360
1360
1360
1260
1260
1260
heat
t K' =
1160
9 .0
2 . 98
2 . 98
0 .00
1165
10 . 0
3 . 48
3 . 48
0 . 00
2 . 525
0 . 02
2 . 480
0 .00
2 . 690
1160
10 . 3
3 . 88
3 . 86
1700
30 . 25
3 . 48
3 . 48
-
1820
10 .5
3 .73
3 .75
+ 0 .02
1840
31
4 . 08
4 . 05
-
0 , 03
2 . 590
2 .685
2 . 660
2720
10 .5
4 . 17
4 . 18
+ 0 .01
2 .815
1150
27 . 2
4 . 17
4 . 15
-
0 . 02
2 . 450
1475
1810
10 .5
10 .0
4 .07
4 .07
4 .08
4 .08
+ 0 .01
+ 0 .01
2 .560
2 .645
substituted
for
201 , helium
(PCO ) 2
PCO2 ' % C
log K' t
was
argon
.
water
- cooled
have
been
tube
error
are
,
discussed
in
Table
.
heats
are
later
.
they
sake
shown
in
%
the
They
are
equal
to
plot
yields
that
weight
deposition
reported
peared
systematic
,
and
, however
only
ratios
,
plot
the
data
log
KI ' =
They
state
are
for
well
suited
carbon
is
.its
activity
at
log
82
,
and
infinite
(a)
The
(b )
The
of
the
a
the
logarithm
of
the
( where
fc = ac / % C ) ,
.
read Ing off . the plot
logic
Similar
plots
will
be
N cisused
The
to
full
the
broken
inlet
tube
of
any
,
the
=
log
is
coefficient
, log
concentration
I
.
KI (T ) log
K1 (T ) '
presented
where
of
dravvn
the
and
parallel
to
the
full
line
THE
MAIN
did
,
not
the
C
( amorphous
potential
).
in
the
Its
effect
gas
and
OF
2CO
to
.
Carbon
lower
only
if
it
could
occurred
(a)
During
the
(b )
at
During
such
mixing
preheating
composition
the
cooling
a short
of
used
distance
and
on
the
from
the
fresh
inlet
gas
in
be
heavier
to
1360
not
and
or
the
C
when
it
crucible
mouth
B
cold
12600
visible
on
tube
the
on
at
series
type
cold
condensation
the
result
since
toward
.
~
heats
hot
the
in
CO
the
wall
Iore
serious
which
,
,
phase
viII
be
.
gas
gas
Other
13
,
it
is
appreciable
of
tends
to
workers
have
to
if
carburization
lighter
,
,
excessive
the
surface
the
gas
an
studiesl2
in
done
the
in
resorted
diffuse
gas
to
suppress
vicinity
here
of
a
the
the
exit
in
path
melt
- metal
full
preheating
temperature
( see
same
it
j
,
.
This
could
not
deposition
a
,
to
vas
.
found
preserve
r \
ddi
-
,
is
the
ratio
(
of
diffusion
similar
Pi
/
Pj
of
/
PCO
detrimental
experiments
thermal
very
ratio
slightly
preserving
the
beneficial
the
mixture
with
on
1 - vhich
to
in
comes
Chipman12
the
gas
authors
and
that
as
to
,
less
of
the
in
the
0
. 03
in
PCO
)
2
?
Dastur
H2
and
-
conditions
H2O
mixtures
bears
error
15600
C
out
of
gas
thermal
(
the
,
the
log
K
son
error
no
and
was
introduced
.
other
basis
comparison
for
with
at
although
measurements
equilibrium
such
)
aresistance
diffusion
is
'
agreement
Richard
large
there
6 .
in
diffusion
,
'
thermal
than
mixtures
,
of
by
B
error
of
similar
fact
no
heats
series
the
K1
temperature
that
A
heats
In
same
confirms
the
.
log
those
the
series
estimating
on
with
at
in
In
the
data
furnace
-
,
at
obtained
gas
Con
A
present
permit
. 5).
series
than
Dennis
as to
Fig
melt
carbon
measurements
so
of
the
of
inert
Comparison
carbon
the
tube
of
because
heavy
i
' \ vhen
+
gas .
