Interfacial Phenomena among Liquid Iron-Carbon Alloy, LiquidSlag, and Solid CaO

YOSHINORI TANIGUCHI and SESHADRI SEETHARAMAN

Interfacial phenomena between hot metal, liquid slag and solid CaO are important to theunderstanding of the desulfurization reaction in hot-metal treatment processes. In the currentwork, the surface tension of molten iron-carbon alloy and liquid slag as well as the interfacialtensions among molten iron-carbon alloy-solid CaO, liquid slag-solid CaO, as well as molteniron-carbon alloy-liquid slag were measured in the temperature range 1623 K to 1723 K(1350 �C to 1450 �C). The sessile drop method has been used for these measurements. Toanalyze the experimental results, two types of graphical analysis programs have been developedto determine the coordinates of the X-ray shadow or charge-coupled device (CCD) image of thedroplet. Furthermore, a software package that uses the Gauss-Newton method to minimize anerror function between the physically observed and a theoretical Laplacian curve has also beendeveloped in this work.

DOI: 10.1007/s11663-012-9639-1� The Minerals, Metals & Materials Society and ASM International 2012

I. INTRODUCTION

IN steelmaking processes including hot metal pre-treatment, the practically used flux for desulfurization isCaO-based and the desulfurization reaction is expressedas follows:

Sþ CaO(s) ¼ CaS(s)þO ½1�

However, it is known that the desulfurization efficiencyis not so high in case only CaO is added to the hotmetal,[1,2] which implies that the liquid slag phase that isformed by the addition of additives has an important rolein desulfurization. In understanding this influence, inter-facial phenomena such as wettabilitiy or interfacialtensions among molten iron-carbon alloy, liquid slag,and solidCaOare some important properties thatmust beconsidered. During the hot metal pre-treatment, carry-over slag from the blast furnace and additives is likely toform a high-basicity, multiple-component CaO-Al2O3-SiO2-based slag. Whereas the experimental studies of theinterfacial tension between iron-carbon alloy and slagsare abundant in literature (as summarized in References 3and 4), these studies were targeted mainly at blast furnaceslags. Only a few measurements of the interfacial tensionof iron-carbon alloy andhigh-basicity slag are available attemperatures at approximately 1673 K (1400 �C), whichis the typical pretreatment temperature for hot metaldesulfurization. Furthermore, to the knowledge of theauthors, no measurement of the interfacial tension

between liquid slag and CaO has been reported. In thecurrent work, the surface tensions of molten iron-carbonalloy and high-basicity liquid slag as well as the interfacialtensions among molten iron-carbon alloy and solid CaO,liquid slag, and solid CaO, and molten iron-carbon alloyand liquid slag weremeasured in the temperature range of1623 K to 1723 K (1350 �C to 1450 �C) by using theX-ray sessile drop method.

II. EXPERIMENTAL

A. Apparatus

A vertical resistance furnace with an X-ray source andgraphite heating elements was used for the surface orinterfacial property measurements. The schematic dia-gram of experimental setup is shown in Figure 1. TheX-ray unit is Philips BV-26 imaging system (Philips,Amsterdam, the Netherlands) with an X-ray source of 40to 105 kV. The furnace was controlled through a pro-portional–integral–derivative (PID) controller. Two setsof Pt-30 pct Rh/Pt-6 pct Rh thermocouples were used.One thermocouple was fixed close to the furnace heatingelements and used to control the furnace temperature.The temperature was controlled within ±1 K over alength of 0.08 m in a reaction tube (alumina tube, innerdiameter [ID]: 0.07 m) in the furnace. The other thermo-couple was set just above the sample to measure thesample temperature. This experimental setup was alsoequipped with a gas cleaning system. Silica gel andMg(ClO4)2 were used to remove the traces of moisture.Ascarite was used to remove the CO2 impurity. Cu andMg chips were kept at 893 K (620 �C) and 753 K(480 �C), respectively, to remove the traces of oxygen.In themeasurement of dynamicwettability between the

slag sample and Pt or CaO, a horizontal furnace with acharge-coupled device (CCD) camera and SiC heating

YOSHINORI TANIGUCHI, formerly Exchange Researcher withRoyal Institute of Technology, SE-100 44 Stockholm, Sweden, is now aManager with Steelmaking Division, Nippon Steel Corporation,Chiyoda-ku, Tokyo 100-8071, Japan. SESHADRI SEETHARAMAN,formerly Professor with Royal Institute of Technology, is now VisitingProfessor, TU Bergakademie Freiberg, 09596 Freiberg, Germany.Contact e-mail: raman@kth.se

Manuscript submitted November 9, 2011.Article published online March 7, 2012.

METALLURGICAL AND MATERIALS TRANSACTIONS B VOLUME 43B, JUNE 2012—587

elements was used. The experimental setup is shown inFigure 2. The furnace was controlled through a PIDcontroller. Two sets of Pt-10 pct Rh/Pt thermocoupleswere used. One thermocouple was fixed close to thefurnace heating elements and used to control the furnacetemperature. The temperature was controlled within±1 K over a length of 0.1 m in a reaction tube (aluminatube, ID: 0.04 m) in the furnace. The other thermocouplewas set just below the sample to measure the sampletemperature. The image-capturing system consists ofobservation windows (borosilicate glass) and a CCDcamera (CV-M10RS; JAIPulnix Inc., San Jose,CA)fittedwith optical zoom lens (ZUIKA AUTO-T 200mm f/4.0;OlympusAmerica, Inc., CenterValley, PA).TheAr gas ofthis systemwas purified by the gas-cleaning system,whichis the similar to that used in the vertical arrangementdescribed previously.

