A Bogue approach applied to BOF slag

An industrial by‐product of the steel industry called basic oxygen furnace (BOF) slag has recently undergone extensive research for high‐end applications outside of road load and landfill. In contrast to the Bogue methodology used with regular Portland cement, BOF slag lacks a quick and straightforward quantitative phase analysis procedure that would allow it to be employed as a high‐end raw material. The main phases of BOF slag (C2S, C2(A,F), Ff, RO‐Phase, and f‐C) can be calculated using the method presented in this paper based on chemical composition.


Introduction
Bogue published his mathematical method to determine the phase quantities of regular Portland cement (OPC) based on its chemical composition approximately a century ago [1].Even though there have been technological advancements like X-ray diffraction analysis to quantify the clinker phases, the Bogue approach gained enormous popularity in the cement and construction industries and is still used today [2][3][4][5].Due to the fact that OPC phase qunataties control hydraulic characteristics, which in turn affect strength [6,7], knowing the phase proportions is essential for quality control.To ascertain the phase quantities of OPC and forecast its performance in mortars, the Rietveld quantitative phase analysis (RQPA) on X-ray diffraction patterns is a useful method.However, due to the intricacy of the X-ray diffraction patterns of OPCs, professional knowledge is needed to precisely determine phase quantities.There have been numerous reports on RQPA's challenges with OPC [4,8].As a result, the indirect method of using the Bogue equations to ascertain the phasesproportions of OPCs continues to be a crucial instrument in the study and production of cement.
It is acknowledged that the production of OPCs by the cement industry contributes significantly (6-7 wt%) to global CO2 emissions.Fuel combustion and CaCO3 decomposition during the calcination process are the main emissions' causes (90 wt%) [9].Utilizing industrial byproducts as supplemental cementitious materials (SCMs) or creating OPC-free binders are two ways to lower CO2 emissions.Basic oxygen furnace slag (BOF slag), also known as Linz-Donawitz slag (LD slag), is an industrial byproduct that has not been extensively employed as SCM or as OPC free binder but the potential [10][11][12].There are three primary benefits: i) the significant production of BOF slag (more than 100 Mt/year globally) [13];ii) the similar chemical composition of BOF slag and OPCs with high CaO and SiO2 concentration of >35 and >10 wt%, respectively [14]; iii) the similar mineralogical composition of BOF slag to OPCs, since the major phases of BOF slag are C2S and C2(A,F) [15,16].The application of BOF slag as SCM [12,17,18] or as a standalone binder through thermal [19], hydrothermal, chemical [11,[20][21][22], and carbonational activation [23] processes has thus come under increased examination.The most typical phases described for BOF slag are shown in Table 1, while the mean chemical composition of BOF slag published in the literature is shown in Table 2 [12].
BOF slag is a complex mineralogical material with a number of phases, hence RQPA is difficult to perform.The difficulty of the RQPA of the BOF slag, which is reflected by a number of causes, frequently results in an erroneous quantification of phase amounts even including falsy identidied phases.Impediments within phases may have an impact on the powder pattern [4] i) solid solutions systems [24,25], ii) significant microabsorption effects when measuring samples containing more than > 10 wt% Fe with Cu-radiation [26][27][28], and iii) the large number of phases (> 5) and therefore resulting peak overlap.These arguments show that precise identification with the Xdiffraction method and RQPA is necessary to ascertain the correct phase amounts of the BOF slag.However, if all of these causes are not addressed, it is extremely likely that inaccurate results will be found, which frequently results in a wrong interpretation of the research's findings.This work offers an alternate and straightforward method for determining the BOF slag phase proportions based on the Bogue technique.In order to convert the chemical composition of BOF slag as determined by X-ray fluorescence (XRF) and Fe-titration into phase amounts, an equation sequence-the Bogue BOF slag model-was developed.In order to produce a reference sample, BOF slag is first sampled from processed batches, then crushed, split, and powdered.A powdered sample of the substance was subjected to XRF, Fe-titration, and RQPA.In order to determine the phase quantities from the chemical composition data, an equation sequence resembling the Bogue equations was created.Then, the simulated phase quantities are evaluated and compared to the associated RQPA values.

