Dephosphorization Kinetics of Bloated Metal Droplets Reacting with Basic Slag Containing TiO₂

Abstract

Although the dephosphorization kinetics of bloated metal droplets reacting with oxidizing slag have been studied in detail in the authors’ laboratory, the mechanism of reaction for slags in a basicity range typical of steelmaking, has been sparsely reported. The current study employed a high temperature furnace equipped with X-ray fluoroscopy to observe the bloating behavior of droplets and tracked dephosphorization kinetics by quenching and analyzing droplets after different reaction times. The mechanism of reaction between bloated metal droplets and slag was studied at 1923 K for slags with basicity range C/S=2.56. The rate and extent of dephosphorization was found to be greater in CMS slags compared to CAS slags due to the faster mass transport and a larger thermodynamic driving force. The kinetic analysis showed that the reaction proceeded in two distinct stages, a fast initial stage followed by a slower stage. The k_m during the first stage of dephosphorization was at least 8 times higher than that during the second stage. This is proposed to be due to a higher internal CO generation rate during the initial stage which increases the rate of surface renewal. The effect of TiO₂ on dephosphorization kinetics was also investigated in terms of thermodynamic driving force.

1. Introduction

Dephosphorization is a key refining reaction in the Basic Oxygen Steelmaking (BOS) process. The reaction partially occurs in the emulsion zone where bloated metal droplets offer a large contact area with slag. The dephosphorization mechanism in the emulsion is complex and linked to decarburization of metal droplets in different ways. CO formation inside the droplet results in droplet bloating, which increases the rate of dephosphorization by increasing droplet residence time in the emulsion.^1,2,3,4,5) On the other hand, decarburization suppresses dephosphorization by consuming available oxygen, thereby lowering the interfacial oxygen potential^{6,7,8,9,10,11)} and the thermodynamic driving force for dephosphorization. The formation of CO bubbles can also enhance the mass transport of phosphorus in metal droplet due to its stirring effect offering a fast surface renewal rate.^12,13)

Several studies have been conducted on dephosphorization kinetics between liquid Fe–C alloys and oxidizing slag.^{7,8,9,10,11,14,15)} However, the experimental conditions in these studies are either at hot metal pretreatment temperatures or use a low basicity slag, neither of which is representative of the BOS process. Manning and Fruehan¹⁶⁾ investigated dephosphorization using basic EAF slags and found that the mass transfer parameter (kA) decreased as the reaction proceeded caused by a change in interfacial area with time due to the capillary effect of the reaction; early in the reaction the oxygen flux was high causing an increase in the interfacial area, as the reaction rate subsided, the area decreased. Dephosphorization kinetics of bloated metal droplets have been investigated under a wide range of experimental conditions by some of the current authors.^11,13,17,18) However, these studies were confined to low basicity slag (mass%CaO/mass%SiO₂=0.9) in the CaO–SiO₂–Al₂O₃–FeO (CAS) system and not the higher basicity slags typically used in the BOS process. In this study, a higher basicity slag (mass%CaO/mass%SiO₂=2.56) in the CaO–SiO₂–MgO–FeO (CMS) system, which is more representative of that used in a BOS vessel, was employed to elucidate the dephosphorization kinetics of bloated metal droplets.

No data has been found in the literature that deals with the effects of TiO₂ on dephosphorization kinetics of liquid Fe–C alloys. The most relevant studies are focused on the effects of TiO₂ on slag properties including viscosity and the phosphorus solubility in 2CaO·SiO₂–3CaO·P₂O₅ solid solution.^{19,20,21,22,23,24,25,26)} Therefore, a further aim of this study was to address this knowledge gap by conducting bloated metal droplet kinetic experiments with slags containing TiO₂.

2. Experimental

2.1. Experimental Setup

A resistance heated vertical tube furnace (Fig. 1) with an 80 mm ID alumina tube was used. The furnace was equipped with X-ray imaging to observe the bloating of droplets in-situ. The pressure change inside the sealed chamber caused by gas evolution was instantaneously measured using a differential pressure transducer. The pressure transducer was calibrated immediately before each experiment by introducing a fixed volume of argon gas into the furnace.

Fig. 1.

Schematic diagram of the furnace.

2.2. Materials Preparation

The details of materials preparation and experimental procedure, identical to those used in previous work by the authors,^11,13,18) are only described shortly here for the convenience of the reader. The Fe–C–P–S droplets were prepared by melting an appropriate quantity of electrolytic iron 99.9% pure, FeP and FeS with graphite (99.999%) in a vacuum arc melter under argon atmosphere of 50.66 kPa. The oxygen content in droplets fabricated in this manner was 50±20 ppm.²⁷⁾ The final droplet composition was confirmed by using ICP-OES and LECO C–S analyzer to be Fe-2.51±0.077 mass% C-0.072±0.005 mass% P-0.007±0.0008 mass% S.

The reagent grade oxides were heated separately to remove absorbed moisture and CO₂, and were added to FeO together to achieve the desired slag composition, which were mixed in a ball mill for 12 hours then used directly for all experiments without pre-melting. The slag composition was measured after each experiment using ICP. The average measured compositions with standard error are given in Table 1. Beside ICP measurements, the authors have also analyzed post reaction samples using XRF fused bead technique, which results show that there is not any significant change in slag composition during the experiment except a minor change in the FeO content, which is expected because of decarburization.²⁸⁾

Table 1. Final slag composition (mass%).

	CaO	SiO2	MgO	FeO	TiO2
Base slag	50.5±0.85	19.6±0.66	6.0±0.83	24.0±1.19
Slag with 5 mass% TiO2	48.0±0.64	18.6±0.37	5.7±0.37	22.8±0.70	5.0±0.58
Slag with 10 mass% TiO2	45.5±1.67	17.6±0.80	5.4±2.41	21.6±0.78	10.0±0.29

2.3. Experimental Procedure

A slag of 25±0.5 g was placed in MgO crucible (44.5 mm ID) located in the hot zone of the furnace and was melted under an argon atmosphere, which was passed through a gas purifying system consisting of columns filled with anhydrous CaSO₄ (drierite) and copper turning furnace. After homogenizing the slag, a 1.0±0.05 g droplet held by a magnet at the top of the furnace, was released by removing the magnet, then fell into the slag via a small hole at the bottom of the alumina tube. The hole in the tube was sized to ensure the droplet was molten prior to passing through. The rod used to support the MgO crucible was held in place by an O-ring and a collar at the base of the furnace. By releasing the collar, the crucible could be dropped into the water-cooling chamber within 1 s. Time zero was defined as the time when the droplet was observed by X-ray to fall into the slag. Samples were quenched at different reaction times and analyzed for phosphorus to track the transient behavior of dephosphorization.

