DOES INTERFACIAL TENSION PLAY THE MOST IMPORTANT ROLE IN SLAG-METAL REACTIONS? AN IMPORTANT ASPECT IN
PROCESS OPTIMIZATION
Du Sichen1 and Jesse F. White2
1Royal Institute of Technology (KTH), Stockholm, Sweden
2Elkem AS, Technology, Kristiansand, Norway
Keywords: Interface, heterogeneous reaction, interfacial phenomena, Gibbs energy Abstract
In view of the nature of heterogeneous reaction of many materials processes, great attention has been paid to the reaction interfaces. Very often, the interfacial tension is given the foremost importance in the study of interfaces in general and slag-metal reactions in particular. As an example, the dependence of entrainment of ladle slag into liquid steel on interfacial tension has been the topic of many researchers.
In the present work, the interface between liquid silicon and CaO-SiO2 slag and the interfacial reaction between silicon and graphite were studied experimentally to gain an insight into the impacts of chemical driving force and interfacial tension on the interfacial phenomena. The results strongly suggested that the chemical driving force could play dominating role in determining the interface, while the interfacial tension would only become important when the slag and metal were reaching equilibrium. Based on the experimental findings, the kinetics of the slag-metal reaction was discussed. Also, the possibility of the entrainment of ladle slag as a source of nonmetallic inclusions was evaluated. The present study would like to draw researchers’ attention regarding the important role of Gibbs energy of the reaction at the interface in the interfacial phenomena and therefore getting an improved understanding of the reaction process.
Introduction
Slag-metal reactions and gas-metal reactions hold the key to successful steelmaking. The former plays also great role in silicon refining. Two-film and surface renewal models had been very popular in describing slag-metal reactions, before the computer became really available to researchers. However, they could only be applied to specific reactors under specific operating conditions, based on which the mass transfer coefficients are optimized. The lack of understanding of the slag/metal interface and the assumption of uniform concentration in the bulk are the foremost factors making the models unrealistic.
It is commonly accepted that most chemical reactions reach thermodynamic equilibrium locally at steelmaking temperatures. To the knowledge of the present authors, the models describing the slag-metal reactions have all made this assumption.[1-4] While the models trying to simulate the
Advances in Molten Slags, Fluxes, and Salts: Proceedings of The 10th International Conference on Molten Slags, Fluxes and Salts (MOLTEN16) Edited by: Ramana G. Reddy, Pinakin Chaubal, P. Chris Pistorius, and Uday Pal TMS (The Minerals, Metals & Materials Society), 2016
slag-metal interface[2-4] have shown good potential of simulating slag-metal interface, the real physical behavior of the slag-metal interface still need very careful study.
Both the formation of inclusions by slag entrainment and inclusion separation to the slag have been discussed by many researchers. A number of publications have been devoted to the separation of inclusion removal to the top slag. The model developed at an early stage assumed that all inclusions reaching the interface between the steel and the slag would be separated from the steel.[5-7] Realizing the importance of interfacial energy and liquid metal film in the removal of inclusions to the slag, researchers have developed models taking these factors into consideration.[8-11] However, in all the modelling approaches, no chemical potential differences between the two phases have been taken into account.
In connection with silicon refining, a number of studies have investigated the wettability and reaction of liquid silicon with different substrates, including graphite and vitreous carbon.[12-17]
The open porosity of the graphite, surface roughness, and not the least, contact time have all been documented to greatly influence the “dynamic wetting” of liquid silicon on graphite.
Although the variation of the contact angle with time has been well known, in process modelling and process optimization the importance has always been given to the interfacial energy. The present work focuses on a discussion regarding whether the chemical driving force has been overlooked when studying the interface and whether the interfacial energy has been given too much importance. The discussion is based on the experimental results obtained under well- defined experimental conditions.
Experimental
Two types of experiments were conducted, namely (1) interfacial reaction between slag and silicon metal, and (2) the wetting behavior of liquid silicon on carbon substrates.
