Prediction of re-oxidation behaviour of ultra-low carbon steel by different slag series

A kinetic model was developed using FactSage Macro Processing to simulate the re-oxidation of ultra-low carbon steel via different oxidising slags. The calculated results show good agreement with experimental laboratory thermal simulation data. Therefore, the model can be used to predict the change behaviour of slag-metal-inclusion in the re-oxidation reaction of liquid steel. It can provide prediction and guidance for an accurate secondary oxidation control process. During the slag re-oxidation process, when the oxygen in the steel is supersaturated and the slag is low in oxidation, it can easily form stick-like and dendritic shape inclusions of Al2O3 in steel. As the (FeO) content increases in slag, the oxygen transfer from slag to steel is evident, and the inclusion size increases, showing clusters and spherical shapes. In addition, supersaturated oxygen in steel easily forms unstable Al2O3-TiOx inclusions with [Ti]. As the components of liquid steel tend to be uniform, the Al2O3-TiOx inclusions will decompose and disappear, forming stable Al2O3 and TiO2 inclusions. The number of inclusions can be reduced by increasing the basicity and the ratio of CaO to Al2O3 in the initial slag.

production. With the development of computer and big data technology, it has become a low-cost and efficient method to study the relatively complex metallurgical reaction process. Thus, The complex metallurgical reaction process that cannot be explained and analyzed before was expressed by big data and computational model, and it was analyzed and discussed. It is proved that the calculation model is more practical and accurate than the traditional metallurgical theory in predicting and analyzing a complex metallurgical reaction process. The method of model prediction has greatly improved the understanding of complex metallurgical reactions. It is of great practical significance for the researchers and operators to optimize the process parameters and improve production efficiency. Recently, some scholars [13][14][15][16][17] proposed some kinetic models, based on thermodynamic theoretical calculation and fluid dynamics equations, which can successfully predict changes in slag, liquid steel, and inclusions at the slag-metal interface. However, these models also have problems, such as decreased prediction accuracy and incomplete prediction of actual production requirements, that accompany changes in thermodynamic data and complex slag systems [18][19][20] .
This study uses ultra-low carbon steel as the research object and develops a kinetic model based on laboratory thermal simulation data combined with FactSage 7.2 Macro Processing software. The model can more intuitively describe the re-oxidation behaviour of slag with different oxidisability than liquid steel and more accurately predict the evolution of slag, liquid steel, and inclusions during the slag-metal interface reaction. It can also formulate more accurate and reasonable control technology for liquid steel re-oxidation.

experimental methods and procedures
Materials. A steel mill was used to produce ultra-low carbon steel. When the steel was RH outbound, five samples were taken from the same ladle, each approximately 100 g. The chemical composition of the samples is shown in Table 1. In this experiment, CaO, SiO 2 , FeO, and MnO were used to simulate the main components of the ladle top slag. Five groups of slag were prepared separately. Their mass fractions are shown in Table 2. These slag systems were prepared and mixed, then placed in a corundum crucible and calcined at 1000 °C for pre-melting before use in the experiments.
Experimental process. In this study, the constant basicity of the experimental I-IV slag was 3.0, and the MnO content was 1%. The experimental IV and V slag series use the same oxidisation and different basicity. The re-oxidation behaviour of the slag upon the liquid steel and the evolution of slag, liquid steel, and inclusions during the slag-metal reaction were studied by changing the oxidation (change in single-variable FeO content) and slag basicity. These changes provide thermodynamic experimental data for the establishment of a kinetic model. The schematic diagram of the experimental device is shown in Fig. 1. A silicon molybdenum furnace was used to provide a stable heat source for the whole experiment. The bottom of the furnace injects Ar gas throughout the experiment. The top of the furnace was sealed with a lid, and Ar gas was introduced into the whole furnace to  Sample preparation. The experimental test analysis steel sample is shown in Fig. 2. The central part of the steel sample was processed into a ϕ5 × 40 mm steel rod. The total oxygen (T. [O]) content in the steel after the reaction was measured by an EMGA-620 oxygen-nitrogen detector, and the remaining elements were analysed by atomic emission spectrometry. Steel cakes of ϕ40 × 15 mm were cut from the bottom of the reaction steel samples from each group, and the inclusions were analysed using an ASPEX PSEM Explore scanning electron microscope, which can detect the number, size, and composition of inclusions in a specified area, in addition to performing conventional electron microscope functions. The composition, size, and area information for each inclusion was analysed using the analysis software of AZtecSteel. The slag composition of each stage of the experiment was obtained by X-ray fluorescence spectrometer analysis. The detection area of all steel sample inclusions in this study was approximately 100 mm 2 . The typical characteristic inclusions in the scanning area were statistically analysed, and inclusions of the same type, shape, and size were not detected repeatedly.