3. Experimental Results

3.1. Droplet Decarburization for Slag with Different TiO₂ Content

Figure 2(a) shows the total CO gas generated for droplets reacting with CMS and CMS-TiO₂ slags as a function of time. In order to make a comparison, the CO gas generation for similar droplets(Fe-2.62 mass% C-0.088 mass% P-0.007 mass% S) reacting with a CAS slag (32 mass% CaO-35 mass% SiO₂-17 mass% Al₂O₃-16 mass% FeO) from the authors’ previous work¹³⁾ is presented in Fig. 2(b). Figure 2(c) reproduced from the authors’ previous study¹¹⁾ was used to demonstrate the decarburization behavior of droplets observed in Figs. 2(a) and 2(b). The figure shows that droplet decarburization can be separated into three sequential stages. Stage I is a slower initial period corresponding to the incubation period for droplet swelling, which is only observed for the case of CAS slag. During Stage II, droplets swell and float up to the foaming slag because of the high CO evolution rate. This is the peak or primary decarburization rate. Stage III is initiated when the fast decarburization subsides, droplets sink back to the dense slag with a lower secondary CO evolution rate. The initial rate is thought to represent a period of mixed internal and external decarburization,^11,13) while the peak rate represents the internal nucleation and growth of CO bubbles. From Fig. 2(a), it can be seen that droplet decarburization follows a continuous curve with an initial rate which is extremely rapid trailing off with time. Examination of droplets using X-ray fluoroscopy shows that the reaction follows two distinct stages. In the initial rapid decarburization stage the droplet starts swelling due to internal CO evolution. Subsequently as the rate slows the droplet floats in the foamy slag then shrinks after a few seconds. Most of the gas appears to nucleate on the external surface once the droplet sinks back into dense slag. Comparing the CMS slags (Fig. 2(a)) with that of the CAS slag (Fig. 2(b)) it can be seen that the initial and peak decarburization rate are slower for the case of CAS slag. In fact, no slower initial decarburization rate is observed for the case of CMS slag. Figure 2 also shows that the decarburization rate for CMS slag is an order of magnitude greater than that of the CAS slag. This greater rate is thought to be due to the greater slag basicity increasing the rate of oxygen transfer to the droplet. The higher decarburization rates in the CMS slags are expected to lead to increased bloating of the metal droplet. In this paper, the change of [C] during reaction was extracted from the pressure transducer results by assuming all the gas formed is CO. This approach was also employed in the authors’ previous studies^11,13,17,18) and showed a good agreement with the LECO results for carbon analysis on post reaction samples (±10 mass% of [C]).

Fig. 2.

Decarburization behavior of droplets with 0.007 mass% S: CO gas generation with time for (a) CMS slag with different content of TiO₂ at 1923 K, (b) CAS slag at 1913 K and (c) Schematic diagram of droplet behavior in terms of CO generation as a function of time Reproduced from Ref. 11), with permission of Springer Nature, 2020. (Online version in color.)

3.2. Droplet Swelling Behavior for Slags with Different TiO₂ Content

Based on X-ray videos, the change in the volume of droplets was determined as a function of time and presented in Fig. 3 for droplets reacting with CMS slag containing different TiO₂ content. No incubation time was observed for droplet bloating using this slag, i.e., droplets swell immediately on entering the slag. It further shows that the maximum volume of bloated droplets increases with increasing TiO₂ content. For comparison, the swelling behavior of droplets using CAS slag¹³⁾ is also presented in Fig. 3. In this case there is a short incubation period before the droplet bloats. This corresponds to the slower initial decarburization period shown in Fig. 2(b). This incubation period represents the time for the oxygen concentration in the droplet to build up and the internal nucleation of CO to become fully established.^11,29) Typically droplets do not bloat until the onset of the more rapid period of internal CO nucleation therefore this initial period has been referred to in the authors’ previous work^11,13) as an incubation period. As shown in Fig. 3, the maximum volume of bloated droplets reacting with CAS slag is almost 3 times that of the droplet reacting with CMS slag containing 10 mass% TiO₂. This observation appears to contradict the results shown in Fig. 2, where the peak decarburization rate for CMS slag is several times higher than for CAS slag. The faster rate could reasonably be expected to increase the maximum volume of bloated droplets. This observation is only possible if the CO bubble escape rate is also much higher for CMS slag. Chen²⁹⁾ investigated the decarburization of 1.0 g Fe-2.87 mass% C-0.01 mass% S droplets reacting with a slag of 31.6 mass% CaO-26.4 mass% SiO₂-12 mass% MgO-30 mass% FeO at 1873 K. The droplet bloating behavior as a function of time observed by Chen²⁹⁾ is also included in Fig. 3. It shows that the maximum volume of bloated droplets observed by Chen²⁹⁾ is higher than that for the base slag but much lower compared to droplets reacting with CAS slag. This may in part be attributed to variations in the slag basicity and viscosity. Several studies^29,30) have shown that while increasing FeO content in the slag has a major effect on droplet decarburization up to about 20 mass% it makes little difference thereafter. Therefore, the authors propose the much faster rate observed in the current work to be caused by other factors. The most likely of these factors responsible for a faster rate would appear to be decreased viscosity.

Fig. 3.

The bloating behavior of droplets under different conditions. (Online version in color.)

