2013 Volume 53 Issue 11 Pages 1974-1982
Non-metallic inclusions have always been the active subject of steelmaking research to improve the steel cleanliness and to develop the so-called oxide metallurgy technology. Inclusions in molten steel form and grow by the sequence of nucleation, chemical and physical growth and removal. Thus, the size distribution of inclusions evolves continuously with time in molten steel, and significant changes in the steel conditions are reflected in the inclusion size distribution as well as in the inclusion chemistry. This study aims to provide a new approach to interpret the inclusion size distributions. The concept of the Population Density Function (PDF) is introduced to objectively represent a given inclusion size distribution. Several possible applications of PDF analysis are presented to demonstrate the advantages of the utilization of the PDF for understanding the inclusion formation mechanism during the steelmaking process. Several ambitious ideas to utilize the PDF for inclusion size control are also presented.
Non-metallic inclusions are a major issue during the production of high performance steels, as they influence the microstructure and structural properties to a large extent. They are often considered as harmful to the final product quality and to the steel processing productivity, so that many industrial efforts are directed towards improving inclusion removal. Another, more positive approach is to use non-metallic inclusions to produce steels with enhanced or tailored properties. In both cases, the key issue is to control the characteristics of the inclusion population in the liquid steel, such as number, composition, morphology, size and spatial distribution.
Non-metallic inclusions can have beneficial effects on the properties of the final product by promoting the formation of a fine-grained structure during phase transformation. This approach, known as Oxide Metallurgy,1,2) utilizes non-metallic inclusions in steel as nucleation sites of acicular ferrite during the austenite to ferrite transformation, leading to a significant increase of the strength of structural steels and the development of tailored microstructures to obtain the desired properties.3) The grain refining can be achieved through a strict control of the nature and the size distribution of the nucleating particles.4) A very fine, narrow size distribution of the nucleating particles should be the aim. Inclusions smaller than 1 μm are inefficient to serve as nucleation sites, whereas larger inclusions are detrimental to steel properties.4)
It is primordial to the steelmaker to understand the mechanism of inclusion formation during the steelmaking process in order to control their presence and to enhance the quality of the final product. In this paper, the concept of the Population Density Function (PDF) to represent a given inclusion size distribution will be introduced. The PDF provides a highly practical and user-independent form of summarizing the properties of a specific inclusion population. Several examples of PDF analysis based on laboratory and real steelmaking plant data will be presented to demonstrate the advantages of the utilization of the PDF for understanding the inclusion formation mechanism during the steelmaking process. Several ambitious ideas about inclusion control will conclude this study. This study aims to provide a new approach to interpret the inclusion size distributions which would foster new ideas for future research.
The size distribution of the inclusion population after deoxidation is the result of a combination of processes of nucleation, growth and removal. Each size distribution is unique and represents the history of the inclusion population. Figure 1(a) shows the predictions, according to the static model of Zhang and Lee,5) of the size distribution of Al2O3 inclusions after deoxidation of steel containing initially 300 ppm O. Figure 1(b) shows the prediction of a similar model by Zhang and Pluschkell.6) By considering the theories of homogeneous nucleation, growth by diffusion and the mechanisms of collision and coalescence, it demonstrates that one or more of these growth processes dominate the growth of inclusions at various stages of the process, involving significant changes in the inclusion size distribution.
It is interesting to note that the calculated size distribution curves (Fig. 1) follow the same general tendency as those obtained experimentally.7,8,9,10,11) The combination of all processes yields size distributions that can be satisfyingly modeled by lognormal functions.7,12) These functions have a quadratic shape in a log-log frequency versus size diagram, as schematically illustrated in Fig. 2. The size distribution is initially narrow (curve t1 in Fig. 2), with a maximum of the number density located at small inclusion size. With time, the size distribution becomes broader and is shifted to larger inclusion sizes (curves t2 and t3 in Fig. 2). The position of the maximum number density is also shifted to the right, while its value decreases. A lognormal-shape size distribution reflects, therefore, the active formation and growth of inclusions, during which net transfer of matter occurs between the steel and the inclusions.
