Optimization of the Two- and Three-Dimensional Characterization of Rare Earth-Traced Deoxidation Products

The importance of recombination is illustrated in Sample 6, with a consequential error between the original and recombined results of approximately 13.60%. The production of this sample differed from Samples 1 – 5 due to a longer reaction time, and as a consequence, more clearly segregated inclusions were found. Concerning the production conditions for the different samples, Sample 6 most resembles industrial samples. 4) Differences between the 2D and 3D characterization of traced NMIs occurred for all samples concerning mean ECDs, tracing rates, and chemical compositions. The mean ECDs and tracing rates decreased for all samples from cross-sections to ﬁ lters. The chemical composition of ﬁ lters shifted to the oxygen corner due to the double-detected carbon signal. Both methods prove to be advantageous for use in further inclusion characterizations since information regarding actual sizes and shapes can be gained by applying sequential chemical extraction as a 3D method


Introduction
The topic of steel cleanness has received a lot of research attention over the last few years. Nevertheless, the influence of different nonmetallic inclusion (NMI) types on mechanical properties [1][2][3] remains somewhat unclarified. A similar uncertainty applies to the cause of the clogging phenomenon [4][5][6] observed during continuous casting. The aim to improve downtimes during production is achieved by getting deeper knowledge about the formation and evolution mechanisms of NMIs. [7,8] Especially the evolution of inclusions in Tistabilized ultra-low carbon steels is the focus of recent research projects since this steel grade is especially prone to clogging. [9,10] Another interesting inclusion type regarding steel cleanness is the MA-spinel. In the study of Deng et al., [11] the formation and evolution of this inclusion type are explained in detail over the steelmaking process.
One option for studying the formation of inclusions and how they behave throughout processing is to use tracing with rare earths (REs), especially La [12,13] and Ce. [14,15] This technique enables the tracking of deoxidation products, such as Al 2 O 3 , across the process. Tracing the changes of alumina inclusions in their morphology and behavior throughout the process is necessary since these NMIs tend to clog in, for example, Ti-stabilized ultra-low carbon steels. The clogging phenomenon is still not entirely clarified. Hence, it is essential to gain more information concerning possible reoxidation processes during production.
The higher deoxidation potential of REs leads to interactions with preexisting alumina inclusions and results in a partial reduction of these deoxidation products. As a result, the REs are bonded to the preexisting inclusions. [12] Several studies have already investigated and described the modification of, for example, alumina inclusions by La [16,17] and Ce. [18,19] Using automated scanning electron microscopy with energydispersive spectroscopy (SEM/EDS), RE-containing inclusions can easily be relocated since these particles appear brighter, due to their higher atomic numbers than the surrounding steel matrix. [16] However, REs modify preexisting deoxidation products and, thus, influence the morphologies, properties, and behaviors of these particles. [17][18][19][20] Different approaches are necessary for characterizing nonmetallic inclusions, as a single technique cannot be used to identify all parameters. The reviews of Kaushik et al. [21] and Zhang et al. [22] describe direct and indirect characterization methods. Additionally, Mayerhofer [23] listed and compared various instruments for evaluating steel cleanness, regarding tested sample size, duration of analysis, detectable inclusion size, and determination of chemical composition, morphology, and spatial distribution. For the 2D characterization of microscopic NMIs, the most applied and comprehensive method is SEM/EDS analysis. Using this technique, information regarding spatial distribution and chemical composition can be determined for small samples. 3D methods can be additionally applied to investigate the actual sizes and shapes of particles since NMIs are randomly cut in cross-section samples. [24] Principally, extraction techniques are divided into chemical and electrolytic procedures. The choice of extraction method and extractant depends on several parameters, such as the stability of the inclusions or the chemical composition of the steel, which must be dissolved. [25,26] 2D and 3D characterization methods for nonmetallic inclusions were compared by Doostmohammadi et al. [27] and Zhang et al. [28] Janis et al. [29] studied the impact of clusters on clogging formation. For this investigation, they extracted clusters by applying the electrolytic extraction technique. The studies by Bi et al. [30] and Nabeel et al. [31] also dealt with the extraction of clusters. Compared to Janis et al., [29] RE-containing clusters were investigated. This kind of cluster differs in its wetting behavior and clogging tendency. These two characterization techniques must be optimized for correct analyses since REs tend to form heterogeneous multiphase inclusions, mainly oxides, oxide-sulfides, or sulfides.
The present work involves characterizing RE-traced alumina inclusions by using different methods. The optimization of characterization methods for RE-containing multiphase inclusions is crucial since the usage of REs, especially Ce, continues to increase primarily for their grain refining effect but also due to further tracing experiments. In addition to a state-of-the-art technique-the automated SEM/EDS analysis-the sequential chemical extraction method and its optimization for these specific inclusion types are also discussed. Concerning the 2D characterization, a double-threshold scan must be implemented for the detection of heterogeneous RE-containing multiphase inclusions. Furthermore, a developed MATLAB tool is essential for the location and recombination of erroneously split particles. The sequential chemical extraction method, a 3D analysis technique, is utilized to determine the actual sizes and shapes of inclusions. Later, the extracted particles are investigated using automated SEM/EDS analysis to obtain the mean equivalent circle diameters (ECDs) of the traced particles. Ultimately, the benefits and disadvantages of 2D and 3D characterization methods are compared.