3.3. Droplet Dephosphorization for Slag with Different TiO₂ Content

The change of [P] as a function of time and TiO₂ content is shown in Figs. 4(a) to 4(c). Also shown in this figure are selected X-ray images of droplets during the reaction. Here, the X axes in Figs. 4(a) to 4(c) have breaks between 6 or 7 s and 15 s where those data were not illustrated in order to clearly demonstrate the difference of droplet dephosphorization during main bloating period (from 1 to 6 s) for each case but at the same time showing the whole picture of the reaction. From Figs. 4(a) to 4(c) it can be seen that once the metal droplet falls into the slag, it starts bloating immediately. Although the digital stills are not clear, the recorded video clearly shows a vigorous gas (CO) generation within the droplet. This bloating/gas generation corresponds to the peak decarburization stage shown in Fig. 2(a). Figures 4(a) to 4(c) also show that the effect of TiO₂ content on droplet dephosphorization is small and the dephosphorization behavior is similar in each case. The [P] in droplet is initially removed rapidly, dropping from 0.072 mass% to less than 0.002 mass% within 1 s and thereafter gradually decreasing. This two-stage dephosphorization behavior of bloated droplets is the result of their decarburization behavior shown in Fig. 2(a). For comparison, the dephosphorization behavior of droplets reacting with CAS slag from the previous study¹¹⁾ is also present in Fig. 4(d) where droplet exhibits a significant phosphorus reversion. In this case, droplets are initially dephosphorized in dense slag and subsequently experience phosphorus reversion in foamy slag due to the sudden increase of decarburization rate and the depletion of FeO from the relatively small liquid volume in the foam. The following renewed dephosphorization is due to the higher FeO in dense slag and the slower decarburization rate, which combine to offer an increase in interfacial oxygen potential. A great detailed explanation on this complicated droplet dephosphorization behavior appeared in Fig. 4(d) can be found in the authors’ previous studies.^11,13,17,18) Unlike the dephosphorization behavior of droplets reacting with CAS slag, the data presented in Figs. 4(a) to 4(c) do not show phosphorus reversion. This observation is likely explained by the high basicity slag employed, which offers a high phosphate capacity resulting in a high partition ratio.

Fig. 4.

Dephosphorization of bloated droplet as a function of time at 1923 K: (a) base slag, (b) slag with 5 mass% TiO₂, (c) slag with 10 mass% TiO₂ and (d) CAS slag at 1853 K Reproduced from Ref. 11), with permission of Springer Nature, 2020. (Online version in color.)

4. Discussion

4.1. Swelling Behavior of Droplets as a Function of Slag Viscosity

In order to investigate the effect of slag viscosity on droplet swelling, the maximum volume of droplets shown in Fig. 3 for various slags were plotted against slag viscosity (ln η) as shown in Fig. 5. Here, Factsage was used to calculate all viscosities used in this paper with the exception of additional data added to Fig. 5 at which the droplet maximum volume was also plotted against viscosity calculated by the Riboub model³¹⁾ for comparison. Decarburization rates for droplets reacting with those slags are listed in Table 2. Here, the secondary decarburization rates listed in Table 2 for the three cases in this study shown in Fig. 2(a), were defined by the slope of CO gas versus time curve after the peak decarburization period. The starting point of period was chosen as the point where the three CO gas curves begin to separate approximately after 1 s as shown in Fig. 2(a). The period of secondary decarburization was enlarged and shown in the small graph embedded in Fig. 2(a). According to the recorded X-ray videos, droplets were swelling and partially floating in foamy slag during the period of secondary decarburization (occurred between 1 and 4 s). After that, metal droplets completely sank back into dense slag and owned relatively lower but similar decarburization rate. The definition of secondary decarburization period was somewhat different from that for the case of CAS slag where it was mostly corresponding to the period when droplets sank back into dense slag.

Fig. 5.

The effect of slag viscosity on the maximum bloated droplet volume.

Table 2. Decarburization rate of metal droplets reacted with different slags.

	Peak DeC. rate×105 (mole/s)	Secondary DeC. rate×105 (mole/s)
This study-base slag	87.17	13.69
This study-slag with 5 mass% TiO2	87.17	25.94
This study- slag with 10 mass% TiO2	87.17	31.15
Chen-CMS slag	39.54
Gu et al.-CAS slag	8.72

Figure 5 shows that the maximum volume of bloated droplets is a linear function of ln η, i.e., it increases with increasing slag viscosity. Although the Riboud model produces different viscosity values from those calculated using Factsage, the trend in relation to the current slags and their effect on the maximum volume of bloated droplets was the same. Therefore, it appears that the maximum volume of bloated droplets increases with the logarithm of slag viscosity. Table 2 shows that the maximum volume of bloated droplets decreases with increasing peak decarburization rate. This observation appears to contradict the previous work,²⁹⁾ which demonstrates that the maximum volume of metal droplet increases with increasing CO generation rate for a fixed slag composition. However, the droplet bloating rate is determined by the balance between CO generation rate and CO escape rate. Thus, the swelling rate of bloated droplet is also strongly dependent on the CO escape rate, which in turn is affected by CO generation rate and viscosity of liquid metal. Both the higher CO generation rate and lower viscosity of liquid metal should lead to a higher CO escape rate. The trend shown in Fig. 5 might be related to the effect of slag viscosity on decarburization behavior of metal droplet. In current cases, the lower viscosity slag would lead to a higher decarburization rate due to the faster transport of iron oxide. This would in turn offer a higher oxygen potential at the slag/metal interface, which would likely reduce the surface tension of the metal droplet, favoring the escape of CO bubbles. This would indicate that the primary effect of lower slag viscosity in increasing CO escape rate is the effect of oxygen potential on surface tension.

4.2. The Effect of TiO₂ Content on Decarburization Rate

According to the oxygen mass balance equation written as Eq. (5) in this section, it is obvious from a strictly mathematical point of view that increasing any one of several terms would increase the rate and we do know that the area increased with the addition of TiO₂ from Fig. 3. However, the cause of the increasing area in the case of bloated droplets is always an increase in the volume of CO gas retained in droplet which typically results from an increase in CO generation rate so the increase in area is an effect rather than a cause. Therefore, the increase in droplet area (A) would be essentially related to the increase of secondary decarburization rate, which occurs with the addition of TiO₂. To explore the potential “Titania effect” on droplet decarburization rate, the analysis of ionic/electronic conductivity was carried out in the following section.