the
tended
in
will
melt
fact
fresh
- v
affect
of
kept
ERROR
- 7 CO2
affect
the
the
,
.
equilibrium
:
in
of
therefore
concentrations
' \ vas
level
diffusion
,
is
alter
deposition
and
deposition
gas
was
presently
Thermal
mole
correspondingly
deposition
carbon
carbon
retained
belo1
to
under
metal
,
ratio
.
reaction
is
,
its
reach
.
experimental
SOURCES
the
81
gas
Diffusion
by
is
gas
the
equilibrium
iron
were
1 - vere
gases
deposition
with
visible
deposits
provided
Thermal
Deposition
Carbon
the
deposition
light
tion
Carbon
B
since
increased
carbon
be
OF
series
b
Heats
gradient
DISCUSSION
13600
the
at
heats
,
of
Type
of
points
except
carburization
of
of
.
errors
been
drawn
according
'\v .
At
13600
C the
through
at
of
or
under
by
concentration
Fig . 4 have
given
belo
C
made
,
spite
limits
.
surfaces
The
carbon
16000
heats
run
In
suppressed
because
constant
%
activity
at
as a unit
lines
on
treatment
line
zero
.
heats
was
discussed
fc
fraction
equilibrium
to
11
.
:
extrapolation
1 -\
discarded
showed
lower
' \ vhen
logarithm
.
were
still
set
1 - vas
log K1 ( T ) ' by
isotherm
T .
which
1150
they
In
to the
defined
.
,
above
,
on
become
dilution
above
1150
were
83
much
( ( PCO ) 2/
should
temperatures
than
conditions
they
to
at
higher
latter
comments
13600
C
and
%
readily
results
a large
. 4.
C as abscissa
its
The
by
suggest
some
interesting
of clarity
, only
the
selected
condition
C .
affected
carbon
PCO2 . % C ) as ordinate
.
case where
the standard
by
13600
be
than
Fig
co -ordinates
. 4 are
at
to
other
2 since
For
the
The
Fig
mostly
recognized
in
an
equilibrium
Tube
is
Crucible
not
likely
under
tested
Graphite
Susceptar
to
on
the
reached
in
.
the
gives
,
of
maximum
fast
' s
data
separation
the
the
Gillespie
available
thermal
to
it
be
consideration
15
is
CO
- flo1
system
,
found
and
temperature
- ving
equation
to
CO2
when
exaggerate
.
gradient
14
If
applied
found
here
,
:
Stand
-
A
log
K
(
~
0
.
13
Fig. S. Mostharmfullocations
for carbondeposition
.
Although
densed iron, was especially efficient in catalyzing
the formation of such a deposit .
the
every
found
of
,
(
bet1
13600
- veen
of
see
Fig
.
ACTIVITY
OFCARBON
IN
. 2
the
LIQUID
4
.
an
This
)
exaggerates
even
larger
is
error
evidenced
known
is
by
saturation
with
to
(
calculation
,
graphite
extrapolation
C
the
error
0
equilibrium
the
of
the
approaching
discrepancy
. Heats retained in series A were free of both types.
Type b could be suppressed by heating the crucible
externally with the graphite susceptor . Type a ap-
step
estimate
CO
saturation
of
the
points
and
CO2
series
B
)
and
data
at
.
IRON
-
CARBONS
Ol
U
T
I ON
S
-
7
A few heats in which conditions were identical in
series A and B show a displacement of the points
of the same order . These facts suggest the existence
of another large error affecting the measurements
in the same direction as thermal diffusion , which ,
according to the authors , is lack of thermal equilibrIum
.
A
by
quantitative
evaluation
lack
of
large
thermal
systematic
from
is
A
it
Equilibrium
The heat transfer from the hot metal to the cold
being
gas is not instantaneous and , for short retention
times , the gas at the interface will contain " cold "
molecules (i .e., the average stored energy is less than
the average at thermal equilibrium ). Fe\ver molecules
will reach the activated state required for
them to react , and reaction rates will be slower .
Chemical equilibrium , which is a balance between
the rates of two opposite reactions , may be displaced
if one of them is slowed . down more than
the
axis
on
same
Fig
Other
.