Conceptual view of the time evolution of inclusion size distributions from active formation and growth of inclusions (t1 to t3, red lines) corresponding to lognormal functions (dotted lines) to chemical equilibrium represented by a straight line (t4, blue line). The size distributions are plotted in a log-log inclusion frequency versus size diagram.
Once the deoxidation reaction is over (supersaturation is low so that no new inclusion can form) and most of the inclusions are removed from the bath, the size distribution tends towards a straight line in a log-log frequency-size diagram (curve t4 in Fig. 2), as it will be described in more detail in section 4.1. In that case, chemical equilibrium is reached and particle sizes are mainly determined by the balance between inclusion attraction and breakage, which strongly depends on surface energy and local steel flow.
These two radically different inclusion size distributions that can be observed in steel represent two fundamentally different processes determining the shape of the inclusion size distribution in steel. Thus, the inclusion size distribution conveys important information on the chemical and physical state of the melt and on possible reoxidation events.
2.2. Interpretation of the Size DistributionThe size distribution is an important tool as it provides a snapshot of the system in time and is shaped by nucleation and growth mechanisms. It is commonly used in the interpretation in nature and in crystallization experiments to estimate important parameters, such as thermal history, growth and nucleation rates. The crystal size distribution (CSD) analysis uses population balance modeling, in which the population density of crystals is the fundamental variable. This technique was developed in the chemical engineering industry in 1971 by Randolph and Larson13) and applied to geologic systems by Marsh.14) In this approach, the distribution of observed crystal sizes in a sample is combined with conservation differential equations describing the balance of crystal numbers growing into and out of a size class in a time Δt. Various theories have been proposed in literature to link changes in CSD shapes with nucleation and growth processes,14,15,16,17,18,19,20,21,22,23,24) as illustrated in Fig. 3. The interpretation of CSDs, the deduction of quantitative information on nucleation and growth rates, and the evaluation of the relative importance of chemical reactions from the shapes of CSDs are complex tasks. Many processes that shape the CSD curve are proportionate and selective, and may affect a limited range of crystal sizes, creating distortions and curvatures in the CSDs. This method of interpreting size distributions has not been applied to inclusions in steel, though inclusion nucleation theories and inclusion growth mechanisms are used to simulate inclusion size distributions.
Representation of the crystal size distribution in a ln(n(d)) versus d following the model of Marsh. The solid line represents steady state nucleation and constant growth rates, while dotted lines and dashed lines show, respectively, coalescence and Ostwald ripening processes causing deviation from the straight line (adapted from Blower et al.16)).
Nowadays, automated feature sizing systems operating on Scanning Electron Microscopes (SEM) are widely used for inclusion analysis. This technique combines the advantages of Energy Dispersive X-ray Spectrometry (EDS) with those of digital image analysis of Backscattered Electron (BSE) micrographs. It provides fast measurements of composition, size and morphology for thousands of particles embedded in the steel matrix, giving a more statistically sound inclusion size distribution in the sample compared to manual inclusion size measurements.
3.1. The Population Density Function to Represent Inclusion Size DistributionsTo draw the size distribution, the frequency of inclusions in a given size bin, nv(LXY), (particle number per volume) is divided by the bin width (LY – LX) as shown in Eq. (1). The latter is the definition of the Population Density Function (PDF)25) and has length–4 units.
| (1) |
Compared to classic (and popular) histograms, this representation of the size distributions eliminates the arbitrariness caused by the choice of the number and the size of the bins defined by the user. The PDF is unique for a given distribution and summarizes the properties of the population. The use of the PDFs is therefore very functional to compare size distributions between different samples or studies. To illustrate this, Figs. 4(a), 4(b) and 4(c) show histograms drawn from the same data set when different definitions of the bins are employed. The respective PDF curve calculated from the histogram is plotted on the diagram. It is clear that, though they represent the same inclusion data set, the three histograms are completely different and can yield different conclusions on the particle size distribution, depending on the choice of the bins. On the other hand, the three PDF curves, which are gathered together in Fig. 4(d), are identical, providing a better way to display the size distribution.