Table 2 shows that the decarburization rates for droplets reacting with TiO₂ bearing slag during the second stage are higher than that for the base slag. This observation is likely the result of faster oxygen transport due to the presence of TiO₂. Titanium in the slag may exist in different valence states, depending on the oxygen potential, slag composition and temperature. Under a certain oxygen potential, the following redox reaction³²⁾ would occur introducing the Ti³⁺/Ti⁴⁺ pair into the slag. Furthermore, it has been suggested that the reduction of Ti⁴⁺ to Ti³⁺ can favor the transportation of oxygen anions, O²⁻.^28,33,34)   

$$Ti{O}_2\left(s\right)=Ti{O}_{1.5}\left(s\right)+1/4O_2\left(g\right)$$(1)

  

$$\mathrm{\Delta }{G}^o=189\mathrm{\hspace{0.17em} }954-48.5T\mathrm{\hspace{0.17em} } \left(J/mol\right)$$(2)

The oxygen in the slag is transported in the form of either O²⁻ or singly charged oxygen species hopping from site to site on silicate chains. Therefore, it is worth exploring whether the Ti³⁺/Ti⁴⁺ pair could enhance oxygen transport in the slag via an electron hopping mechanism similar to that seen with the Fe²⁺/Fe³⁺ pair.^{35,36,37,38,39)} In this study where the CMS–FeO–TiO₂ slag was employed, sufficient reduction of Ti⁴⁺ to Ti³⁺ might occur to allow the hopping mechanism to operate at least close to the slag/metal interface. As the oxygen potential decreases, the ratio of Ti³⁺/Ti⁴⁺ in the slag will rise. In this study when the metal droplet first fell into slag, oxygen in the slag would be depleted locally due to the drastic decarburization as shown in Fig. 2(a), which would significantly alter the ratios of Ti³⁺/Ti⁴⁺ and Fe²⁺/Fe³⁺ pairs in the vicinity of slag/metal interface according to the following “coupling” reaction.   

$$Ti{O}_2+FeO=Ti{O}_{1.5}\left(s\right)+Fe{O}_{1.5}$$(3)

The interfacial oxygen potential in Table 4 calculated according to Eq. (5) is the direct result of this vigorous decarburization behavior. Tranell et al.⁴⁰⁾ found that the correlation between oxygen potential and the ratio of Ti³⁺/Ti⁴⁺ can be closely predicted by Eq. (4). This equation is used here to estimate the ratio of Ti³⁺/Ti⁴⁺ for slags containing TiO₂,   

$$log\frac{X_{T{i}^{3+}}}{X_{T{i}^{4+}}}=-\frac{\mathrm{\Delta }{H}^o}{2.3RT}-log\frac{{\gamma }_{Ti{O}_{1.5}}}{{\gamma }_{Ti{O}_2}}+\frac{\mathrm{\Delta }{S}^o}{2.3R}-0.25log{P}_{O_2}$$(4)

where X represents the cation fraction of mobile ions, ΔH^o and ΔS^o are the standard enthalpy and entropy for reaction (1) respectively. γ_i is the activity coefficient of species i in the slag, $P_{O_2}$ is the oxygen partial pressure in equilibrium with the slag and R is the gas constant.

Table 4. Calculated ionic/electronic conductivity for different slags.

TiO2 (mass%)	$log{P}_{O_2}^i$ (atm)	$\frac{X_{F{e}^{3+}}}{X_{F{e}^{2+}}}$	$\frac{X_{T{i}^{3+}}}{X_{T{i}^{4+}}}$	Total ionic conductivity (S/cm)	electronic conductivity attributed to Fe3+/Fe2+ (S/cm)	electronic conductivity attributed to Ti4+/Ti3+ (S/cm)
0	−10.73	0.065		2.674	0.152
5	−9.83	0.098	0.031	2.634	0.191	0.002
10	−9.50	0.114	0.026	2.599	0.190	0.008

The oxygen potential at the slag/droplet interface was calculated by balancing the oxygen supply from FeO in the slag and oxygen consumption by carbon in the metal via Eq. (5).   

$$k_{FeO}\left(C_{FeO}^b-C_{FeO}^i\right)=\frac{1}{A}\frac{d{n}_{CO}}{dt}$$(5)

Here, $\frac{d{n}_{CO}}{dt}$ is the decarburization rate (mole/s), C_FeO is the concentration of FeO (mol/cm³), A is the surface area of droplet (cm²), k_FeO describes oxygen transport in the slag conceptually defined as the mass transfer coefficient for FeO (cm/s). $C_{FeO}^i$ may be expressed in terms of oxygen activity at the interface, and the concentration of FeO in the bulk slag, $C_{FeO}^b$, may be expressed as a function of the initial concentration of FeO modified by the amount reduced (dn_FeO). A more detailed derivation and substitution of Eq. (5) can be found in the authors’ previous studies.^11,13,17)

According to Eq. (5), the interfacial oxygen potential can be calculated if one knows k_FeO in the slag, and vice versa. In the previous work,¹⁷⁾ the authors found that k_FeO was a function of iron oxide content in slag. The correlation was employed in this study to calculate k_FeO for slags with different TiO₂ content. These values are listed in Table 3. Using Eq. (5), k_FeO in the dense CAS slag was calculated to be 1.0×10⁻² cm/s at 1853 K in the authors’ previous study.¹⁷⁾ With the value of k_FeO for CAS slag, k_FeO for slag containing different TiO₂ content can be estimated by using Eq. (6), which is a consequence of either the Stokes-Einstein or the Eyring equation (Eq. (7)) combined with Higbie’s penetration theory,⁴¹⁾   

$$k_s\propto {\left(\frac{T}{\eta }\right)}^{1/2}$$(6)

  

$$D\propto \frac{T}{\eta }$$(7)

where D is the diffusivity of species in liquid slag (m²/s), η is the viscosity of slag (Pa·s), k_s represents the mass transfer coefficient in slag (cm/s) and T is the temperature (K).

Table 3. Calculated k_FeO for TiO₂ bearing slag.

TiO2 (mass%)	η(pa·s) from Factsage Calc.	kFeO × 102 (cm/s) based on function of iron oxide	kFeO × 102 (cm/s) based on Eqs. (6)–(7)	Droplet surface area (cm2) at 1 second
0	0.027	5.04	2.39	2.08
5	0.029	4.43	2.31	3.05
10	0.03	3.90	2.27	4.11