BOF slag sampling
The used BOF slag is derived from the Tata Steel IJmuiden, the Netherlands The data set consists of 21 bulk samples from the 0 -25 mm BOF slag production referenced with "B" that were sampled in the time period of 13.03.to 24.09.2020.Each bulk sample represents approximately the average of weekly BOF slag production at the steel plant.The BOF slag samples of the size 0 -2.5cm were taken during a quality monitoring investigation from processed batches that contained multiple (> 50) basic oxygen furnace heats (each 30 tons of BOF slag per heat) approximately every 9 days.The samples were taken according to standard NEN 7302:1999.Additionally, the chemical composition of five finer samples (0 -1 mm) referenced with "F" and six coarser samples (4 -5.6 mm) referenced with "C" are used that were derived by sieving the bulk samples and analysed.Because finer fractions of BOF slag are more oxidized (i.e., have lower FeO/Fe2O3) and weathered than coarser fractions, the addition of these samples allows for a wider range of FeO/Fe2O3 and degree of weathering to be covered [29].In order to cover this wide range of phase composition, these samples were added to the study.

Sample analysis
Samples of BOF slag are subjected to a two-step process for XRF analysis.In order to eliminate volatiles, the sample is heated to 1000 °C in the first phase, and the loss on ignition (LOI) is noted.Lithium borate (Li2B4O7:LiBO2 = 65:35) was employed in a second process to create fused beads in a weight-proportion of 1:10.On a PANalytical Axios, samples are analyzed, and the components Al2O3, CaO, Cr2O3, MgO, MnO, P2O5, SiO2, TiO2, V2O5, and Fe total are quantified.
Fe can be found in BOF slag in three separate Fe species (Fe metallic, Fe 2+ , and Fe 3+ ), according to other investigations [20,30,31].The redox titration method, based on the titration with potassium dichromate and the brominemethanol titrimetric method, is used to quantitatively identify the various Fe species for each sample.Following that, Fe metallic and Fe 2+ are calculated in accordance with ISO 5416-2006 andISO 9035:1989.By subtracting the titration results from the XRF-determined Fe total , Fe 3+ is calculated.
For the quantitative phase analysis with the Rietveld method, additional sample preparation is required prior to the analysis [26].As an internal standard, 0.4 wt% Si metal is added to 3.6g of BOF slag sample.The material must be ground to a grain size under 10 µm in order to have repeatable results [26].This is accomplished by employing a Retsch McCrone micronizer with a 20-minute milling cycle and 7 ml of cyclohexane.After drying for 5 min at 70 °C in a furnace, samples were back-loaded into metal sample holders for XRD analysis.To prevent microabsorption with the Fe-rich materials during the XRD measurement, Co-radiation is favored over Cu-radiation [26,27,32].XRD measurement were carried out on a Malvern PANalytical XpertPro with a Co-tube (Kα1 1.7901, Kα2 1.7929 ) and Pixel 3D detector.A fixed divergence slit setting of 0.5° and 0.04 rad soller was used for the measurements.The measurement's 2Theta range was 10 to 120 degrees.
For the Rietveld quantitative phase analysis, Table 3 lists the structures that were taken from the ICDS or PDF database along with the stoichiometry for each structure.For Rietveld quantification the actual measured compositions of the slag phases are used as the derived with EDS-Spectral Imaging and PARC quantification [14,34].