Interfacial reaction between slag and silicon
The mixing crucibles and impellers were made of Mersen 2020 graphite. The impeller was 45 mm high and 15 mm wide. The mixing crucible was fabricated by boring four 18-mm diameter holes into a graphite blank in such a manner as to create an internal volume with a quatrefoil profile. The resulting four vertical protrusions acted as baffles to prevent bulk rotation of the melt and consequent generate vortex. A schematic diagram of the setup is provided in Fig. 1, with the details of the crucible arrangement shown in (b). A description of the setup can be found in a previous publication.[18] A stirring motor was used to drive a graphite impeller that stirred the melt. The stirring motor and support tube were fastened to a motorized belt drive that allowed the vertical movement of the crucible assembly in and out of the hot zone of the furnace.
To seal the moving mechanical components, radial shaft seals were used between the impeller shaft and support tube, and between the support tube and the cooling chamber.
CaO–SiO2 slags, designated Slag A B, and C were prepared prior to the experiments by fusing high-purity fused silica and calcium oxide in a graphite crucible. The silicon was polycrystalline, semiconductor-grade purity. Boron was added either to the slag phase (in the form of SiB6) or to the metal phase (in the form of H3BO3) at an initial concentration of approximately 436 ppm. In preparation for each heat, 40 grams of silicon chips were placed in the bottom of the mixing crucible, and 40 grams of slag constituents were placed on the top. After placing the mixing
crucible into the holding crucible, the whole assembly was fastened onto the end of the stainless steel support tube.
The impeller blade was lowered until it rested on the top of the material in the mixing crucible. The reaction tube was then sealed, evacuated and back-filled with argon.
Thereafter a flow of argon gas (0.05 l min-1) was kept throughout the experiment.
When the target temperature in the hot zone of the furnace was reached, the crucible assembly was lowered to rest at a position in the reaction tube at about 1573 K to preheat the crucible for 15 minutes to minimize thermal shock to the alumina reaction tube. The crucible assembly was then lowered into final position in the hot zone of the furnace. When the impeller was in position (10 mm above the bottom of the mixing crucible), the stirring motor was engaged (zero-time t = 0).
At the end of an experiment, the crucible assembly was rapidly retracted out of the furnace into the water-cooled quenching chamber by raising the stainless steel support tube with the motorized belt drive. A high flow of argon gas was immediately initiated to expedite quenching of the samples. Photographs and micrographs were taken of the crucible cross-sections.
Interfacial phenomena between liquid silicon and carbon substrates
The experimental apparatus was a high-temperature sessile drop apparatus as depicted in Fig. 2 A detailed description can be found in a previous paper.[19] The main component of the setup was a horizontal tube furnace and an alumina reaction tube (70 mm
inner diameter). The reaction tube was sealed with O-rings on its ends by an internally water-cooled quenching chamber on one end, and the other end had a water-cooled aluminum cap with a sealed quartz glass window. The reaction gas entered on the window end and exited the quenching chamber. A carriage made of graphite held the specimen in the hot zone of the furnace. The carriage was threaded onto a water-cooled pushrod (sealed with a packing). The pushrod was fastened to a motorized screw drive that enabled the precise positioning and
movement of the specimen to reproducibly control heating rates. The measurement thermocouple was a Type C (W / W–5 % Re), and was mounted axially in the pushrod and carriage, with the tip inside the carriage body positioned directly under the substrate. A gas train prepared the
Fig. 2 Experimental setup for contact angle measurements
14 1
5
3
13 15
4 4
(See Fig. 2) 2
11
11 12
8
6 7
9
10
(b)
Fig. 1 Experimental setup
Parts:
1. Tube furnace; 2. Alumina tube;
3. Water‐cooled quenching chamber;
4. O‐ring seal;
5. Stainless steel support tube;
6. Graphite support tube;
7. Stainless steel coupling;
8. Stainless steel impeller shaft;
9. Graphite impeller shaft;
10. Graphite impeller;
11. Radial shaft seal;
12. Stirring motor;
13. Measurement thermocouple;
14. Ar mass flow controller; 15. Gas outlet.
(b)
reaction gas mixture when needed. High-purity argon gas was metered using a Bronkhorst mass flow meter (± 0.5 % accuracy).