4
,
Sources
When
of
no
to
,
inlet
,
gas
much
show
that
both
that
equilibrium
,
for
a
points
to
the
line
are
the
ordinate
being
as
minor
preserved
of
errors
(
just
.
been
become
the
on
ratio
have
errors
precision
A
,
how
so
errors
,
the
series
determine
parallel
large
present
assess
In
of
Error
such
are
be
equilibrium
only
of
the
can
contribution
thermal
the
slope
of
)
joint
distance
the
going
cooling
composition
all
The
when
preheating
may
gas
.
in
when
of
One
,
displaced
. ,
to
of
temperature
. e
lack
.
independent
given
i
possible
contributes
are
(
the
and
introduced
possible
steps
B
as
diffusion
error
not
natural
merely
each
of Thermal
series
for
interpreted
without
lack
to
which
substituted
thermal
the
is
error
series
gas
of
equilibrium
discussed
of
interest
measurements
log
KI
'
.
due
impurities
,
to
flow
carbon
analysis
measurement
)
,
the other . This may happen in two ways:
and
(a) The reactants being equally " cold " in both ,
one reaction requires more activation energy than
the other , or
(b) Activation energies being equal , the reactants
for one reaction are " colder " than for the other .
temperature
simultaneously
A
At
high
that
were
log
- carbon
Ki
'
~
contents
equilibrium
,
0
,
or
"
such
that
:
. 033
the
reaction
. . . , , ' as
so
pseudoequilibrium
slow
, "
could
not
be
approached
theoretically
Short of any better working hypothesis , the mechanism
proposed by Doehlemann16 for carburization
and decarburization of austenite is applied to liquid
Iron :
decarb
.
CO2 ,
' CO + 0 (adsorbed)
carbo
decarb
.
0 (adsorbed) + C ,
' CO
carbo
result
the
sign
. . . vere
slo'YV
ho
. . . vever
as
0
\
,
the
fast
and
its
, 7
.
0
%
in
a
1
8- S0LUTES IN LIQUID IRON OR STEEL
. 2
reaction
" , ' ity
ox
)
mina
,
suppressed
in
a
even
,
at
on
the
C
at
temperatures
\
t
15600
good
0
.
11
at
vas
.
It
17600
C
that
the
spectacular
at
carbon
could
sets
than
.
be
Alu
-
formed
fluctuations
a
limit
carbon
deposition
to
this
study
.
OF
THE
C
DATA
AND
CALCULATIONS
,
three
equilibrium
with
agreement
less
here
of
THERMODYNAMIC
r
' s
temperature
INTERPRETATION
established
)
high
Independently
reaction
the
evidence
surface
" \ vith
.
crucible
high
and
melt
and
Aluminum
alwa
\
the
will
interval
the
,
was
percentage
presented
(
15600
at
200
be
data
temperature
)
' gen
through
.
equilibrium
or
particles
or
to
melt
)
weight
led
good
with
points
accuracy
those
.
of
Richard
have
They
been
are
son
also
and
coefficient
,
were
materials
larshall
. 01
crucible
the
with
l \
0
control
the
of
carbon
1660
to
than
found
range
' gen
CO
lower
with
reached
,
=
according
vays
melt
the
%
]
was
the
rapidly
1760
If .it is assumed that the reactants be equally " cold ,"
decarburization is, therefore , slowed down more
than carburization .
Had the activation energies turned out to be
equal , the same conclusion could be reached by
arguing that the CO2 molecules (reactants in decarburization ) which have more degrees of freedom
may be expected to stay " colder " than CO molecules
(reactants in carburization ). In all cases, therefore
, if the mechanism is correct , the total effect is
a displacement of equilibrium
towards higher
carbon content , this is indeed found by experiment .
\
and
in
increased
One may , therefore , write :
.