Experimental Section
The 2D and 3D characterizations of RE-traced nonmetallic inclusions were performed on six samples. Samples 1 to 5 were produced in a high-frequency remelting (HFR) furnace (Linn High Therm GmbH, Eschenfelden, Germany) on a laboratory scale. Electrolytic iron with a high oxygen content of %330 ppm was used for the trials. The samples were melted at temperatures slightly above the liquidus temperature of pure iron (1550-1570°C) under an inert atmosphere. After a short dwell time, the melts were centrifugally cast at a high mean cooling speed. Aluminum was added through a drilled hole for deoxidation. As a consequence, mainly aluminum oxides were formed. Besides Al, either La or Ce was additionally alloyed; hence, the deoxidation products, Al 2 O 3 NMIs, were traced using these elements. A detailed description and a schematic illustration of the single states of the samples' production in an HFR furnace could be found in Thiele et al. [32] The production route differs for Sample 6. This sample was produced in a resistance-heated Tammann-type furnace (Ruhrstrat HRTK 32-Sond.) and heated to 1600°C under an inert atmosphere. Al was added to the melt for deoxidation, and 6 min later, La, wrapped in an Al foil for alloying to prevent oxidation. After 10 s of stirring, the melt was held for 10 min, slowly cooled to 1350°C, and then quenched in water. Inclusion types similar to those in Samples 1-5 were formed in this process; however, larger inclusion sizes were observed as a result of slower cooling. A previous study by Dorrer et al. [33] illustrates the experimental setup of a resistance-heated Tammann-type furnace. Furthermore, the addition of alloying elements over the process is explained.
The chemical compositions of the raw material and the investigated samples for the 2D and 3D characterizations are listed in Table 1. The composition of Sample 6 differs in the case of C and Al contents compared to the samples produced using HFR. Three different alloying concepts were used for the REs. In Samples 1 and 3, REs were put in a steel tube. In Samples 2, 4, and 6, REs were wrapped in Al foil, and in Sample 5, ferrocerium was used as an alloying element. The influence of the alloying concepts on the output of REs has previously been discussed by Thiele et al. [32] The composition in terms of REs varies across the six samples, depending on the various alloying concepts and furnaces used.

Characterization Methods for RE-Traced Nonmetallic Inclusions
Two methods were used in this study to characterize nonmetallic inclusions-one 2D and one 3D approach. For the 2D analysis, cross-section samples were investigated using manual and automated SEM/EDS. With this technique, information regarding the NMIs' spatial distributions, chemical compositions, and number per square millimeter could be obtained for a predefined sample area. For the 3D characterization method, the particles in the steel samples must be isolated from the steel matrix to reveal the entire morphology of the particles and provide additional information about their individual sizes. The 3D characterization method used in this research work was the sequential chemical extraction technique. All particles containing >0.1 wt% La or Ce were defined as traced NMIs.

Sequential Chemical Extraction
The sequential chemical extraction technique was used to separate nonmetallic inclusions from the steel matrix. The principle of extraction is to dissolve the surrounding steel matrix with acid without dissolving or modifying the NMIs. An essential advantage of sequential chemical extraction is the conservation of rather unstable inclusions, such as sulfides, on the filters. [25]  By using samples with a high surface-to-volume ratio, a greater amount of matrix could be dissolved in the same amount of time. In addition, the samples must be thoroughly cleaned so that no corroded passages or scale residues were left on the sample and the dissolution of the steel matrix was not affected. As a next step, the steel sample was put inside a beaker. A 3% nitric acid solution was added as an extracting agent until the sample's surface was completely covered. Reactions causing the dissolution of already-extracted NMIs, such as sulfides, were inhibited by utilizing the sequential technique. The precipitation was steadily pipetted every 15 min and subsequently transferred into another beaker. A schematic illustration is shown in Figure 1.
The total duration of the sequential chemical extraction for this study was 1 h. A vacuum filtration system with polycarbonate filters was utilized to separate the extracted inclusions via consecutive filtering with different pore sizes (12 and 1 μm). The 12 μm filter mainly removed matrix and grinding residuals. Extracted NMIs were primarily found on the 1 μm filter since many inclusions were in the microscopic range. After drying the filter on air for 12-14 h, the filters were cut and stuck on pin sample holders with high-purity, double-sided, conductive carbon adhesive pads. The pins were sputtered with carbon to achieve optimized high-resolution SEM measurements. Automated SEM/EDS analyses of the extracted particles were possible due to the carbon layer on the surface of the filters.

