Evolution of the Inclusion Population During the Processing of Al-killed Steel

The increasing demand for higher inclusion cleanliness levels motivates the control over the formation and evolution of inclusions in the steel production process. In this work, the evolution of the chemical composition and size distribution of inclusions throughout a slab production process of Al-killed steel, including ladle furnace (LF) treatment and continuous casting (CC), was followed. The initial solid Al2O3 and Al2O3-MgO inclusions were modified to liquid Al2O3-CaO-MgO inclusions during LF treatment. The evolution of the size distributions during LF treatment was associated with the growth and removal of inclusions, as new inclusions were not created after the deoxidation process, according to a population density function (PDF) analysis. Additionally, the size distributions tended to be similar as the LF treatment progressed regardless of their initial features, whereas they differed during CC. Analysis of the upper tails of the distributions through generalized extreme values theory showed that inclusion distributions shifted from larger to smaller sizes as the process progressed. There were great changes in the distributions of large inclusions throughout the LF treatment and between the end of the LF treatment and the start of the CC process. Additionally, distributions of large inclusions differed at the end of the LF treatment, whereas such differences decreased as CC progressed.


Introduction
The inevitable presence of inclusions in steel products has led steelmakers to pay particular interest to the control of inclusions by focusing on decreasing the number and size and controlling the morphology and chemical composition [1,2]. Successful control of the inclusion population requires knowledge of its formation and evolution throughout the steelmaking process.
Recent papers analyzed the origin and characterization of populations of inclusions [3,4]. In Al deoxidized steels, the deoxidation product solid Al2O3 can have different morphologies depending on the degree of saturation of dissolved aluminum and oxygen [4].
The Al2O3 inclusions can be modified via inclusion-steel reactions. Consequently, inclusion modification depends on the chemical evolution of the liquid steel during treatment in a ladle furnace (LF), which in turn depends on the addition of alloying elements, reactions of the steel with slag and refractory, and the homogenization of liquid steel [4][5][6][7][8][9]. After Al2O3 inclusions form, they can subsequently transform into Al2O3-MgO inclusions [9,10]; however, inclusions of the type Al2O3-MgO-CaO have been observed during ladle furnace treatment [6,7]. At the end of LF treatment, the composition of the inclusions is modified by Ca addition to form liquid inclusions of the Al2O3-CaO type [11]. The Ca treatment efficiency seems to depend on the type of inclusions present before the modification treatment, i.e., Al2O3 or Al2O3-MgO inclusions, [5,10,[12][13][14] and the homogenization of dissolved Ca in the liquid bath [15]. In addition, a decrease in temperature occurs progressively in the operations following the LF treatment, i.e., transfer of the ladle to the continuous casting (CC) station and the CC process, and the thermodynamic conditions of the liquid steel-inclusion interactions change and consequently the chemistry of the inclusions can be modified. On the other hand, a desirable inclusion population implies low numbers and small sizes of inclusions, which is reached through the efficient removal of inclusions during LF treatment and subsequent operations.
The removal of inclusions during LF treatment depends on numerous factors, such as the chemical compositions and sizes of the inclusions, flow pattern of the liquid steel, and slag properties [5]. Once the LF treatment is finished, the transport of the ladle to the continuous casting station and the CC operation itself provide an additional opportunity for flotation and removal of inclusions [7].
On the other hand, the inclusion size distribution is commonly represented by a histogram and a plot of the frequency of inclusions as a function of the inclusion size, assuming a normal distribution [16,17]. These representations provide limited information on the inclusion population. Instead, the formalism proposed by Higgins that introduces the concept of the population density function (PDF) can be used [18]; the PDF is unique for a given inclusion population and provides information on the formation and evolution of inclusions [17]. On the other hand, the use of the generalized extreme values (GEV) theory based on Murakami et al.'s pioneering work [19] has been used to describe the large particle size tail of the distribution. For example, Ekengren and Bergström [20] described the upper tail of inclusion size distributions in industrial-scale samples. More recently, Castro et al. [21] and García et al. [22] used GEV theory to describe the evolution of the upper tail of the inclusion size distribution throughout the steelmaking process.
Thus, the improvement of inclusion cleanliness implies knowledge about the evolution of the inclusion population throughout the steelmaking process. The present work presents the characterization of inclusion populations in samples obtained in 4 heats conducted at an industrial scale facility. A sampling procedure was used throughout the steelmaking process, including the LF treatment and CC. The chemical composition of inclusions was estimated to follow its evolution throughout the steelmaking process.
Furthermore, the inclusion populations were characterized in terms of their size distributions.
The PDF concept was used to analyze and explain the evolution of the size distributions, whereas GEV theory was used to describe the evolution of the upper tail of the size distributions.