In preparation for each experiment, the silicon piece and the graphite substrate were first cleaned with ethanol and then placed on the carriage. The carriage was positioned in the quenching chamber, and the whole system was then sealed. The reaction tube was evacuated with a vacuum pump and back-filled with argon. To start the run, a flow of reaction gas and the furnace control sequence were initiated. The flow rate of the inlet gas was fixed at 0.02 l min-1. The temperature was ramped up to 1703 K (1430 °C) at 2 degrees per minute. The variation of the sample was followed by video recording.
At the end of each experiment, the carriage was rapidly withdrawn from the furnace into the water-cooled quenching chamber by activating the mechanical drive. In some of the tests the specimens were quenched shortly after melting started, while in other tests the silicon was given time to completely wet the graphite substrate so that dynamic changes in infiltration could be observed. Still images were extracted from the video files.
Results
Interfacial reaction between slag and silicon
Figure 3 and Figures 4 show photographs of the crucible cross-sections for the heats where boron was added to the slag phase or metal phase, respectively. Note that mixing was stopped prior to quenching, and that the mixing conditions were kept constant in all the experiments. At short reaction times of t = 30 seconds and t = 60 seconds, (Figure 3(a) and (b), Figure 4(a) and (b), it can be seen with the naked eye that the interfacial boundary between the metal phase and slag phase is markedly irregular, and that there are countless small yet visible metal droplets entrained in the slag phase. By 300 seconds of reaction time (Fig. 3d and Fig. 4d ), the interface is smooth, and the slag phase color has transformed from grey to green. To show this aspect
clearer, Fig. 5(a) and 5(b) show LOM micrographs at 50× magnification of the bulk slag phase at t = 30 s and t = 300 s. At 30 seconds reaction time, metal is finely dispersed in the slag phase as
a) Heat 7, 30s b) Heat 8, 90s c) Heat 24, 180s d) Heat 6, 300s
Fig. 3 Changes in characteristics of slag–
metal interface, slag phase doped with boron
a) Heat 16, 30s b) Heat 17, 90s c) Heat 23, 180s d) Heat11, 300s Fig. 4 Changes in characteristics of slag–
metal interface, metal phase doped with
irregularly formed droplets of varying size, indicting thereby that the interfacial area is very large at this stage. In contrast, under the same mixing conditions at t = 300 s (Fig. 5b), the slag phase is nearly devoid of metal droplets. Higher magnification (500x) reveals that only very tiny metal droplets less than 5 micrometers in diameter are left in the slag phase.
Fig. 6 shows the change in boron concentration with increasing reaction time for the slag being doped with boron or the metal phase being doped with boron. In the case of boron addition into the metal phase, the concentration decreased exponentially and leveled out by about 300 seconds. When boron was added to the slag phase, the concentration in the metal phase increased and leveled out. Since the total amount of boron was added to the system was equal in each case, these two curves converge at 300 seconds. The converging of the curves indicates strongly that slag and metal have almost reached equilibrium after 300 seconds.
Fig. 7 shows the variation of calcium concentration in the metal phase as a function of reaction time and mixing speed (rpm).
The calcium concentration in the silicon increases with time as CaO in the slag is reduced. It is readily apparent that a stirring speed greater than 100 rpm does not appear to increase the rate of calcium transfer. With stirring, by 600 seconds the calcium concentration in the slag reaches around 0.5 mass %Ca. Note that the variation of the concentration is very small after 300 s, within the experimental uncertainties.
Interfacial phenomena between liquid silicon and carbon substrates
The starting time, t = 0 (designated t0) was assigned to when the silicon was completely molten.
It took only a few minutes for the molten silicon to completely spread and infiltrate the graphite.