.
t:.H I(rorward
) > t:.H I(backward
) + 7500 cal
al
analyzed
. 01
0
,
was
of
was
[
Aluminum
reaction
t:.Ho = 7500 cal
+
concentration
Chipman
CO2 (g) + Fe (1) = CO (g) + FeO (1)
impurities
acti
Ox
C
.
the
charge
Step I is rate controlling . The difference bet ,veen
the heats of activation for the for ,vard and the
back \\"ard reactions is equal to AH (I )' the heat of
reaction (I ), a low estimate of which may be obtained
by the standard heat of the reaction :
obtained
%
ll
con
than
. 005
and
(step II )
the
smaller
f
(step I )
of
in
Den
-
control
nis at the same temperature. At 14600C, a single
heat, sho\ving no net reaction under conditions
where reaction rates were high, is taken as defining
equilibrium within the accuracy of the method.
This point fits the temperature dependenceof the
equilibrium found by Richard son and Dennis at
higher temperatures.
At 1360and 12600C, the equilibrium lines could
not be determined in the present \vork. Reliable
data are limited at the present time to the solubility
limit and the equilibrium of graphite with CO and
CO2. Successfulexperimental work is still needed
between 2% carbon and saturation.
In view of the modest contribution of this work,
it seemsdesirable to propose a joint interpretation
of all the data available. All of the experimental
points of Richard son and Dennis and of the authors
have been plotted in Fig. 6. The choice of (1 -
To
proceed
further , two assumptions
are made :
(a) The intercepts of the isotherms ( i .e., values of
log KJ are a linear function
of I IT \ vhich , in view
of the relationship
:
dlog Kl d (l / T ) -
~
- 2 .3R
is equivalent
to assuming that the standard heat
of reaction 1 is independent
of temperature .
(b ) The slopes of the isotherms are proportional
to l / T , following
the treatment of the iron -carbon
system by Darken and Gurry .17 These authors assume
the relationship
:
log ' Yc = _ .-4- ( 1 T
where A is a constant .
a log KIf
5 .40
a(l -
.I\ 'FC2
)
Hence :
a log "Yr
=
NFe2)
= - -A
j\ rFe2)
T
a (t -
5 .2
All slopes may , therefore , be calculated from the
15600 C isotherm , the value of A being A = - 4450 .
A tentative
general expression for the activity
coefficient
is therefore
5 .0
4 .8
.)
log
'Yo
=-4450
T (1- 1\Fc2
_ _4 .6
~
0 0
- 4 .4
The data at 17600 C are used along with the
previous equation
for log- YC
. to establish the tem perature dependence of Kl with the following result
:
42
4 .0
3 .8
I
E
o /}
Il
,
' ~ !-
- 7280
log
Kl=---:r- +7.98
.
utectlc
( 1153 C )
3 .60
0
0 .05
010
0 . 15
020
0 . 25
0 . 30
0 . 35
These
0 .40
son
I - N2
Fe
equations
and
Equilibrium of carbon with CO- CO2 mixtures.
K1' = p2CO
/ (PCO2. Nc).
activity
carbon
the
15600
abscissa
permits
a
linear
extrapolation
known
melt
.
carbon
saturated
for
data
other
to
a
content
point
and
The
determined
gas
ratio
relative
temperatures
by
of
the
position
will
isotherms
have
be
log
..1 ( (
K1
=
'
log
=
Kl
15600
C
and
isotherm
may
+
( Pco
-
the
gas
The
presently
type
is
may
be
'
=
4 . 02
+
2 . 43
( 1
-
the
4 . 02
i ~ tercept
15600
and
C
.
is
over
the
value
the
the
of
last
ent
log
term
~ re
range
Kl
conform
- carbon
solutions
of
the
producer
-
thermodynamic
the
data
equation
I8
:
C
( graphite
)
=
2CO
( g ) ;
K
=
~
~
+
8 . 85
graphite
is
C
=
according
to
Chipman
:
1 . 34
+
2 . 54
~ n
along
X
10
-
3 t
( OC
)
:
these
equations
are
sho1
,
values
of
the
log
KIf
line
of
1vere
calculated
saturation
in
/ ' yrFe2 )
determined
represents
of
+
of
%
experimentally
equation
Fig
where
from
by
- workers19
and
KI
( g )
solubility
co
From
log
to
T
defined
by
high
constant
known
log
and
best
than
required
.