Description of the steelmaking process
This study involved the production of an Al-killed steel slab by the electric arc furnace (EAF)-LF-CC route ( Figure 1). 1. A mix of directly reduced iron and scrap is the raw material used to produce primary steel in the EAF. After chemical composition and temperature adjustment, the steel is tapped into a 150-ton ladle. During that operation, a deoxidizer, ferroalloys, and slag-forming agents are added to the stream of liquid steel. After the tapping operation, the ladle is transported to an LF station, and the steel treatment starts with the adjustment of the chemical composition of the slag and the homogenization of the

Plant trials
Four successive plant production heats of a low-carbon aluminum-killed steel were studied. The heats corresponded to the first four heats of a 24-heat casting sequence. The chemical composition of the batches of steel at the end of the LF treatment is presented in Table 1; carbon and sulfur contents were determined by the Leco technique, and other elements were determined by optical emission spectrometry. As the first stage of the experimental procedure, liquid steel was sampled during the LF treatment and at the CC mold using a cap-protected lollipop-type sampler. The samples were labeled according to their site and time of collection, as indicated in Table 2. The liquid steel samples were obtained in duplicate at each step: one sample was used for chemical analysis, and the other was used for characterization of the inclusion population.
Furthermore, slag samples were drawn along with the samples of liquid steel in LF. X-ray fluorescence spectrometry was used to measure the elemental composition of slag and estimate its chemical composition and conversion to typical oxides, Table 3.

Inclusion size distribution and statistical analysis
Selected surfaces of the specimens were metallographically prepared to estimate the amount and size of inclusions. Each lollipop-type sample was axially sectioned, and one of the fresh surfaces was progressively dry ground using 80-, 220-, 300-, 500-, 800-, and 1000-  The analysis of the inclusion size distributions was conducted using the concept of PDF proposed by Higgins [18]. The PDF is expressed by the following: where ( ) is the frequency of inclusions in each size bin (particle number per bin volume), ( − ) the bin width is expressed in units of length -4 . This treatment assumes that a log-normal distribution can be used to fit the experimental data [18,24]. Additionally, a statistical analysis based on the statistical GEV theory was conducted to characterize the upper tail of the inclusion populations [16]. A detailed statistical background has been presented in previous papers [21,22], so only the necessary details specific to this paper are included here. In general, the GEV distribution was fitted to the experimental dataset of inclusion sizes, and the scale, shape, and location parameters were estimated. If the k parameter (shape parameter) is greater than zero, then the probability distribution function is expressed by: and the CDF (cumulative distribution function) is given by the following equation: where σ is the scale parameter, z is the reduced variable (x-μ)/σ, and μ is the location parameter.
To analyze the reliability of the resulting GEV distributions, the Anderson-Darling test was used to evaluate the goodness of fit of the GEV distribution to the experimental data.
Thus, the resulting A-D statistic values, A 2 n, expressed by were compared, for a given confidence interval, to a given critical value estimated by the Monte Carlo method. In the A n 2 expression, F(xi) is the CDF of the GEV distribution, n is the total number of observed inclusions, and xi is the i-th measurement of inclusion size. If the k value is greater than zero, then the upper tail of the distribution does not tend to a finite value, and accordingly, a survival function S(x) is used instead as a cleanliness parameter.
S(x), the complement of the CDF expressed by S(x)=1-CDF, represents the probability of having inclusions larger than a given size.

