Surface Tension and Wettability of Liquid Fe-16mass%Cr-S Alloy with Alumina

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Surface Tension and Wettability of Liquid Fe-16 mass%Cr-S Alloy with Alumina
Zushu Li
1;
*
,Masafumi Zeze
2
and Kusuhiro Mukai
1
1
Department of Materials Science and Engineering,Faculty of Engineering,Kyushu Institute of Technology,Kitakyushu 804-8550,Japan
2
Yawata R&D Lab,Technical Development Bureau,Nippon Steel Corporation,Kitakyushu 804-8501,Japan
The surface tension and wettability of liquid Fe-16mass%Cr-S alloy with alumina substrate at 1823Kand the temperature dependence of
surface tension of liquid Fe-16mass%Cr-S alloy in the temperature range of 1808-1883Kwere measured using the sessile drop technique.The
surface tension and contact angle of liquid Fe-16mass%Cr-S alloys with alumina substrate decreased markedly with increasing sulphur
concentration in the alloys.The variation of surface tension of liquid Fe-16mass% Cr-S alloys with sulphur activity can be described by the
following equation:
1g
¼ 1640 182lnð1 þ157a
S
Þ (mass%O=0.0037-0.0075,mass%S  0.195) (mN/m).The interfacial tension between
liquid Fe-16mass% Cr-S alloys and alumina substrate,calculated using Young’s equation,can be expressed by the following equation:

s1
¼ 2170 220lnð1 þ237a
S
Þ (mass% O=0.0037-0.0075,mass% S  0.195) (mN/m).The work of adhesion between liquid Fe-16mass%
Cr-S alloys and alumina had a tendency to increase with increasing sulphur concentration.The temperature coefficient of surface tension,
d=dT,for Fe-16mass% Cr-S system in the temperature range of 1808-1883K increased with increasing sulphur concentration,and changed
from negative to positive value when the sulphur concentration exceeded 20mass ppm.
(Received June 16,2003;Accepted August 6,2003)
Keywords:surface tension,temperature coefficient of surface tension,interfacial tension,contact angle,liquid iron-16mass% chromium-
sulphur alloys,sulphur
1.Introduction
In the continuous casting process,some non-metallic
particles,such as deoxidation products,mould powder,may
be transported along with injected argon bubbles by the
molten steel flow to the solidifying metal interface.These
foreign particles (solid particles and bubbles) can get
entrapped at the solidifying interface of steel and result in
inclusions and bubble-related defects in the cast-product.The
behaviours of these foreign particles in front of solidifying
interface,(i.e.pushing or engulfment by a solidifying
interface) are related to interfacial tension gradients induced
by both the concentration and temperature gradients formed
in the boundary layer in the front of the solid-liquid
interface.
1)
Particle entrapment is also related to the wett-
ability of the inclusion with liquid steel.
2)
Consequently,the
knowledge of the surface tension of iron-chromiumalloy and
its wettability with alumina is necessary to reduce inclusion
and bubble entrapment in Cr-steels.
Keene
3)
compiled the reported data of the surface tension
of liquid Fe-Cr alloys,and concluded that the large discrep-
ancy of the surface tension between investigations is
probably due either to varying concentrations of surface-
active impurities such as O and S in the alloy samples or to
inaccurate experimental techniques.The oxygen or sulphur
contamination of steels has been recognized as a major
problem in steel processing.
Tret’yakova et al.
4)
determined the effect of oxygen up to
110 mass ppm on the surface tension of liquid Fe-Cr alloys
with less than 1.0 mass% Cr.Nogi et al.
5)
measured the
surface tension of liquid Fe-Cr alloys up to 100mass%Cr by
the levitated droplet method in an Ar-H
2
gas atmosphere at
2023 K.Fe with the purity of 99.99 mass% and two kinds of
Cr,that is puratronic Cr and electrolytic Cr,were used in their
experiments.The oxygen and sulphur contents in the samples
are as follows:for electrolytic Cr,with 5000 
6000 mass ppm O and 250 mass ppm S before levitation and
15mass ppm O and 180 mass ppm S after levitation,for
puritronic Cr,with 20  30mass ppm O and 10 mass ppm S
before levitation and <1mass ppm O and <1 mass ppm S
after levitation.They clarified that the difference between the
two results for puratronic and electrolytic grades of Cr is due
to the difference in the oxygen and sulphur contents in these
samples.Chung and Cramb
6)
measured the surface and
interfacial properties of Fe-30 mass%Cr-S alloys in contact
with alumina,and found that both the surface tension of Fe-
30mass%Cr-S alloys and the contact angle between the alloy
droplet and an alumina substrate decreased with increasing
sulphur content.In order to elucidate the metal flow in the
weld pool in the plasma environment,McNallan and
Debroy
7)
calculated the effects of temperature and compo-
sition on surface tension of Fe-Ni-Cr alloys containing
sulphur,and found that until up to about 2400 K the surface
tension of Fe-18 mass%Cr-S alloy is somewhat higher than
that for the binary Fe-S alloy.This is in contradiction with the
fact that the addition of chromium to liquid iron results in a
decrease in the surface tension.
3,6,8)
The stainless steel containing about 16mass%Cr is one of
important stainless steel grades.In order to reduce inclusion
and bubble entrapment in this grade of stainless steel,it is
necessary to study the effect of Oand S on the surface tension
and its wettability with solid substrate.The surface tension
and wettability of liquid Fe-16 mass%Cr-O alloy with
alumina have been reported in the previous paper.
8)
In this
study,the effect of S on the surface tension of liquid Fe-
16mass%Cr alloy and its wettability with alumina substrate
has been determined using the sessile drop technique.
2.Experimental
A Fe-16 mass% Cr alloy with 30-40 mass ppm O,
10mass ppm N and 3 mass ppm S was prepared by using