(a) to (c): Histogram and PDF representations of the size distribution of an identical data set using three different bin definitions. The three PDFs curves are superimposed in (d).
The classical inclusion size analysis technique gives access to two dimensional data, resulting from the intersection of the three dimensional inclusions with a plane. The estimate of the parameters in three dimensions calls upon stereology methods.17,25) The conversion of two-dimensional to three-dimensional data can be done using the program CSDCorrections that includes a correction method for the “cut-section” and the “intersection-probability” effects.25,26) A detailed description of the calculation method is provided by Higgins.25) The raw data set of the equivalent diameters and the measured area are given as input to the software. The overall shape of the particles must be estimated using four parameters, namely the three aspect ratios (short, intermediate and long dimensions) and the degree of roundness. Based on the two-dimensional raw data and the overall shape parameters, the software calculates the PDF curve, the total number and the total volume percentage of particles, and the goodness of the fit.
3.3. Statistical Distributions to Represent Inclusion Size DistributionsThe shape of the size distribution is remarkably linear or quadratic in a logarithmic representation. Consequently, the most relevant statistical distributions to describe size-frequency distributions are respectively fractal (or power law) and lognormal distributions.23) These distributions are entirely defined by two adjustable parameters. That is, the information in the size distribution of thousands of inclusions can be summarized by only two parameters. This representation of the size distribution in such a concise way has the advantage of enabling a more efficient exchange of information between studies and an easier comparison between several size distributions. As chemical and physical processes such as nucleation, growth, breakage, agglomeration, sintering and removal of inclusions shape the inclusion size distribution with time, the two parameters of the statistical distribution might represent the contribution of a given process to the size distribution. Moreover, the statistical properties of the distribution, such as the mode, the median, the standard deviation, etc. are easily accessible and facilitate the comparison of size distributions. Definitions of the fractal and lognormal distributions and their properties can be found elsewhere.27,28)
In this section, our recent efforts on the applications of inclusion PDF analysis for real plant sampling data are presented. The plant data are from two different steel works, Tata Steel Europe, Ijmuiden, the Netherlands and Hyundai Steel, South Korea.
4.1. Evolution of Al2O3 Inclusions in Al-killed SteelZinngrebe et al.29) investigated the evolution of non-metallic inclusions in the series of Ti-alloyed Al-killed steel samples during the entire secondary steelmaking and casting processes using Automated Image Analysis (AIA) implemented with the aid of SEM-EDS technology. The series of samplings were performed in the secondary steelmaking plant of Tata Steel Europe, Ijmuiden work. The inclusion analysis technique using the EDS spectrum and the data conversion process to inclusion population density function (PDF) were performed based on the measurements of thousands of inclusions. Figure 5(a) shows the evolution of the PDF of Al2O3 inclusions with secondary steelmaking process (after Al deoxidation in RH-OB, after stirring station, and during casting), which is regenerated from the results of heat B1 published in reference.29)
As can be seen, the inclusion PDF just after Al deoxidation shows a lognormal shape, which clearly demonstrates the nucleation of new inclusions, where net mass transfer between solute and inclusion takes place. The PDF changes to a power law distribution with time (linear function in the log-log plots), when chemical equilibrium between solute and inclusions is reached. One of the most important findings by Zinngrebe et al.29) is that the PDF in all investigated heats approached the so-called ‘reference line’ within a rather short mixing time (less than 10 min), which is plotted as a dashed line in Fig. 5(a). The average slope of the reference line is –3.5. When chemical equilibrium is reached, the inclusion population size distribution is governed by the competing processes of coalescence/growth and collision/breakage.