Optimization of the Automated SEM/EDS Measurement
The automated SEM/EDS analysis has to be optimized when analyzing RE-traced inclusions. In general, inclusions are detected due to a gray scale difference in the backscattered electron (BSE) image since the contrast of the image is highly dependent on the material's atomic number. Thus, classical oxide inclusions appear darker than the surrounding steel matrix. Conversely, REs appear brighter than the surrounding steel matrix in BSE images. In most cases, the detection of the entire RE-containing NMIs is inhibited since traced deoxidation products are mainly multiphase inclusions with brighter and darker parts depending on the dominating element. Particles brighter than the steel matrix can be detected in addition to the darker ones using a double-threshold scan with the automated SEM/EDS measurement. In this study, a field-emitting SEM (JEOL 7200 F; JEOL Germany GmbH, Freising, Germany) equipped with a 100 mm 2 SDD-EDS detector (Oxford Instruments Ultim Max 100; Oxford Instruments GmbH NanoAnalysis, Wiesbaden, Germany) was used for the characterization of the NMIs. The EDS spectra were collected by an area scan. The SEM software AZtec Feature (AZtec 5.0, Oxford Instruments GmbH NanoAnalysis, Wiesbaden, Germany) was utilized for automated particle analysis. The main measurement parameters for the automated SEM/EDS analyses were a beam energy of 15 keV, a probe current of 14 PC, a working distance of 10 mm, and a resolution of 2048 Â 1024 px at an EDS evaluation time per particle of 1 s. Different settings were required for crosssection samples and filters in terms of resolution and magnification. The resolution for cross-sections was 2048 px at a magnification of 200Â, and for filters, 1024 px at 400Â.
The use of a double-threshold scan means that a section is scanned twice. In this case, the thresholds were set in a manner to ensure that all particles darker than the matrix were detected first. The second step involved obtaining information regarding the brighter particles.
The same SEM was used for the 3D characterization, in which manual and automated SEM/EDS analyses of the extracted NMIs were performed.

