Solubility, Permeability, and Diffusivity of Oxygen in
Solid Iron
J. H. Swisher and E. T. Turkdogan
The solubility of oxygen in zone-refined iron was
determined in the temperature range.from 881" to
1350°C. The solubility in a iron at 881°C m s found
to be about 2 to 3 ppm; in y iron, the solubility was
found to increase from about 2 to 3 ppm at 950°C to
about 25 ppm a t 1350°C. The permeability of oxygen
in an iron -0.1 pct A1 alloy zvus determined in the y
iron range, using an internal oxidation technique.
By combining the permeability and solubility data,
the diffzisivity of oxygen in y and a iron was calculated. The oxygen dlffusivity in solid iron may be
s ~ i m m a r i z e da s follows:
y
iron:
For 6 iron and
approximately
f o r a iron:
log D
= -
logD
=--
7+
5100
T
0.76
- 1.43
IN a recent paper, Hepworth, Smith, and ~ u r k d o ~ a n '
reported on the solubility, permeability, and diffusivity
of oxygen in 6 iron, together with permeability data
for oxygen in a iron. In the present investigation,
similar measurements were made in the y phase r e gion. In addition, a solubility measurement was performed in the CY phase region to permit calculation of
the diffusivity of oxygen in a, iron. References to early
work on this subject a r e given in the previous publication .'
EXPERIMENTAL
Solubility Measurements. The oxygen solubility was
determined by equilibrating cylindrical samples 0.3
in. diam by 14 in. long of zone-refined iron in water
vapor -hydrogen gas mixtures. The zone -refined iron
was prepared by B. F. Oliver of this laboratory, using
an apparatus and technique described
Six zone-melting passes were used to achieve a total
impurity level of about 30 ppm. Of this 30 ppm, the
combined nickel and cobalt content was about 20 ppm,
oxygen was 4 ppm, and all oxidizable impurities l e s s
than 1 pprn each.
A vertical resistance furnace wound with molybdenum wire was used for the experiments. The temperature was measured before and after each experiment with a Pt/Pt-10 pct Rh thermocouple. In the g a s
train, flow r a t e s of hydrogen and argon were measured
with capillary flow meters, and the resulting mixtures
were passed through a column containing 90 pct oxalic
acid dihydrate and 10 pct anhydrous oxalic acid to obtain predetermined ratios of H z 0 to Hz. The vapor
p r e s s u r e of Hz0 above this mixture a s a function of
temperature is well-known.4 The exit g a s was anaJ. H. SWISHER and E. T. TURKDOGAN are with Edgar C.
Bain Laboratory for Fundamental Research, U.S. Steel C o r ~ . .
Research center, Monroevi l le, Pa.
Manuscri~tsubmitted Auaust 12. 1966. ISD
..
426-VOLUME 239, APRIL 1967
lyzed periodically for H20, and good agreement (+3
pct) with the calculated composition was obtained.
The zone-refined iron specimens were held in the
furnace for a sufficient length of time for equilibration, e . g . , 18 h r a t 1350°C and 1 week a t 881°C, then
quenched in a brine solution. After removing the s u r face oxide from the samples by machining, duplicate
analyses were obtained by a combined vacuum fusioninfrared method; oxygen analysis was reproducible
within 2 ppm.
Permeability Measurements. The permeability of
oxygen in alloys containing about 0.1 pct A1 was determined by internal oxidation and measurement of the
subscale thickness a s a function of time. The experimental alloys were prepared by adding aluminum to
electrolytic iron (grade 104A plastiron) that had p r e viously been vacuum-carbon deoxidized. The resulting
ingots contained about 20 pprn 0, 100 pprn C, 40 pprn
Si, 50 pprn Mo, 20 pprn P, 20 pprn S, and 20 pprn Zr
a s the principal impurities. After hot rolling the ingots
to 1-in.-thick slabs, specimens were machined from
the stock in the form of rectangular plates, 4 by 5 by
2 in.
The general procedure for the permeability experiments was the same a s those for the solubility measurements. The specimens were cooled in a reducing
atmosphere rather than quenched, however, in order to
maintain a clean surface for measurement of the subscale thickness. This measurement was made on a
polished c r o s s section of each specimen, using a microscope with a micrometer stage. The inclusions
formed a t the lowest temperature 1033°C were too
small to be seen with an optical microscope. An electron micrograph showing the size and shape of individual particles i s shown in Fig. 1. The dark band in
the picture is a boundary between two subgrains. The
subscale thickness in these samples was measured
with an optical microscope after heavily etching in
2 pct nital, which gave contrast between the subscale
and the unoxidized zone.