In this case, the substrate actually fractured during infiltration due to internal stresses as also described by Israel et al..[20] It should be mentioned that the “contact angle” observed in a non-
0 100 200 300 400 500 600
0 50 100 150 200 250 300 350 400 450
t [seconds]
[B] [ppm]
Metal phase doped with B Slag phase doped with B
0 100 200 300 400 500 600
0 0.1 0.2 0.3 0.4 0.5
t [seconds]
[Ca] [mass %]
0 rpm 50 rpm 100 rpm 200 rpm 400 rpm
Fig. 6 Boron concentration as a function of time Fig. 7 Ca concentration as a function of time a) Heat 7, t = 30 s, 50×
b) Heat 11, t = 300 s, 50×
Fig. 5 Optical micrographs of the slag phase
equilibrium system is not a fundamental property but a reaction of the system and its tendency to go towards equilibrium. Hence, the term “apparent contact angle” is used in the current study for all further discussions.
The change in apparent contact angle as a function of time for the three different graphite grades at rapid heating rate are presented in Fig. 8. In every one of these runs, the specimen was pushed at the same velocity (corresponding to a rate of temperature increase calculated to be 6.6 K/s) into the hot zone of the furnace at 1703 K (1430 °C). It is evident that there are clear differences in the dynamic wetting behavior of these graphite grades. For all of the graphite grades tested, the apparent contact angle decreased linearly with time until approaching equilibrium, corroborating the observation of Israel et al.[20]. Silicon melting on Grade A in Test SD1 started out at a high apparent contact angle and did not attain an equilibrium contact angle until after over 250 seconds; this is expected since this is an isostatically pressed, dense graphite grade with low open porosity. The initial apparent contact angle for Grade C, surprisingly, was quite similar to Grade A grade despite having the highest open porosity since it is an extruded graphite quality. Melting on Grade B (the vibration molded quality), in contrast, started at a low apparent contact angle and was completely wetted in just under 150 seconds, although the initial rate of spreading differed.
Discussion
Importance of Gibbs energy change.
The variation of the contact angle between two phases that are not in equilibrium is well reported and documented.[12-17] The present discussion would not focus on this variation, since this kind of variation is inevitable. It is essential to have an in-depth understanding of the dynamic nature of wetting behavior in order to make this type of measurement useful for the development and optimization of any materials process. Note that the situation described by Young’s law is only valid for systems in thermodynamic equilibrium. In a system under non-
equilibrium conditions, the interfacial tension between liquid silicon and graphite, Si/C, varies with time. Unfortunately, Si/C is not measureable in reality. Exactly as in the case that the activity of a component cannot be defined and measured in a non-equilibrium system, the interfacial tension Si/C term cannot be defined and measured in this system since molten silicon and carbon cannot exist in thermodynamic equilibrium. Actually, the variation of the apparent contact angle is not only a result of the change in Si/C, but also due to the change in the total Gibbs energy between the two states:
Re action
GTot G A
[1]
where GReactionis the Gibbs energy of the reaction to form silicon carbide by graphite and liquid Si, and Ais the interfacial energy term. Hence, a scientific consideration of the dynamic variation in this system (see Fig. 8) should really be based on Eq. [1]. For this reason, the observed contact angle should strictly be called an “apparent contact angle”.
0 50 100 150 200 250 300
5 10 15 20 25 30 35 40 45 50 55
SD7 SD1
50.63 46.92 A B C
Contact Angle [degrees]
Time [s]
0 d/dt Grade
22.19 -0.093 -0.170 -0.185
0.952 0.932 0.986
SD4
r-squared
1 atm Ar 6.6 K/s heating rate
Fig. 8. The contact angle of Si(l) on different graphite substrates as a function of time.
It is expected that the mechanism and rate of the reaction are directly related to the experimental conditions, e.g. in the present case, the type of substrate and the heating history. The variation of the apparent contact angle is in fact a measure of the reaction rate. In order to properly utilize this type of measurement in a proper scientific manner for process optimization, a good understanding of the reaction mechanism including the effects of the substrate properties and the heating history is required. The apparent contact angle or the apparent interfacial energy between a liquid and either solid or another liquid would, no doubt, vary with time if the two phases in contact are not in equilibrium. The variation rate may be high or low depending on the system.
One must be careful when using the value of apparent interfacial energy reported in the literature, since the value is system dependent.