Recombination Tool for Heterogeneous Nonmetallic Inclusions
During the automated SEM/EDS analysis, RE-containing multiphase inclusions were separated into two sections-a Ce/Laenriched one and one containing light elements, such as Al-oxides-as shown in Figure 2a,b. The colors represent the two different user-defined thresholds. Inclusions 1 and 2 (marked in blue) belong to the higher threshold value and Inclusion 3 (labeled in red) to the lower. This splitting process leads to a systematic error in the subsequent evaluation because one multiphase inclusion is treated as several individual parts. To address this problem, a MATLAB tool was developed and used to identify and merge parts of the inclusions that initially belonged together. The input data for this tool are the measurement results of the automated SEM/EDS analysis exported from AZtec Feature as an Excel file, which contains the morphological parameters and the chemical composition for every measured inclusion.
The first step of the recombination process is to identify particles that were split due to the double-threshold scan. Therefore, the algorithm iterates over all measured particles of the higher threshold value and examines a defined merging-condition with every low threshold inclusion. Within this examination, parameters for the shape and distance of the corresponding inclusions Figure 1. Schematic representation of sequential chemical extraction equipment (adapted from Mayerhofer [23] ).
www.advancedsciencenews.com www.aem-journal.com are calculated. When the heavy-element particle is below a defined distance (Equation (1)) to the compared light-element particle, the merging condition is fulfilled, and the algorithm combines them to form a postprocessed inclusion. The merging condition for putting the split inclusions together is set as follows Distance Center defines the space between both centroids. The calculation of Distance Shape depends on the shapes of both inclusions. SafetyFactor is included to compensate for the difference between a measured and a calculated inclusion shape caused by the limitation to using only two geometric forms with the available data and the low resolution of the automated SEM/EDS analysis. This factor reduces the distance between the two centroids and increases the possibility that inclusions are merged. The value for SafetyFactor was set as 3 μm, which was empirically determined by testing the algorithm on different datasets and validating the results by reviewing whether the inclusion findings were correct. The resulting output of the cluster finding process is a list of inclusions with their supposed partners, which will be merged in the next step to redisplay a split RE-traced heterogeneous NMI. The IDs of the listed inclusions can be searched in the original data from the automated SEM/EDS measurement with the AZtec Software. The validation is done on a random basis by manually comparing the supposed heterogeneous inclusions with the original SEM images.
The three different possibilities for the merging conditions are listed below: 1) Both inclusions are equiaxed: Distance Shape is the sum of both ECDs. 2) One inclusion is equiaxed, the other one elliptical: Distance Shape is the sum of the ECD for the equiaxed inclusion and the ellipse radius in the direction of the connection line for the elongated inclusion. The centroids of both inclusions define the connection line. 3) Both inclusions are elliptical: Distance Shape is the sum of both ellipses' radii in the direction of the connection line.
During the automated SEM/EDS analysis, the AZtec Feature software determines morphological parameters such as the aspect ratio (Equation (2)), ECD, length, breadth, and direction of the particles.
The algorithm uses those parameters to calculate a theoretical inclusion shape, simplified as a circle or an ellipse. The aspect ratio defines the distinctive feature between the two geometric forms. Inclusions with aspect ratios below a certain threshold value are treated as circular; otherwise, the shape will be set as an ellipse. This is important for the Distance Shape parameter in the mergingcondition (Equation (1)). Equiaxed inclusions can show an aspect ratio higher than 1 because the lengths and breadths do not necessarily need to be perpendicular. This is the case for squared shapes, which have an aspect ratio of 1.41 and, therefore, represent the algorithm's threshold value. For circular-treated inclusions, the ECD determines the radius for the calculated shape. For elliptical inclusions, the magnitude of the major axis is defined by the particle's length and the magnitude of the minor axis by the particle's breadth. A particle's direction represents the inclination angle between the horizontal and major axes. Figure 2c shows the calculated shapes of three different inclusions on the same particle that was used as an example in Figure 2a. Inclusions 1 and 2 have an aspect ratio higher than 1.41 and, therefore, they are treated as ellipses. The aspect ratio of Inclusion 3 is lower than 1.41; hence, it is represented as a circle.
The magnitude of the ellipse radius in a specific direction for the possibility of one equiaxed and one elliptical inclusion can be calculated using Equation (3). All variables in this equation are defined during the double-threshold scan. The length of the particle determines the value 2a (major axis of the ellipse) and the breadth of the particle determines the value 2b (minor axis of the ellipse). α is the inclusion's direction and describes the angle of inclination between the horizontal axis, x, and the inclusion's length value. θ is the angle between the major axis of the ellipse and the direction of the second particle. Depending on the value of α, either Equation (4) or (5) is used for the calculation of θ. Δy and Δx describe the distances along the vertical and horizontal axes, respectively, between the centers of the area.  www.advancedsciencenews.com www.aem-journal.com Figure 3 shows two inclusions with their corresponding geometric parameters. The radius r 1 of the elliptical inclusion is defined by Equation (3). Due to the circular shape of Inclusion 2, the ECD determines the value of r 2 . In this example, the sum of r 1 and r 2 is smaller than the distance between the centers of the area. Therefore, these inclusions will not be merged.
After validating all of the merging conditions, the algorithm's output is a list of inclusions. The user can review the results by comparing the listed entries with their representations in the actual SEM image. The respective inclusions can be manually removed from the list if discrepancies arise. Afterward, the inclusions in the finalized list are merged by calculating a new chemical composition based on the area-weighted percentage of their corresponding parts. The final output of this tool is an Excel file including the corrected number of inclusions with all of their properties.