Recently, the same inclusion analysis was performed by Hyundai Steel30) for Al-killed low-carbon steel. Their analyzed data are plotted in Fig. 5(b). Because the analysis was based on routine sampling practice, the Al2O3 inclusion PDFs were analyzed after Al deoxidation in the RH-OB and at the tundish during casting. Interestingly, the reference line suggested by Zinngrebe et al.29) is still valid at Hyundai Steel. This can possibly mean that the reference line representing the dynamic equilibration of the Al2O3 inclusion population is similar regardless of the steelmaking plant if the secondary steelmaking practice is similar. This makes sense considering that the dynamic equilibration profile is mainly governed by the physicochemical properties of the non-metallic inclusions such as interfacial tension and thermodynamic equilibrium constant.
4.2. Diagnosis of Reoxidation EventsAny chemical and/or physical modification in the state of the steel melts is instantaneously reflected in the inclusion size distribution. Disturbances in the steelmaking process by reoxidation events can be easily diagnosed from the appearance of the lognormal shape of the inclusion size distribution. A reoxidation process involves the nucleation and growth of new oxide inclusions, producing a strong lognormal PDF profile. Thus, the occurrence of such undesirable processing effects can be detected both qualitatively, and evaluated quantitatively, with the PDF analysis.
Zinngrebe et al.29) reported that the inclusions size distributions (in the form of PDF) in a certain heat largely deviated from the reference line after the stirring station. For instance, the normalized PDFs of Al2O3 inclusions in their results (heat B5) are drawn in Fig. 6(a). The PDFs were normalized by taking the exponential of the difference between the measured ln(PDF) and the reference line in order to see the deviation more clearly: the reference line has a constant value of 1 in Fig. 6(a). These size distributions exhibit a well-defined lognormal shape, which is typically observed during active inclusion formation and growth. Zinngrebe et al.29) concluded that this happened due to a reoxidation event at the stirring station (most probably by the accidental formation of an open-eye during gas stirring). The reoxidation of the steel produced new Al2O3 inclusions, which yielded a lognormal size distribution similar to that observed after the deoxidation event.
The inclusion PDFs in Fig. 5(b) from Hyundai Steel are shown as normalized PDFs in Fig. 6(b). According to the researchers in Hyundai Steel,30) the steel cleanliness became worse in the tundish compared to that after Al deoxidation in the RH-OB. As can be seen clearly in Fig. 6(b), the lognormal PDF of Al2O3 inclusions occurred in the tundish. This is most probably due to steel reoxidation by low-quality reducible refractory linings in the tundish.
4.3. Nozzle CloggingNozzle clogging is one of the issues raised by non-metallic inclusions. There are two possible known causes of nozzle clogging: (i) accumulation of pre-existing non-metallic inclusions in molten steel on the nozzle wall and (ii) reoxidation of steel near the nozzle wall by the nozzle refractory and/or air penetration through the nozzle refractory. A combination of both causes can take place depending on the situation during plant operation.31)
Figure 7 shows one of the PDF analyses performed on non-metallic inclusion deposit in the tundish well near the Submerged Entry Nozzle (SEN) taken in plant during the casting of Al-killed low carbon steel.32) As can be seen in the optical micrographs of the sample in Fig. 7(a), layers of non-metallic inclusions accumulated on the surface of the tundish well area, forming layers of agglomerated inclusion with solidified steel in-between. The inclusion chemistry is Al2O3. However, the inclusion chemistry cannot tell whether the inclusions were deposited from pre-existing Al2O3 inclusions from the bulk steel or were generated in that area by steel reoxidation. The inclusion PDF can provide more insight into the deposit formation. The PDFs of the inclusions in the deposit are plotted in Fig. 7(b) against the ‘reference line’ for matured Al2O3 inclusions existing in the bulk tundish steel. As mentioned in section 4.1, the Al2O3 inclusion population produced after Al deoxidation has reached a steady state, producing a power-law distribution named the ‘reference line’. Clearly, the inclusions accumulated on the tundish wall exhibit lognormal PDFs, similar to the inclusions produced by reoxidation in Fig. 6. That is, new inclusions have formed and grown in the deposit, creating a deviation from the reference line. Therefore, from this inclusion PDF analysis, the origin of the inclusions causing tundish well clogging can be understood. In the present case, the analysis of the PDF suggests that reoxidation played a role in the deposit formation, though agglomeration of pre-existing inclusions has certainly contributed to some extent. It should be noted that clogging in the tundish well and in the SEN is affected by numerous factors related to casting operations and secondary steelmaking practices. Therefore, inclusion size distributions in deposits should be regarded on a case-by-case basis. It can be emphasized that the PDF analysis for non-metallic inclusions can give a good clue to understand the origin of clogging formation.
