Evaluation of Surface Tension and Adsorption for Liquid Fe–S Alloys

ISIJ International, Vol. 42 (2002), No. 6, pp. 588–594

Joonho LEE and Kazuki MORITA1)

Graduate Student, The University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-8656 Japan. E-mail: [email protected] 1) Department of Metallurgy, The University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-8656 Japan. (Received on December 11, 2001; accepted in ﬁnal form on February 16, 2002)

Surface tension of liquid iron is strongly inﬂuenced by the adsorption of sulfur. In this study, surface tensions of liquid Fe–S alloys at 1 823 K were measured by the sessile drop technique in a puriﬁed argon at- mosphere. Experimental results were compared with the model based on Butler’s equations considering the effect of size and interactions of the adsorbed elements assuming that the system was composed of Fe–“FeS” binary. The model could evaluate the surface tension and the adsorption of sulfur more reasonably rather than a simple ideal adsorption model. In the calculations, excess free energy expanded by Margules’ series over the entire composition range of Fe–FeS system was used. KEY WORDS: surface tension; adsorption of sulfur; Butler’s equation; Margule’s series; sessile drop technique.

sorption for liquid iron containing surface active elements. 1. Introduction Bernard and Lupis6) indicated that differences in size of the Surface tension of liquid iron is considerably decreased adsorbed elements and interactions between them cause de- by the adsorption of the surface active elements which are viations of experimental results from an ideal adsorption known to be present in large concentrations at a surface. behavior, and Eq. (1) is only valid near the saturation stage, Thus, preferential adsorption of surface active elements at a since adsorbed elements may exclude adjacent sites from surface can be predicted by accurate surface tension values. occupancy. Belton7) developed a two-step isotherm model, Among the surface active elements, sulfur is one of the which considers repulsive interactions between surface ac- most important elements in steelmaking processes. There- tive elements on liquid iron. However, the surface tension fore, it is essential that the surface tension of liquid iron values obtained by the two-step model are indistinguishable containing sulfur should be evaluated properly. from those by the ideal adsorption model,1) because he used Usually, the surface tension of liquid iron containing sul- reported values scattered by more than 0.2 N/m. By some fur, s, has been given by the simple ideal adsorption model other groups, there have been several attempts to explain (so called Szyszkowski equation) proposed by Belton.1) the surface tension of liquid iron containing surface active elements based on Butler’s equations, considering the equi- ss RTG ° ln(1K a ) ...... (1) Fe S S S librium between a bulk phase and a monolayer at the sur- 8) where s Fe, G S°, KS and aS are surface tension of pure iron, face. Tanaka and Hara calculated the surface tension of surface adsorption of sulfur at saturation, adsorption coeffi- liquid Fe–O alloys with a regular solution model. In their cient and activity of sulfur with respect to 1 mass% as stan- calculations, the alloy was regarded as a Fe–“FeO” system. dard state, respectively. Most of the experimental results of Likewise, Hajra et al.9) calculated the surface tension of surface tension of liquid iron containing sulfur were ex- molten Fe–S alloy regarding the alloy as a Fe–“FeS” sys- pressed as an ideal adsorption isotherm of Eq. (1).2–4) tem. They assumed that the system follows a sub-regular 8,9) However, the derived value of KS varies from 185 to 365. model. These previous models agreed with the experi- Chung and Cramb4) asserted that surface tension curves mental results within 0.2 N/m. They, however, ignored in- may not be very sensitive to values of the adsorption coeffi- teractions or extrapolated thermodynamic data of interac- cient. Meanwhile, Lupis5) found that the adsorption of sur- tions for dilute solutions to high content regions, although face active elements such as sulfur in an ideal adsorption the surface may be highly occupied by sulfur and oxygen. model disagrees with the experimental observations which Recently, Hajra and Divakar10) have explained the surface yield a much steeper rise of the adsorption curve. There- tension of the liquid Fe–S–O system based on the modified fore, it is believed that Eq. (1) is not proper to evaluate the Butler’s equations. However, this model still uses the first sulfur adsorption on liquid iron. order interaction coefficients of dilute solutions. According- Recently, attention has been paid to the development of a ly, in order to evaluate surface tension and adsorption of more general relationship between surface tension and ad- sulfur for Fe–S alloys more accurately, it is necessary to de-

© 2002 ISIJ 588 ISIJ International, Vol. 42 (2002), No. 6 termine a moderate excess free energy equation across the composition range. In this paper, surface tensions of Fe–S alloys were measured using the sessile drop technique. At the same time, a thermodynamic model calculation of surface tensions for Fe–S alloys based on Butler’s equations was presented. By comparing the model calculation with the experimental results, the surface adsorption of sulfur on liquid iron could be deduced.