electrolytic iron (15 C,<10 P,6 S,<5 Si,1 Mn,1 Cu,6 N,70
*
Present address:Department of Materials,Imperial College London,
Prince Consort Road,London SW7 2BP,UK
Materials Transactions,Vol.44,No.10 (2003) pp.2108 to 2113
#2003 The Japan Institute of Metals
O in mass ppm) and 99.9 mass% Cr (6 O and 3 N in
mass ppm).
8)
The samples for measuring the surface tension
of liquid Fe-16 mass%Cr-S (0.0003mass%) alloys were
cylindrical pieces (about  8 mm  8mm,3 g) cut from the
ingot of Fe-16 mass%Cr alloy.The samples for measuring
the surface tension of liquid Fe-16 mass%Cr-S alloys
containing higher than 0.0003 mass% S were constituted by
two cylindrical pieces ( 8mm6mmand  8mm2mm)
cut fromthe ingot of Fe-16 mass%Cr alloy.The desired mass
of high purity FeS agent was added to a hole drilled in the 
8mm6 mmcylindrical piece and covered by the  8mm
2mm piece.All the alloy pieces were polished with sand-
paper to remove any surface oxide and cleaned with acetone
using an ultrasonic automatic washer.The high purity Al
2
O
3
(99.8%) plate (25.7 mm25.7mm2.5 mm) was used as a
substrate in this study.The surface of Al
2
O
3
plate was
washed with ethanol,dried and used without touching the
surfaces,in order to avoid any possible contamination.
The experimental apparatus for surface tension measure-
ments consisted of a LaCrO
3
heating element furnace,gas
purification system,oxygen sensor,a photographic system
and a digital system(computer).The experimental technique
has been described in the previous paper.
8)
Only the
difference will be introduced in this paper.
In this study,all the measurements were carried out in a
purified Ar atmosphere with the oxygen partial pressure of
less than 10
19
MPa in the gas outlet.The surface tension of
liquid Fe-16 mass%Cr-S alloys was measured at 1823 K.The
temperature dependence of surface tension of liquid Fe-
16mass% Cr-S alloys was determined by measuring the
surface tensions of some liquid Fe-16 mass% Cr-S alloys at
1808,1845 and 1883 K.
The droplet profile of liquid Fe-16 mass%Cr-S alloys was
photographed using a camera fitted with a telephotographic
lens ands a bellows in a fixed magnification of the photo-
graphed image.The photographs of the droplet of liquid
alloys were taken every 0.18 ks.The measurement time was
5.4 ks for one experimental run.The surface tension of liquid
Fe-16 mass% Cr-S alloys remained almost constant during
the experiment.The mean values of surface tension measured
in the latter 1.8 ks were adopted for all the above experi-
ments.After the experiments,the content of O,S and Nin the
specimen was analyzed.The following analytical methods
were adopted in this study:the infrared adsorption and
thermal conductimetric method after fusion in a He gas flow
for N and O,and the infrared adsorption method after
combustion in an induction furnace for S.
The surface tension of liquid Fe-16 mass%Cr-S alloys was
calculated from the image contour of the droplet using
Rotenberg’s method.
9)
The density of liquid Fe-16 mass%Cr
alloys was derived from the relation (Mg/m
3
)=7.034-
0.00567w
Cr
at T ¼ 1823 K and the mass% of Cr,w
Cr
< 24,
which was obtained by the sessile drop method
10)
without
considering the effect of sulphur content.The densities of Fe-
16mass%Cr-S alloys at 1808,1845 and 1883 K were the
values measured using the sessile drop method in this study
and calibrated by the value of 1823 K by Sharan et al.
10)
The
maximum measurement error was estimated to be 2% for
the surface tension and 0:5% for contact angle.
3.Results and Discussion
The measured surface tension and contact angle of liquid
Fe-16 mass%Cr-Salloys with alumina were shown in Table 1.
Activities of oxygen and sulphur,a
O
and a
S
,were calculated
by considering their coefficients using the recommended
interaction coefficients.
11)
The calculated values using eqs.
(3) and (5) described below were also listed in Table 1.
3.1 Surface tension of liquid Fe-16 mass%Cr-S alloys
The measured surface tension of liquid Fe-16 mass%Cr-S
alloys is plotted as a function of sulphur activity and
logarithm of sulphur activity in Figs.1 and 2.The effect of
sulphur on surface tension of liquid Fe-30 mass%Cr alloy
determined by Chung and Cramb
6)
and that of liquid Fe by
Belton,
12)
Ogino et al.
13)
and Jimbo et al.
14)
was also drawn
for comparison.Belton
12)
obtained the Szyszkowski-type
equation,which is shown later in eq.(1),for liquid Fe-S
alloys by treating the data obtained by Kozakevich and
Table 1 Surface tension of liquid Fe-16mass%Cr-S alloys measured at
1823K.
w
O
w
S
a
O
a
S