The
the
high
other
about
represented
' Yc
represented
known
the
at
:
' 1\ ' c
is
be
log
the
is
valid
is
concentrations
for
not
temperatures
equilibrium
reaction
and
lines
) 2
PCO2
The
of
is
modification
what
Richard
carbon
expression
,
at
of
at
. the
graphite
of
discussed
equations
The
however
slight
CO2
The
.
data
authors
of
.
C
,
and
1 ~ ith
as
the
concentrations
C ,
the
of
2 %
coefficient
1560
)
and
below
Fig. 6.
NFe2
reproduce
Dennis
by
log
liquid
' Yo
the
.
6 .
The
correction
.
at
,
compositions
written
ACTIVITYOF
CARBON
lines
are
whereby
The
the
A
fi Otted
is
expression
best
fit
of
is
to
made
those
a
log
obtained
points
by
function
KI
of
a
temperature
remaining
when
unchanged
log
' Yo
is
-
9
:
IN
LIQUID
IRON
- CARBON
SOLUTIONS
4350
.
log'YC
= - T [1 + 4 X 10-4(T - 1770
)](1 - J\.Fe2
)
The lines of Fig . 6 are drawn to conform to this
equation , and values of log yo are shown in Fig . 7.
Second , the
the
solidus
experimental
to yield
the
of
Smith
at
temperature
the
lines
extrapolated
12000
C
gas ratios
isotherms
straight
" ,'ere
( the
) , 1260 , 1360 , and
corresponding
equilibrium
parallel
1. 0
data
concentrations
on
were
a plot
.
In
drawn
to
highest
14600 C
doing
so ,
as a set of
of
0
OlD
OID
OID
OlD
I Dq -
O.
I DI') N
~
~ ...
r
I()
-
log
-
and
O.
Third
the
.
, the
liquid
The
gas
alloys
temperatures
O.
, and
agreement
ratios
obtained
were
of
liquidus
line
the
log
with
K1 ' was
calculated
the equilibrium
:). pplied
at
to
the
same
.
lines
of Fig .
6 is fair . It could
be improved
by selecting
a solidus
line slightly
concave
downward
, since the location
~
0\ O .
of
0
choice
O.
Darken
the
of
final
the
both
and
Gurry17
lines
O.
Thermodynamic
O.
.
.
.
.
.
0 . 24
from
points
solidus .
solidus
O.
activity
is rather
sensitive
In fact , the
and
liquidus
preferred
to
to
uncertainty
is such
calculate
the
regarding
that
those
data .
Summary
The experimental data and the thermodynamic
implications of the above treatment regarding the
reactions of CO - CO2 mixtures with carbon in solution
or as graphite and the various solution and
Nc
Fig . 7 .
.1~c
~
.LV
\ rFe
spaced on the assumption
that the heat of transfer
of carbon
from
gas to metal
is independent
of
temperature
O.
0.I~Fe
S: . - . - ; - ; - versus
PCO2
1
\ TC )
( P
')
1.0
Activity coefficient of carbon in liquid iron (mole fraction
basis ).
O.
Figure 8 is a translation of Fig . 7 on the weight percentage basis, and the line earlier proposed by
Chipman2 O is shown on the same graph .
Comparison
with
Data
o.
o.
on Austenite
The data of Smith21 on the equilibrium of carbon
o.
in austenite with CO- CO2 mixtures may be extrapolated
across the two -phase field where austen" -u
ite is in equilibrium
with liquid alloys . The
points placed on the liquidus line on Fig . 6 have
been calculated in a manner to be described here .
c:7' o .
c
o.
First the liquidus and solidus lines of the iron carbon , diagram were redrawn on the follovving
o.
basis: the eutectic was taken at 11530 C17 and 4.27%
carbon19 and the peritectic at 14990 C and 0.53%
carbon .17 The experimental points of several investigators
O.
, 22, 23, 24, 25when corrected to fit the above
end points , define the liquidus used here . The
0.1
agreement with the line proposed by Darken and
Gurry17 is very close. The end points of the solidus
are taken at 14990 C, 0.16% carbon , and at 11530 C,
2.01% . Short of any justified choice among the
widely scattered experimental determinations
of
Fig. 8.
the solidus , a straight line was drawn between the
basis}.
two end points .