Table 3 shows that k_FeO for CMS slag calculated using the previously developed empirical correlation is at least 4 times higher than that for CAS slag, whereas k_FeO based on Eqs. (6)–(7) is only approximately 2 times higher. This result is expected if one considers the distinct influence of iron oxide and basicity on both ionic/electronic conductivity in the slag; and the fact that k_FeO increases with increasing total electrical conductivity as demonstrated in previous work by the authors.⁴²⁾ This observation is to some extent consistent with experimental results found in the study of Barati and Coley⁴³⁾ where the total electrical conductivity increased at least by a factor of 3 as basicity increased from 0.5 to 2.0 under similar oxygen potentials to those seen in the current work. In this study and a previous one¹⁷⁾ the authors expressed oxygen transfer conceptually as mass transport of FeO which is common throughout the literature. However, it is more realistic to consider that oxygen is in abundance throughout the slag and its “transport” merely requires the charge transport for supporting its release. Under this transfer mechanism, one would expect a higher value of “k_FeO” than k_s predicted by Eqs. (6) and (7) that describe the transport of other species in the slag. This is also the most likely the reason that the reported values in the literature^9,30,44,45) of k_FeO for high iron oxide/basic slag were up to the order of 10⁻² cm/s. Knowing the k_FeO calculated from the correlation developed in the author’s previous study¹⁷⁾ based on experimental data, the interfacial oxygen potential for all three cases after the peak decarburization period, was calculated based on Eq. (5) and presented in Table 4. The calculated $P_{O2}^i$ for slags containing TiO₂ is higher than for those without TiO₂, mainly due to the different reaction behavior with droplets as shown in Figs. 3 and 4. Metal droplets reacting with TiO₂ bearing slag have higher surface area thereby lowering the balance term of $\frac{1}{A}\frac{1}{k_{FeO}}\frac{d{n}_{CO}}{dt}$ in Eq. (5). By assuming the droplets are spherical the reader can see the changing surface area of bloated droplets at any given time in Fig. 3 where the dynamic volume of droplets, measured based on X-ray videos is presented as a function of reaction. Here, for the convenience of the reader, the surface areas of droplets at 1 s reaction time, i.e., after the primary decarburization period is over, were listed in Table 3.

Using the diffusion-assisted charge transfer model for electronic conduction in the slag,³⁵⁾ the electronic conductivities for different slags in this study were calculated and listed in Table 4. Full details of the model can be found elsewhere.³⁵⁾ The method for calculating Fe³⁺/Fe²⁺ ratio of iron silicate slags at a given oxygen potential and temperature was proposed in that work³⁵⁾ as well by summarizing data reported in literature. The Ti³⁺/Ti⁴⁺ ratio for slag containing TiO₂ in this study was calculated based on Eq. (4). In the equation, the ratio of ${\gamma }_{Ti{O}_{1.5}}$/${\gamma }_{Ti{O}_2}$ was extrapolated from the study of Tranell et al.³⁹⁾ who investigated the effect of basicity (mass%CaO/mass%SiO₂) ranging from 0.55 to 1.25, on the ratio of activity coefficients of titanium oxides. Tranell et al. also demonstrated that the ratio of ${\gamma }_{Ti{O}_{1.5}}$/${\gamma }_{Ti{O}_2}$ is independent of the titanium oxidation state when the mole fraction of TiO_1.5 is greater than 0.02. Using Eq. (7), values of $D_{Ca}^{2+}$, $D_{Fe}^{2+}$ and $D_{Ti}^{3+}$ in the slag are calculated based on reported values,^35,46) which are measured under the different experimental temperature and slag composition from this study. Here, the ionic/electronic conductivity in slag contributed from iron oxide and titanium oxide was calculated separately.

The data in Table 4 show that the total electronic conductivity contributed from Fe²⁺/Fe³⁺ and Ti³⁺/Ti⁴⁺ pairs increases as decarburization proceeds due to the decreasing of $P_{O2}^i$, which favors the reduction of Ti⁴⁺ to Ti³⁺ and promotes the oxidation of Fe²⁺ to Fe³⁺. However, the electronic conductivity contributed from Ti³⁺/Ti⁴⁺ pair is very limited, and even the total electronic conductivity is more than an order of magnitude lower than the ionic contribution. This indicates that in the current work, with basic slags, the ionic component of conductivity is much higher and is likely to play the greater role in charge balancing.

Using a four-electrode technique, Liu et al.³⁹⁾ measured the electronic and ionic conduction properties of TiO_x–CaO–SiO₂ at various oxygen potentials. Their study showed that the electronic conductivity for slag containing 7.5 mass% TiO₂ at 1843 K was around 0.154 S/cm under a similar oxygen potential to that listed in Table 4. Even if it is assumed that the electronic conductivity is similar to that measured by Liu et al.³⁹⁾ and therefore the contribution of the titanium couple becomes similar in magnitude to that of iron, the electronic contribution still remains relatively insignificant under the conditions prevailing here. Therefore, it seems unlikely that the “Titania effect” on the secondary decarburization behavior is related to electronic conductivity. The authors currently are not able to offer a definitive explanation for the higher secondary decarburization rate for slags containing TiO₂. A more detailed investigation is required to understand the Titania effect on oxygen transport in the basic slag.

4.3. Dephosphorization of Bloated Droplet as a Function of TiO₂ Content

TiO₂ behaves as an acidic oxide in basic slags, thus according to the calculated results from Factsage and Riboub model,³¹⁾ the slag viscosity increases with increasing TiO₂ content and is expected to decrease the phosphate capacity $C_{P{O}_4^{3-}}$ as shown in the author’s work.⁴⁷⁾ By reviewing relevant literature, some of the current authors⁴⁷⁾ developed the following correlation to calculate the $C_{P{O}_4^{3-}}$ for TiO₂ bearing BOS slags.   

$$\begin{array}{l}log{C}_{P{O}_4^{3-}}=\frac{46\mathrm{\hspace{0.17em} }141}{T}+0.020\left(CaO\right)-0.010\left(MnO\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-0.077\left(P_2{O}_5\right)-0.102\left(Si{O}_2\right)- 0.059\left(F{e}_{t}O\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-0.040\left(MnO\right)-0.084\left(A{l}_2{O}_3\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-0.079\left(Ti{O}_2\right)\mathrm{\hspace{0.17em} } 0.080\left(V_2{O}_5\right)-3.475\end{array}$$(8)

All components in Eq. (8) are in mass%. The phosphorus partition ratio (L_P) was then calculated using Eq. (9), assuming the oxygen potential is determined by Fe–FeO equilibrium. It is not unreasonable to assume that the oxygen potential was determined by Fe–FeO equilibrium in this case based on the recorded X-ray videos at which the droplet decarburization after 5 minutes of reaction was believed to be in a negligible magnitude if not completely ceased. Furthermore, according to Fig. 2(a), the decarburization rate dropped dramatically and was as low as the order of magnitude of 10⁻⁶ mole/s after only one minute of reaction, which would hardly cause any significant reduction on FeO content where it was higher than 20 mass% in the slag.   

$$L_P=\frac{C_{P{O}_4^{3-}}{P}_{O_2}^{5/4}{f}_P{M}_P}{K_P{M}_{P{O}_4^{3-}}}$$(9)

where K_P is the equilibrium constant for phosphorus gas in equilibrium with phosphorus in liquid iron, f_P is the Henrian activity coefficient for [P], and M_i is the molecular weight in g/mol and $P_{O_2}$ is oxygen partial pressure in atm.