Fig. 1-Electron micrograph of internally oxidized 0.003-in.thick Fe-0.1 c t A1 specimen after reacting 17 h r i n wet hydrogen (pH2&~2
= 0.50)a t 1033OC. Magnification about 6000
times.
TRANSACTIONS O F THE METALLURGICAL SOCIETY OF AlME
At the two higher temperatures, i . e . , 1152" and
1352"C, the inclusions were large enough to be r e solved using an optical microscope. The photomicrograph in Fig. 2 shows a specimen that had been internally oxidized a t 1152OC f o r 80 h r with p ~ ? o / p=~0.20.
,
There was no evidence for enhanced diffusion along
grain boundaries in any of the samples.
The stoichiometry of the inclusions formed was
studied by extraction of the inclusions from selected
samples, using a bromine-methyl acetate solution.
The oxygen to aluminum ratio in the extracted material
was determined using X-ray diffraction and spectrographic analysis.
RESULTS
Oxygen Solubility. The experimental results for
1350°C a r e plotted in Fig. 3, and the solubility data for
-.
all temperatures a r e summarized in Table I. The oxygen concentration data listed in column 3 of Table I
were obtained by analyzing specimens after equilibration in H20-H2mixtures close to the composition r e quired for wustite formation. In all cases, the raw
data were corrected in column 4 for a blank of 4 ppm
0 . This correction was made f o r the following r e a sons. The oxygen content of purified iron could not
be reduced below 4 ppm in several zone-refining
passes, nor could oxygen be removed by annealing for
18 hr in purified hydrogen a t 1350°C. Therefore, it
is believed that this oxygen concentration corresponds
either to oxygen that i s combined with trace amounts
of impurities such as zirconium and aluminum, or to
a n analytical blank in the vacuum fusion analysis for
oxygen. In the previous work on oxygen solubility in
6 iron, the solubility was sufficiently high that a blank
correction was unnecessary. However, for temperatures below 1200"C, this correction becomes an appreciable portion of the total oxygen; therefore the
reported solubility data for lower temperatures a r e
l e s s accurate.
The oxygen concentration in equilibrium with wustite was obtained by extrapolation of the data to the
critical ~
~ ratio for
~ wustite
~ formation
/
derived
p
~
f r o m the equilibrium data of Darken and ~ u r r ~ ?
In Fig. 3 , corrected values for the equilibrium oxy-
Unoxidized zone
Fig. 2-Photomicrograph of internally oxidized 0.250-in.thick Fe-0.1 c t A1 specimen a f t e r reacting 80 h r in wet hy= 0.20) a t 1ISTC. Magnification about 20
drogen
times.
1 .o
0.8
0.6
0.4
AT pHI,/p,,
= 0.89
0.2
0
8
Fig. 3-Determination
1350°C.
16
p p m OXYGEN
24
of the oxygen solubility in y iron a t
TRANSACTIONS OF THE METALLURGICAL SOCIETY O F AlME
30
Fig. 4-Variation of subscale thickness with time for 0.086
pct A1 alloy a t 1033°C with pH2dpH2
= 0.20.
VOLUME 239, APRIL 1967-427
~
aen content a r e plotted a s a function of P ~ . , ~ f/ oPr ~ ~
temperature of 1350°C. The critical P ~ , ; / P ~ ,*for
wustite formation was checked by progressively increasing the ratio until visual oxidation of the sample
occurred. The value obtained was equal to that calculated from the data of Darken and Curry, i .e., PH,O/PH,
= 0.89, within the experimental uncertainty (k0.01).
Permeability. Data plots describing the rate of internal oxidation of the Fe-A1 alloys a r e given in Figs.
4 to 6. The data a r e plotted in the form of square of
depth of penetration v s time to show the parabolic nature of the internal oxidation reaction.