Investigation of Al2O3 inclusions accumulated near the tundish well region.32) (a) Optical micrographs of the sample. The dotted area on the left-hand side micrograph is enlarged on the right-hand side micrograph. (b) PDF of the inclusions at different locations in the deposit. Sample locations are indicated in (a).
For the active utilization of non-metallic inclusions (oxide metallurgy) for acicular ferrite formation, the control of non-metallic inclusion size distribution is critical. Size distributions of primary oxide inclusions produced by deoxidation of Fe-10 wt% Ni alloy with Al, Si, Zr, Ti, Ce, etc. have been extensively measured by Suito’s group.7,8,10,33,34) A potentiostatic electrolytic extraction was employed to dissolve the metal sample. The particles were collected on a filtration membrane and observed by using SEM. The size of each particle on the micrograph was obtained by using a semi-automated image analyzer. In these studies, the particle size distributions are represented by the number of particle per unit volume as a function of the log of the particle size. The size distributions of ZrO2, Al2O3, MgO and CaO–Al2O3 inclusions from the study of Nakajima et al.,33) those of SiO2 from the study of Karasev and Suito,8) and those of MnO–SiO2 from the study of Ohta and Suito10) were transformed into PDFs following the procedure explained in section 3. Each size distribution has a holding time of 600 s.
The experimental size distributions represented as PDF are indicated by markers in Fig. 8. As seen in the figure, most of the size distributions have a clear quadratic shape in a log-log PDF versus inclusion size diagram, which can be estimated using the lognormal distribution. The shape parameter σln and the scale parameter m defining the lognormal distribution for each size distributions were obtained from the quadratic fit and listed in Table 1. The dotted lines in Figs. 8(a) and 8(b) represent the estimated lognormal distribution for each experimental size distribution. A possible secondary particle formation might have occurred during Mg deoxidation, explaining the hump that forms in the MgO size distribution between 0.1 and 0.3 μm diameter in Fig. 8(a). Similarly, bimodal curves are observed in the size distributions of SiO2 and MnO–SiO2 particles in Fig. 8(b). The curves at small inclusion size correspond to secondary particles that are produced during rapid cooling and solidification of the melt. As seen in Fig. 8(b), nucleation and growth of secondary particles also yield a lognormal size distribution. The curves at large inclusion size correspond to primary oxide particles and were used to estimate the lognormal distributions. In the case of MnO–SiO2 particles, the separation between primary and secondary particle size distributions is clear, resulting in a good fit of the primary particle size distribution data. However, the separation is more ambiguous in the case of SiO2 particles, resulting in a larger error on the parameters of the lognormal distribution.
Representation of experimental particle size distribution of various oxide inclusions in a log-log inclusion diameter d (μm) versus PDF (mm–4) for a holding time of 600 s. The full markers represent the experimental distribution, while the dotted lines indicate the lognormal distribution estimated from the experimental data. Experimental data are taken from (a) Nakajima et al.33) and (b) Karasev and Suito8) and Ohta and Suito.10)
Suito and Ohta7) derived the geometric standard deviation of the size distributions of different deoxidation particles for various holding times. The observed trends were extrapolated to zero holding time to estimate the spread of the size distribution soon after nucleation. They found that the geometric standard deviation increases with an increase in the interfacial energy between oxide and liquid Fe. The latter was explained using the homogeneous nucleation theory, in which the nucleation rate decreases with an increase in the interfacial energy. They concluded that, in order to obtain a narrow size distribution, oxides with low interfacial energy with liquid Fe are required.
