ISIJ International
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Chemical and Physical Analysis
Quantitative Analysis of Mineral Phases in Iron-ore Sinter by the Rietveld Method of X-ray Diffraction Patterns
Toru TakayamaReiko MuraoMasao Kimura
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2018 Volume 58 Issue 6 Pages 1069-1078


Analysis techniques for quantifying crystal structures of mineral phases and their fractions in iron ore sinters have been developed using the Rietveld analysis of X-ray diffraction patterns and applied to iron ore sinters of different mechanical strength, which were prepared by laboratory-scale sinter pot testing. The Rietveld analysis successfully determined the phase fractions and structural parameters for co-existing phases such as hematite (α-Fe2O3), magnetite (Fe3O4), multi-component calcium ferrites or silico-ferrite of calcium, and aluminum (SFCA:Ca2(Ca,Fe,Al)6(Fe,Al,Si)6O20 and SFCA-I:Ca3(Ca,Fe)(Fe,Al)16O28) and other minor phases. The strength of the iron ore sinter correlated with the quantity of magnetite and not simply with that of the calcium ferrites determined by this method. The lattice constants of calcium ferrites differed among the specimens; moreover, no clear difference was observed among iron oxide phases. These results show that the Rietveld analysis provides crucial information for controlling the sintering process and suggests the phase fractions.

1. Introduction

Sinter is an important feedstock material for the steel industry and accounts for more than 70% of the iron sources charged into blast furnaces. Recently, deterioration in the sinter quality has been a concern due to the degradation of the quality of iron ore resources. Therefore, it is necessary to develop a technique of quantitatively analyzing the sinter microstructure, which significantly affects the sinter quality, in order to accurately estimate the effects of raw iron ore variations on sinter quality.

Many studies have been conducted to understand the mechanism of sinter microstructures.1,2,3,4,5,6,7,8) The sinter microstructure evolves as follows: (1) the calcium ferrite melt is formed by a sintering reaction that progresses at non-equilibrium during the first few minutes. (2) Then, the melt diffuses and spreads in the surrounding iron ore particles. (3) Finally, the melt is cooled down and forms complex microstructures, wherein hematite (α-Fe2O3), magnetite (Fe3O4), calcium ferrites, and silicate slag are present as the main phases; they are complexly distributed together with the pores and are responsible for the development of sinter characteristics (strength, reducibility, reduction degradation, etc.). In particular, the characteristics and the formation reactions of calcium ferrite (as calcium ferrite melts and bonds with the nucleus particles of iron ores) have been investigated because these reactions comprise the key mineral phase in a sinter ore.

Hancart et al.1) reported that calcium ferrites in sinter are multi-component continuous solid solutions containing gangue components such as silico-ferrite of calcium and aluminum (SFCA). Inoue and Ikeda then clarified that the SFCA is an alternate crystal structure of pyroxene and spinel modules.2) Hamilton et al.3) determined a crystal structure model of SFCA {Ca2(Ca,Fe,Al)6(Fe,Al,Si)6O20} as an aenigmatite structure by X-ray single crystal structural analysis. Mumme et al. elucidated a SFCA-I {Ca3(Ca,Fe)(Fe,Al)16O28} and a SFCA-II {Ca4(Fe,Al)20O36} as SFCA homologues with different chemical compositions and crystal structures.4,5) Sugiyama et al. determined the crystal structure of the SFCAM phase wherein magnesium is a solid solute in SFCA by X-ray single crystal structural analysis.6) Webster et al.7) conducted high-temperature in situ experiments using X-ray diffraction (XRD) and clarified that SFCA-I formed before SFCA during the heating process. Kimura and Murao performed high-temperature in situ XRD experiments using synchrotron radiation and laser-microscopy at different heating and cooling rates. They showed that the phase transition temperature of calcium ferrite formation varies with supercooling and proposed the first “continuous cooling transformation diagram for sinter” as a commercial process guideline.8)

Microscopically, the calcium ferrite microstructure in sinter was observed to have an acicular or columnar morphology due to the differences in formation conditions.9,10) It is reported that acicular calcium ferrite tends to be contained in a high-reducibility sinter and it is formed in a low gangue content area in a low temperature sintering reaction.10)