Results and Discussion
Kinetic prediction of slag-steel-inclusion reaction during slag re-oxidation process. The re-oxidation behaviour of liquid steel via slag in the ladle mainly involves the chemical reactions and processes as shown in Fig. 3. During the oxidation reaction, R1 and R3 determined the rate and direction of the slag-metal interface reaction. When the diffusion of [O] in steel is a limiting link, oxygen will diffuse from the slag to the liquid steel. At this time, the oxidation reaction R4 between oxygen and deoxidised elements such as [Al] s and [Ti] in the steel occurs in inside of liquid steel. When the mass transfer of (SiO 2 ), (FeO) and (MnO) in the slag phase is a limiting link, the oxidation reaction occurs in the slag-metal interface, that is, the R2 reaction, occurs. When the chemical potential of oxygen in the slag-metal phase is relatively close, the oxidation reaction is simultaneously restricted by mass transfer of [O] in steel and (SiO 2 ), (FeO) and (MnO) in slag. The slag-metal interface is in equilibrium, and no obvious re-oxidation behaviour will occur at this time.
The accuracy and validity of the hypothesis conditions will be checked and corrected by the test data of the steel sample and slag sample. To facilitate the establishment and calculation of the model, the thermodynamic experiment and the kinetic model need to make the following assumptions: (1) In the thermal simulation experiment, when the slag is added to the steel to participate in the reaction, the slag reaction step size is Δt = 5% m slag 21 .
(2) The slag-metal interface reaction can reach an equilibrium state.  I  I-5  I-10  I-15  I-20  I-25  I-30   II  II-5  II-10  II-15  II-20  II-25  II-30   III  III-5  III-10  III-15  III-20  III-25  III-30   IV  IV-5  IV-10  IV-15  IV-20  IV-25  IV- Table 3. Sample number with regard to different slag and reaction time. In the FactSage software, the Macro Processing module was invoked to create a balanced reaction program. All input data for the model are based on the data from this thermal simulation experiment, and reference data are appropriately cited. The output data were all organised into data lists or Microsoft Excel tables, which were processed and plotted into corresponding charts at a later stage 22 . All the major chemical reactions in Fig. 3 were formed into small programs by the Macro Processing code. All thermodynamic reaction equilibrium phase diagrams were calculated using FactPS, FToxid, and FTmisc databases in FactSage software under adiabatic conditions 23 .

Model validation.
To verify the accuracy of the model, the data adopted in this study were mainly based on the thermal simulation experiment, and a few references are cited. The basic conditions and data used in the reaction of slag I with ultra-low carbon steel were selected randomly as the input data for the kinetic model. The actual experimental value was compared with the output data calculated by the model, and the results are shown in Fig. 4. The inner diameter of the zirconia crucible used in the experiment was 60 mm, and the height was 80 mm. Thus, the reaction area of the interface is 0.0028 m 2 . The densities of slag and steel used in the calculation were, respectively, 2500 kg/m 3 and 7200 kg/m 3 . The mass transfer coefficient of steel in this kinetic model can be estimated through the fitting experiment by measuring the concentration changes of [Al] s , [Ti], and [Si] in the steel, and repeated modifications were carried out to obtain the best fitting parameters. Figure 4 shows that when the estimated mass transfer coefficient of steel is 1.25 × 10 −5 m 3 /s, the calculated results of this kinetic model show good consistency with the experimental values under the same conditions, which fully indicates that the mass transfer coefficient value can meet the calculation needs of the existing model.
The total oxygen (T. [O]) content in steel includes dissolved oxygen in liquid steel and oxygen in inclusions. When the slag oxidises the liquid steel, the chemical potential of the dissolved oxygen in steel and the oxide in slag tends to gradually balance, and the floating removal rate of the inclusions also has a significant impact on the oxygen in the inclusions.  [O] content in steel. Therefore, it can be considered that the kinetic model can meet actual production needs and provide prediction and guidance for the formulation of an accurate re-oxidation control process.