Information obtained on the stoichiometry of inclusions formed in the internally oxidized samples is
summarized in Table 11. The oxygen/aluminum atom
ratio in the oxide, r , taken for use in the permeability
calculations, i s based primarily on spectrographic
analysis of the extracted inclusions. The accuracy of
weight gain measurements was limited by vaporization
of iron a t the high temperatures and oxidation of the
surface of the specimens during cooling. Although not
quantitative, the X-ray diffraction patterns a r e in
agreement with the spectrographic analyses.
a
DISCUSSION
For the equilibrium reaction
Hz (1 atm) + 0 (1 pct sol) = Hz0 (1 a t m )
[ 11
TIME, hr.
Fig. 6 - V a r i a t i o n o f s u b s c a l e t h i c k n e s s w i t h time f o r 0.125
pct A 1 alloy at 1352°C.
Table I. Oxygen Solubility Data
oc
PH,O/pH,
ppm 0,
analysis*
ppm 0.
correctedt
88 1
95 1
1049
1250
1350
0.544
0.580
0.643
0.708
7.5
6.5
9.
18.5
3.5
2.5
5.
14.5
Temp,
80
40
120
TIME, hr.
( s e e Fig. 3)
For Fe-FeO
Eq~ilibrium'~~
K'
pHZO/pHI
PPm 0
1554
2320
1286
488
362
0.56
0.63
0.70
0.83
0.89
3.6
2.7
5.4
17.0
24.6
*Results listed a r e based on the average of duplicate analyses on the
same specimen.
h he raw data are corrected for a 4 ppm blank (see text).
Fig. 5 - V a r i a t i o n o f s u b s c a l e t h i c k n e s s with time f o r 0.125
pct A 1 alloy f o r 1152°C w i t h pHZ0IpH2
= 0.20.
Table I I . Summary of Data o n o x i d e Stoichiometry
S a m ~ l eNumber
Data
Temp, O
P c t A1
C
PH,O/PH,
X-ray identification
Analysis of extracted inclusions*
Weight gain
r value taken
r
P5
D-13
D-21
D-31
D-27
1033
0.086
0.20
1152
0.125
0.20
1352
0.125
0.10
1352
0.125
0.20
FeAl,O,
FeAI,O,
A1203
1352
0.125
0.40
FeAAO, > AI,O,
1.87
{;:''
1.53
2.06
1.8
2.0
FeAI,O,
t
1.68
AI,O,
-
-
-
1.5
1.7
1.9
+r = oxygen/aluminum atom ratio in the oxide; calculated from total analysis for iron and aluminum in inclusions assuming a l l iron i s divalent and a l l
aluminum trivalent.
428-VOLUME 239, APRIL 1967
TRANSACTIONS O F THE METALLURGICAL SOCIETY O F AlME
where the standard s t a t e s a r e given in parentheses
and K is the equilibrium constant. The temperature
dependence of K i s shown in Fig. 7 f o r a and y iron
f r o m the present study and for 6 iron f r o m the previous work.' The line I i s f o r liquid i r o n , the data
having been taken f r o m a critical survey of the published work.6
It is difficult to estimate the limit of uncertainty
in the r e s u l t s ; the uncertainty range indicated in Fig.
7 for the present data is f o r an assumed e r r o r of * 2
pprn in the reported oxygen solubilities. Despite this
possible range of uncertainty, the r e s u l t s for y iron
appear to be interconsistent; these data a r e well r e p resented by the line drawn in Fig. 7. It may be r e called that the oxygen solubility measurements a t tempted by Kitchener et a1 .7 indicated the solubility to
be about 30 i 30 pprn in y iron; t h i s previous observation i s supported by the present findings.
In drawing the line f o r the bcc phase, m o r e weight
is given t o the high-temperature data f o r 6 iron because the previously measured solubilities a r e considered t o be more accurate. The recommended
solubility line in Fig. 7 for the bcc phase gives an
oxygen solubility of 1.6 pprn in CY iron at 881°C, a s
compared with the corrected observed value of
3.6 ppm.
F o r the purpose of interpolation, the data s u m m a r ized in Fig. 7 may be represented by the following
equations :
5000
bcc iron (approx): log K = - - 0.79
T
fcc iron:
4050 + 0.06
log K = T
liquid iron:
log K
=
7050 - 3.20
7'
TEMPERATURE, 'C
To facilitate other thermodynamic computations, the
following free-energy equations may be derived from
the data cited above f o r the solution of oxygen in iron:
Reaction: +02(1a t m )
=
0 (1%)
[GI
bcc iron: AF" = -37,190 + 10.20T c a l per g-atom 0
(approx for CY iron range)
[ 71
fcc iron: h F o = -41,860 + 14.46 T cal per g-atom 0
[81
liquid iron: AF" = -28,000 - 0.69T cal p e r g-atom 0
[ 91
The phase equilibrium diagram given in Fig. 8 for
the iron-rich side of the F e - 0 system i s derived by
combining the solubility data summarized in Fig. 7
with the relevant equilibrium data of Darken and Gurry
on the F e - 0 system.5 The monotectic, eutectoid, and
peritectoid invariant t e m p e r a t u r e s a r e computed in
the usual manner f r o m the available heats of phase
transformation of irone1' and the oxygen solubilities.