Many studies have reported on the microstructure of sinter and the crystal structure of multi-component calcium ferrite. However, crystallographic studies of calcium ferrite have mostly been performed not using sinter ore samples on a sintering pot test scale (10-kg scale) or a commercial scale but using single crystals or laboratory-scale samples because it is difficult to analyze multi-component calcium ferrites in actual sinter ore, which is a polycrystalline sample. Therefore, a highly accurate throughput technique that is able to analyze the mineral phases in sinter ore is required.

A technique for identifying and analyzing the mineral phases in sinter ore could provide new knowledge concerning the sintering reaction behavior and the mechanism of sinter quality. In particular, identification and quantitative evaluation of calcium ferrite phases having different chemical compositions and crystal structures in sinter ore are important because calcium ferrites are affected by the sintering reaction and contribute to the sinter quality. However, such quantitative analyses of mineral phases, including multi-component calcium ferrites, are rarely performed.

In this study, we used the Rietveld method,11,12) an analysis technique that uses powder XRD patterns to determine the crystal structure and quantify the co-existing crystalline phases, to evaluate the sinter microstructure. It is difficult to quantify the calcium ferrite phases contained in a sinter ore by the simple deconvolution of their diffraction peaks because their diffraction peaks overlap. Furthermore, the crystal structure and the composition of the calcium ferrite in the sinter ore often do not agree with the findings of calcium ferrite models in a standard XRD database. Therefore, quantification using the reference intensity ratio and other conventional methods that use the standard XRD pattern are difficult. In contrast, the Rietveld method calculates the crystal structure parameters of mineral phases based on initial crystal structure models including lattice constants and atom coordinates and their mass fractions. Then the whole simulated XRD patterns are compared with the actually measured ones, and these parameters are determined by the least square method to minimize the residual. The absence of diffraction peaks at specific regions in the XRD pattern can also be used as information to refine the crystal structure parameters. Consequently, multiple phases with overlapping diffraction peaks can be quantified with high accuracy. Moreover, the crystal structures of materials that are continuous solid solutions having a complicated crystal structure and a wide solid solution range such as multi-component calcium ferrites can also be determined by refinement of lattice constants, atom coordinates, and other crystal structure factors. In addition, the results of the Rietveld method exhibit high repeatability and low arbitrariness as far as using the same initial model and the fitting procedure.

In this study, the crystal structures, fractions and crystal structure parameters of the mineral phases in sinter ore samples whose mechanical strengths differed, were determined quantitatively by the Rietveld method including the verification of the efficacy of the method. Then, the results of mass fractions and crystal structure parameters of mineral phases in the sinter ore were compared to consider their chemical composition and mechanical strength.

2. Experimental

2.1. Sample Preparation

The starting materials of iron ore sinter, known as quasiparticles, are agglomerated materials composed of iron ores (sinter feed or pellet feed), limestone, silica stone, olivine, and coke breezes. The limestone was blended with the main components to a CaO content of 8.2 mass%, and silica and olivine were also added to a CaO/SiO2 basicity of 1.6 by weight. Coke breezes and water were also added to 4.5 mass% and 7.0 mass%. The raw mixture was then granulated in a drum mixer for 5 min to produce quasiparticles.

The sinter samples were prepared by charging the quasiparticles into a cylindrical sinter pot with a diameter of 300 mm and height of 600 mm while taking care to prevent size segregation. Further, they were burned in the sinter pot (Fig. 1(a)). The charge weight and density of the quasiparticles were 60 kg and 1.62 t/m3, respectively. The top surface layer of the charged quasiparticles in the sinter pot was fired using burners for 90 s. The exhaust gas was sucked downward with a blower at a constant negative pressure of 8 kPa. Thermocouples were inserted in the top layer (Sample A), middle layer (Sample B), and bottom layer (Sample C) of the sinter pod to measure the temperatures in the respective layers. The measured temperatures are shown in Fig. 1(b).

Fig. 1.