In this study, the longest reaction between a metal droplet and slag was 5 minutes at which time the decarburization was approaching completion. Therefore, the content of phosphorus in metal and slag with unit of mass% after 5 minutes of reaction was used to calculate the maximum L_P according to Eq. (10),   

$$L_P=\frac{\left(\%P\right)e}{\left[\%P\right]e}=\frac{\left(\%P\right)max.}{\left[\%P\right]min.}$$(10)

The calculated L_P based on Eqs. (9) and (10) were presented in Fig. 6 to demonstrate the influence of TiO₂ on dephosphorization. This figure shows that both predicted and experimental L_P decrease with increasing TiO₂ content. However, the measured values are more than two orders of magnitude lower than predicted ones. This much lower measured L_P is just because of the difficulty in measuring the equilibrium value in this case which is further evidenced by the good fit of the theoretical value in the kinetic plots shown in Fig. 7(a). In addition, the authors⁴⁷⁾ conducted slag/steel L_P measurements with similar slag compositions and found that the range of L_P is between 100 and 200. Employing BOF-type slags, Assis et al.⁴⁸⁾ also carried out phosphorus equilibrium study between liquid iron and slags and found that slags with basicities higher than 2.5 (V ratio) and around 20 to 25 mass% FeO can offer a L_P greater than 500. Therefore, it is not unreasonable in this study to accept the theoretical L_P is of the order of 10².

Fig. 6.

The effect of TiO₂ content on phosphorus partition ratio.

Fig. 7.

Dephosphorization data from Fig. 4 are replotted as a function of time: (a) using Eq. (13) and (b) using Eq. (11). (Online version in color.)

4.4. Dephosphorization Kinetics of Bloated Metal Droplet

It is well established that dephosphorization kinetics are limited by mass transfer of phosphorus in the slag, metal or both phases.^{6,7,8,9,10,11,16)} The rate equation for mixed control by mass transfer in both slag and metal phase can be expressed as Eq. (11),   

$$\left({\displaystyle \frac{W_m}{{\rho }_{m}A}}{\displaystyle \frac{1}{1+{\displaystyle \frac{W_m}{L_P{W}_s}}}}\right)Ln\left[\left(1+{\displaystyle \frac{W_m}{L_P{W}_s}}\right){\displaystyle \frac{{\left[P\right]}_b}{{\left[P\right]}_o}}-{\displaystyle \frac{W_m}{L_P{W}_s}}\right]=-k_{o}t$$(11)

where k_s and k_m are respectively the mass transfer coefficients for phosphorus in slag and metal with units of cm/s, ρ_m and ρ_s are densities of metal and slag with units of g/cm³, W_m and W_s are the respective masses of metal and slag in g.

In Eq. (11), the overall mass transfer coefficient, k_o, with units of cm/s is defined as   

$$k_o={\displaystyle \frac{1}{{\displaystyle \frac{{\rho }_m}{k_s{\rho }_s{L}_P}}+{\displaystyle \frac{1}{k_m}}}}$$(12)

As shown in Fig. 6, the predicted value of L_P for slags employed in this study is of the order of 10². With such a high value, the rate controlling step for dephosphorization is more likely to be mass transfer in metal phase, i.e., $k_o={\displaystyle \frac{1}{{\displaystyle \frac{{\rho }_m}{k_s{\rho }_s{L}_P}}+{\displaystyle \frac{1}{k_m}}}}\cong k_m$. This assumption is valid even for the high decarburization rate at the beginning of reaction. The higher decarburization rate would lead to a larger k_m due to the bubble stirring effect. However, assuming k_FeO is a reasonable estimate for k_s,^6,7,17) k_sL_P remains much greater than k_m under the condition of high decarburization rate according to values of k_FeO listed in Table 3 and k_m shown in Fig. 7(a). Therefore, the following integrated rate equation for phosphorus transfer in metal can be used to determine k_m:   

$$Ln\left[\frac{{\left[P\right]}_b-{\left[P\right]}_e}{{\left[P\right]}_o-{\left[P\right]}_e}\right]\left(\frac{{\left[P\right]}_o-{\left[P\right]}_e}{{\left[P\right]}_o}\right)\left(\frac{W_m}{{\rho }_{m}A}\right)=-k_{m}t$$(13)

where [P]_o, [P]_b and [P]_e are the initial, bulk and equilibrium concentration of phosphorus in metal droplet with units of mass%. Here, [P]_e was calculated based on predicted L_P presented in Fig. 6.

All data shown in Fig. 4 except the case of CAS slag were plotted in Fig. 7(a) according to Eq. (13). Whilst Eq. (11) representing mixed control rate equation was adapted in the previous study¹³⁾ to calculate k_o for the case of CAS slag because of its low L_P, i.e., less than 10. Those data were also presented in Fig. 7(b) for comparison. In that case, the time plotted starts from the time when the droplet was estimated to have dropped back into the dense slag for the second stage of dephosphorization. The initial phosphorus was taken at the same time. For CAS slag, k_m for the initial and the second stages were obtained from Eq. (12) by knowing k_s and L_P. Again, this approach on the analysis of dephosphorization kinetics for CAS slag can be found in the authors’ previous study.¹³⁾ Since the change of [P] in stage II ranges from maximum 0.0018 to 0.0007 mass%, which is small relative to the scale employed in Fig. 4 ranging from 0 to 0.08 mass%, changes in [P] are not readily observable. However, when the same data is plotted on a Ln basis according to Eq. (13), the change with time in stage II is much more observable. As seen in Fig. 7(a), each data set is well represented by two slopes representing two different k_m for phosphorus in metal droplet. In plotting Fig. 7(a), it has been assumed that k_m was same for all slags in stage I as the data does not justify any attempt to distinguish. This is probably because the mass transport of oxygen in stage I is sufficiently rapid as to not be rate controlling resulting in the same decarburization rates for all slags and therefore the same stirring and dephosphorization rates. It also assumes that the first reaction stage ends at the first data point in stage II. While there is no way of knowing that the stage I did not end earlier, this approach offers the most conservative possible estimate of the k_m in stage I. The k_m estimated for stage I are at least 8 times higher than the values determined for stage II of dephosphorization.