1g


1g


1g

(mass%) (mass%) (10
4
) (10
4
) (mN/m) (mN/m) (mN/m) (

)
0.0050 0.0003 8.9 1.9 1634 1635 1651 155
0.0054 0.0003 9.6 1.9 1615 1635 1645 154
0.0069 0.0003 12.2 1.9 1610 1635 1622 147
0.0050 0.0003 8.9 1.9 1664 1635 1651 155
0.0042 0.0047 7.4 30.5 1592 1569 1599 140
0.0075 0.0074 13.2 47.8 1545 1538 1518 140
0.0037 0.0118 6.5 76.4 1492 1497 1535 136
0.0045 0.0270 7.9 174.4 1352 1400 1425 143
0.0047 0.0620 8.1 399.0 1296 1279 1302 137
0.0061 0.1050 10.4 672.0 1201 1195 1197 134
0.0075 0.1950 12.5 1234.3 1090 1091 1077 130

1g
(mN/m) is the experimental value of surface tension,and 

1g
and 

1g
(mN/m) are calculated values using eqs.(3) and (5),respectively.
0
0.04
0.08
0.12
1200
1600
2000
Sulphur Activity,
a
S
Surface Tension,
lg/mN
.
m
σ
-1
Fe-16Cr-S Present work, 1823K
Fe-30Cr-S Chung and Cramb
6)
Fe-S Belton
12)
Fe-S Ogino et al.
13)
Fe-S Jimbo et al.
14)
Fig.1 Surface tension of liquid Fe-16mass%Cr alloys as a function of
sulphur activity at 1823K.
Surface Tension and Wettability of Liquid Fe-16mass%Cr-S Alloy with Alumina 2109
Urbain
15)
using the empirical equations for expressing the
relationship between the surface tension of water solution
and adsorption proposed by Szyszkowski.
16)
The
Szyszkowski-type equations for liquid Fe-S alloys by Ogino
et al.
13)
and Jimbo et al.
14)
were obtained by using the
recently determined surface tension values of pure iron,
1910 mN/m and 1913 mN/m respectively which are higher
than that used by Belton
12)
(1788 mN/m) and treating the
experimental data obtained by themselves and other inves-
tigators based on Szyszkowski’s equation.The experimental
results of surface tension for liquid Fe-16 mass%Cr-S alloys
obtained in the present work show the same tendency with
that of liquid Fe-S alloys that sulphur is strong reactive
element in the liquid Fe-16 mass%Cr alloys.
The obtained values of surface tension for liquid Fe-
16mass%Cr-S alloys are lower than that of the Fe-S alloys
determined by Jimbo et al.
14)
about 80(a
S
¼ 0:12)-250(a
S
¼
0:0006) mN/m.It can be ascribed to the addition of
16mass%Cr to the liquid alloys as shown in the previous
study
8)
and the oxygen difference between liquid Fe-
16mass%Cr-S alloys in the present study and liquid Fe-S
alloys.The dependence of the surface tension of liquid Fe-Cr
alloys on Cr content,compiled by Keene,
3)
is
d=dw
Cr
(at%)=7.5 mNm
1
[at%Cr]
1
.Subsequently,the
depress of the surface tension value of liquid iron due to
the addition of 16mass%Cr can be estimated to be
130 mNm
1
.This value can be considered to be consistent
with the difference of the surface tensions between liquid Fe-
16mass%Cr-S alloys in the present work and that of the Fe-S
alloys determined by Jimbo et al.
14)
The effect of the oxygen
content difference in the samples on the difference of the
surface tensions between liquid Fe-16 mass%Cr-S alloys and
Fe-S alloys can not be discussed because the oxygen content
in the samples of Fe-S systems in the cited reference
14)
is
unclear.
The obtained values of surface tension for liquid Fe-
16mass% Cr-S alloys are only 20(a
S
¼ 0:12)-40(a
S
¼
0:0006) mN/m higher than that of liquid Fe-30 mass%Cr-S
alloys determined by Chung and Cramb,
6)
which is smaller
than the values estimated by using the dependence of surface
tension on Cr content compiled by Keene.
3)
It may be due to
that the oxygen activities in the present experimental
samples,ð6:5 13:2Þ 10
4
(the oxygen content is
0.0037-0.0075 mass%) is higher than that in the samples of
Chung and Cramb,
6)
ð0:2 0:3Þ 10
4
,deoxidized by
aluminium.According to the previous report,
8)
if the oxygen
activity in the Fe-16 mass%Cr alloys is reduced from ð6:5 
13:2Þ 10
4
to ð0:2 0:3Þ 10
4
,the surface tension of
liquid Fe-16 mass%Cr will increase from 1640mN/m to
1750 mN/m by 110 mN/m.Therefore,if considering the
effect of oxygen content in the samples,the present results
are consistent with that of Fe-30 mass%Cr-S alloys by Chung
and Cramb.
6)
Since sulphur acts as a surface-active element in a liquid
Fe-16 mass%Cr-S alloy,the behaviour of sulphur adsorption
can be described by the Szyszkowski-type equation as
follows:
12)

1g
¼ 
0
1g
RT
0
S(Fe-Cr)
lnð1 þK
S(Fe-Cr)
a
S
Þ ð1Þ
where 
1g
and 
0
1g
are the surface tension of liquid Fe-
16mass%Cr-S alloys and liquid Fe-16 mass%Cr alloys both
with 0.0037-0.0075 mass%oxygen in the present study (mN/
m),
0
S(Fe-Cr)
is the saturated surface excess concentration of
sulphur for the (Fe-Cr)-S pseudobinary melt relative to the
Fe-Cr solvent (major component) at the Gibbs dividing
surface of 
S(Fe-Cr)
¼ 0,K
S(Fe-Cr)
is the adsorption coefficient
of sulphur at the surface of Fe-16 mass%Cr melt and a
S
is the
sulphur activity in the Fe-16 mass%Cr-S melt,R is gas
constant and T is Kelvin temperature (K).