(a) Schematic illustration of the sinter pot test and (b) heating patterns of each layer in the pot.

After the sintering reaction was completed, the sinter cake removed from the sinter pot was divided into three equal parts in the vertical direction. The shatter index test (SI test, JIS M8711:2011, by the Japanese Standards Association) was performed using the divided sinter cakes (Table 1). Samples of 5 mm or more in particle size were pulverized to an average particle size of about 10 μm in a vibration mill and subjected to a powder XRD measurement and a chemical composition analysis. The chemical compositions were determined by the following methods: the total iron content (JIS M 8212), the acid soluble iron (II) content (JIS M 8213), the calcium content (JIS M 8221), the silicon content (JIS M 8214), and the aluminum content (JIS M 8220).

Table 1. Results of a shatter test of each layer.
SampleSI (mass%)
Sample A73.3
Sample B85.9
Sample C89.7

※SI: Weight fraction of grains over +5 mm in diameter after shatter test.

In addition, the standard specimens of calcium ferrites were synthesized by sintering of powder oxides for verification of the analytical accuracy of the Rietveld method.

2.2. XRD Measurement

The pulverized sinter specimens were filled into a sample holder: a glass plate with a hollow (width: 20 or 18 mm, depth: 0.2 mm) with care not to cause preferred orientation of grains, and the specimens were examined by XRD measurement. XRD patterns were obtained using Cu Kα radiation as an X-ray source (40 kV and 40 mA) with the focused X-ray optics using a Rigaku Ultima III XRD system. We selected a one-dimensional detector (D/teX Ultra, Rigaku) and a Kβ filter.

The measurement conditions were a 2θ range of 10°–140° with a 2θ step of 0.02°, a step scan speed of 1°/min, and a divergence slit (DS) of 2/3°. The DS value of 2/3° was determined to obtain a sufficient irradiation area in the high angle range, as far as maintaining a sufficient angle resolution is concerned, because the mineral phase distribution in the sinter specimen is expected to have large inhomogeneity. The relatively large DS value of 2/3° results in the situation where the region irradiated by an X-ray beam is larger than that of the sample in a range of 2θ of 10°–19°, where the diffracted intensities were corrected by a factor of 1.66 × 10−1/sinθ. Moreover, it was confirmed beforehand that the radiation scattering from the sample holder had no influence on the determination accuracy of the Rietveld analysis.

2.3. The Rietveld Analysis

2.3.1. Overview of the Rietveld Analysis11,12)

The Rietveld analysis, which is the least square refreshment technique of powder XRD, optimizes scale factor (s), crystal structure factor (FK), preferred orientations (PK), and other parameters of each mineral phase by calculating the diffraction intensities in the i-th step (fi(x)) of each phase, as given by Eq. (1);11,12) this analysis is performed until the best fit is obtained between the observed powder diffraction pattern and the sum of the calculated patterns of each phase.   

f i (x)=s S R ( θ i )A( θ i )D( θ i ) K m K | F K | 2 P K L( θ i,K )Φ(Δ2 θ i,K ) + y b (2 θ i ), (1)
where x represents the structure parameters used for the calculation of diffraction patterns (e.g., lattice constants, atomic coordinates, atomic displacements). FK is the crystal structure factor of the K-th Bragg reflection; L(θi,K) is the Lorentz polarization and multiplicity factor; θi,K is the Bragg angle; SR(θi) is the sample surface roughness correction factor; A(θi) is the absorption factor; D(θi) is the constant irradiation correction factor; K is a value indicating the type of reflection contributing to the Bragg reflection intensity; mK is the multiplicity of the K-th Bragg reflection; Φ(Δ2θi,K) is the reflection profile function; and yb(2θi) is the background intensity at the ith step.

The relative weight (mass) fraction of phase h in a mixture is given by   

R h = ( s h Z h M h V h ) / ( j s j Z j M j V j ) (2)
where sj and sh are scale factors of the phases j and h; Zj and Zh are the numbers of formula units of the phases j and h in a unit cell; Mj and Mh are the mass of the formula unit of the components j and h; and VjVj are the unit cell volumes of the components j and h.