According to Higbie’s penetration theory⁴¹⁾ expressed as Eq. (14), assuming the CO bubbles are the same size at different stages, the ratio of k_m in the initial stage to that for the second stage would be equal to the square root of the ratio of the CO gas velocities expressed as Eq. (15),   

$$k_m=2{\left(\frac{D\mu }{\pi d}\right)}^{1/2}$$(14)

  

$$\frac{k_{m1}}{k_{m2}}={\left(\frac{{\mu }_1}{{\mu }_2}\right)}^{1/2}$$(15)

where D represents the diffusivity of phosphorus in metal with unit of m²/s;⁴⁹⁾ d is the diameter of CO bubbles(cm); and μ is CO gas velocity(rate of CO formation/surface area with units of cm/s); subscript 1 and 2 represent initial stage and second stage, respectively. For calculating k_m using penetration theory, taking the velocity and the diameter of metal droplet would be appropriate if the droplet velocity was significant. However, in the current study the velocity of metal droplet was relatively slow. The authors’ assertion in the current case is that stirring occurs inside metal droplet, through continuous generation and escape of CO bubbles. With this mechanism, the surface renewal rate is a function of CO gas velocity and bubble diameter.

The predicted ratio of k_m1 to k_m2 for all conditions was calculated using the decarburization and droplet surface area data, given in Table 5. The predicted ratio is at least a factor of 5 lower than the measured ratio. Based on Fig. 7(b), the determined k_m1 and k_m2 from our previous study¹³⁾ were 6.16×10⁻² and 1.66×10⁻² cm/s, respectively. The calculated ratio of k_m1 to k_m2 using the Eq. (15) for that case was also presented in Table 5. In this case the measured ratio was only a factor of two higher than the predicted. Different k_m at different stages can be attributed to, firstly the effect of oxygen and carbon activities on CO bubble sizes formed inside droplet at different stages, and secondly the percentage of CO generated on the surface of metal droplet. The influence of these two factors on k_m will be discussed in the following section. The influence of the change of [C] on viscosity of metal droplet was neglected in this study. Ostrovski et al.⁵⁰⁾ measured the influence of [C] on viscosity of Fe–C alloys at 1823 K and showed that the viscosity decreased from 8.5×10⁻⁷ down to 7×10⁻⁷ m²/s when the [C] increased from 0 up to 4.3 mass%. The maximum [C] change in the current study was 1.9 mass%, which assuming the viscosity change with carbon is linear would make less than 10% change in viscosity.

Table 5. Ratio of the initial to final value of k_m.

	μ at initial stage (cm/s)	μ at second stage (cm/s)	Predicted ratio based on Eq. (15)	Measured ratio	Predicted ratio based on Eq. (21)	Percentage of internal deC.
Base slag 5 mass%	68.5	6.5	3.2	15.4	7.0	20.9
TiO2 slag 10 mass%	64.2	10.2	2.5	17.4	5.7	10.6
TiO2 slag	21.2	10.0	1.5	8.7	3.6	17.5
CAS slag	2.0	0.7	1.7	3.7	2.7	54.4

In recent work,^13,18) the authors showed that the bubble size effect could be included in calculating the k_m by considering the formation of a CO bubble (reaction (16)⁵¹⁾) and combining Eqs. (18) and (19) with penetration theory. Thus k_m can be calculated via Eq. (20),   

$$\left[C\right]+\left[O\right]=C{O}_g$$(16)

  

$$log{K}_{CO}=\frac{1\mathrm{\hspace{0.17em} }160}{T}+2.003$$(17)

  

$$K_{CO}=\frac{P_{ve}}{h_C{h}_O}$$(18)

  

$$\mathrm{\Delta }P=\left(P_{ve}-P_l\right)=\frac{2\sigma }{r^{*}}$$(19)

  

$$k_m={\left[\frac{h_C{h}_{O}D\mu }{\pi \sigma }{K}_{CO}\right]}^{1/2}$$(20)

  

$$\mathrm{T}\mathrm{h}\mathrm{e}\mathrm{n},\mathrm{\hspace{0.17em} } \frac{k_{m1}}{k_{m2}}={\left[\frac{\frac{h_{C1}{h}_{O1}{\mu }_1}{{\sigma }_1}}{\frac{h_{C2}{h}_{O2}{\mu }_2}{{\sigma }_2}}\right]}^{1/2}$$(21)

where h_C and h_O are the henrian activity in liquid iron of carbon and oxygen respectively, σ represents the surface tension of liquid metal (N·m⁻¹), which is calculated via the correlation developed by Chuang et al.,⁵²⁾ r^* is the radius of critical nucleus of the CO bubbles with unit of cm, P_ve is the pressure in the bubble at equilibrium (supersaturation pressure) in atm, P_l is the liquid pressure (1 atm).

According to Eqs. (18)–(19), the bubble size would be expected to be smaller if, as is likely, a higher oxygen potential, was operating during the initial stage of the reaction. Therefore, instead of assuming the same bubble size, different values based on local conditions, should be considered in Eq. (20) at different stages. Since the resolution of X-ray fluoroscopy isn’t high enough to observe CO bubbles and their sizes in this study, the authors were left with no choice but to analyze the data based on the theoretically expected change in bubble size with driving force. As stated in section 4.2, it is reasonable to assume the interfacial oxygen potential for metal droplets in the dense slag is determined by the Fe–FeO equilibrium due to the high basicity and high FeO content offering a fast oxygen transport in the slag. With this assumption, the radius of CO bubbles formed at different stages for all cases were calculated based on Eqs. (18)–(19) and shown in Tables 6 and 7. Here, the initial [C] and [O] measured by LECO analyzer presented in Section 2.2 were used to calculate h_C at stage I using interaction parameters⁵⁰⁾ based on Eqs (22)–(23), whilst the [C] derived from the data shown in Fig. 2(a) was employed to calculate h_C at stage II. The first order of interaction parameter was employed here since the second order of that is not applicable. This approach is identical to the one used by other researchers who studied bloated droplets.^29,53) Furthermore, for calculating h_C only [C] and [P] changed whilst the dissolved content of other elements were assumed to be identical to the initial measured value. The [C] and [P] of droplet at stage II after primary decarburization was listed in Table 7. With the assumption that h_O was determined by Fe–FeO equilibrium, then K_Fe, $a_{Fe}^i$ and γ_FeO defined in Eq. (5) were used to calculated its value at which γ_FeO was obtained via the correlation developed by Basu et al.⁵⁴⁾   

$$h_C=f_C\left[\%C\right]$$(22)

  

$$log{f}_C=e_C^C\left[\%C\right]+e_C^S\left[\%S\right]+e_C^P\left[\%P\right]+e_C^O\left[\%O\right]$$(23)

Table 6. Calculated radius of CO bubbles at the initial stage.