Two-Dimensional Characteristics of Traced Inclusions
The 2D characterization was performed using automated SEM/ EDS analyses of cross-section samples and the subsequent application of the recombination tool. The data files from the automated SEM/EDS measurements were then used to determine the number of particles and the typification of NMIs. All particles without nonmetallic bonding partners were removed before the inclusions were rated in the respective single-phase classes (O, S, and N) or multiphase classes (OS, ON, NS, and ONS). The typification of the classified inclusions depends on which metallic bonding partner was present. In the HFR-produced samples that were investigated, over 99.5% of all measured NMIs were alumina inclusions. For Sample 6, approximately 85.0% of all detected particles were alumina inclusions. The other NMIs were preexisting silicon and manganese oxides from the raw material. As a result, only traced and untraced Al 2 O 3 NMIs were observed in this study. The tracing rate was % 98.23 AE 1.16% across all samples. Particles with a mean ECD of at least 1 μm were detected within these measurements. Across all cross-section samples, the mean ECD was %2.33 AE 0.42 μm. Sample 6 had a significantly higher mean value of 3.16 μm and the largest standard deviation of 1.56 μm. The inclusions were mostly globular, with a mean aspect ratio of %1.35 AE 0.08. The number of NMIs per square millimeter varied for the samples produced in HFR between 158.48 Nr/mm 2 for Sample 3 and 369.70 Nr/mm 2 for Sample 5, as shown in Table 2. Sample 6, produced in a heat-resistance furnace, had the lowest inclusion density with 51.45 Nr mm À2 . Figure 4 shows three separate Ce-traced Al 2 O 3 inclusions in Sample 4. Due to the use of a double-threshold scan, the particles were erroneously split up into seven smaller particles depending on their different grayscales. In Figure 4, the three brighter parts are marked in blue, and the four darker ones in red. By using the developed MATLAB tool, the particles, which fit together, were found and merged into three heterogeneous NMIs.
The relative numbers and percentage of the recombined NMIs and their corresponding parts (pseudoinclusions) can be seen in Table 2. In addition, the consequential errors between inclusions in the original and recombined results were calculated and listed. The error is defined as the difference between the percentage of Figure 3. Example of an elliptical and circular inclusion with the corresponding geometric parameters (adapted from Meng et al). [35]  pseudo-NMIs and assembled NMIs after using the recombination tool. Between 0.45% and 1.75% of the detected Al 2 O 3 inclusions in Samples 1-5 originally fit together. Sample 6 had a significantly higher amount of erroneously split multiphase inclusions, with a total of 13.60%.
Changes in the main parameters, such as the mean ECDs, chemical compositions, and tracing rates, were investigated and compared before and after applying the recombination tool. Table 3 lists the mean ECDs values for the Al 2 O 3 -NMIs before and after recombining. The mean ECDs were almost unchanged, with a slight increase in standard deviation for Samples 1-5. For Sample 6, the mean ECD increased by over 0.27 μm to a mean value of 3.43 μm. After recombining the particles, the mean RE contents decreased, and the standard deviations were minimized for all six samples. Concerning the tracing rates, no changes were observed for any sample.

Three-Dimensional Characteristics of Traced Inclusions
In Figure 5, 2D and 3D inclusion mappings of Sample 3 are compared. The chemical distribution of NMIs was similar to the investigation of the cross-section. Hence, the NMIs were finely dispersed and heterogeneous for the five samples produced in the HFR furnace. Moreover, the RE oxides were brighter and mainly in the center of the inclusions.
The inclusions in Sample 6 (as seen in Figure 6) show a stronger segregation tendency and a tighter separation between the different phases of the complex inclusions. The NMIs are larger and have greater RE-containing areas in multiphase inclusions than Samples 1-5.
The topography of the extracted particles can be investigated in more detail with the secondary electron (SE) image. By comparing the BSE image with the SE image for Ce (Figure 7), it was determined that the supposed-centered RE-containing    www.advancedsciencenews.com www.aem-journal.com parts of the NMI were effectively agglomerated Ce oxide on the surface of the alumina inclusion. As shown in Figures 5 and 7, the morphology of traced alumina inclusions primarily consists of relatively globular and hexagonal NMIs. No elongated or cubic RE-containing alumina inclusions were detected with manual SEM/EDS measurements for these samples. Automated SEM/EDS measurements were performed, similar to the 2D characterization. Therefore, the 1 μm filter containing the extracted inclusions was coated with carbon before the investigation. All particles seemed brighter on the BSE images in the SEM/EDS since the inclusions were no longer surrounded by steel matrix and mounted upon conductive carbon adhesive pads. Due to this, only one grayscale was required as a detection-limiting automated measurement. The analyzed areas were minor concerning the high number of extracted inclusions on the filters. The measured area for each filter varied between 2 and 20 mm 2 since the extracted NMIs were irregularly distributed on the filters. The areas of the cross-section samples were relatively constant, however, at %10 mm 2 each. Figure 8 illustrates the number of Al 2 O 3 inclusions per square millimeter on the 1 μm filter and the number of traced inclusions. The number of inclusions varied considerably for all samples. Samples 2 and 3 had similar particle densities of 1932 and 1891 Nr mm À2 , respectively. In contrast, the difference between Samples 4 and 6 was substantial. Sample 6 had the lowest density, with 44.85 Nr mm À2 , while Sample 4 was %80 times denser, with over 2620 Nr mm À2 . The particle density of Sample 5 was somewhere in the middle, at 1487 Nr mm À2 , and that of Sample 1 was relatively low, at 569 Nr mm À2 .
The percentage of RE-traced particles was high for Samples 1, 3, and 5, with over 97.5% of a similar value to those of the    Lower values and variations were found between the standard deviations of the filter samples compared to those of the cross-section samples. Only Al 2 O 3 inclusions were found in the cross-section samples following SEM/EDS analyses. In addition to traced and untraced alumina inclusions, residuals from beaker glassesmainly silicon oxides-were also detected on the filters. These residuals were likely produced by the attack of the acid that was used for the chemical extraction. These erroneously detected inclusions were excluded from the evaluation to better compare the 2D and 3D analyses.