S(Fe-Cr)
can be determined by calculating the slope of the
surface tension to the logarithm of the sulphur activity curve
(Fig.2) according to the Gibbs adsorption equation.

S(Fe-Cr)
¼ ð1=RTÞ  ðd
1g
=d lna
S
Þ
T
ð2Þ
where 
S(Fe-Cr)
(mol/m
2
) is the surface excess concentration
of sulphur relative to the Fe-Cr solvent at the Gibbs dividing
surface of 
(Fe-Cr)
¼ 0.
The slope of the surface tension to the logarithm of the
sulphur activity curve (Fig.2) becomes almost constant in the
sulphur content of above 0.062 mass%(a
S
¼ 0:04).By fitting
the slope of surface tension versus logarithm of sulphur
activity to experimental data at high sulphur activity,the term
RT
0
S(Fe-Cr)
was found to be 182 mNm
1
.The surface
tension value of liquid Fe-16 mass%Cr alloy,
0
1g
,was
obtained to be 1640 mN m
1
by extrapolating the exper-
imental data to that the sulphur concentration equals 0.By
inserting these values into eq.(1) and by fitting eq.(1) to the
experimental data using the least square method,the term
K
S(Fe-Cr)
was found to be 157.The variation of surface tension
of liquid Fe-16 mass%Cr-S alloys with sulphur activity
(a
S
5 0:12) can thus be expressed by (mN/m):

1g
¼ 1640 182 lnð1 þ157a
S
Þ ðmN/mÞ
ðmass%O ¼ 0:0037 0:0075;mass%S 5 0:195Þ ð3Þ
On the other hand,there is oxygen of 0.0037-
0.0075 mass% in all the samples,the practical systems can
be considered as Fe-16 mass%Cr-S (0.0003-0.195mass%)-O
-8
-6
-4
-2
0
800
1200
1600
2000
Fe-16Cr-S present work
Fe-30Cr-S Chung and Cramb
6)
Fe-S Belton
12)
Fe-S Ogino et al.
13)
Fe-S Jimbo et al.
14)
ln
S
a
Surface Tension,
lg/mN
.
m
σ
-1
Fig.2 Surface tension of liquid Fe-16mass%Cr alloys as a function of
logarithm of sulphur activity at 1823K.
2110 Z.Li,M.Zeze and K.Mukai
(0.0037-0.0075mass%) alloys.Ogino et al.
13)
expressed the
surface tension of Fe-S-O systems by assuming that the
additive property for the effects of O and S on the surface
tension is applicable.Therefore,the effect of oxygen in the
Fe-16 mass%Cr-S alloys can be corrected as follows.

1g
¼ 
0
1g
RT
0
O(Fe-Cr)
lnð1 þK
O(Fe-Cr)
a
O
Þ
RT
0
S(Fe-Cr)
lnð1 þK
S(Fe-Cr)
a
S
Þ ð4Þ
where 
0
1g
is the surface tension of liquid Fe-16 mass%Cr
alloys (mN/m),
0
S(Fe-Cr)
is the saturated excess surface
concentration of Fe-16 mass%Cr-O alloys at the Gibbs
dividing surface of 
(Fe-Cr)
¼ 0 (mol/m
2
),K
O(Fe-Cr)
is the
adsorption coefficient of oxygen at the surface of Fe-
16mass%Cr melt.
The surface tension of liquid Fe-16 mass%Cr-S (0.0003-
0.195 mass%)-O(0.0037-0.0075 mass%) alloys can be given
by eq.(5) by combining the results of Fe-16 mass%Cr-O
alloys reported in the previous paper
8)
with the present
results.The calculated results using eqs.(3) and (5) as shown
in Table 1,are in good agreement with the experimental
results.