Background correction was carried out by the B-spline method function, and the split pseudo-Voight function was used as a profile function. The preferred orientation correction was performed by the March–Dollase function.

In this study, we refined the following structure parameters x: crystal structure factors and lattice constants of mineral phases, the profile and background functions. The peak width parameters that depend on the X-ray optics were excluded from this analysis. Moreover, the isotropic temperature factor in the crystal structure factors was also excluded. At first, refinements of all crystal structure parameters of the SFCA and SFCA-I were considered but they could not converge due to the too large numbers of the constituent atoms in the SFCA and SFCA-I structures. Therefore, the atomic coordinates of oxygen atoms, which contribute less to the crystal structure factors compared with metal atoms, were fixed. It was separately confirmed that fixing the atomic coordinates of oxygen atoms did not significantly affect the relative weight fraction and the other parameters of the mineral phases.

The goodness-of-fit (S) in the analysis was judged by the weighted pattern reliability index Rwp; these are given by Eqs. (3) and (4), respectively.   

R wp = [ i w i { y i - f i (x) } 2 i w i y i 2 ] 1 2 (3)
S= [ i w i { y i - f i (x) } 2 N-P ] 1 2 (4)
where wi is statistical weight; yi is observed intensity at the i-th step; N is the number of observation points; and P is the number of parameters adjusted. The Rietveld analysis was performed using software PDXL Version 2.0 (Rigaku Co.).

2.3.2. Choice of Appropriate Crystal Structure Models

It is important to set the initial crystal models for the mineral phases in the sinter ore specimens for profile fitting by the Rietveld analysis. According to the results of preliminary experiments with various sinter ore samples, we determined the crystal structure models for major phases as follows (Table 2): α-Fe2O3,13) Fe3O4,14) multi-component calcium ferrite SFAC phase3) and SFCA-I phase,4) dicalcium silicate Ca2SiO4,15) and a type of silicate slag were selected as the main component phases in sinter. We also included some minor phases: wustite (FeOx), likely to form in a strongly reducing atmosphere near coke,14) and dicalcium ferrites (Ca2Fe2O5)16) and CFF (Ca2Fe15.51O25),17) pseudo-binary calcium ferrites are likely to form when little or no gangue melts in a calcium ferrite melt, though these mineral phases sometimes could not be clearly observed structurally by XRD. We also included α-SiO2 phase, which may come from ore-derived gangue and/or is added intentionally for basicity adjustment, though the crystallinity of α-SiO2 phase is often too low to be detected by XRD.

Table 2-1. Main parameters of crystal structures for major mineral phases used as initial structural models.
Crystal phaseMajor phases
α‐Fe2O3Fe3O4Ca2.8Fe8.7Al1.2Si0.8O20 (SFCA)Ca3.14Fe15.48Al1.34O28 (SFCA-I)Ca2SiO4
Crystal structureSpace Group: R-3c,
a=0.50352 nm,
b=0.50352 nm,
c=1.37508 nm,
V=0.301921 nm3
Space Group: Fd-3m,
a=0.84045 nm,
b=0.84045 nm,
c=0.84045 nm,
V=0.593657 nm3
Space Group: P1,
a=0.90610 nm,
b=1.00200 nm,
c=1.09200 nm,
V=0.781762 nm3
Space Group: P1,
a=1.03922 nm,
b=1.05945 nm,
c=1.17452 nm,
V=1.105700 nm3
Space Group: P21/n,
a=0.55160 nm,
b=0.67620 nm,
c=0.93292 nm,
V=0.346991 nm3
ReferencesPerkins et al.13) (ICDD: 01-080-2377)Fjellvåg et al.14) (ICDD: 01-089-0688)Hamilton et al.3) (ICDD: 01-080-0850)Mumme et al.4) (ICDD: 00-052-1258)Mori et al.15)
(ICDD: 01-076-3608)
Table 2-2. Main parameters of crystal structures for minor mineral phases used as initial structural models.
Crystal phaseMiner phases
Fe0.925O (FeO)Ca2Fe15.51O25 (CFF)Ca2Fe2O5α‐SiO2
Crystal structureSpace Group: Fm-3m,
a=0.43064 nm,
b=0.43064 nm,
c=0.43064 nm,
V=0.079863 nm3
Space Group: R32,
a=0.60110 nm,
b=0.60110 nm,
c=9.46900 nm,
V=2.962977 nm3
Space Group: Icmm,
a=0.56432 nm,
b=1.50701 nm,
c=0.54859 nm,
V=0.466541 nm3
Space Group: P1,
a=0.49160 nm,
b=0.49170 nm,
c=0.54070 nm,
V=0.113118 nm3
ReferencesFjellvåg et al.14)
(ICDD: 01-089-0686)
Karpinskii et al.16)
(ICDD: 01-078-2301)
Berastegui et al.17)
(ICDD: 01-089-8668)
Pakhomov et al.18)
(ICDD: 01-077-1060)