The above discussion does also apply to the system of slag-metal reactions. Note that the interfacial tension between silicon and slag at the initial stages of the experiments (corresponding to Fig 3a, b and Fig.4a, b) cannot be measured as a physical property. Only at the final stage, when the two phases have reached equilibrium, the interfacial tension can be determined. The authors would like to draw people’s attention that the system in Fig. 3a (Fig. 4a ) is not the same as the system shown in Fig.3d (Fig.4d), since the compositions of both phases have changed. It emphasizes again that one should be careful when using the value of interfacial energy reported in the literature. To explain the observation that slag-metal system rapidly generates a very large interfacial area that decreases with reaction time (see Figs. 3-5), the overall driving force, viz. the total change in the Gibbs energy of the system between the initial and the final states is also described by eq. [1]. Considering the chemical reaction involved, the Gibbs energy term
action
GRe
is related to the following reaction,
) ( ) 2 ( ) 1 2 ( ) 1
(s Sil SiO2s Cal
CaO [2]
with
Q RT G G2 2o ln
[3]
Hence, eq. [1] can be rewritten as
A G GTot
2 [1’]
As pointed out in a previous section, the apparent interfacial tension that is observed indeed depends on the total GTotand not only on .
At the initial stages of the process, the two phases are far from equilibrium with respect to calcium, i.e. G2is very negative, and therefore it is the dominating term in Eq. [1’]. The extremely low apparent interfacial tension would result in a large interfacial area between slag and silicon, facilitating emulsion formation. As the two phases approach chemical equilibrium (G2 approaches zero), the second term, A in Eq. [1’] becomes increasingly important. To reach the minimum Gibbs energy level, the system would prefer a minimum interfacial area at the latter stage of the process, which explains the drastic decrease in the interfacial area as equilibrium is approached.
Mechanical agitation inputs kinetic energy into the system and therefore facilitating the break-up and dispersion of metal droplets into the slag phase. At this point where theG2has almost reached zero, with 100 rpm mixing speed, there is not enough energy imparted to the melt to
maintain the slag–metal emulsion, and the metal phase re- coalesces. It is strongly felt that a process optimization concerning the slag-metal interfacial phenomena would be unrealistic when the chemical potential is excluded in the consideration and only the interfacial tension is highlighted. In metallurgical and material processes, chemical reactions always take place at the interface, e.g. in the present case: slag-silicon or silicon-graphite. Overlooking of the chemical reaction and too much emphasis on interfacial tension would mislead the modelling and optimization of the process.
Although the variation of the contact angle with time has been well known, in process modelling and process optimization the foremost importance has always been given to the interfacial energy. In the consideration of the interfacial phenomena, the
Gibbs energy term in eq.[1] is very often overlooked. As seen in the case of both slag-metal reaction and silicon-graphite reaction, the apparent interfacial energy is in fact a function of the kinetic conditions. While the contact angle (interfacial energy) could be somehow followed dynamically, the contribution of the Gibbs energy term can very often be dominating in the dynamically followed apparent interfacial energy. This dominating behavior has been evidently seen in the initial stages (before 90 s) of the slag-metal reaction.
As a matter of fact, in the case of study of both slag entrainment into liquid steel forming inclusions and inclusion separation to the slag phase, almost all the models have neglected the Gibbs energy term in eq. [1].
Possibility of slag entrainment into liquid steel Formation of inclusion by slag entrainment has been discussed by many researchers. The mechanism of droplet formation is illustrated in Fig. 9, which is reproduced from the publication by Krishnapisharody and Irons[21]. The authors came to the conclusion that the momentum of interfacial shear was not significant for emulsification of oil but it is rather triggered by Kelvin-Helmholtz instability when two stratified fluids are in relative motion. One important fact is that the phenomenon illustrated in the above figure is evidence for the formation of slag droplets. On the other hand, the size of the droplets formed in this manner has so far been at the millimeter scale. No evidence has so far been reported for the formation of slag droplets less than 20-30 µm, which are the potential source of inclusions. To form certain amount of inclusions in this size range and even smaller would need a considerably large amount of energy.