B. Experimental Method

1. Interfacial property measurementThree types of iron-carbon alloys and seven different

slags CaO-Al2O3-SiO2-MgO-MnO were used for the

measurements. Two of the iron-carbon alloys werestandard specimens, and the other was a carbon satu-rated iron. The compositions of the alloys are shown inTable I. The carbon and sulfur contents of carbonsaturated iron were analyzed using a LECO combustion-infrared spectrometer (LECO Corporation, St Joseph,MI). The standard specimen powders were set in a dense,sintered Al2O3 tube (ID: 0.006 m) and premelted inpurified Ar stream at 1723 K (1450 �C) for 0.5 hours.The carbon saturated iron was prepared by mixing 96mass pct electrolytic iron and 4 mass pct graphitepowders. It was set in a graphite crucible and premeltedin a purified Ar stream at 1673 K (1400 �C). The sampleswere soaked at this temperature for 20 hours to homog-enize them. As shown in Table I, the carbon content ofthe carbon saturated iron was 6.01 mass pct. Thiscontent is obviously higher than the saturated concen-tration of carbon at 1673 K (1400 �C).[3] Carbon con-tamination might occur from the crucible. However, theexcess carbon is expected to be free carbon according to aFe-C binary phase diagram.[5]

The slag samples were prepared by mixing appropri-ate proportions of CaO, Al2O3, SiO2, and MgO reagentpowders. The oxide powders were calcined at 1273 K(1000 �C) for 12 hours in a muffle furnace to removeany trace of moisture before mixing. It was set in a Ptcrucible and premelted in a purified Ar stream at 1673 K(1400 �C) for 2 hours. The compositions of the slags areshown in Table II.While carrying out the measurement, the samples

were set on CaO or graphite substrates for surfacetension measurements and placed in CaO crucibles forinterfacial tension measurements. The CaO substratesand crucibles were supplied by Tsukuba Ceramic Works(Tsukuba, Japan). The surfaces of the samples werepolished to the extent possible as the substrate couldabsorb moisture easily from the atmosphere and may beruined. For this reason, the surface roughness could notbe estimated. The substrate or crucible was set in anAl2O3 holder. A Pt foil (0.025 9 0.025 m, thickness 2.5 9

Ar

Thermocouple (Pt-30 pct Rh/Pt-6 pct Rh)

Sample

Reaction tube

CaO substrate

Pt foil

Al2O3 holder

High temperature window

Ar

X-ray source Image unit

Fig. 1—Schematic diagram of experimental setup of the vertical fur-nace with an X-ray image analyzer.

Ar/CO/CO2

Thermocouple (Pt-10 pct Rh/Pt)

Sample

Heating element

Reaction tube

Ar/CO/CO2

CaO substrate

Pt foil Al2O3 tray

Borosilicate glass window

CCD camera

Al2O3 rail

Fig. 2—Schematic diagram of experimental setup of the horizontalfurnace with a CCD camera.

Table I. Experimental Compositions of Iron-Carbon Alloy

(wt pct)

No. C Si Mn P S

C42 4.22 0.017HM 4.73 0.35 0.34 0.084 0.0177CS 6.01* 0.005

*The carbon content is higher than the saturated concentration.[3]

Table II. Experimental Compositions of Liquid Slag

No. CaO Al2O3 SiO2 MgO MnO

X01 49.92 38.40 7.68 4.00X02 50.00 50.00C01 52.00 40.00 8.00C02 49.92 38.40 7.68 4.00C03 47.32 36.40 7.28 4.00 5.00C04 44.72 34.40 6.88 4.00 10.00C05 50.00 30.00 6.00 4.00 10.00

588—VOLUME 43B, JUNE 2012 METALLURGICAL AND MATERIALS TRANSACTIONS B

10�4 m) was set between the CaO substrate or crucibleand the Al2O3 holder to prevent the reaction of CaOwith Al2O3 at a high temperature. The holder was thenpositioned inside the furnace at room temperature, andthe system was evacuated to 103 Pa. Purified Ar gas at aflow rate of 300 mL/min was then introduced into thereaction tube, and the temperature was increased at aconstant rate of 5 K per minute. When the temperaturereached the target temperature, the shape of the samplewas investigated by X-ray imaging and recorded for 1 to3 hours. In view of the experimental failures, which arecommon for these measurements, some experiments,where the images might not be clear, were repeated andthe clearest images were selected. These still images wereused to calculate the surface or interfacial tension andthe contact angle.

2. Dynamic wettability measurementCaO-Al2O3-SiO2-MgO-MnO slag samples and Pt or

CaO substrates were used for the measurement. It wasfound in preliminary experiments that the use ofgraphite substrate could lead to the formation of gasbubbles in the sample, which are not detectable in theobservation using the CCD camera. In contrast, Jimboand Cramb[6] mentioned that the surface tension mea-surement under wetting conditions (contact angle islower than 90 deg) might have a large error. In view ofthis, the graphite substrate was used in limited cases inthe current measurements where high wetting conditionswere suspected. The slag samples were prepared bymixing appropriate proportions of CaO, Al2O3, SiO2,MgO, and MnO reagent powders. The sample waspressed into a small pellet of 0.1 to 0.2 g and set on a Ptor CaO substrate. The compositions of the slags areshown also in Table II. The furnace was heated to thetargeted temperature with the sample at the cold end ofthe furnace. After the experimental temperature wasattained, the sample was pushed to the even temperaturezone. The sample attained the experimental temperaturein less than 7 minutes. The sample could be observedcontinuously, and when the melting was complete andthe temperature was stable, the images were recorded.

The experimental procedure for the MnO-containingslag was almost the same as in the interfacial propertymeasurement. However, a gas mixture of CO-CO2 wasused to control the equilibrium oxygen partial pressureof Mn-O reaction. The shape of the sample wasinvestigated and recorded using the CCD camera.

In all these cases, selected experiments were repeatedto confirm the experimental observations.