The shape parameter of the lognormal distribution, σln, is a measure of the skewness and spread of the distribution. In order to obtain similar findings as Suito and Ohta,7) the shape parameters derived from the experimental size distributions measured at a holding time of 600 s are compared, in Fig. 9, with the interfacial energy between oxide and liquid Fe at 1600°C taken from Suito and Ohta7) (Table 1). The correlation between spread of the distribution and interfacial tension observed by Suito and Ohta7) is clearly seen between the shape parameter of the lognormal distribution and the interfacial tension. The latter demonstrates that the interfacial tension has a significant influence on the spread of the size distribution during nucleation and growth (especially via Ostwald ripening). The PDF representation of the particle size distribution combined with a lognormal distribution is an easy and effective way to obtain valuable and concise information on the physical and chemical processes occurring during nucleation and growth. In addition, the influence of important physical processes and properties are gathered in only two parameters that summarize the entire inclusion size distribution.
Correlation between the shape parameter of the lognormal distribution, σln, derived from experimental and predicted particle size distributions of various oxide inclusions and the interfacial tension between the oxide and liquid Fe.
Numerical simulations5,6,11,35,36,37,38,39,40,41) have been extensively used to simulate inclusion size distributions in molten steel in order to understand the inclusions behavior in the melt and control their size distribution. Among the mathematical models, population balance equations have been used by Zhang and Pluschkell,6) Zhang and Lee,5) Kwon et al.40) and Lei et al.41) to build a general nucleation-growth model that can predict time-dependent particle size distribution of inclusions. The predicted number density of inclusions as function of inclusion size, as mentioned in section 2.1, is qualitatively very similar to experimental size distributions. Therefore, the predicted size distributions of Al2O3 from the results of Zhang and Lee5) and those of ZrO2 and Al2O3 in molten steel from Lei et al.’s study41) were converted into PDFs and plotted in Fig. 10 using solid markers. The calculated size distributions were taken for a holding time of 600 s to enable comparison with the experimental size distributions from previous section.
Representation of predicted particle size distribution in a log-log inclusion diameter d (μm) versus PDF (mm–4) for a holding time of 600 s. The full markers represent the size distribution based on the mathematical models of Lei et al.41) and Zhang and Lee,5) while the dotted lines indicate the lognormal distribution estimated from the predicted data.
As seen in Fig. 10, the two size distributions from Lei et al.’s calculations41) show a clear quadratic shape in the given inclusion size range, which can easily be estimated by lognormal distributions. The shape and scale parameters of the lognormal distributions are listed in Table 1, and the estimated lognormal distributions from the predicted data are plotted as dotted lines in Fig. 10. Though the size distributions of Al2O3 and ZrO2 seem similar, small differences can be noticed in the adjustable parameters of the lognormal distributions. In the case of Zhang and Lee’s predicted results5) for Al2O3 inclusions, the typical lognormal shape is clearly observed in the small size range between 0.08 and 0.8 μm, as indicated by the dotted line in Fig. 10. Above 0.8 μm, the predicted size distribution deviates from the lognormal distribution and tends to be linear in a log-log diagram.
Different values of interfacial tension between the inclusion and liquid Fe were employed in the mathematical models: Zhang and Lee5) used 0.5 N m–1 for Al2O3, whereas Lei et al.41) used 1.1 N m–1 for ZrO2 and 1.6 N m–1 for Al2O3. The relation between the shape parameter of the lognormal distributions from the predicted size distributions and the interfacial tension is compared with the experimental data in Fig. 9. As can be seen, the relation between shape parameter and interfacial tension is in good agreement with the experimental trend. As these mathematical models are built on nucleation and growth theories, they can provide very useful information to determine which mechanisms and properties have a significant influence on the spread or other important characteristics of the inclusion size distribution.