1g
¼ 1750 304 lnð1 þ383a
O
Þ
182 lnð1 þ157a
S
Þ ðmN/mÞ ð5Þ
If it is assumed that the surface-active element adsorption
consists of a monolayer,it is possible to estimate the area A
occupied by each adsorbed sulphur on the surface by using
eq.(6):
A ¼ 1=ð
0
O(Fe-Cr)
NÞ ð6Þ
where N is Avogadro number (6:022 10
23
mol
1
).
The saturated surface excess concentration of sulphur on
liquid Fe-16 mass%Cr-S alloys (
0
S(Fe-Cr)
) is 12:2 
10
6
mol/m
2
,with the average area occupied by one sulphur
ion,A,13:2 10
20
m
2
.The average area occupied by one
sulphur ion determined by experiments for Fe-S melts at
1823-1873 K is ð11:2 15:6Þ 10
20
m
2
(mean 13:0 
10
20
m
2
).
3)
The average area occupied by one sulphur ion
determined by Chung and Cramb
6)
for Fe-30 mass%Cr-S
melts at 1823 K is 13:6 10
20
m
2
.Therefore,the average
area occupied by one sulphur ion on the surface of the Fe-
16mass%Cr-S alloys obtained in the present studies is almost
the same to that of Fe-S and Fe-30 mass%Cr-S systems.
3.2 Interfacial properties of liquid Fe-16 mass%Cr-S
alloys with alumina
Figure 3 shows the contact angle of liquid Fe-16 mass%Cr-
S alloys with alumina at 1823K.As shown in Fig.3,the
contact angle between liquid Fe-S alloys and alumina
remains almost unchanged in the range of a
S
< 0:2 at
1823 K determined by Ogino et al.
17)
and Nogi and Ogino.
18)
However,the contact angle of liquid Fe-16 mass%Cr-S alloys
with alumina decreases with increasing sulphur content in the
samples.The contact angle of liquid Fe-16 mass%Cr-S alloys
and alumina in the low sulphur content of (0.0003mass%) is
higher than that of liquid Fe-S alloys with alumina
determined by Ogino et al.
17)
and Nogi and Ogino.
18)
It can
be concluded that the wettability between liquid Fe-S alloys
and alumina has been changed by adding Cr to the alloys.The
tendency for liquid Fe-16 mass%Cr-S alloys is similar to that
for liquid Fe-30 mass%Cr-S alloys by Chung and cramb.
6)
Young’s relation (7) allows an estimate of the interfacial
tension between liquid metal and solid substrate (
s1
) based
on the values of the surface tension of the metal (
1g
) and the
solid (
sg
) and the contact angle of the metal on the solid ():

s1
¼ 
sg

1g
cos  ð7Þ
The interfacial tension between liquid Fe-16 mass% Cr-S
alloys and solid alumina (Fig.4) was calculated using the
measured data of the contact angles between liquid Fe-
16mass%Cr-S alloys and solid alumina,the measured
surface tensions of liquid Fe-16 mass%Cr-S alloys and the
reported data of the surface tension of solid alumina
(755 mN/m).
6,18)
The surface tension is also plotted in
0
0.2
0.4
0.6
80
o
100
o
120
o
140
o
160
o
Fe-16Cr-S Present work 1823K
Fe-30Cr-S Chung and Cramb
6)
1823K
Fe-S Ogino et al.
17)
1823K
Fe-S Nogi and Ogino
18)
1823K
Sulphur Activity,
S
Contact Angle,
θ
a
Fig.3 Contact angle between liquid Fe-16mass%Cr alloys and alumina
substrate as a function of sulphur activity at 1823K.
-8
-6
-4
-2
0
500
1000
1500
2000
2500
lna
S
Surface, Interfacial Tension,
lg
, σσ
sl/mN
.
m
-1
sl
=2170-220ln(1+237a
S
)
lg
=1640-182ln(1+157a
S
)
σ
σ
Fig.4 Interfacial tension between liquid Fe-16mass%Cr alloys and
alumina substrate as a function of logarithmof sulphur activity at 1823K.
Surface Tension and Wettability of Liquid Fe-16mass%Cr-S Alloy with Alumina 2111
Fig.4 for comparison.
The sulphur behaviour at the interface between liquid Fe-
16mass%Cr-S alloy and alumina substrate may also be
described by the Szyszkowski-type equation as follows:
12)