Re-oxidation behaviour of ultra-low carbon steel by different oxidisability slags.
To predict the re-oxidation behaviour of ultra-low carbon steel with differing oxidising slag, the process of oxidisation was simulated by FactSage Macro Processing. For the materials used for the model calculations, the steel was 100 g, and the five groups of different oxidising slags were 30 g each. The specific components of steel and slag systems are shown in Table 1 and Table 2, respectively. The calculated temperature was 1853 K.
When the slag interacts with ultra-low carbon steel, reactions (1-7) may occur in the slag-metal interface and the inside of liquid steel.   Fig. 6a. The model calculation shows that the oxygen generated by the inclusions mainly comes from the self-dissociation reaction of (SiO 2 ) in the slag, and the [Si] content in steel increases significantly. In addition, because of the low (FeO) content in the slag, its activity is also lower. Therefore, under the influence of slag interfacial tension, there is no large-scale self-dissociation reaction to transfer oxygen to the steel 20 . Therefore, it can be inferred that the oxidation property of slag to liquid steel is mainly affected by (SiO 2 ), but not by the (FeO) in slag. At this point, reactions (1) and (3) occur in the slag-metal interface. As the (FeO) content in the slag increases to 2%, the total number of inclusions in the steel increases slightly, as shown in Fig. 6b. [O] content in the steel increases sharply. The oxygen transfer from slag to liquid steel is obvious, and the total inclusions in the steel increase correspondingly. Figure 6c indicates that when the reaction proceeds to approximately 25 minutes, TiO 2 inclusions appear in the steel and Al 2 O 3 inclusions decrease. During the whole reaction process, the oxidation of [Al] s occurred in steel before [Ti] in the early stage of the reaction, and a large number of Al 2 O 3 inclusions were formed. This is mainly because the binding force of aluminium to oxygen is much greater than that of titanium to oxygen. As the reaction proceeded, the [Al] s content in the steel decreased in the later stages of the reaction, and some oxygen immediately oxidised the [Ti] to form TiO 2 inclusions. According to the test results from the steel samples after the reaction, there was no significant change in [Si] content in the steel. Therefore, it can be inferred that the oxygen in steel mainly comes from the decomposition reaction of (FeO) in the slag. Moreover, its decomposition reaction inhibits the self-dissolution reaction of (SiO 2 ) in the slag. The oxidation of slag mainly manifested as the (FeO) content in the slag, which is not directly related to the (SiO 2 ) content in the slag. At this point, main reactions (2) Fig. 6c, it can be seen that the total inclusions decrease throughout the whole reaction process. This is mainly due to the increase in Al 2 O 3 inclusions generated in the early stage of the reaction to the slag, which improves the w(CaO)/w(Al 2 O 3 ) in the slag, a condition conducive to improving the slag's ability to absorb the inclusions. Figure 6d,e show the re-oxidation behaviour of liquid steel via slag with the same oxidation properties but a different basicity. By comparing the calculation results in Fig. 6e,d, it can be seen that the basicity of slag has a great influence on the inclusions in steel. According to Fig. 6e, TiO 2 and Ti 2 O 3 inclusions began to appear in the steel at approximately 25 min into the late stage. The analysis shows that this is due to the increase in basicity. Meanwhile, the Al 2 O 3 formed in the early stage of the reaction also increases the w(CaO)/w(Al 2 O 3 ) of slag. These two aspects are conducive to inhibiting the premature oxidation of [Ti] in steel and avoiding the premature formation of Ti inclusions. The Al 2 O 3 -TiO x solid solution phase appears in the steel at a later stage of the reaction. This is due to the decrease in [Al] s content in steel in the later reaction stage and [Ti] may combine with a high concentration of oxygen. This forms a solid solution phase with TiO x as the core and Al 2 O 3 as the outer layer. This is consistent with the results in ref. 24 .With the solidification of liquid steel, the Al 2 O 3 -TiO x solid solution phase has no time to rise and remove, so it remains in the steel to form inclusions. Such inclusions are unstable and can be removed by raising the temperature of the liquid steel and increasing the duration of ladle bottom blowing. Main reactions (2), (3), (4), (5), (6), and (7) occur in the slag-metal interface and on the inside of the liquid steel. It can be seen from the comparison of Fig. 6d,e that with the increase in slag basicity, total inclusions in steel can be reduced, and the purity of liquid steel can be improved. Figure 7 shows the stable phase diagram of Al-Ti-O inclusions formed in steel at 1853 K. This was calculated using the FactPs, FToxid, and FTmisc databases in Evolution of inclusions in steel during slag re-oxidation process. The steel samples at all stages of the experiment were examined and analysed by Aspex. To reflect the difference in the change of characteristic inclusions in the steel, this study selected three groups of steel samples with different slag oxidation and basicity change time points for comparative analysis, as shown in Fig. 8.      www.nature.com/scientificreports www.nature.com/scientificreports/ conclusion predicted by the model. The morphology of inclusions shows that Al 2 O 3 -TiO x inclusions generally have a spherical shape with TiO x as the nucleation centre and a size of 4-6 μm, and the edges are covered by Al 2 O 3 . According to research by Park 26 and Doo 27 , when Ti-Fe alloy is added to steel, it will lead to locally high [Ti] or [O] concentration. Al 2 O 3 -TiO x inclusions are easily formed in the locally high [Ti] concentration area. In this study, the [Ti] distribution in steel after melting with ultra-low carbon steel was relatively uniform. There was no locally high [Ti] concentration region. Therefore, the formation of Al 2 O 3 -TiO x inclusions was caused by high oxidising slag rather than the local oxidation of [Ti]. After bottom blowing and standing, the composition of the liquid steel was uniform. The Al 2 O 3 -TiO x inclusions decomposed and disappeared, forming stable Al 2 O 3 and TiO 2 inclusions. These experimental results are consistent with those predicted by the model.