2. Theory

2.1. Butler’s Equation Fig. 1. Schematic diagram of surface tension measurements. Butler’s equations for A–B binary system can be ex- 11) pressed as Table 1. Chemical analysis of electrolytic iron used in the ex- periment. [mass%] RT  1 X s  σσP ln B  A b SA  1 X B  1 Ex,s s Ex,b b ((,)GTXGTXA B A (,))B SA samples on a high purity (99.95 mass%) alumina boat with RT  X s  an alumina cover were placed at the center of a mullite re- σ P ln B  B b action tube. (I.D.: 0.040 m, O.D.: 0.050 m) The samples SB  X B  were prepared with high purity electrolytic iron (see Table 1 Ex,s s Ex,b b 1) and FeS (99.9 mass%), and concentrations of oxygen and ((,)GTXGTXB B B (,))B ...... (2) SB sulfur in the samples were analyzed by LECO analyzers after experiments. The temperature was well adjusted by P where R, T, s i , Si are the gas constant, the absolute temper- PID controller with a Pt–30%Rh/Pt–6%Rh thermocouple ature, the surface tension and molar surface area of the pure located by the heating element, which was preliminarily ¯Ex,s s element i, respectively. G i (T, Xi ) is the partial excess free calibrated by the temperature of the exact position where a s energy of i in the surface as a function of T and Xi (the liquid droplet was settled. ¯Ex,b b mole fraction of i in the surface). G i (T, Xi ) is the partial The experimental procedure was as follows. Cubes of b excess free energy of i in the bulk as a function of T and Xi alloy samples weighing about 1–2 g were ground on edges (the mole fraction of i in the bulk). Si is calculated from the and corners and polished on faces with a grinder, then molar volume Vi on the assumption that the elements occu- washed in acetone by a ultrasonic cleaner and dried before 5) py a close-packed configuration in a monolayer. (i A or being placed on ceramic substrates. Al2O3 (or graphite for B.) FeS) was used as a substrate in order to prevent the reaction of the molten alloy with the substrate. Contamination from S 1.091·N 1/3V 2/3...... (3) i A i substrates was negligible in this study. After the specimen where NA is Avogadro’s number. Thus, in calculations based assembly was settled at the center of the furnace, the reac- on Butler’s equations, it is necessary to know the surface tion chamber was sealed and evacuated, and then purified tension and density of each component element of pure Ar gas was introduced at a flow rate of 0.3 l/min STP. Then, state and the excess free energy between the component el- the system was heated to the experimental temperature ements. However, if B is a surface active element such as (1 823 K). Once the sample was melted, measurements of sulfur, it is impossible to determine physical properties surface tensions were started. such as surface tension and density of the component B at The shape of the sessile drop of the liquid alloy on the such high temperatures. Hence, such system can be regard- ceramic substrate was monitored by a digital video camera ed as A–AB pseudo binary one.8,9) for 30–60 min. Several selected still images then could be directly converted into image files. The digitized dots were used to calculate the surface tension with a computer pro- 3. Experimental gram that has been developed by Jimbo et al.13) The sessile-drop method was employed in the present investigation. This technique proved to be one of the most 4. Results and Discussion popular techniques to determine surface tension of molten metals after Bashforth and Adams empirical equation.12) 4.1. Surface Tension of Fe–S Recently, Jimbo et al.13) have developed more accurate way The experimental results of the surface tension for Fe–S of non-subjective and numerical determination of surface alloy were the same or slightly higher than the reported val- tension. ues measured by the sessile drop technique. In Fig. 2, the The experimental apparatus is shown in Fig. 1. A SiC experimental and reported results were shown as a function heating element furnace was used in this study. The alloy of sulfur content for comparison. Data after Kozakevitch14)