C. Data Acquisition and Calculation Method

The droplet images were converted to black and white,and then a graphical analysis program was used toconvert the images to the coordinate data sets. Thisprogramwas developed in the currentwork. The programdetermines the coordinates of points along the dropletprofile automatically. However, some X-ray images,especially the images of slag droplets, were analyzed byusing another graphical analysis program because thecontours were slightly unclear, which would lead to

uncertainties during the black-and-white conversion.This program, which developed as part of the currentwork, was used to determine manually the coordinates ofpoints along with the droplet contour. This softwaredigitizer can be operated fully on a computer screen, andthe pointer of it can be navigated by the pixel of the screenwith keyboard operation. Thus, there is no need for ahigh-accuracy pointing device for its use. The dataacquisition was repeated several times to check theaccuracy of the image analysis.The coordinate data were then used to calculate the

surface or interfacial tension and the contact angle witha computer program. The software package (developedas a part of the present work) uses the Gauss-Newtonmethod to minimize an error function between thephysically observed and a theoretical Laplacian curve.The details of the program are given in Appendix. Theseprograms use Microsoft Visual C++ 2005 and work onMicrosoft Windows XP or Vista operating systems(Microsoft Corporation, Redmond, WA).

III. RESULTS AND DISCUSSION

A. Reliability of the New Program

To apply the newly developed computer program tothe analysis of the surface or interfacial tension mea-surements, the accuracy of the program must be checkedbefore its use. This process was carried out at the firststage of the current work. If an actual experimentalresult is used for this purpose, then it is possible that thecalculated result will contain the error of image analysis.Thus, the droplet contours computed based on thefollowing Laplace’s equations[7] were used for theaccuracy check:

xiþ1 � xi ¼ Ri cos/iD/ ½2�

ziþ1 � zi ¼ �Ri sin/iD/ ½3�

Ri ¼1

qgc ðh� ziÞ þ 2

b�sin/xi�x0

½4�

where /i is the turning angle measured between thetangent to the droplet contour at the point (xi, zi) andthe vertical axis, q is the density difference, g is theacceleration from gravity, c is the surface or interfacialtension, h is the height of the droplet, b is the radiusof curvature at the top of the droplet, and x0 is thex-coordinate of the droplet center. Because these equa-tions only give the right half of droplet curvature, theleft side of curvature was calculated as follows:

xleftsidei ¼ 2x0 � xi ½5�

xleftsidei ¼ zi ½6�

Eight types of the droplet contours were computed.Four of them were calculated based on the followingconditions: the droplet weight: 5 9 10�4 (kg), densitydifference: 3000 (kg/m3), surface tension 600 (mN/m),

METALLURGICAL AND MATERIALS TRANSACTIONS B VOLUME 43B, JUNE 2012—589

and the contact angle: 60, 90, 120, and 150 (deg). Theseare targeted at slag droplets. The other four werecalculated based on the following conditions: the dropletweight: 1 9 10�3 (kg), density difference: 7000 (kg/m3),surface tension 1600 (mN/m), and the contact angle: 60,90, 120, and 150 (deg). These are targeted at metaldroplets. D/ of 0.0001 was used for the calculations.When a calculated contour was obtained, a set of data

points was selected arbitrarily from the coordinates, andthen the same numbers of the left side points werederived by using Eqs. [5] and [6]. Then, these coordi-nates were used for the surface tension calculation as‘‘calibration’’ points. The calculated droplet shapes areshown in Figures 3 and 4, and the numerical values ofdensity, surface tension, and contact angle are summa-rized in Table III. As shown in these figures andTable III, the calculation accuracy of the program thathas been developed in the current work is goodThe program was also compared with other pro-

grams. One is the software developed at the Departmentof Materials Science and Engineering, Carnegie MellonUniversity and the other is the software developed byKrylov et al.[8] A set of coordinate data listed in Table Iin Krylov et al.’s paper[8] was used for the calculation.The results are shown in Table IV. It is clear fromTable IV that all the calculation results agree well witheach other. Thus, the new developed program wasconsidered to be reliable and applied for the analysis ofthe current work. The general accuracy of the currentmeasurements was estimated to be less than ± 10 pct.

B. Interfacial Properties Between Fe-C Alloys and CaO

The experimental results are shown in Table V. Thedensities of C42 (4.22 mass pct C) at 1623 K (1350 �C)and 1673 K (1400 �C) were calculated using the follow-ing equation:

q ¼ 7:03� 5:36� 10�4ðT� 1665Þ ðg/cm3Þ½9� ½7�

The average density of 4.5 mass pct C (7030 kg/m3)[3]

and that of 5.0 mass pct C iron-carbon alloy (6990kg/m3)[3] at 1673 K (1400 �C) was used as the density ofhot metal (HM) (4.73 mass pct C). The density of 5.5mass pct C iron-carbon alloy (6700 kg/m3)[3] was used asthe density of carbon saturated iron (CS) (6.01 mass pctC). In Table V, the interfacial tension was calculated byYoung’s equation.[10]

cSL ¼ cSL � cLV cos h ½8�

where, cLV is the surface tension of the iron-carbonalloy, h is the contact angle, and cSV is the surface

–0.5 –0.4 –0.3 –0.2 –0.1 0 0.1 0.2 0.3 0.4 0.5 0.60

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Horizontal Distance from Droplet Center (10–2 m)

Ver

tica

l Dis

tanc

e fr

om S

ubst

rate

(cm

)

1600–601600–901600–1201600–150

Fig. 3—Theoretical and calculated droplet shape. The surface ten-sion is 600 mN/m.

–0.5 –0.4 –0.3 –0.2 –0.1 0

0.1 0.2 0.3 0.4 0.5 0.6 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Horizontal Distance from Droplet Center (10–2 m)

Ver

tical

Dis

tanc

e fr

om S

ubst

rate

(cm

)

1600–60 1600–90 1600–120 1600–150

Fig. 4—Theoretical and calculated droplet shape. The surface ten-sion is 1600 mN/m.