Mean ECDs of the NMIs in Cross-Sections and Filters
The values of the mean ECDs in Table 4 refer to all measured Al 2 O 3 inclusions. Samples 1-5 exhibited discrepancies in mean ECD of at least 0.01 μm between traced and untraced NMIs. Sample 6 had a slightly higher deviation of %0.25 μm between traced and untraced NMIs on the filter. Since the tracing rates were high across all samples, the mean ECDs can be related to RE-containing NMIs. Figure 9 shows ternary systems of RE-Al-O for each sample. A comparison between the chemical compositions of traced alumina inclusions is possible after 2D and 3D analyses.

Distribution of Traced NMIs in the Ternary System RE-Al-O
The chemical composition for each cross-section sample ranged from 25 to 45 wt% for O, 5 to 50 wt% for REs, and 8-60 wt% for Al. Rare exceptions were also found; these deviated NMIs were mainly located in areas with higher La content. Groups of isolated NMIs with values up to 80 wt% for La or Ce were detected.
Compared to the cross-section samples, the chemical compositions of extracted NMIs differed in several ways. Higher oxygen contents were measured for all NMIs on filters. The NMIs on filters for Samples 1-5 ranged from 50 to almost 100 wt% for O, 1 to 35 wt% for REs, and 2-25 wt% for Al. Single NMIs with higher RE concentrations were also detected. The extracted inclusions for Sample 6 were lower in oxygen content (20À65 wt%), more varied in La content (15À65 wt%), and slightly higher in Al content (5À40 wt%).

Evaluation of Sequential Chemical Extraction Technique
Extractions offer the possibility to investigate the morphologies of NMIs in more detail compared to the 2D analyses of crosssection samples, in which inclusions are randomly cut. [24] In addition to allowing the determination of the actual sizes and shapes of inclusions, extractions enable the distinction between large multiphase inclusions and clusters of NMIs, which may be detected as one particle when using automated SEM/EDS measurements of cross-sections.
One particular advantage of the sequential chemical extraction technique is that the dissolution of RE-containing Al 2 O 3 -inclusions can be inhibited with this method, even if the behavior of La-and Ce-containing NMIs was not known before. Further benefits of this method compared to the electrolytic extraction are the simple setup, the possibility of using stronger acids if necessary, and suppressed formation of FeCl 2 . [34] Especially, the last point is crucial for investigations of filters in the SEM. Although previous studies [23,25,34] have shown that unstable inclusions such as Ca-containing NMIs or sulfides remain on the filter following extraction with the sequential procedure, this has not yet been confirmed for RE-containing inclusions.
Despite the benefit of extracting even less stable inclusions, this method also has some disadvantages. An oxide layer is gradually formed during the sequential chemical extraction, delaying interactions between the steel sample and the extracting agent; thus, the reaction speed is reduced. Other extraction methods, especially electrochemical techniques, may be faster but are also more likely to dissolve less-stable inclusions, such as sulfides. Another disadvantage is that the acid interacts with the beaker glass. As a result, residuals from the beaker, mainly SiO 2 NMIs, contaminate the filter; hence, a correction of the SEM/ EDS measurement results concerning SiO 2 NMIs is required. Furthermore, it is recommended to use new pipettes for every extraction to prevent contamination with the inclusions from previous extractions.
After comparison of the benefits and detriments, the sequential chemical extraction technique with 3% nitric acid suits for extractions of unstable NMIs and NMIs, whose dissolution behavior is not entirely clarified.