10- S0LUTES IN LIQUID IRON OR STEEL
1.0
2 .0
3 .0
Percent
4 .0
5 .0
6 .C~
c
Activity coefficient of carbon in liquid iron (weight -percentage
Broken line based on data of Marshall and Chipman.20
dilution processes for liquid iron -carbon alloys are
summarized '*' in the following statements and equations log
. In particular , expressions are given for the
activity of carbon with respect to both graphite and
the infinitely dilute solution as standard states. The
free-energy equations are well established because
they follow directly from the experimental data .
The heat terms in equations 4 to 7 that follow
should not be considered as accurate since they are
very sensitive to small errors in the temperature
coefficients .of free-energy terms .
C
4350
' YC =
(
log Kl = - 7280
- -r
)
A Hs
The standard state is defined by ac/ Nc = 1 when
Nc = O. The enthalpy term , A.H1o = + 33,300 cal
is an average for the experimental range and is
assumed to be independent of T .
When it is desired to express carbon concentration
in ", eight per cent , making ac/ [% C] = 1 when
+
4
[C ]
=
A Fs
=
Fc
=
Hc
=
5400
X
10 - 4 ( T
equations
change
for
mole
fractions
carbon
in
from
3
-
i\ TFe2 )
(5)
0
-
0
Fc
( graphite
)
=
AF4
+
AF3
0
-
Hc
+
( graphite
)
(1
NFe2
5810
-
)
gIve
,lving
Noand
NFeo
The
gra
phi
te-sa
tura
red
disso
gra
free -energy
and
en te in a solution
phI
activity
solution
the
of
follows
:
If
ac
'
and
,,/ c '
referred
( sat
to
.)
=
I
are
the
activity
graphite
as
and
the
activity
standard
coefficient
state
,
then
ac
'
and
log
ac
log
' YC
'
=
log
1\ TC
=
log
' YC
+
log
I
' Yc '
1180
+
-
-
0 . 87
T
C
( graphite
)
- 7280
log
K]a=--~ + 6.65
CO2 (g) + C (graphite ) = 2CO (g)
38 ,700
-
~ F 6
~ H6
(2)
40 .5 T
For
- 8460
log K2 = y
) ] (1
logac(sat
.) = - 1180
T + 0.87
AFlaO= 33,300- 30.40T
=
1770
( l\ TC)
[% C] = 0, the equation becomes
t:.F2
-
the
These
thalpy
7.98
+
[1
T
graphite
of
(1)
CO2(g) + [C] (inf. Dll.) = 2CO(g)
AF1O
= 33,300- 36.5T
-
-
to
N
is
7500
a
c
mean
( sat
cal
.)
=
[ C
=
0
=
Hc
=
5400
]
( sat
( sat
.)
.)
+
temperature
=
0 .2 ,
C
( "\ ' Cl )
the
heat
( 6 )
-
Ho
( graphite
5810
[ 1
-
of
15000
of
solution
-,"
)
Fe2
( sat
.) ]
corresponding
of
graphite
.
+ 8.85
=
C
=
RT
( "VcJ
( 7 )
The enthalpyterm is an averagebetween39,700cal
at 11500 C and 37 ,900 cal
Bureau
of Standards
at 20300
' data .
C , based
= 5400 -
a2
National
AF7
In
al
C (graphite ) = [C] (inf . Dll .)
AF3
on
AH7
(3)
=
5810
( i V ~' el
-
J.\ ' ~' e2 )
The last is a general expression for the heat of dilution
.
4 .00T
- 1180
log K3 = --y -
+ 0.87
References
The enthalpy term ~ H3 = 5400 cal is the heat of
solution of graphite in the infinitely dilute solution .
1. .J. Chipman , Tran .5. /im . ,) ()c. }\ letals , 22, 385 ( 193-4) .
2. N . J . Petch , ] . Iron Steel II /st ., 145, III ( 1942) .
3 . I -I . C . Vacher
[ C] (inf . diI .) = [C] (.iVc)
(4)
t'J-F4x = + 19,900[1 + 4 X 10- 4( T - 1770) ]
-
NFe2)
-
0
t'J-H4 = Hc - Hc (inf . diI .) = 5810(1 - .LVFe2
)
The excess partial molar free energy of carbon
AF 4:1: and its relative partial molar enthalpy AH4
are obtained directly from the equation for activity
coefficient
. See
Ref
:
. 26 .