s1
¼ 
0
s1
RT
0
S(Fe-Cr,Al
2
O
3
)
lnð1 þK
S(Fe-Cr,Al
2
O
3
)
a
S
Þ ð8Þ
where 
0
s1
is the interfacial tension between liquid Fe-
16mass%Cr alloys with 0.0037-0.0075 mass% oxygen and
alumina (mN/m),
0
S(Fe-Cr,Al
2
O
3
)
(mol/m
2
) is the saturated
excess concentration of sulphur at the interface between the
(Fe-Cr)-S pseudobinary melt and alumian substrate at the
Gibbs dividing surface of 
(Fe-Cr)
¼ 0 supposing that Al
2
O
3
is chemically inert for Fe-16 mass%Cr-S melts,K
S(Fe-Cr,Al
2
O
3
)
is the adsorption coefficient of sulphur and a
S
is the sulphur
activity in the Fe-16 mass%Cr-S melts.
At the above mentioned Gibbs dividing surface,the excess
concentration of sulphur at the interface between liquid Fe-
16mass%Cr-S alloys and alumina,
S(Fe-Cr,Al
2
O
3
)
can be
obtained from Gibbs adsorption isotherm (9):

S(Fe-Cr,Al
2
O
3
)
¼ ð1=RTÞ  ðd
s1
=dln a
S
Þ
T
ð9Þ
From Fig.4,it can be seen that the slope of interfacial
tension curve with logarithm of sulphur content remains
almost constant at the sulphur content of larger than
0.0062 mass%.By fitting the slope of interfacial tension
versus logarithmof sulphur activity to experimental data,the
term RT
0
S(Fe-Cr,Al
2
O
3
)
was found to be 220 mN/m.The
interfacial tension value of liquid Fe-16 mass%Cr alloy,
0
s1
,
was obtained to be 2170 mNm
1
by extrapolating the
experimental data to that the sulphur concentration equals
0.By inserting these values into eq.(8) and by fitting the
equation to experimental data,the term of K
S(Fe-Cr,Al
2
O
3
)
was
found to be 237.The variation of interfacial tension with
sulphur activity (mass%S 5 0.195) can thus be written by
(mN/m):