Fig. 2. Surface tension of Fe–S alloy as a function of sulfur content at 1 823 K. and Dyson et al.15) showed relatively lower values even for pure iron as 1.788 and 1.754 N/m, respectively. Samples of Halden et al.17) contained oxygen from 0.0006 to 0.3 mass%. Among the reported values, those of Keene et al.18) are noticeable. They measured the surface tension of Fe–S alloys using a levitation technique at 1 923 K, which elimi- nated the possibility of contamination by substrates. In Fig. 2, only selected data of Keene et al. containing less than 0.005 mass% of oxygen were presented. It is expected that in a lower sulfur content region the surface tension at 1 923 K is lower than that of 1 823 K, whereas in a higher sulfur content region that of 1 923 K is higher, because temperature coefﬁcient of surface tension (ds/dT) changes from negative to positive by increasing sulfur content.19) However, even in a lower sulfur content region, the surface tension values of Keene et al. showed higher values than other experimental data. In the present investigation, oxygen remained constant at 60 ppm. Therefore, it is considered that the reported values using the sessile drop technique may contain more than 60 ppm of oxygen. Effect of oxygen on the surface tension of Fe–S alloys Fig. 3. Re-estimation of the surface tension for Fe–S alloy with- can be considered, if we assume the effects of both sulfur out oxygen as a function of sulfur content at 1 823 K. and oxygen on the surface tension in the manner of Ogino et al.20) Ogino suggested the following equation for the sur- 1.8900.299 ln(1110a ) (N/m) ...... (5) face tension of Fe–O–S alloys. s O From Eqs. (4) and (5), we may conclude that samples of ss RTG ° ln(1K a )RTG ° ln(1K a ) ....(4) Fe O O O S S S the present study may have higher surface tensions by where G i°, Ki and ai are the surface adsorption of element i 0.151 N/m without oxygen. In Fig. 3, re-estimated values at saturation, adsorption coefﬁcient and activity of element are shown as a function of sulfur content. The re-estimated i, respectively. Equation (4) shows that oxygen and sulfur values are higher than the previous models by 0.150–0.350 have no mutual interactions. At least, this equation may be N/m. Since ideal adsorption models suggested by Belton1) applied to the samples of low oxygen and sulfur levels of and Jimbo et al.3) and the two-step model by Belton7) used the present study. Taking the values of Kasama et al.,21) the reported values using the sessile drop technique, it is Belton22) suggested Szyszkowski equation for the surface believed that the reported models were lowly estimated for tension of Fe–O alloys at 1 823 K as some reasons such as oxygen contaminations.

Fig. 4. Effect of temperature on the density of FeS. Fig.5. Variation of the surface tension of FeS with temperature.

4.2. Thermodynamic Model Calculation The data of this study is slightly higher than that of other In order to evaluate the sulfur adsorption on liquid iron, a researchers.31–33) Considering that the surface tension of proper thermodynamic model that reasonably describes the pure materials generally decreases by increasing tempera- resulting surface tension for the Fe–S system is required. In ture, the negative temperature dependence of the present re- the model calculation of the present study, Fe–S system was sults seems to be reasonable. regarded as Fe–“FeS” system based on Butler’s equations. Each parameter was introduced as follows. 4.2.2. Excess Free Energy Chipman34) calculated the excess free energies of the 4.2.1. Physical Properties of Pure Elements Fe–“FeS” system from the phase diagram of the Fe–S sys- The accurate values of density and surface tension for Fe tem. He had taken the data of g from the phase diagram and FeS are assessed as follows. There are a number of Fe (pure liquid iron was taken as the standard state) and calcu- studies on the surface tension of pure iron. In order to avoid lated g by Gibbs–Duhem equation. In the present work, oxygen contamination by ceramic substrates, some investi- FeS through a similar but more general way, the values of g gators have used the levitation technique. Using this tech- Fe and g could be calculated at 1 823 K across the composi- nique, Kasama et al.,21) Lee et al.,23) and Brooks24) have re- FeS tion range using Margules series. ported the surface tension of pure iron at 1 823 K as 1.913, 1.919 and 1.884 N/m, respectively. In the calculation of this 1 1 1 γα α2 α3 α4 ⋅⋅⋅ paper, the value of 1.913 N/m was used as the surface ten- ln Fe1234XXXX FeS FeS FeS FeS sion of pure iron, while the value of 7.10103 kg/m3 as the 2 3 4 density of pure iron suggested by Jimbo et al.25) ...... (8) The density and surface tension of FeS were measured si- 1 1 1 multaneously in this work using the sessile drop technique. γβ β2 β3 α4 ⋅⋅⋅ ln FeS1234XXXX Fe Fe Fe Fe Figure 4 shows the density of FeS as a function of tem- 2 3 4 perature. The density of FeS slightly increases with in- ...... (9) creasing temperature, which is unusual. Kawai et al.,26) Applying Gibbs–Duhem equation with ignoring coefﬁ- Henderson,27) and Schenck et al.28) found very similar tem- cients a ’s and b ’s higher than i4, one can obtain a and perature dependence of the density of FeO that increases i i 1 b as zero, and Eqs. (8) and (9) can be rewritten by Eqs. with elevating temperature. In this study, the partial pres- 1 (8-1) and (9-1). sure of sulfur was not controlled, and the reason of the increase in the density of FeS with increasing temperature is ln γ 1 1 1 unclear at present. Nevertheless, the reported values of FeS ααXX α2 ...(8-1) 29) 3 3 30) 2 23FeS 4 FeS Kozakevitch (4.1010 kg/m at 1 723 K) and Elliot ()1 X Fe 2 3 4 3 3 (3.88 10 kg/m at 1 473 K) are very close to the present ln γ 1 1 1 results. Assuming that density data is represented by a lin- FeS ββXX β2 ...... (9-1) 2 2 233 Fe4 4 Fe ear function of temperature, the density of FeS can be ex- ()1 X FeS pressed by the following regression equation. In this study, data of g Fe were taken from the phase dia- 3 3 35) 34) r FeS 2.26 10 1.21T (kg/m ) ...... (6) gram with the same manner as Chipman (Table 2). Then, ln g /(1X )2 can be plotted as a function of X at The results of surface tension of FeS are shown as a Fe Fe FeS 1 823 K as shown in Fig. 6. These values could be ex- function of temperature in Fig. 5. pressed by a second order equation graphically, yielding 3 s FeS 0.650 0.155 10 T (N/m) ...... (7)