Comparison of Two-and Three-Dimensional Characteristics
SEM/EDS analysis is the current state-of-the-art method for the characterization of NMIs. This analysis technique provides information regarding the number of NMIs per square millimeter, spatial distributions, and types of NMIs; however, the actual sizes and shapes of NMIs cannot be determined using this method. The error between the actual mean ECDs of the inclusions and the ones measured using automated SEM/EDS analysis of cross-sections is substantial since inclusions are randomly cut during sample preparation. [24] Therefore, 3D characterization methods become further necessitated. The sample areas of the investigated filters analyzed by SEM/EDS differed significantly from those of the cross-sections. The lack of uniform measurement areas results from the random, inhomogeneous distribution of the inclusions on the filters. Furthermore, the inhomogeneous distribution on the filters prevents the determination of spatial distribution. Moreover, corrections concerning residuals from beaker glass, mainly SiO 2 NMIs, must be performed following the analyses of the extracted particles. www.advancedsciencenews.com www.aem-journal.com Additionally, matrix residuals may adhere to single inclusions after an incomplete extraction, which requires further correction. The percentage of traced inclusions was over 80% for all samples. The tracing rate was even higher for Samples 1, 3, and 5, with over 97.5%. One explanation for the lower number of REmarked inclusions in Samples 2 and 4 could be the different alloying concept compared to Samples 1, 3, and 5, resulting in the additional formation of small, untraced deoxidation products. The use of a heat-resistance furnace for Sample 6 led to higher losses for Al and La. Furthermore, a lower number of NMIs per square millimeter were formed in the heat-resistance furnace. The reason for this is the longer dwell time resulting in agglomeration and enhanced removal of existing inclusions. Additional Al entered the melt with the alloying of La, and small inclusions were formed, similar to those in Samples 2 and 4.
By comparing the mappings of Samples 3 and 6 (in Figure 5  and 6), the RE-containing areas in Sample 3 were finely distributed within the alumina inclusions and not as clearly separated as those in Sample 6. This difference in the phase distribution of heterogeneous RE-containing inclusions could be due to the longer reaction time in the resistance-heated furnace and the segregation tendency of REs. Another distinction between these two production routes can be seen in the sizes of the NMIs. Slightly larger NMIs appeared in Sample 6, which could be due to slower cooling conditions or due to agglomeration tendencies of small NMIs caused by the longer dwell times in this furnace.
In addition, another finding was that the determined mean ECDs for the filters were smaller than for the cross-section samples. Concerning these results, many inclusions may have been below the detection limit since they were partly covert in crosssection samples. After extraction, the actual sizes of inclusions of at least 1 μm become visible, and the total mean ECD of the samples lowers. Karasev et al. previously commented on this phenomenon. [25] No reliable statements can be made about the number of NMIs per square millimeter in the sample or their spatial distributions on filters compared to cross-section samples. These characteristics primarily depend on the selected section of the filter.
As shown in Figure 10, extracted inclusions can also be very close to each other so that an automated measurement can detect them as one mesoscopic irregular-shaped particle instead of many partly globular finely dispersed multiphase (Al, La) oxides.
The ternary systems in Figure 9 show the different distributions of RE-containing Al-oxides of the cross-sections and filters from automated SEM/EDS measurements of each sample. The compositions of the majority of the NMIs in cross-section samples were in the range of complex REAl 11 O 18 inclusions (19.2 wt% RE, 41.0 wt% Al, and 39.8 wt% O), similar to the distribution described in Thiele et al. [32] In addition, accumulations of several inclusions were detected in all samples; these had similar compositions to that of the complex REAlO 3 (65.0 wt% RE, 12.6 wt% Al, and 22.4 wt%). Particularly for Sample 6, many inclusions were found with compositions similar to that of the complex REAlO 3 . A lower number of extracted particles were located in the oxygen corner of Sample 6 compared to the other samples since more matrix residuals were on the filters, weakening the carbon signal.
Concerning the extracted particles, the chemical compositions shifted to higher oxygen values. The cause behind this change to the oxygen corner was a falsification during SEM/EDS measurements. An oxygen bias occurs due to the double carbon signals that reach the detector simultaneously since the filters are mounted upon an adhesive carbon pad. The detector cannot correctly allocate the signal because oxygen has approximately twice the energy level of carbon. [16,34] Furthermore, the composition of the single extracted inclusions scatters in a broader range than the NMIs on the cross-section.
The characterization of RE-traced NMIs is improved due to the implementation of a double-threshold scan in the automated SEM/EDS measurement of cross-section samples. The usage of the sequential chemical extraction technique with 3% nitric acid as an extractant was essential since the stability of RE-containing inclusions in different extracting agents and methods was not entirely clarified before this study.
Due to the aforementioned reasons, the investigation of filters mainly delivers additional information regarding the morphologies of NMIs and, for multiphase inclusions, also regarding their phase distributions. However, an automated SEM/EDS analysis of cross-section samples cannot be replaced by filter investigations since information regarding the distributions and chemical compositions is not provided.