As mentioned previously, the predicted size distributions at 600 s by Zhang and Lee5) deviates from the lognormal distribution for inclusions larger than 0.8 μm and tends to be linear in a log-log diagram. This tendency is clearly observed in the evolution of the size distributions as a function of holding time (Fig. 1(a)). At a holding time of 30 s, the size distribution becomes suddenly broader as the right-hand side of the size distribution is shifted to larger inclusion size. The subsequent deformation of the size distribution becomes more pronounced with holding time. From a holding time of approximately 60 s, part of the size distribution follows a linear relationship in a log-log diagram. The same behavior can be observed in the calculation results of Zhang and Pluschkell6) for holding times of 100 and 1000 s (Fig. 1(b)). In both studies, the slope of the line seems to remain almost unchanged with holding time. To investigate further this feature, the PDF of the predicted particle size distributions from Zhang and Pluschkell6) at 1000 s and from Zhang and Lee5) at 600 s were calculated and shown in Fig. 11. A linear fitting of part of the PDF was performed to obtain the slope of the line (power-law distribution). Interestingly, both predicted size distributions yield a similar slope. The slope of the predicted size distribution by Zhang and Lee5) is 3.43, whereas that by Zhang and Pluschkell6) is 3.35. Even more interesting, these slopes are very close to that of the reference line observed in industrial samples, 3.5 (see section 4.1). Such mathematical models are very useful to understand the chemical and physical processes behind the formation and evolution of the inclusion population in liquid steel. Further investigations would be required to determine which mechanisms and properties (such as interfacial tension) drive the establishment of this reference line and how the slope of the reference line can be changed.
Representation of predicted particle size distribution in a log-log inclusion diameter d (μm) versus PDF (m–4). The full markers represent the size distribution based on the mathematical models of Zhang and Pluschkell6) for a holding time of 1000 s and Zhang and Lee5) for a holding time of 600 s, while the dotted lines indicate the linear fit estimated from the predicted data.
In this paper, the concept of PDFs to represent inclusion size distributions was presented along with the methods to calculate the PDF and the advantages of using statistical distributions to summarize them. Examples of currently available inclusion size distribution were collected, converted into PDFs and analyzed in a systematic manner. Both laboratory and in-plant sampling data proved that the inclusion PDF can provide a good insight into the evolution of the inclusion size distribution during the process. According to recent sampling data from real steel plants, the size distributions of non-metallic inclusions (mainly Al2O3) generated by deoxidation or reoxidation show a lognormal type PDF just after their formation in molten steel. The size distributions then evolve toward a power law type PDF with time, which is also predicted by numerical models. Steel reoxidation events could be identified in the inclusion PDF plots. This implies that the inclusion PDF can be effectively used as an internal probe to diagnose chemical reaction events during the secondary steelmaking process. For example,
i) inclusions formed through reactions with refractories or slag can be easily determined: if liquid steel is highly reduced after the deoxidation stage, non-metallic inclusions can form as a result of oxygen transfer from the slag and/or refractories to liquid steel (steel reoxidation). The newly formed inclusions should exhibit a lognormal PDF distribution.
ii) if nozzle clogging is due to the deposit of existing inclusions from molten steel on the nozzle wall, the size distribution of the deposited inclusions would show a power law type PDF. If the inclusion size distribution in the clogging deposit has a lognormal shape, the active formation of new inclusions through nucleation and growth took place, suggesting that an additional source of oxygen exists in that area.
Although the current knowledge on inclusion PDF can give a rough idea of the occurrence of reoxidation phenomena and a rough control of the inclusion size distribution for oxide metallurgy applications, the following techniques should be further developed to obtain more accurate inclusion size distribution data: (i) adequate sampling technique with minimizing reoxidation during sampling and secondary precipitation during cooling, and (ii) automated inclusion analysis technique with minimizing the noise data. Numerical simulations of inclusion nucleation/growth/removal in conjunction with CFD simulation should be investigated to understand their effects on the PDF. Fundamental physical properties such as interfacial tension between liquid steel and inclusion depending on melt composition and inclusion type are key information to perform numerical simulations of inclusion evolution during the secondary steelmaking process.
The authors would like to thank Mr. J.-B. Lee from Hyundai steel for providing their in-plant inclusion analyses data.