Modelling framework
Each modeling strategy has a distinct goal.The purpose of this study is to forecast the BOF slag phase amounts in relation to the primary phases.Regarding modeling of the phase proportions of BOF slag, it is also important to realize that BOF slag is a highly variable industrial by-product since steel companies [35] are primarily focused on the right composition of the steel and the composition of BOF slag follows to serve this goal.Due to the wide variety of input of blast furnace metal and output steel compositions, there are also a wide variety of slag compositions that are produced in the basic oxygen steelmaking process.These compositions can vary not only between steel plants [12,36], but even during the production of a single steel plant [15].For instance, according to [12], the CaO and SiO2 content of the examined BOF slags ranges from 34 to 57 wt% and 7.7 to 36 wt%, respectively.As a result, the composition of the BOF slag phase will likewise vary greatly.Instead of more extreme chemical compositions, the modeling seeks to forecast the phase proportions of BOF slag for normal BOF slag chemical compositions.We recommend the following definition for typical BOF slag composition: BOFS values for average chemical composition are [12] ±5 wt% (Table 2).It should be made clear that if single converter heats are accumulated over a longer length of time (> one week) and processed together, BOF slag output of a steel factory may be highly stable (±3 wt% CaO).
Additionally, despite the fact that OPC and BOF slag exhibit certain similarities in their chemical and phase compositions [12] and that both are crystalline materials with initially relatively low amorphous contents (< 5 wt%) [3,37], the modeling technique is slightly different, due to the presence of many Fe species, including metallic Fe, FeO, and Fe2O3 (Fe metalic , Fe 2+ , and Fe 3+ , respectively).The only Fe species found in OPC is Fe 3+ , also known as Fe2O3, and it is solely incorporated into the C2(A,F).In contrast, C2(A,F), RO-Phase, Ff, and metallic Fe are all present in BOF slag along with other Fe species.Due to the difficulty of recovering all metal droplets from BOF slag, the metallic Fe is typically about 1 wt% [38].The FeO/Fe2O3 ratio in BOF slag can vary significantly (at least 0.6 -6.8 by mass) [39,40], even within steel plants, as will be demonstrated, where several heats intended to reduce chemical variability and continuously comparable cooling techniques are used.Additionally, dichromate titrimetry is typically used to determine the Fe speciation rather than XRF [41].
The common BOF slag phase assembly and the genesis of certain phases must be understood in order to determine the common BOF slag chemical composition.Since we follow the Bogue method, cement notation will be utilized for phase names rather than the standard mineral names found in the literature (Table 1).In BOF slag, the most prevalent phases are C2S, C2(A,F), RO, f-C, and Ff.The following phases are also possible: C3S, CF (Fe-Perovskite), Cc, and CH.Understanding how these phases form is crucial in order to calculate the normative phase proportions.The phases Cc and CH are weathering byproducts of C2S and f-C, as already shown by [35].They are unstable and lose their volatile content at high temperatures > 800 °C.and would form f-C at steelmaking process conditions.As a result, Cc and CH should be included in form of their f-C equivalent in the modeling of the phase assemblage.The cooling conditions and CaO content [15,30] of the BOF slag play a large role in the formation of C3S.The presence of considerable levels of C3S (> 3wt%) cannot be taken into account in the modeling calculations because C3S = C2S + f-C.However, under industrial cooling circumstances (i.e.slow cooling) this exsolution reactionwill take place and C3S decomposes and CaO values are typically lower than the boundary of 47 wt% set by [15] for C3S formation.Lastly, Ff, referred to as magnetite or spinel, is another secondary phase that only develops in oxidizing conditions.but is unstable with standard oxygen furnace settings [42].The generation of Ff is mostly dependent on the cooling conditions during the post-processing of the BOF slag [16,33,43].In BOF slag under industrial cooling settings, f-C originates from three different sources: undissolved flux particles [44,45], exsolution from C3S that forms alongside C2S, and eutectic f-C that occurs at the conclusion of the crystallization sequence.It's possible that the f-C content is highly changeable and difficult to forecast because these origins depend not only on the total CaO content but also on the cooling conditions and oxygen blowing time in the basic oxygen steelmaking process.
Therefore, the provided model will have limitations for BOF slags with high CaO (> 47 wt%) and more unusual cooling processes (such as air granulation), in which case C3S may be preserved.The most prevalent phase in BOF slag (> 35 wt%) is C2S, which typically exists in two polymorphs: β-C2S and α'-C2S [14].Both polymorphs are classified as C2S in the modeling approach.FeO, MgO, MnO, and trace levels of CaO ( 5 wt%) make up the solid solution known as the RO-phase, also known as wuestite in the literature [12,15,46].To sum up, the modelling is targeting a phase assemblage that consists of C2S, RO-phase, C2(A,F), Ff, and f-C based on the ordinary BOF slag chemical compositions and slow cooling circumstances are typically relevant in the industrial BOF slag processing.
The following step will determine which oxides are present in which phases or create solid solutions.Assigning the oxides to their appropriate phases based on known phase compositions [14,34].Minor oxides (<5 wt% of the bulk composition of the BOF slag), such as V2O5, Cr2O3, P2O5 TiO2, are categorized into a single phase in agreement with their dominant partitioning behaviour.The RO-phase contains MgO, FeO, MnO, and trace amounts of CaO (<5 wt%) in a solid solution.The modeling also makes the assumption that all of the Cr2O3, MgO, and MnO are integrated into the RO-Phase in agreement with observations [30].It is assumed that the RO-phase is devoid of CaO to simplify the modeling.For the same reasons, it is assumed that Fe2O3 and FeO make up Ff pure.Although TiO2 is partially present in C2, it predominantly reports to the the C2(A,F) phase.Hence, in the model all of the TiO2 and Al2O3 is assigned to C2(A,F) [14,47,48].In addition, C2(A,F) contains small amounts of Fe2O3 and CaO.As C2S, C3P, and C3V make up a solid solution system, in the model C2S includes all SiO2, P2O5, and V2O5 and a significant portion of CaO.Table 4 provides the summary of the oxides' assignments to their host phases.It is necessary to assume that a portion of the Fe total (i.e., the sum of Fe metallic , Fe 2+ , and Fe 3+ ) was initially Fe 3+ that formed during the basic oxygen furnace process (i.e., Fe2O3) and is incorporated into C2(A,F), while the remaining Fe 3+ is used to form the secondary Ff phase which formed during cooling, this in order to calculate the appropriate f-C at the end of the modeling sequence.However, the precise percentage of the initial Fe 3+ that is contained in C2(A,F) depends on the Fe total .However, it is known that the initial Fe 3+ /Fe total in the fundamental oxygen furnace fluctuates between 0.25 and 0.33 based on internal records from the Tata Steel facility IJmuiden.Hence, the BOF slag phase composition is modelled with three Fe 3+ /Fe total ratios (0.25, 0.292 and 0.33).X Fe total is the quantity of Fe total in mass, and ωi is the original Fe 3+ /Fe total ratio.While the remaining Fe2O3 is believed to be created secondarily and hence affects the amount of Ff.