Table 2. Activity of iron in liquid solutions Fe–FeS.

Fig. 7. Effect of the value of b on the surface tension of liquid Fe–S alloy at 1823K.

Table 3. Physical properties of the components for the calculation of the surface tension of the liquid Fe–S alloy.

2 Fig. 6. Plot of ln g Fe /(1 XFe) as a function of XFe for the graphical determination of polynomials across the composition range at 1 823 K. ment (Fe or FeS) has the same value, and the net bonding energies in the surface have the same concentration depen- ln γ dence as those in the bulk phase, the partial excess free en- Fe 379.. 519XX 253 .2 ...... (10) ergy ratio between the surface and the bulk phase is deter- 2 FeS FeS ()1 X Fe mined only by the coordination number ratio (bZ s/Z b) as Eq. (13). The error of this ﬁtting is within 0.2% across almost the ¯Ex,s s ¯Ex,b s entire concentration region. Then we can decide the each G i (T, Xi ) b ·G i (T, Xi ) ...... (13) value of a , a and a . From Eq. (10), the following equa- 2 3 4 Note that for b0 Eq. (13) yields an ideal adsorption tion is obtained by Gibbs–Duhem equation. model. For b1, interactions between adsorbed elements ln γ are equal to those in the bulk phase. In calculations for a FeS 107.. 156XX 253 .2 ...... (11) non-ideal adsorption model, the value of b was suggested 2 Fe Fe ()1 X FeS as 1/2–1 by many researchers.5,11,36,37) Figure 7 shows the effect of b on the surface tensions, when b varies from zero From Eq. (11), we could obtain the g° by inserting X →1. FeS Fe to one. It is shown that the resulting surface tension values Then the value of g° was obtained as 2.04 at 1 823 K. FeS for non-ideal models (b1/2–1) were higher than those for Chipman34) has obtained the value of g° as 1.95 and 2.14 at Fe the ideal model (b0) by 0.054–0.109 N/m at most. In this 1 873 K and 1 773 K respectively by both experiments and calculation for the non-ideal adsorption model, the value of calculations, with which our value was in reasonable ac- b employed 0.83 suggested by Tanaka et al.,11) which con- cord. Then, we can also deduce the excess free energy as sidered the relaxation of the surface. The surface tension Eq. (12) based on the three parameters equation suggested values at b0.83 differ from other non-ideal adsorption by Lupis.5) models only within 0.035 N/m, which is less than the exper- Ex G XFe XFeS(31XFe 17XFeS 13XFe XFeS) (kJ/mol) imental errors. The necessary input data for Eq. (2) are ...... (12) summarized in Table 3. It is likely that elements having mutual interactions in a 4.2.3. Model of the Surface Tension for Fe–S bulk phase also show interactions with each other at a sur- In Fig. 3, results of model calculation for ideal and non- face. Assuming that the coordination number of each ele- ideal adsorptions are shown with the re-estimated values