The a iron/wustite phase boundary is based on the
line drawn in Fig. 7 for the bcc phase and not on the
experimental value of 3.6 pprn 0 for 881°C which i s
probably in e r r o r by about 2 ppm.
In previous studies involving kinetics of internal
oxidation, permeability h a s usually been defined a s
the product of solubility and diffusivity. For the
present purpose, it i s more convenient t o define
permeability a s the quotient, D/K, where D is the
oxygen diffusivity and K is the equilibrium constant
given by Eq. [2].
The permeability equation to be derived is based
on the following assumptions and approximations:
i ) The oxygen content of the iron a t the surface of
the specimen is in equilibrium with the oxygen partial
p r e s s u r e in the g a s phase.
i i ) The oxygen content of the iron in the oxidized
r i m d e c r e a s e s linearly from the surface to essentially z e r o a t the interface between the oxidized and
unoxidized zones.
iii ) The aluminum concentration and diffusivity in
the alloy a r e such that counterdiffusion of aluminum
can be neglected.
E r r o r s arising f r o m these simplifying assumptions
7+WUSTITE
DISTRIBUTION RATIOS:
3
t-
[%OI
[%OI,
to4/ T
Fig. 7-Temperature dependence of oxygen solubility constant K = P ~ O / P H [%OI
~
f o r u and y iron (results of present
work); for 6 iron (results for previous worki); for liquid
iron (critical compilation of previous studied).
TRANSACTIONS OF THE METALLURGICAL SOCIETY O F AlME
0.054;
[%O]
-2
= 0.52;
[%OI,
['/.O],
r 1.1
[%OI,
a l WUSTITE
Fig. 8-Iron
side of the F e - 0 phase diagram.
VOLUME 239, A P R I L 1967-429
will be negligibly small in the interpretation of the
permeability data presented here. For the above conditions. the kinetics of internal oxidation i s an application of Fick's f i r s t law:
The amount of oxygen transported a c r o s s the unit a r e a
of the specimen i s given by the mass balance equation:
where
p i s the density of iron,
where
[ ' ~ l ] is the aluminum concentration in the original
material,
(in/& i s the instantaneous flux of oxygen into the
specimen, g-atoms per sq cm s e c ,
v is the oxygen/aluminum atom ratio in the oxi-
[ i s the instantaneous thickness of the oxidized
dized layer.
layer,
By combining Eqs. [ l o ] and [ I l l and converting oxygen
concentration to weight percent,
c i s the oxygen concentration at the surface in
equilibrium with the g a s phase,
D i s the diffusion coefficient of oxygen in iron.
Upon integration,
TEMPERATURE,
OC
where
Values of D/K obtained from Eq. [ 131 a r e now inde pendent of P ~ , ~ and
/ P a~function
~
of temperature only.
The values of D/K derived from the experimental
results a r e given in Table 111 and in Fig. 9, where
log D/K i s plotted against the reciprocal of the absolute temperature. The r e s u l t s of other investigat o r ~ ' ~ a- r' e~ a l s o included in Fig. 9. Except f o r the
data of ~ e i j e r i n g , " the present work i s in good a g r e e ment with previous studies. The oxygen permeability
in y iron may be represented by the following equation
for the line drawn in Fig. 9:
D
fcc iron: logK
= - 12'870
--
T
+ 0.70
The corresponding expression obtained previously by
n ' bcc iron i s a s
Hepworth, Smith, and ~ u r k d o ~ a for
follows:
D
10'100
bcc iron: log - = - -- + 0.64
T
K
7
6
8
9
IO'/T
Fig. 9-Temperature dependence of oxygen permeability in
y iron. 8 , present work: - 0 . 1 pct Al; A V , Schenck et a1 .:lo
0 . 2 5 to 0 . 8 1 pct Al, 0 . 2 4 to 1 . 6 pct Si; 0 ,
Bohnenkamp and
Engell:I1 0 . 2 4 pct Si; i; , h ~ c i j e r i n g : '0.97
~ pct A l .