Table III. Reliability of the Surface Tension and Contact Angle Calculation

No. Weight (kg)

Density Difference(kg/m3) Surface Tension (mN/m) Contact Angle (deg)

Condition Results Condition Results Condition Results

600-60 5 9 10�4 3000 2999 600 599.09 59.99 60.00600-90 5 9 10�4 3000 3000 600 600.43 90.01 90.00600-120 5 9 10�4 3000 3000 600 599.94 120.02 120.02600-150 5 9 10�4 3000 3000 600 600.22 150.02 150.001600-60 1 9 10�3 7000 6999 1600 1599.75 60.01 60.011600-90 1 9 10�3 7000 7000 1600 1601.69 90.03 90.021600-120 1 9 10�3 7000 7000 1600 1599.71 120.02 120.021600-150 1 9 10�3 7000 7000 1600 1600.63 149.99 149.98

590—VOLUME 43B, JUNE 2012 METALLURGICAL AND MATERIALS TRANSACTIONS B

tension of solid CaO. The surface tension of solid CaOwas calculated using the following equation:

cCaO ¼ 895� 0:16T ðmN/mÞ½11� ½9�

Furthermore, the activity of sulfur was calculatedusing the interaction coefficients given in a data sourcebook.[12] It is to be noted that the activity of sulfur in thecarbon saturated iron alloy was calculated using thesaturated carbon concentration of 4.90 mass pct at

1673 K (1400 �C).[3] Figure 5 shows the surface tensionof Fe-4 mass pct C alloy and the contact angle betweenthe alloy and CaO along with the sulfur content innatural logarithm. Figure 6 shows the relationshipbetween sulfur activity and surface tension of Fe-4 masspct C alloy. In Figures 5 and 6, the reported values byLee and Morita[13,14] as well as Jimbo et al.[15] are alsoshown for comparison. It is clear from the figures thatthe current results including the carbon saturated iron-carbon alloy are in good agreement with their results.Variations of the surface tension and the contact angleare shown as a function of time in Figure 7. As shown inthis figure, the surface tension increased slightly withincreasing time. During the measurement, the temper-ature was increased from 1623 K to 1673 K (1350 �C to1400 �C). It was expected that the surface tension would

Table IV. Comparison among the Surface Tension Calculation Programs

Points*

Density (kg/m3) Surface Tension (mN/m) Contact Angle (deg)

A B C A B C A B C

1-24 2445 2446 2444 223.35 223.02 220 81.20 81.20 801,2,5-24 2446 2447 2446 220.71 220.31 219 81.36 81.36 811,2,7-24 2447 2447 2448 220.87 220.25 221 81.38 81.39 811,2,10-24 2455 2455 2456 231.29 230.26 231 81.13 81.16 81

*This item is the same with that of Table 1 in Krylov et al.[8]

A: Present work.B: The software developed at the Department of Materials Science and Engineering, Carnegie Mellon University, Pittsburgh, PA.C: The software developed by Krylov et al.[8]

Table V. Interfacial Properties Between Iron-Carbon Alloy and CaO

No. Temp [K (�C)] Density* (kg/m3) Surface Tension (mN/m) Contact Angle (deg) Interfacial Tension (mN/m) aS

C42 1623 (1350) 7053 1157 138 1497 0.0499C42 1673 (1400) 7026 1210 136 1515 0.0499HM 1673 (1400) 7010 1104 122 1204 0.0620CS 1673 (1400) 6700 1519 143 1833 0.0175�

*Reference values.[9]�Calculated using the saturated carbon concentration of 4.90 mass pct at 1673 K (1400 �C).[3]

400

600

800

1000

1200

1400

1600

–8 –7 –6 –5 –4 –3 –2 –1 080

100

120

140

160

Surf

ace

Ten

sion

(m

N/m

)

Lee and Morita[12]Present work (C42)

ln(mass pct S)

Con

tact

Ang

le (

deg)

Lee and Morita[12]Present work (C42)

Fig. 5—Surface tension of Fe-4 mass pct C alloy and contact anglebetween the alloy and CaO at 1623 K (1350 �C).

10 –3 10–2 10–1 100400

600

800

1000

1200

1400

1600

1800

2000

as

Present work (C42)

Lee and Morita (on Al2O3)[13]

Lee and Morita (on CaO)[12]

Jimbo et al.[14]

Present work (CS) at 1673K (1400 °C)

Present work (HM) at 1673K (1400 °C)

Surf

ace

Ten

sion

(m

N/m

)

Fig. 6—Relationship between sulfur activity and surface tension ofFe-4 mass pct C alloy at 1623 K (1350 �C).

METALLURGICAL AND MATERIALS TRANSACTIONS B VOLUME 43B, JUNE 2012—591

decrease with the increasing of temperature. However,the surface tension maintained almost the same valuewith that at 1623 K (1350 �C). In contrast, the contactangle decreased slightly with the increase in time. Leeand Morita[13] reported that the reaction between Fe-4mass pct C-S alloy, and solid CaO leads to theformation of a new product layer of CaS. Thus, it isconsidered that the formation of CaS layer causes thesechanges.

C. Surface Tension of CaO-Al2O3-SiO2-MgO Slags

As mentioned earlier, in view of the high wettabilityof these slags, graphite substrates were used for thesemeasurements. The experimental results are shown inTable VI.Because there is no reported value of thedensity of high-basicity CaO-Al2O3-SiO2-MgO slag at1673 K (1400 �C), the estimated density value calculatedusing the regular solution approximation model[16] wasused in the current work. The value is 2912 kg/m3.During the experiment, the evolution of gas bubbles wasobserved at the interface between the droplet and thesubstrate as shown in Figure 8, which was attributed topossible reaction between the slag and the substrate andthe consequent evolution of CO gas. In the current

experiments, only the images that have no bubble in thedroplets were analyzed. As shown in Table VI, thecontact angle is higher than 90 deg, and the surfacetension is in good agreement with the value that wascalculated using the surface tension factor.[17]

Even though the analysis was done with the imagethat has no bubble in the droplet, it is possible that gasevolution would affect the surface tension measurement.Because it is considered that the reaction between SiO2

and carbon causes the evolution of CO gas,[3] the surfacetension of the 50 pct CaO-50 pctAl2O3 slag (in mass pct)was measured for a comparison. The measurement wasconducted at 1723 K (1450 �C). In case of this slag, thedensity data at 1723 K (1450 �C) have been reported.However, these values range from approximately 2.75 to3.0 in a data source book.[4] Thus, the density was alsocalculated using the regular solution approximationmodel. The value is 2844 kg/m3. While carrying out thismeasurement, the existence of a bubble was observed inthe first few minutes. However, no gas evolution wasobserved afterward. Figure 9 shows the comparison

between the current work and the literature.[18–20] Asshown in the figure, the current work is in goodagreement with the result by Sikora and Zielinski.[19]

800

1000

1200

1400

1600

0 5 10 15 20 25 30 35120

130

140

150

160

Surf

ace

Ten

sion

(m

N/m

)

Surface tensionTemperature

Time (min)

Con

tact

Ang

le (

deg)

Tem

pera

ture

(K

)Contact angleTemperature

1593

1613

1633

1653

1673

1693

Tem

pera

ture

(K

)

1593

1613

1633

1653

1673

1693

Fig. 7—Change in surface tension of Fe-4 mass pct C alloy and con-tact angle between the alloy and CaO as a function of time.