	Base slag	Slag with 5 mass% TiO2	Slag with 10 mass% TiO2	CAS slag
hO	0.102	0.101	0.10	0.068
hC	10.4	10.4	10.4	11.4
Pve (atm)	427.5	421.7	421.2	328.5
σ (N m−1)	1.19	1.20	1.20	1.10
r × 106 (cm)	5.52	5.61	5.62	6.60

Table 7. Calculated radius of CO bubbles at the second stage.

	Base slag	Slag with 5 mass% TiO2	Slag with 10 mass% TiO2	CAS slag
hO	0.102	0.101	0.10	0.068
hC	2.20	2.04	1.67	4.64
Pve (atm)	90.6	82.9	67.7	133.3
σ (N m−1)	1.19	1.20	1.20	1.13
r × 105 (cm)	2.60	2.85	3.49	1.67

Table 8. Metal droplet composition for calculating h_C at stage II (mass%).

	[C]	[P]	[O]	[S]
Base slag	1.15	0.0019	0.005	0.007
Slag with 5 mass% TiO2	1.10	0.0011	0.005	0.007
Slag with 10 mass% TiO2	0.97	0.0013	0.005	0.007
CAS slag	1.74	0.06	0.005	0.007

The results in Tables 6 and 7 demonstrate that the radius of CO bubbles formed at stage I of dephosphorization is approximately one order of magnitude smaller than those formed at stage II due to the decrease of carbon activity as reaction proceeds, which provides lower supersaturation pressure of CO gas. Smaller CO bubbles lead to faster surface renewal, resulting in higher k_m for the initial stage of dephosphorization. Taking the effect of bubble size into account, the ratio of k_m1 to k_m2 for all conditions was recalculated based on Eq. (21), and given in Table 5. This brings the predicted ratios more into line with the measured values. However, the new predicted ratios are still approximately 3 times lower than measured values for slag with 5 mass% TiO₂.

One possible reason for this discrepancy is that the nucleation of CO bubbles for stage II is more likely to occur at the surface of metal droplet due to the decreasing driving force for CO nucleation. In other words, the CO nucleation in stage II is composed of a small fraction of internal nucleation and a larger portion of surface nucleation. The stirring offered by CO bubbles formed at the surface does not contribute significantly to mass transfer in droplet, which would explain a much lower k_m at stage II compared with that in stage I where there is a large fraction of CO is formed inside the droplets. Assuming the nucleation of CO bubbles at stage I fully occurs inside droplet and the stirring offered by internal CO nucleation is the only contribution to the measured k_m for both initial and second stages, then one can back calculate the fraction of internal CO nucleation at stage II using measured ratios of k_m1 to k_m2 based on Eq. (21). The calculated fraction of internal nucleation at stage II was also presented in Table 5. It shows that only less than 20% of CO nucleation occurs inside metal droplet at stage II for all three cases, which therefore would make a very limited contribution to enhance mass transport of phosphorus via bubble stirring. However, in the case of CAS slag, a large portion of CO nucleation (around 54%) may occur inside droplet due to a high remaining carbon activity. The aforementioned analysis shows that the combination of the formation of bigger CO bubble and the occurrence of surface decarburization at stage II leads to a much lower k_m than that at stage I. According to calculated results listed in Tables 6 and 7, this observation is mainly attributed to the significant decline of carbon activity in metal droplet at stage II resulting from the vigorous CO evolution at stage I. The decline of carbon activity leads to a lower supersaturation pressure of CO, which eventually causes the formation of bigger CO bubble and the occurrence of surface decarburization.

In this study, the extremely fast reaction as shown in Fig. 4 and the insufficient kinetic data especially at stage I, would render it improper to make any general conclusions on the influence of TiO₂ on dephosphorization kinetics of bloated metal droplet. In this sense, the authors believe the traditional flat metal bath experimental setup will be more proper to elucidate the TiO₂ effect on generic dephosphorization behaviors. However, the current study does confirm that the highly basic CMS slag provides very favorable conditions for dephosphorization of bloated metal droplet compared to the previous study¹³⁾ where low basicity CAS slag is employed. In the authors’ view, the most significant finding of this study is that with BOS type of slag the dephosphorization rate of metal droplets is extremely fast (complete in less than 4 s) relative to the residence time of the droplet (a few seconds to 60 s for bloated droplets).¹⁾ The overall dephosphorization rate may be calculated at any time during the blow by knowing the local equilibrium partition and the rate of droplet generation.

5. Conclusion

The decarburization and dephosphorization behavior of bloated metal droplets reacting with slags containing different TiO₂ content were analyzed in detail to elucidate the influence of TiO₂ on dephosphorization kinetics. The following conclusions may be drawn from the analysis.

(1) The rate and extent of dephosphorization for metal droplet was found to be greater in CMS-TiO₂ slag compared to CAS slag due to the faster mass transport and a larger thermodynamic driving force.

(2) The observation of maximum volume of bloated droplet increasing with increasing slag viscosity was likely due to the effect of slag viscosity on CO bubble escape rate of bloated droplet by affecting oxygen transport therefore the surface tension of metal droplet.

(3) Both the predicted phosphorus partition ratio (L_P) and the measured ones were found to be decreased with increasing TiO₂ content in the slag.

(4) For all the cases of CMS slag, the k_m at stage II was at least 8 times lower than the one at stage I because of the following two factors. Firstly the size of CO bubble formed at stage I was approximately one order of magnitude smaller than those formed at stage II. Secondly the small fraction of internal decarburization (less than 20%) occurred at stage II, which cannot offer effective surface renewal to enhance mass transport of phosphorus in metal phase.

Acknowledgements

Funding from the Australian Research Council Industrial Transformation Research Hubs Scheme (Project Number IH130100017) is gratefully acknowledged.

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