Chemical analysis
The chemical compositions of the inclusions were estimated using energy dispersive spectroscopy. Approximately 10 inclusions per sample were selected for analysis under a Phillips XL30 ESEM scanning electron microscope equipped with an EDAX Pegasus analyzer. The inclusions were classified as simple or complex; those that exhibited only one phase were labeled "simple", those that contained two phases were "complex": In complex inclusions the major phase was identified as the "matrix", and other phase was identified as "secondary".

Evolution of the chemical composition of inclusions
The evolution of the chemical composition of inclusions throughout the sequence of steel samples is shown in Figure 2.

Path of inclusion modification
To illustrate the modification path of inclusions through the processing of liquid steel, the contents of Al2O3, CaO, and MgO in the analyzed inclusions were normalized and plotted on the Al2O3-CaO-MgO ternary diagram at 1873 K. This diagram was calculated using Thermocalc software [25] and the Slag2 database ( Figure 3).    To illustrate the evolution of the inclusion population throughout the steelmaking process, Figure 6 shows the evolution of the probability density function for Heat C, assuming a normal distribution. It was observed that the upper tail of the distributions shifted towards smaller sizes with the advance of the process, and that the means of the distributions  To go deeper in the analysis of the evolution of the inclusion populations throughout the process, PDFs were calculated using Equation (1) based on the Higgins formalism [21].

Distribution size
To estimate the frequency of inclusions per unit volume, the 2D inclusion population information obtained by image analysis was transformed to 3D data via a procedure based on the Saltikov method [30,31]. The logarithmic representation of PDFs calculated for each sampling stage in LF treatment, LF samples, and all 4 heats is shown in Figure 7. Figure 7.a shows the PDFs corresponding to the LF-I samples, whereas those for LF-II and LF-III are shown in Figure 7.b. In general, the PDFs showed linear power law behavior [24]. The reference lines included in Figure 7 were estimated by considering the averages of data for inclusion sizes smaller than 9 m, where the fitting to the linear behavior was remarkable.
The linear behavior indicated that there was no formation of new inclusions during the LF treatment, e.g., inclusions formed from reoxidation, and the observed evolution was associated with the growth and removal of inclusions [32,33]. The data for the LF-I samples (Figure 7.a) were farther from the reference line than the LF-II and LF-III data (Figure 7.b). This was associated with the intense transient deoxidation process that delayed the approach to dynamic inclusion-steel equilibrium at the beginning of LF treatment. For the LF-II samples, it was thought that equilibrium was reached. Furthermore, the Ca addition seemed to not modify the inclusion population because similar behavior was exhibited by samples from LF-II and LF-III; however, instead, it is believed that the changes associated with the growth and/or removal of inclusions during the interval between the Ca addition, the LF-II samples, and the LF-III samples were not significant enough to be detected by the measurement procedure used in this study. The Regarding the reference line, there were slight differences with respect to those of the LF samples. The slope shifted slightly to larger inclusion sizes and log (PDF) values, but the steepness of the slope was practically the same. These slight differences were attributed to the scattering of the data. It is worth noting that the CC-II samples of Heat A were less close to the reference line, which suggested that there was a deviation from the "standard" casting process. It is worth noting that the analysis in this paper applied strictly to inclusions smaller than 9 m, which were used to obtain the reference lines. For larger inclusions, the data scattering restricted the analysis and suggested a deviation from the described behavior.