Table VI. Surface Tension of Liquid Slags

No. Temperature [�C (K)] Density* (kg/m3)

Surface Tension (mN/m)

Contact Angle (deg)Measured Calculated�

X01 1673 (1400) 2912 573 576.7 132.81X02 1723 (1450) 2844 580 — 139.38X02 1673 (1400) — 587� 623.2 —

*Calculated using the regular solution approximation model.[16]�Calculated using the surface tension factor.[17]�Estimated from the result at 1723 K (1450 �C).

Fig. 8—X-ray image of a CaO-Al2O3-SiO2-MgO slag on a graphitesubstrate at 1673 K (1400 �C).

592—VOLUME 43B, JUNE 2012 METALLURGICAL AND MATERIALS TRANSACTIONS B

The surface tension of the slag at 1673 K (1400 �C) wasestimated using the temperature coefficient of –0.14 mN/mÆK.[4] The value of 587 mN/m is close to the value ofthe surface tension of the CaO-Al2O3-SiO2-MgO slag butsmaller than the value calculated using the surfacetension factor. As mentioned, the estimated density of2844 kg/m3 is used in the current work. Ogino et al.[21]

reported the density of this slag at 1823 K and 1973 K(1550 �C and 1700 �C). The values are approximately2900 kg/m3 at 1823 K (1550 �C) and approximately2700 kg/m3 at 1973 K (1700 �C),[22] respectively. If therelationship between the density and temperature islinear, then the density of the slag at 1723 K (1450 �C) isexpected to be approximately 3000 kg/m3. In this case,the surface tension of the 50 pct CaO-50 pct Al2O3 slag(in mass pct) at 1723 K (1450 �C) is recalculated to be612 mN/m and that at 1673 K (1400 �C) was estimatedto be 619 mN/m. This is in good agreement with thevalue calculated using the surface tension factor. Thus,subsequent investigation of the density is considered tobe required, but it has not been done in the current work.

D. Iron-Carbon Alloy in Contact with a Liquid Slag

1. Iron-carbon alloy and hot metal in contactwith a liquid slag

The iron-carbon alloys were melted with 49.92 pctCaO-38.4 pct Al2O3-7.68 pct SiO2-4 pct MgO slag (inmass pct) in CaO crucibles. The experimental results areshown in Table VII, and one of the X-ray images isshown in Figure 10. As shown in this figure, the metal

showed a near-circular shape in the slag. The results arecompared with those reported in the literature[23,24]

(Figure 11). Despite the difference of the slag composi-tions, these results agree with each other. It is consideredthat this is because the effect of SiO2 content on theinterfacial tension is small if the carbon content of themetal is higher than 4 mass pct.[25] The interfacial tensionbetween the slag and solid CaO were also calculatedusing the present results; Eqs. [8] and [9] and are shownin Table VII. A difference is found between the valuesbut it may be because of the image analysis error. Basedon the results, the contact angle between the slag andsolid CaO is expected to be approximately 60 deg.

2. Carbon-saturated iron-carbon alloy in contactwith a liquid slagThe carbon-saturated iron was melted with 49.92 pct

CaO-38.4 pct Al2O3-7.68 pct SiO2-4 pct MgO slag (inmass pct) in a CaO crucible. In the measurement, the

500

550

600

650

700

750

Temperature (K)

Surf

ace

Ten

sion

(m

N/m

)

Present workZielinski and Sikora[18]

Sikora and Zielinski[19]

Esshov and Popova[20]

1723 1773 1823 1873 1923 1973

Fig. 9—Relationship between temperature and surface tension of 50mass pct CaO-50 mass pct Al2O3 slag.

Table VII. Interfacial Tension Among Iron-Carbon Alloy,Liquid Slag, and Cao at 1673 K (1400 �C)

No.

ContactAngle (deg)

Interfacial Tension(mN/m)

EstimatedContact

Angle (deg)Alloy/CaO Alloy/slag Slag/CaO Slag/CaO

C42 169 1142 370 63.5HM 166 951 295 54.8

Fig. 10—X-ray image of a Fe-4 mass pct C alloy in a CaO-Al2O3-SiO2-MgO slag at 1673 K (1400 �C), 10 min.

Fig. 11—Relationship between temperature and interfacial tensionbetween iron-carbon alloy and liquid slag.

METALLURGICAL AND MATERIALS TRANSACTIONS B VOLUME 43B, JUNE 2012—593

droplet floated on the slag phase as shown in Figure 12.Because the place of the triple point is not clear in theimage, it is difficult to calculate the actual interfacialtension between the alloy and the slag. However, thisindicates that the wettability between the carbon satu-rated iron and the slag is bad. As mentioned in SectionII–B–1, the carbon content is higher than the saturatedconcentration. Thus, the alloy has excess free carbon.The carbon might exist at the interface between the metaland the slag and might affect the wettability betweenthem. To verify this assumption, the cross-sectionanalysis is required but the crucibles and slags alwayscame apart after cooling. One possible reason might bethat the slags expanded during solidification. Thus, theinvestigation could not be completed in the current work.