No real quantitative model has so far been developed to describe the slag-metal emulsification. A simple model based on energy balance was suggested by Wu in his PhD thesis.[22] As seen in Fig. 10, interfacial tension has a great impact on droplet size. The influence of gas flow rate on droplet size is obvious when interfacial tension between slag and liquid metal is big. Otherwise, the effect is weak. It is seen that droplets smaller than 50µm can only form when the interfacial
Fig. 10 Model predictions for droplet sizes at different conditions (Reproduced from Ref. [22])
Fig.9 Detachment of emulsified droplet in an oil- water model (Reproduced from Ref.[21])
tension is low, e.g. 0.1 N/m. On the other hand, droplets formed with higher interfacial tensions, e.g. 0.7 N/m are usually bigger than 0.2 mm, which would float up easily. These bigger droplets would not form inclusions.
Note that as discussed earlier in the present work, the slag- metal reaction at the initial stages of the ladle treatment would dramatically lower the apparent interfacial tension between slag and metal. It could be lower than 0.1 N/m, though the equilibrium interfacial tension is usually between 0.5 and 1 N/m. The variation of apparent interfacial tension along the process would offer us an opportunity for process optimization regarding inclusion entrainment and inclusion removal.
To verify the results from the laboratory study, three samples of slag-metal interface taken around the open-eye in the gas stirred ladle at Uddeholm Tooling (currently Uddeholm AB) were investigated to evaluate the presence of slag entrainment in the steel.[23-25]
Fig. 11 illustrates this aspect clearly. Fig.11a presents a photograph of an opened sample showing slag-metal interface in the case of gas-stirring mode, while Fig. 11b presents the LOM photograph of the steel sample in contact with the slag (magnification – 50 X). The results strongly suggest further systematic study is needed for an in-depth understanding of slag-metal interface in the ladle treatment.
Fig.12 presents series of photomicrographs taken from the three samples, respectively. While the first picture in each series shows the surface of the steel in contact with slag, the lowest picture shows the steel part about 20 mm from the slag-metal interface. Note that almost all the dot spots are pores. No visible amount of slag is observed in any of the three samples. The results are in very good accordance with the semi empirical model suggested by Wu in his PhD thesis.[22]
Note that these sample were taken when the slag was almost in equilibrium with the liquid metal.
The situation could be very different when the top slag has just been added to ladle (the slag and steel are far from equilibrium at this stage). In this stage, the Gibbs energy term in eq.[1] might play great role in determining the slag-metal interface, the entrainment of slag and even the removal of inclusions. It is strongly felt that an optimization of the ladle process considering the
Fig.12 Series of photomicrographs taken from the three samples
(a)
(b)
Fig.11 (a) slag‐metal interface in the case of gas‐stirring mode,[23] (b) LOM photograph of the steel sample in contact with the slag [25]
function of Gibbs energy term in eq.[1] in determining the slag-metal interface would be essential with respect to slag-metal reaction and steel cleanness. The present work would function as a starting point to initiate a discussion about the importance of Gibbs energy change in determining the behavior of interface. It is hoped that this discussion would lead to better process models.
Conclusion
The interface between liquid silicon and CaO-SiO2 slag and the interfacial reaction between silicon and graphite were studied experimentally. The results revealed evidently that the chemical driving force could play dominating role in determining the interface, while the interfacial tension would only become important when the slag and metal were reaching equilibrium.
In the case where the two phases are not in thermodynamic equilibrium, it is impossible to measure the interfacial tension. This is similar as the situation where equilibrium chemical potential cannot be determined in a non-equilibrium system. The apparent interfacial tension measured is in fact a kinetic parameter that depends greatly on the experimental conditions, but not a physical property of the system. The measured values cannot be used to other experimental conditions.
The possibility of the entrainment of ladle slag as a source of nonmetallic inclusions was also evaluated on the basis of the above findings. The present study would like to draw researchers’
attention regarding the important role of Gibbs energy of the reaction in the interfacial phenomena. The study would also raise a question whether the interfacial tension determined at equilibrium condition can be applied to a non-equilibrium system.
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