s1
¼ 2170 220lnð1 þ237a
S
Þ ðmN/mÞ
ðmass%O ¼ 0:0037 0:0075;mass%S 5 0:195Þ ð10Þ
The saturated excess concentration of sulphur
(
0
S(Fe-Cr,Al
2
O
3
)
) at the interface between the alloy and the
alumina substrate was found to be 14:5 10
6
mol/m
2
,with
the average area occupied by one adsorbed sulphur,A,
11:1 10
20
m
2
.This value is near to the average area
occupied by one sulphur ion S
2
in the liquid Fe-S alloy,
10:63 10
20
m
2
,in the form of closely packed with the
sulphur ion radia of 1:84 10
10
m,
19)
but much higher than
3:7 10
20
m
2
of liquid Fe-S alloys with alumina by
supposing that the sulphur exists in the form of sulphur
atom.It can be concluded that the sulphur exists in the form
of S
2
at the interface of liquid Fe-16 mass%Cr-S alloys and
alumina.
The work of adhesion of liquid Fe-16 mass%Cr-S alloys
with alumina at 1823 Kcan be calculated using Young-Dupre
equation (eq.(11)) and shown in Fig.5.
W
ad
¼ 
1g
ð1 þcos Þ ð11Þ
As can be seen in Fig.5,the work of adhesion of liquid Fe-
16mass%Cr-S alloys with alumina at 1823K has a tendency
to increase with increasing sulphur content in the samples.
3.3 Temperature dependence of the surface tension of
liquid Fe-16 mass%Cr-S alloys
Figure 6 showed the surface tension of liquid Fe-
16mass%Cr alloys with sulphur content in the temperature
range of 1808-1883 K.The temperature dependence of the
surface tension of liquid Fe-16 mass%Cr-S alloys obtained in
this study was shown in Fig.7 together with that for pure
Fe,
20)
Fe-S alloys,
20–23)
Fe-18Cr-Ni-S alloys.
7,24–26)
The
temperature dependence of the surface tension of liquid Fe-
16mass%Cr-S alloys d=dT increased with increasing
sulphur content,and changed fromnegative to positive value
when the sulphur content exceeded 20mass ppm.
4.Conclusion
The surface tension and the wettability of liquid Fe-
16mass% Cr-S alloy on an alumina substrate at 1823 K and
the temperature dependence of the surface tension of liquid
-8
-6
-4
-2
0
0
500
1000
Fe-16mass%Cr-S, present work
lna
S
Work of Adhesion, W
sl
/mN
.
m
-1
Fig.5 Work of adhesion as a function of logarithm of sulphur activity at
1823K.
1800
1850
1900
1400
1600
1800
Surface Tension,
lg/mN
.
m
σ
-1
Tem
p
erature, T/K
3 mass ppm S
50 mass ppm S
77 mass ppm S
Fig.6 Surface tension of liquid Fe-16mass%Cr alloys as a function of
temperature.
2112 Z.Li,M.Zeze and K.Mukai
Fe-16 mass%Cr-S alloy in the temperature range of 1808-
1883 Kwere measured using the sessile drop technique in the
sulphur content range of less than 0.195 mass%.The
following results were obtained:
(1) Sulphur was found to be strongly surface active in liquid
Fe-16 mass%Cr alloys.The variation of surface tension of
Fe-16 mass%Cr alloys with sulphur activity can be described
by the following equation:

1g
¼ 1640 182 lnð1 þ157a
S
Þ ðmN/mÞ
ðmass%O ¼ 0:0037 0:0075;mass%S 5 0:195Þ
(2) The contact angle of liquid Fe-16 mass%Cr-S alloys with
alumina decreased markedly with increasing sulphur content
in the samples.
(3) The interfacial tension of liquid Fe-16 mass%Cr-S alloys
and solid alumina,calculated using Young’s equation,can be
expressed by the following equation:

1g
¼ 2170 220 lnð1 þ237a
S
Þ ðmN/mÞ
ðmass%O ¼ 0:0037 0:0082;mass%S 5 0:195Þ
(4) The temperature dependence of the surface tension of
liquid Fe-16 mass%Cr-S alloys d=dT increased with in-
creasing sulphur content,and changed from negative to
positive value when the sulphur content exceeded
20mass ppm.
Acknowledgements
The authors would like to thank Marika Iwami,under-
graduate of Kyushu Institute of Technology (KIT) for her aid
of the experiments,Ms.Rika Umegane (KIT) for her careful
analysis on the experimental samples and Professor K.C.
Mills of Imperial College London for his kind suggestions.
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0
100
200
300
400
-1
-0.5
0
0.5
1
Sulphur Content, W
S
/mass ppm
Temperature Coefficient, d /dT(mN/mK)
σ
Fe-18Cr-8Ni(170-1030 mass ppm S)
0.66±0.14 mN/mK exp. 1823-2073K Grant et al.
24)
Fe-18Cr-8Ni exp. 0.58mN/mk
Keene et al.
26)
Fe-16Cr exp. 1808-1883K Present work
Fe-18Cr-8Ni cal. 1800-1900K Mcnallan et al.
7)
Fe cal. 1800-1900K Sahoo et al.
23)
316 steel exp.1823-2073K Mills et al.
25)
Fe exp. 1823-2023K Popel et al.
22)
Fe exp. 1823-2023K Gupt et al.
21)
Fe -0.23~-0.6mN/mK compiled by Nogi et al.
20)
Fig.7 Temperature coefficient of surface tension of liquid metals (Fe,Fe-
16Cr,Fe-18Cr-8Ni) with sulphur content in the melts.
Surface Tension and Wettability of Liquid Fe-16mass%Cr-S Alloy with Alumina 2113