E. Dynamic Wettability between CaO-Al2O3-SiO2-MgO-MnO Slags and CaO

The measurement was carried out using the horizontalfurnace with a CCD camera. In the measurement, MnO-containing slags were used. Because the slag is possiblyaffected by the oxygen potential of the gas phase, theeffect of atmosphere was measured using Pt substrates atthe beginning. Change in the contact angle between theslags without MnO and Pt in Ar stream is shown withtime in Figure 13. As shown in the figure, the contactangle of these slags decreased with the increasing oftemperature but kept a constant value after the temper-ature reached at a steady value of 1673 K (1400 �C). Nosubstantial difference in the contact angle was observedbetween the two slags. However, in an additionalexperiment in which Ar stream was used, a 5 mass pctMnO-containing slag spread widely within a few min-utes after the droplet formation. Because the furnaceused for this measurement was not equipped with adeoxidation furnace in the gas-cleaning system, it isconsidered that the traces of oxygen in Ar gas were notremoved sufficiently. Thus, a gas mixture of CO-CO2

was used for the MnO-containing slags. The results wereshown in Figure 14. As shown in this figure, two sets ofgas mixtures (CO/CO2 = 20/23 and 30/80) were appliedfor the measurement, but no substantial change in thecontact angle was observed during the measurement.Therefore, a gas mixture of CO-CO2 (CO/CO2= 20/23,PO2

= 3.3 9 10�4 Pa) was used for the followingmeasurement. The experimental results are shown inTable VIII, and a variation of the contact angle betweenthe slags and CaO is shown as a function of time inFigure 15. In Table VIII, the surface tensions of theslags were calculated using the surface tension factor.[17]

As shown in the figure, the contact angles between theslags and CaO are lower than that between the slags andPt. The effect of MgO addition on the wettabilitybetween the slag and solid CaO is not clear, but thecontact angle between the slag and solid CaO decreasedwith the MnO addition. In case of the MnO-containingslags, the contact angles are almost constant with thecomposition. This might be because the contact angle istoo low to detect the difference. The interfacial tensionsbetween the slags and solid CaO were calculated usingthe derived surface tensions (Eqs. [8] and [9]) and areshown in Table VIII. It is also clear that the values ofthe interfacial tension and the contact angle are lowerthan the values shown in Table VII. Therefore, it is

Fig. 12—X-ray image of a carbon saturated Fe alloy in a CaO-Al2O3-SiO2-MgO slag at 1673 K (1400 �C), 2 min.

0 10 20 30 40 50 60 70 80 90 100 11020

25

30

35

40

45

50

Time (min)

Con

tact

Ang

le (

deg)

Tem

pera

ture

(K

)

C01C02

Temperature

1593

1693

1673

1653

1633

1623

Fig. 13—Change in contact angle between CaO-Al2O3-SiO2-MgOslag and Pt in Ar stream as a function of time.

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 1500

10

20

30

40

50

0

0.2

0.4

0.6

0.8

1

Time (min)

Con

tact

Ang

le (

deg)

CO

/CO

2

C03 (MnO=5 mass pct) C04 (MnO=10 mass pct)

CO/CO2

Fig. 14—Change in contact angle between CaO-Al2O3-SiO2-MgO-MnO slag and Pt in CO-CO2 stream as a function of time.

594—VOLUME 43B, JUNE 2012 METALLURGICAL AND MATERIALS TRANSACTIONS B

considered that the reactions between the slags and CaOaffect the wettability between them.

F. Discussion on the MnO Addition for Desulfurization

Although care was taken to ensure the absence ofnonsmooth surface, it is still necessary to take this aspectinto account by considering that the interfacewas actuallya composite interface[26] between the particle and hotmetal. This void part decreases the interfacial area fordesulfurization reaction. However, if liquid slag coexistswith them, the liquid slag will infiltrate the interface andincrease the interfacial area of the reaction. This isbecause the interfacial tension between the slag and hotmetal and that between the slag and solid CaO are smallerthan the surface tension of hot metal and that of solidCaO. Based on the current results, the MnO additionincreases the wettability between the liquid slag and solidCaO. Thus, the MnO-containing slag is expected toinfiltrate the composite interface with relative ease.Furthermore, in view of the temperature decrease of hotmetal during transportation from a blast furnace to asteelmaking plant, the carbon content of the hot metal atthe steelmaking plant is likely to be saturated in concen-tration, and the precipitation of carbon (graphite) parti-cles might exist in the metal. It is known that thewettability between a particle and metal affects theparticle penetration size.[13,27] Therefore, there is a pos-sibility that the reduction of the carbon concentration atthe interface between the particle and hot metal would

improve the wettability between them and decrease theparticle penetration size. In this regard, MnO decreasesthe carbon content by the following reaction:

C(s) + MnO(1) = Mnþ CO(g) ½10�

At the same time, the MnO addition itself increasesthe sulfide capacity at a low oxygen potential.[28] Ahigher MnO content in the slag might increase theoxygen potential of the slag and decrease the sulfurdistribution ratio, but a small amount of MnO additionis expected to be useful for desulfurization.

IV. CONCLUSIONS

In the current work, the surface tension of the liquidiron-carbon alloys and liquid slags, and the interfacialtensions among molten iron-carbon alloys, a liquid slag,and solid CaO were measured experimentally at 1623 Kto 1723 K (1400 �C to 1450 �C) using the sessile dropmethod. The measured surface and interfacial tensionvalues are in good agreement with the literature. In thedynamic wettability measurement, the contact anglebetween liquid slag and solid CaO decreased with theaddition of MnO. It is considered that the reactionbetween the slag and CaO causes the change.In the analysis of the experimental results, two types

of graphical analysis program and numerical solution ofLaplace’s equation developed in the current work wereused. The accuracy of the numerical solution is alsoshown in this article.