EH
. Ha milton
4 . H . C . " acher , ] . Research
t'J-F4 '= RT In .i\ TC+ t'J-F4x
(1 -
and
,
Trans
. / 1 .1 . ,~I .E ., 95 ,
124 (1931).
lVatl . Bur . Standards
(1933).
5. S. Matoba , Honda Anniv . Vol ., 548 (1936) .
6. G . Ph ragmen and B . Kal1ing , ] ernkontorets
199 (1939).
, II , 541
Ann ., 123,
7. S. Marshall and J. Chipman , Trans. 'Am . Soc. j\[ Etais, 30,
695 (1942).
8. F . D . Richard son and WE
49, 171 (1953).
9 . O . A . Esin
and
. Dennis , Trans . Faraday Soc.,
L . K . Gavrilov
, lzves
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the eutectic
composition .
Darken
used 4.24% , ,",'hile
Chipman and Rist used 4.27%.19
RICHARDSON
discussed briefly some of the experimental
difficulties inherent in a system ,vhere heating is by induction
and a cold gas impinges on the surface of the
melt
. These
conditions
could
be
ex Dected
to
havf 'c ~ n
14 .
influence on the constant KI ' and on the temperature
measurement . CHIP~rAN and RICI-IARDSONagreed that the
general effect would tend to lead to too -low results , as
shown in the experimental points on the right side of
Fig . 4.
WAGNERbrought out the fact that in a gas like CO2
there are several degrees of freedom . Equilibrium
in -
volving the vibrational energy is probably not readily
attained . Therefore , it seems likely that CO2 is not in
equilibrium
with the melt , and on Richardson 's question
, he surmised that this effect would tend to shift KI '
as shown in Fig . 4.
PEARSONdescribed a program of research being conducted
in the Chemical Laboratories of B .I .SiR .A . in
London . Initially
the interest was in measuring the
activity of carbon in iron -carbon alloys , but in reviewing
the picture , it ,,,'as decided that although the CO/ CO2
ratio in equilibrium with liquid iron did not give trouble
at lo,v carbon leiels , it would in the high carbon
ranges . As a result , the H2 / CH4 reaction ,vas tried . A
mixture of hydrogen and methane was circulated over a
liquid iron -carbon alloy contained in a lime crucible.
The gas was recirculated
Discussion
continuously
and ,vas analyzed
in an infrared gas analyzer. Equilibrium ,vas established
in approximatel )' t"'.o hours. It ,,,'as run for
another two hours to be sure. Subsequently, the
DARKENpointed out that in his laboratory the)' had
methane -hydrogen gas was replaced with argon , the sample
made similar calculations several )'ears ago. They concluded was quenched , and analyzed for carbon . The general
that the eutectic point pro\'ided the most reliable
accuracy of the method ,vas checked by using iron contained
in graphite crucibles . Their results checked with
source of information . The activities at point E of
Fig. 7 could be calculated from the thermod)'namic
the existing data on methane . A quick calculation from
properties of iron , the temperature and composition of
data sent recently from England showed that the results
the eutectic, and the assumption that the activity coefficients
agreed reason ably well ,vith Fig . 7. Up to 0.16 atom
approach unity at high temperatures.
fraction of carbon , the agreement is good . At No = 0.18,
CHIPMANsaid that their calculations did not include
they begin to drop a little bit below the line given .
the thennodynamic functions of iron , but that log KIf at
MORRISinquired ,vhether the presence of the waterthe eutectic was calculated from the graphite-gas equilibrium cooled Vycor tube influenced the temperature measurement
and the eutectic composition. The result was reaby changing the emissivity of the iron surface.
sonably close to Darken's previous calculation. The
CHIP~!AN said that it did not , as the emissivity values are
discrepancy may be due in part to the values taken for
for cold surroundings .
12- S0LUTESIN LIQUIDIRON OR STEEL