Analyses of the upper tail of size distributions
For each sample, the measured size distributions were fitted to the GEV distribution, and the goodness of fit was estimated. Table 4 shows the GEV distribution parameters, k, μ and σ, and the A-D statistics and critical values, A 2 n, and CV obtained by tests of the goodness of fit. It was observed that practically all the tests, except one gave a good fit to the GEV distribution, as the calculated A-D statistics were smaller than the critical value estimated by the Monte Carlo method. The values of the shape parameter k are plotted in Figure 9. In almost all the fitted distributions, the k value was positive; therefore, the upper tail of each large inclusion distribution decayed to infinity. Furthermore, the k values are greater in the LF samples than in the CC samples, which means that there was a higher probability of finding large inclusions in the LF samples. This behavior is shown for Heat C in Figure 10, which shows the probability density function obtained from the calculated GEV model. It was observed that as the process went forward, the probability density function shifted to smaller inclusion sizes.  The comparison among heats of the probability density functions of the last three liquid steel samples, LF-III, CC-I and CC-II, is shown in Figure 11. It is worth noting that there were great differences among the probability density functions at the LF-III stage, particularly the locations and shapes of the upper tails, and these differences decreased progressively in the C-I and C-II samples. This result indicated that inclusion populations tended to resemble each other as the process progressed because large inclusions were removed in subsequent operations after Ca addition, as described previously in the section on PDFs.
The survival function S(x) was used to analyze the evolution of the inclusion populations. Figure 12 shows the variation in S(x) throughout the steel sampling sequence for the heats and three "critical" inclusion sizes: 20, 40 and 60 m. These values were chosen based on the location of the PDFs shown in Figure 11.b and 11.c. corresponding to the CC samples, whose inclusion populations were expected to be like those in the solidified product.  The results showed that inclusion populations evolved significantly during the LF treatment regardless of the inclusion size and that differences were observed between the LF-III and CC samples. Figure 13 shows that during the LF treatment, initial large inclusions and large inclusions that resulted from the growth of small inclusions were removed. The

Conclusions
In this paper, the evolution of the chemical composition and size distribution of inclusions in samples obtained throughout a plant-scale slab production process was followed. Two approaches were used to analyze the size distributions: (1) estimation of PDFs following the Higgins formalism [18] to obtain information on the behavior of the global inclusion population, and (2) GEV theory to describe the upper tail of each size distribution.
Thus, the following conclusions can be drawn.
-Solid Al2O3 and Al2O3-MgO inclusions formed by the deoxidation process were modified by Ca to form partly-liquid low-CaO Al2O3-MgO-CaO inclusions. This modification was associated with the steel-slag interactions during the LF treatment, which provided dissolved Ca. This result agrees with that reported in the literature, which states that such types of inclusions are modified even at low Ca contents.
-Inclusions of Al2O3-MgO-CaO with low CaO content were modified into fully liquid inclusions with an Al2O3/CaO ratio of approximately 1.25 and MgO contents lower than 10% through a CaFeAl wire treatment.
-The PDF approach allowed us to follow the evolution of inclusion size distributions throughout the process. Great changes in LF treatment and between the end of the LF treatment and the start of the CC process were observed. The PDF analysis revealed that new inclusions were not formed during the LF treatment; hence, the observed changes were associated with the growth and removal of inclusions. Furthermore, size distributions were similar at the end of the LF treatment regardless of their initial features. Differences among size distributions during the CC process were associated with variations in the residence time of inclusions in the liquid steel from the Ca addition to the progressive CC.
-The use of the GEV approach led to determining the form of the upper tails of the distributions, which in turn allowed us to follow their evolution and make a reliable comparison of the size distributions. Thus, the analysis of the shape parameter showed that the upper tail of each large inclusion distribution decayed to infinity.
Regarding the evolution of the large inclusion distributions, they shifted to smaller sizes as the process advanced, and the changes were more appreciable in the LF treatment than in the CC process. Furthermore, great differences between the end of the LF treatment and the start of the progressive CC process were observed, and they were more apparent as the CC process advanced. This highlighted the importance of the increased residence time of inclusions in the liquid steel from the Ca addition to the progress of the CC operation. On the other hand, the probability of finding an inclusion larger than a given "critical" inclusion size and the cumulative distribution function were estimated, which was used to analyze their evolution throughout the steelmaking process for each of the studied heats as well as the comparison among distributions of different heats.