ACKNOWLEDGMENTS

The authors express their sincere gratitude to Dr.Taishi Matsushita and Dr. Lidong Teng of the Divi-sion of Materials Process Science, Royal Institute ofTechnology for their support and valuable discussions.The author also is grateful to Professor L. Holappa,Dr. E. Heikinheimo (Laboratory of Metallurgy, HelsinkiUniversity of Technology), and Dr. M. Nakamoto (for-merly with the Laboratory of Metallurgy, Helsinki Uni-versity of Technology is now with the Laboratory ofMaterials and Metallurgy Renaissance in InnovativeIron & Steel Technology, Graduate School of Engineer-ing, Osaka University, Osaka, Japan) for their help inthe dynamic wettability measurement and discussions inthe surface tension calculation.

APPENDIX. SURFACE TENSION AND CONTACTANGLE CALCULATION

Theory and Calculation Method

Suppose that a total of N data points was selectedfrom the observed droplet contour. An error functionbetween the physically observed and a theoreticalLaplacian curve is defined as follows:

Table VIII. Wettability Between Liquid Slag and CaO at

1673 K (1400 �C)

No.Contact

Angle (deg)Surface

Tension* (mN/m)Interfacial

Tension (mN/m)

C01 16 581 55C02 15 577 57C03 7 580 39C04 8 584 37C05 6 588 30

*Calculated using the surface tension factor.[17]

0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

Time (min)

Con

tact

Ang

le (

deg)

Tem

pera

ture

(K

)

C01 (CaO/Al2O3/SiO2 = 52/4/0 C02 (CaO/Al2O3/SiO2/MgO = 49.92/38.4/7.68/4

Temperature

C04 (CaO/Al2O3/SiO2/MgO/MnO = 44.72/34.4/6.88/4/10 C04(CaO/Al2O3/SiO2/MgO/MnO = 50/30/6/4/10

1573

1673

1693

1713

1733

1653

1633

1613

1593

C03 (CaO/Al2O3/SiO2/MgO/MnO = 47.32/36.4/7.28/4/5

Fig. 15—Change in contact angle between CaO-Al2O3-SiO2-MgO-MnO slags and CaO as a function of time. The numerical valuesshow mass pct.

METALLURGICAL AND MATERIALS TRANSACTIONS B VOLUME 43B, JUNE 2012—595

E ¼XN

n¼ 1

oxn � xnð Þ2þ ozn � znð Þ2n o

¼XN

n¼ 1

en ½A1�

where oxn and ozn are the x and z coordinates ofobserved nth point, and xn and zn are those of the nearestpoint on the theoretical curve from the observed point.The values of xn and zn can be calculated by usingEqs. [2] to [6]. Thus, the error function E is given bythe following four variables:

q1 ¼ hq2 ¼ 2

b

q3 ¼ qgc

q4 ¼ x0

½A2�

Hence, Eq. [A1] is rewritten as

E q1; q2; q3; q4ð Þ ¼XN

n¼1 en q1; q2; q3; q4ð Þ ½A3�

If the variables are increased Dq1, Dq2, Dq3, and Dq4,respectively, then Eq. [A3] is expressed as

E q1 þ Dq1; q2 þ Dq2; q3 þ Dq3; q4 þ Dq4ð Þ

¼XN

n¼1 en q1 þ Dq1; q2 þ Dq2; q3 þ Dq3; q4 þ Dq4ð Þ½A4�

The conditions of an extremum in the value of theerror function are given by

@Eðq1 þ Dq1; q2 þ Dq2; q3 þ Dq3; q4 þ Dq4Þ@qk

¼ @PN

n¼1 enðq1 þ Dq1; q2 þ Dq2; q3 þ Dq3; q4 þ Dq4Þ@qk

¼ 0; ðk ¼ 1; 2; 3; 4Þ [A5]

Dq1, Dq2, Dq3, and Dq4 are computed by solving Eq.[A5]. Then the new variables

qk ¼ qk þ Dqk k ¼ 1; 2; 3; 4ð Þ ½A6�

are substituted into Eq. [A4], and Eq. [A5] is repeateduntil the value of error function E becomes sufficientlysmall.

Finally, the surface tension is given by

c ¼ qg

qfinal3

½A7�

The contact angle h is calculated by using Eq. [2]through [4] with the following values and given by:

h ¼ qfinal1

2

b¼ qfinal2

qgc¼ qfinal3

x0 ¼ qfinal4

½A8�

h ¼ /i ðat zi � 0Þ ½A9�

where qkfinal (k = 1, 2, 3, 4) are the values of qk under the

convergent condition.The volume of the droplet can be calculated by using

Eqs. [A10][29] and [A11]

Volume ¼ pb2x2

b2

b� 2 sin h

xþ bh

b2

� �½A10�

b ¼ qgb2

c½A11�

where x is the radius of the droplet on the substrate.

Actual Calculation Procedure

To obtain the accurate calculation results of thesurface tension and the contact angle, it is important togive the initial values of variables that are sufficientlyclose to the optimum values. Otherwise, if poor initialvalues are given, the convergent calculation mightdiverge. Appealing attempts that eliminate this disad-vantage of the Gauss-Newton method are the introduc-tion of graphic visualization of the initial condition anduser-definable initial values.When the data of observed coordinates are loaded,

the program automatically starts calculation of thedroplet contour by using Eqs. [2] through [4] with thefollowing start values:

h = q1 = maximum value of the z coordinate ofobserved points2b ¼ q2 = fixed valueqgc ¼ q3 = 0 (c = infinity)x0 = q4 = defined in the data file

Then the x-way distance between the observed pointthat has minimum value of z coordinate and thecalculated contour are computed. If the distance islarger than the threshold value, q2 = q2 + dq2 issubstituted into Eq. [4] and the calculation is repeateduntil the distance is smaller than the threshold value.The results are shown graphically. In case that the giveninitial values are not good, the user can change thevalues of q1, q3, and q4 manually and reevaluate theinitial value of q2. These procedures are shown inFigures A1 and A2. Figure A1 shows a graphic of theinitial condition estimated by the program. In the figure,the squares express the observed points on the right sideof the defined droplet center (x = x0). The circles in thefigure express those on the left side of the droplet center,and they are rotated 180 deg with respect to x = x0.Because the droplet profile has symmetry with respect tothe actual droplet center, Figure A1 indicates that thequality of the observed points or the defined x0 value isnot appropriate. In this case, the value of x0 isintentionally changed for explanation. Figure A2 showsa graphic after a user modification.Two more attempts to eliminate the disadvantage of

the Gauss-Newton method are applied to the convergent

596—VOLUME 43B, JUNE 2012 METALLURGICAL AND MATERIALS TRANSACTIONS B

calculation. In the convergent calculation, Eq. [A7] ismodified as follows:

q2 ¼ q2 þ aDq2 ½A12�

where a is a damping factor,[30] 0<a £ 1. Furthermore,once the convergent condition is obtained, the programwill start recalculation automatically using qk

final (k = 1,2, 3, 4) as the initial values. It will be repeated until thevalue of qfinal3