Optimization of Evaluation Regarding RE-Traced NMIs
The recombination of split-up multiphase inclusions is essential for correctly analyzing the data of automated SEM/EDS measurements after double-threshold scans. Without this correction, the number of NMIs per square millimeter and the mean ECDs of the inclusions would be incorrect. Due to the erroneous split-up, many small inclusions were detected before merging the NMIs. Hence, more NMIs per square millimeter are detected, and as a result, the mean ECDs are slightly lower before applying the recombination tool.
In addition to the mean ECDs, the chemical compositions of the split multiphase NMIs also changed after merging. Most notably, the mean RE-contents in the samples were reduced. www.advancedsciencenews.com www.aem-journal.com Before recombination, mainly small parts of the detected inclusions contained high amounts of La and Ce, which negatively impacted the mean value. The recombination tool corrects the chemical composition depending on the area fractions of the recombined parts of the NMI. Therefore, small, incorrectly split, highly RE-concentrated particles no longer influence the mean RE content. The tracing rate did not change after recombining the inclusions because low contents of REs were detected in the Al 2 O 3dominated parts of incorrectly split particles, and inclusions are defined as "traced" if containing at least 0.1 wt% of La or Ce. The number of incorrectly separated RE-containing multiphase inclusions compared to the number of correct inclusions was very low for Samples 1-5, with a maximum error of 1.75% for Sample 4, compared to 13.60% for Sample 6. The error is significantly bigger for the sample produced in the resistance furnace since longer interaction times between REs and alumina inclusions occurred. Therefore, most inclusions are not completely segregated or segregated enough to be split up by the double-threshold method. Hence, the recombination tool is necessary to prevent an incorrect evaluation of the automated SEM/EDS measurement results for RE-containing particles.
Meng et al. [35] discussed the merging of erroneously split RE-containing multiphase inclusions. Their study inspired the development of the recombination tool used in this work. The percentage of merged multiphase inclusions was larger in the study conducted by Meng et al. [35] since a higher BSE image resolution was set and submicroscopic NMIs were detected. By applying these settings in combination with the double-threshold scan, multiphase inclusions were more frequently split into smaller parts below 1 μm. As a result, more submicroscopic and microscopic particles were identified when detecting heterogeneous NMIs. The drawback of these settings is a higher measurement time due to the requirement of higher-resolution BSE images. The measurement of submicroscopic inclusions is seldom applied in industry, as detecting them requires increasing the measurement time, and NMIs from industrial samples show larger areas due to a more precise separation of multiphase inclusions, similar to Sample 6.
All extracted particles appeared brighter in the SEM compared to the inclusions on cross-section samples since filters were mounted upon carbon adhesive pads. Hence, traced multiphase inclusions were not divided into smaller NMIs, so no recombination was required for the NMIs on filters.
This MATLAB tool fits, especially for samples with clearly separated areas of the traced multiphase NMIs, such as Sample 6 or industrial samples, since rare earth elements tend to segregate and modify existing deoxidation products after a sufficient reaction time. [20,36]

Conclusion
Based on the performed experiments and evaluations, the following conclusions can be drawn: 1) A sequential chemical extraction was implemented for the 3D investigation of NMIs. This optimized method can be used for inclusions whose behaviors are not entirely researched, such as RE-traced Al 2 O 3 , since even less-stable NMIs, such as sulfides, can remain stable. The extraction output depends on both the duration of the whole extraction and the surface-to-volume ratio of the sample. 2) The 3D analysis of extracted particles offers an additional method to determine other characteristics of NMIs, such as the actual sizes and morphologies of the particles. The analysis of the extracted particles was performed using SEM/EDS measurements. The automated measurement of filters does not replace the analysis of crosssections, as the particles are inhomogeneous and randomly distributed.
3) The detection of RE-traced NMIs in cross-section samples implicates the need for a double-threshold scan with the automated SEM/EDS analysis. Due to the tendency of REs to modify deoxidation products, it is necessary to recombine the split-up multiphase inclusions with the developed MATLAB tool. Within this tool, the evaluation is corrected concerning the actual number of inclusions per square millimeter, the mean ECD, the mean chemical composition, and the number of clusters. The importance of recombination is illustrated in Sample 6, with a consequential error between the original and recombined results of approximately 13.60%. The production of this sample differed from Samples 1-5 due to a longer reaction time, and as a consequence, more clearly segregated inclusions were found. Concerning the production conditions for the different samples, Sample 6 most resembles industrial samples. 4) Differences between the 2D and 3D characterization of traced NMIs occurred for all samples concerning mean ECDs, tracing rates, and chemical compositions. The mean ECDs and tracing rates decreased for all samples from cross-sections to filters. The chemical composition of filters shifted to the oxygen corner due to the double-detected carbon signal. Both methods prove to be advantageous for use in further inclusion characterizations since information regarding actual sizes and shapes can be gained by applying sequential chemical extraction as a 3D method.