Fig. 8. Effect of the molar surface area on the surface tension of Fig. 9. Plot of exp[(s Fe s)/RTGFeS° ] 1 as a function of sulfur liquid Fe–S alloy at 1 823 K. activity for the graphical determination of an ideal adsorption coefficient of sulfur at 1 823 K. excluding the effect of oxygen. The non-ideal adsorption model is in reasonable accordance with the experimental results. It is believed that the slight difference between the non-ideal model and experimental results may be caused by the simple assumption of Ogino et al.20) The non-ideal adsorption curve shows higher values than the ideal adsorption curve especially in the low sulfur concentration region. The difference between these two models appears to be maximum when the sulfur content in the bulk phase is about 0.005 mass%. Similar behaviors were found in the study on Cu–O system by Sasaki et al.38) using data of Gallios et al.39) It is noticeable that most of the previous results could be expressed by Szyszkowski equation, which assumed that the molar surface area is constant and atoms adsorbed on the surface have no interactions. Figure 8 shows the difference of the surface tension values between the non-ideal adsorption model (b0.83) and the ideal adsorption models assuming S SFe or S SFeS. The surface tension values of the ideal adsorption model assuming SS deviate from Fe Fig. 10. Surface adsorption of sulfur as a function of sulfur con- the non-ideal adsorption model by 0.466 N/m at most, tent at 1 823 K. whereas those assuming S SFeS are very close to the non- ideal adsorption model. In the latter case, the surface ten- 1 823 K may be given by Eq. (14). sion deviates from the non-ideal model less than 0.040 N/m. It is considered that the effect of the change in the s 1.913 0.217 ln(1 123aS) ...... (14) molar surface area could be compensated for the change in It can be concluded that the surface tension of Fe–S alloy interactions between the adsorbed elements at the liquid without oxygen can be estimated reasonably by the model iron surface when SS . Therefore, it is considered that, FeS calculation of the non-ideal adsorption, whereas it can be assuming that the molar surface area is equal to the surface also expressed as a form of the ideal adsorption style equa- adsorption of sulfur at saturation, the surface tension can be tion (Eq. (14)) within errors of 0.040 N/m. expressed as a form of Szyszkowski equation. Graphically, we may determine the ideal adsorption coefficient of sulfur 4.2.4. Surface Adsorption of Sulfur in Eq. (1) as 123 at 1 823 K by plotting (exp[(s Fe s)/ Surface adsorption of sulfur on liquid iron can be ob- RTG FeS° ] 1) as a function of sulfur activity with respect to tained by Eq. (15). 1 mass% as standard state (Fig. 9). It is shown that the slope of regression line in Fig. 9 may vary from 113 to 158 X s ΓΓ FeS ...... (15) depending on the regression range, which explains why the S FeS s s SXFe Fe SFeS X FeS adsorption coefficients for the ideal adsorption model dif- fered with investigators.2–4) Consequently, as a form of The sulfur adsorption variations against the sulfur content Szyszkowski equation, the surface tension of Fe–S alloy at are shown in Fig. 10. Those for the non-ideal adsorption

593 © 2002 ISIJ ISIJ International, Vol. 42 (2002), No. 6 model show more rapid increase than the ideal adsorption 4) Y. Chung and A. W. Cramb: Steel Res., 70 (1999), 325. model at about 0.005 mass% of sulfur. Thus, it may be con- 5) C. H. P. Lupis: Chemical Thermodynamics of Materials, North- cluded that an ideal adsorption model is not proper to eval- Holland, Amsterdam, (1983), 176, 347. 6) G. Bernard and C. H. P. Lupis: Metall. Trans., 2 (1971), 2991. uate sulfur adsorption on the liquid iron. In the non-ideal 7) G. R. Belton: Metall. Trans. B, 24B (1993), 241. adsorption model, it is considered that the sudden decrease 8) T. Tanaka and S. Hara: Z. Metallkd., 90 (1999), 348. of surface tension at around 0.005 mass% is caused by the 9) J. P. Hajra, M. G. Frohberg and H.-K. Lee: Z. Metallkd., 82 (1991), fast increase in sulfur adsorption in this concentration re- 718. 10) J. P. Hajra and M. Divakar: Metall. Mater. Trans. B, 27B (1996), 241. gion. 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