� �jþ1ð Þth� qfinal3

� �jth

becomes smaller than the

threshold value. Here, qfinal3

� �jth

is the value of q3 under

the jth convergent condition. Therefore, the programestimated initial values can be used in most cases. Theresults are also shown graphically. Thus, the reliability

of the computation results can be estimated. The actualprogram window is shown in Figure 5.

REFERENCES1. T. Takaoka, Y. Kikuchi, and K. Yamada: CAMP-ISIJ, 1998,

vol. 11, p. 765.2. Y. Kawai, T. Takaoka, Y. Kikuchi, and K. Yamada: CAMP-ISIJ,

1999, vol. 12, p. 132.3. The Iron and Steel Institute of Japan: Physical and Chemical Data

Book for Iron- and Steelmaking, Ironmaking, The Iron and SteelInstitute of Japan, Tokyo, Japan, 2006.

4. Slag Atlas, 2nd ed., VDEh, Verlag Stahleisen GmbH, ed.,Dusseldorf, Germany, 1995.

5. T.B. Massalski, ed.: Binary Alloy Phase Diagrams, vol. 1, ASM,Materials Park, OH, 1986.

6. I. Jimbo and A.W. Cramb: ISIJ Int., 1992, vol. 32, pp. 26–35.7. T. Tanaka: Bull. Iron Steel Inst. Jpn., 2003, vol. 8 (3), pp. 161–66.8. A.S. Krylov, A.V. Vvedensky, A.M. Katsnelson, and A.E.

Tugovikov: J. Non-Cryst. Solid, 1993, vols. 156–8, pp. 845–48.9. I. Jimbo and A.W. Cramb:Metall. Trans. B, 1993, vol. 24B, pp. 5–

10.10. T. Young:Miscellaneous Works, vol. 1, G. Peacock and J. Murray,

eds., Dover Publications, London, U.K., 1805.11. D.T. Livey and P. Murray: J. Am. Ceram. Soc., 1956, vol. 39,

pp. 363–72.12. Japan Society for Promotion of Science: Steelmaking Data

Sourcebook, Gordon and Breach Science Publishers, New York,NY, 1988.

13. J. Lee and K. Morita: ISIJ Int., 2004, vol. 44, pp. 235–42.14. J. Lee and K. Morita: Steel Res., 2002, vol. 73, pp. 367–72.15. I. Jimbo, A. Shara, and A.W. Cramb: Trans. ISS, 1995, vol. 16,

pp. 45–52.16. K. Nakajima: Tetsu-to-Hagane, 1994, vol. 80, pp. 593–98.17. R.E. Boni and D. Derge: Trans. AIME, 1956, vol. 206, pp. 59–64.18. M. Zielinski and B. Sikora: Prace IMZ, 1977, vol. 29 (3–4),

pp. 157–65.19. B. Sikora and M. Zielinski: Huntnick., 1974, vol. 41 (9), p. 433.20. G.S. Esshov and E.A. Popova: Russ. J. Inorg. Chem., 1964, vol. 9

(3), p. 361.21. K. Ogino, S. Hara, and E. Shibahara: Tetsu-to-Hagane, 1972,

vol. 58, p. S388.22. A. Nishiwaki and K. Ogino: Tetsu-to-Hagane, 1985, vol. 71,

p. S121.23. A. Adachi, K. Ogino, and T. Suetaki: Tetsu-to-Hagane, 1964,

vol. 50, pp. 1838–41.24. B. van Muu, H.W. Fenzke, and H.J. Eckstein: Neue Hutte, 1985,

vol. 30, p. 341.25. J.L. Bretonnet, L.D. Lucas, and M. Olette: C.R. Acad. Sci. Paris,

1977, vol. 285, p. 45.26. K. Mukai: Kouon-yutai-no-kaimen-butsuri-kagaku, Agne Gijutsu

Center, Tokyo, Japan, 2007.27. Y. Hino, Y. Nakai, I. Sumi, S. Nabeshima, and Y. Kishimoto:

CAMP-ISIJ, 2007, vol. 20, p. 89.28. Y. Taniguchi, N. Sano, and S. Seetharaman: ISIJ Int., 2009, vol.

49, pp. 156–63.29. F. Bashforth and J.C. Adams: An Attempt of Test the Theories of

Capillary Action, Cambridge University Press, Cambridge, U.K.,1883.

30. Y. Rotenberg, L. Boruvka, and A.W. Neumann: J. Colloid Inter.Sci., 1983, vol. 93, pp. 169–83.

0 0.1 0.2 0.3 0.4 0.5 0.60

0.1

0.2

0.3

0.4

Horizontal Distance from Droplet Center (10–2 m)

Ver

tical

Dis

tanc

e fr

om S

ubst

rate

(cm

)

q1 = 0.247q2 = 5.093q3 = 0q4 = –0.01

Fig. A1—Example of initial condition of surface tension calculation.

0 0.1 0.2 0.3 0.4 0.5 0.60

0.1

0.2

0.3

0.4

Horizontal Distance from Droplet Center (10–2 m)

Ver

tica

l Dis

tanc

e fr

om S

ubst

rate

(cm

)

q1 = 0.254q2 = 4.615q3 = 10q4 = 0

Fig. A2—Example of initial condition after user modification.

METALLURGICAL AND MATERIALS TRANSACTIONS B VOLUME 43B, JUNE 2012—597