[ 151
By combining these equations with those given for
the equilibrium constant K in Eqs. [3] and [4], the
temperature dependence of the oxygen diffusivity in
bcc and fcc iron may be evaluated:
For oxygen diffusivity
in bcc iron (approx
for cr iron range):
log D
= -
5 100
- 1.43 [16]
T
--
Table Ill. Permeability and Diffusivity of Oxygen in Gamma Iron
PH,O/FH,
'C
1033
1152
1352
1352
1352
0.20
0.20
0.40
0.20
0.10
D
wt pct A1
i*
0.086
0.125
0.125
0.125
0.125
oxygen/aluminum atom ratio in the oxide.
'1n computing diffusivity D from U / K the equilibrium constant
2.0
2.0
1.9
1.7
1.5
d(cl)/df,
cm2 per s e c
1.80 x
1.30 x
3.53 A
1.93 x
1.12 x
10lo-'
1010lo-'
-log- K
9.339
8.318
7.207
7.217
7.206
0,
cm2 per s e c '
6.64 r lo-'
3.34 r 10"
1.93 Y 10"
1.88 r 10"
1.93 x 10-
*i =
430-VOLUME 239, APRIL 1967
K
taken i s that given by Eq. [4] for y iron.
TRANSACTIONS O F THE METALLURGICAL SOCIETY O F AlME
The permeability of oxygen in an iron -0.1 pct A1
alloy was determined in the y iron range, using a n
internal oxidation technique. The internal oxidation
reaction was found to follow parabolic behavior, and
no evidence for preferential diffusion along grain
boundaries was obtained.
The diffusivity of oxygen in y and a iron was calculated f r o m the combined permeability and solubility
data. The oxygen diffusivity values were found to be
close to published values for carbon and nitrogen in
solid iron.
ACKNOWLEDGMENT
f c c IRON
The authors wish to thank the following members of
this laboratory: B. F . Oliver for the zone-refined
iron, L. Zwell f o r the X-ray diffraction work, P. R.
Swann and W. F . Kindle for photomicrographs, R. S.
Walsh for assistance with the experiments, and J. F .
Martin and his associates in the Applied Research
Laboratory of U.S. Steel Corp. for oxygen analysis.
I
REFERENCES
1097
Fig. 10-Comparison of oxygen, carbon, and nitrogen diffusivi t i e s in bcc and fcc iron. D o in bcc and f c c : p r e s e n t and p r e vious work;' D c in b c c : Smith;13 D c in f c c : Smith;l4 D N in
b c c : F a s t and verrijp,15 Grieveson and ~ u r k d o ~ a n ; ' " ~ in
f c c : Grieveson and Turkdogan.17
For oxygen diffusivity
in fcc iron:
log D
8820 +
= - -
T
0.76 [17]
I t should be emphasized that the temperature d e pendence of oxygen diffusivity in bcc iron becomes a p proximate only a t temperatures below those for 6
iron. This i s self-evident from the preceding discussion of oxygen solubility in a iron, Fig. 7 and Eq. [3].
For comparison purposes, the interstitial nitrogen,
carbon, and oxygen diffusivities in bcc and fcc iron
a r e summarized in Fig. 10.
CONCLUSIONS
From direct measurements of the oxygen solubility
iron, the solubility i s found to vary from 2 o r 3 ppm
a t 950°C to about 25 ppm a t 135WC. A single measurement for a iron a t 881°C yielded an oxygen solubility
of 2 to 3 ppm.
y
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"J. L. Meijering: .Acla Met., 1955, vol. 3, pp. 157-62.
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14R. P . Smith: Trans. Met. Sac. AIME, 1964, vol. 230, pp. 476-80.
1 5 J . D. Fast and M. B. Verrijp: I . Iron S t e e l lnst., 1955, vol. 180, pp.
337-43.
L6
P . Grieveson and E. T . Turkdogan: Trans. ,Met. .Sac. AIME, 1964,
vol. 230, pp. 1604-09.
I7
P . Grieveson and E. T. Turkdogan: Truns. ,\let. Sac. AIME, 1964, vol.
230, pp. 407-14.
VOLUME 239, APRIL 1967-431