conclusions
(1) The kinetic model developed by the Macro Processing module in the FactSage software program can predict the re-oxidation behaviour of ultra-low carbon steel via slag with different oxidisabilities. The calculated results of the model show good agreement with the experimental data from the laboratory thermal simulation. This model can predict and guide the accurate secondary oxidation control process for the actual production.
(2) During the slag re-oxidation process, when w(FeO)% = 1%, the oxygen that generates inclusions is mainly derived from the self-dissociation reaction of (SiO 2 ) in the slag. With the increase in (FeO) content, the oxygen transfer from slag to steel is marked. The oxygen in steel mainly comes from the decomposition reaction of (FeO) in the slag. Moreover, the decomposition reaction of (FeO) suppresses the self-dissociation reaction of (SiO 2 ) in the slag. In addition, the oxidation of [Ti] in steel can be suppressed by increasing the basicity and ratio of CaO to Al 2 O 3 in the initial slag, while the number of inclusions can be reduced.
(3) When the oxygen in steel is supersaturated and the slag is low in oxidation, stick-like and dendritic inclusions of Al 2 O 3 form easily. As the oxidation of the slag increases, the size of the inclusions increases, and it presents clusters and spheres shape. In addition, the supersaturated oxygen in steel easily forms unstable Al 2 O 3 -TiO x inclusions with [Ti]. As the components in the liquid steel tend to be uniform, Al 2 O 3 -TiO x inclusions decompose and disappear, forming stable Al 2 O 3 and TiO 2 inclusions.