Modelling formulations
Form the above mentioned framework conditions the following equations follow which are based on [1,5]: →   = (  −   ) +   +   +   (6) These equations are the molar balancing equations that describe the formation of the major BOF slag phases (C2S, C2(A,F), Ff and RO-Phase and ωi is the initial Fe 3+ /Fe total at the end of the BOF-process.When the equations 1 -7 are transferred to mass proportions using molar masses of element oxides in each phase the following equations are derived: With these equation one can calculate directly the phase wt% from the oxide wt% of the chemical analysis, without the conversion to mol%.As such these equations are easily applicable to any oxide composition data for BOF slag.

Compositional differences between grain size fractions
The chemical composition and RQPA results of the samples are used to compute and validate the precision of the Bogue BOF slag model Appendix, respectively (Tables 1  and 2).The reported phase proportions are significantly influenced by the sample type (B, C, or F).When compared to B and C-type samples, the RQPA C2S values for the F-type samples are much lower.For instance, the mean C2S for F16-F20 is 32.6 wt%, while the averages for B16-B21 and C16-C21 are 40.7 wt% and 42.8 wt%, respectively.The higher amount of weathering products (WP; the sum of Cc, CH, and amorphous) in the F-type samples-15.1 wt% on average (F16-F20) against 1.9 wt% on average (B16-B20)-confirms this as well.The RQPA results for the RO-Phase and Ff amounts reveal decreasing and increasing phase amounts, respectively, from C-type over B-type to F-type samples, which illustrates how oxidation relates to fragmentation of BOF slag.From coarser to finer grain sizes, the increase in Fe2O3/Fe total was already noted by [29,49].With a mean of 18.8 wt% for the F16-F20 samples and a higher mean of 19.6 wt% for the B16-B20 samples, the RQPA results of C2(A,F) appear to be unaffected by oxidation and weathering.The increase in Fe2O3 from weathering is therefore correlated with formation of Ff.

Effect of varying initial Fe 3+ /Fe total (ωi) on the modelled phase quantities
The combined chemical composition data from XRF and Fe titration (Appendix Table 1) are applied here as input values for the Bogue BOF slag equations (Equations 8 -12) to calculate the phase quantities, which are then compared to the RQPA data in Figure 1.
The modelled phase quantities for three selected ωi (0.25, 0.292 and 0.33) are shown in Figure 1 and demonstrate that the ωi has no effect on the modelled C2S contents as to be expected since C2S does not incorporate Fe in the model.Its amounts solely depend on the bulk chemical SiO2, P2O5, and V2O5 contents.The ωi, on the other hand, has a major impact on C2(A,F), as the contents of C2(A,F) depend on the Fe 3+ availability defined the ωi.As a result an increase in the simulated C2(A,F) mean from 19.6 wt% (ωi = 0.25) to 23.3 wt% (ωi = 0.33) is found for the entire sample suite.Conversely, since the simulated amount depends on the remaining Fe2O3 concentration, the amount of Ff is also affected.The model yields an average of 7.3 wt% Ff for all samples at the lowest ωi ratio.
The model predicts incorrectly negative values for Ff in one sample at the highest ωi of 0.33 because more Fe2O3 is assumed than found by titration analysis.Consequently, more Ff is generated the lower the ωi is set and diminished FeO affects the RO-Phase levels in the model.As a result, the means of the modelled RO-Phase amounts rise from 22.7 wt% (ωi = 0.25) to 23.7 wt% (ωi = 0.33), on average.The computed f-C is related to the CaO left over after satisfying the C2S and C2(A,F) rules of the model, and is also affected by the ωi.A higher ωi causes more C2(A,F) to develop and subsequently results in less CaO available for f-C.As a result, f-C values are the lowest for ωi of 0.33 and the highest for ωi of 0.25.

Comparison between normative and RQPA phase quantities
Figure 1 A-C present the comparison between the normative and RQPA phase quantities.For all three ωi the C2S is overestimated in model calculation.There are multiple reasons that could explain the modelled overestimation: i) the exclusion of C3S in the model, whereas small amounts of C3S could be present in the BOF slag (<3 wt%) [15], ii) all V2O5 is assumed to be incorporated in C2S, while C2(A,F) also incorporates V2O5 [50] and iii) that the C2S is partially weathered during storage.The latter assumption appears realistic because the F-type samples have structurally the lowest amount of C2S and significantly higher amorphous, Cc and CH [35].C2(A,F) values are the closest to the 1:1 linear correlation for the lowest ωi of 0.25 and overestimated by the Bogue BOF slag calculation when an higher ωi is assumed (Figure 1c).Also modelled Ff values are best matched at the lowest ωi value of 0.25.In contrast modelled RO-Phase values are the closest to the 1:1 linear correlation when a higher ωi of 0.33 is assumed and on average somewhat underestimated by the Bogue BOF slag model.The f-C values are the closest and best modelled when a higher ωi value of 0.33 is taken, whereas it seem that at ωi of 0.25 the Bogue BOF slag model slightly overestimates the f-C.Even though the bulk of the points plot the closest to 1:1 linear correlation at ωi of 0.33 some f-C values are negative therefore ωi of 0.25 appears more realistic.Moreover, due to outside storage and subsequent weathering of the BOF slag, the initial f-C could have been significantly higher than the RQPA value in the norm-calculation for the lower ωi of 0.25 [35].
To summarize, the lowest used ωi of 0.25 gives probably the most accurate phase estimations for initial BOF slag phases.However, due to outside storage C2S and f-C have been lost by weathering and are therefore overestimated by the Bogue BOF slag model compared to the actual sample values from RQPA.Moreover, a significant lower reporting of C2S in the RQPA is caused by ignoring the presence of small quantities of C3S in the norm calculations and by assigning all V2O5 to C2S.These shortcomings can be addressed in future improvements of the Bogue BOF slag model to give more realistic phases estimations.Also the weathered character of the BOF slag should be considered based on a correction using the loss on ignition determined prior to the XRF analysis.

Conclusions
BOF slag is known to be one of the most complicated materials to perform a RQPA based on multiple peak overlap and multiple solid solution systems.This study presented a simple and quick tool to model quantities of major BOF slag phases C2S, C2(A,F), Ff, RO-Phase and f-C based on a bulk chemical composition analysis.Using this Boque slag norm calculation, steel companies and scientist working with BOF slag can quickly predict BOF slag phases amounts without the use of XRD and Rietveld knowledge.
The Bogue norm calculation strongly depends on the initial Fe 3+ /Fe total (ωi) of the BOF slag which is needed in order to discriminate how much Fe 3+ is accommodated by primary C2(A,F) and how much by secondary formed Ff.For the BOF slag of Tata Steel IJmuiden the best ωi value seems to be 0.25.However a variable ωi depending on the amount of Fe total could also be considered, but it should be noted that for each converter heat the ωi may vary, so a plant average is more suitable, if large average process lots are described with the Bogue BOF slag model.
The presented Bogue BOF slag norm calculation still requires some improvement in order to be able to predict actual phase quantities for the major BOF slag especially after weathering because weathering changes the phase assemblage.The simplest and least time consuming way to perform this correction is to use the loss on ignition determined prior to XRF analysis, but this development still needs statistical assessment.
For the future, it is planned to continue with I routine RQPA measurements of produced slags and compare these to the Boque slag norm values.to improve the model.Moreover, the chemical compositions of the major BOF slag phases can be calculated from the model and compared to measured data of chemical phase analysis from SEM-EDS.

Table 3
[13]chiometry and ICSD/PDF Nr. database codes used for the structures in the RQPA of BOF slag samples.It should be noted that a fixed stoichiometry is in all cases.The specific stoichiometry that is used for C2(A,F) is calculated from chemical compositions determined by large area phase mapping analysis (PARC) on average BOF slag samples from the Tata Steel plant IJmuinden[13].