The Rietveld analysis was conducted by refining the parameters of mineral phases step by step; first, profile functions and lattice constants of phases in the order of α-Fe2O3 to α-SiO2, as shown in Table 2, were simultaneously refined. Then, the crystal structure factors of the major mineral phases from α-Fe2O3 to Ca2SiO4 were sequentially refined. Only lattice constants and profile functions were refined for minor phases.

3. Results and Discussions

3.1. Evaluation of Quantification Accuracy of the Rietveld Analysis

The mixture samples were prepared with different ratios of dicalcium ferrite (Ca2Fe2O5) and monocalcium ferrite (CaFe2O4) single-phase samples synthesized by solid solution of CaCO3 and Fe2O3 powders to evaluate the quantification accuracy of the Rietveld analysis. The mass fractions of the mineral phases in the mixture samples were determined by the Rietveld analysis of XRD patterns and were compared with the nominal weight fraction of the mixture. The lattice constants and reflection profile parameters were refined in the Rietveld analysis. The relationship between the nominal weight fraction of the mixture and the mass fraction of the mineral phases determined by the Rietveld analysis is shown in Fig. 2. The mass fraction determined by the Rietveld analysis agreed well over the entire range with a relative error of about 7%. For samples with a mix ratio of 10% or less, the relative error is about 10%–25% and higher than the average; however, the error is low enough compared with the errors expected in conventional quantification techniques of XRD such as comparing the intensity of each peak independently.

Fig. 2.

Relationship of nominal weight fraction of mixture of Ca2Fe2O5 and CaFe2O4, and its quantitative value determined by the Rietveld analysis.

3.2. Mass Fractions of Mineral Phases and their Relationship with Sintering Conditions

Figure 3 shows the identification results of the XRD patterns of samples. The differences of the main peak intensities of calcium ferrites and other phases were found. However, the differences were small and it is difficult to refine the ratio and crystal structure of the constituent phases by comparison of the specific peak intensities alone.

Fig. 3.

XRD patterns of sinter samples A, B and C. ●: α-Fe2O3, ○: Fe3O4, ◇: SFCA, ◆: SFCA-I, ▲: Ca2SiO4, ◎: FeO, ■: CFF, △: SiO2.

The Rietveld analysis results of these XRD patterns are shown in Fig. 4 and Table 3. The measured and calculated XRD patterns are shown in the upper part of Fig. 4 and the residual differences between the two are shown in the lower part of Fig. 4. Table 3 shows the results of the Rietveld analysis: mass fractions of mineral phases in the samples, the reliability factor Rwp, and the goodness-of-fit indicator S (Eqs. (3) and (4), respectively). In the sinter samples, the reliability index Rwp is about 2.0% and the goodness-of-fit indicator S is less than 1.1, suggesting that the analysis is statistically good.12)

Fig. 4.

Comparison of the measured (solid line) and the calculated (dotted line) XRD patterns of sinter samples A, B and C. The differential of the profiles were shown in the bottom region of the figure.

Table 3. Phase fractions of mineral phases in sample A, B and C determined by the Rietveld analysis.
Sample namePhase fractions (mass%)Rwp (%)S
α‐Fe2O3Fe3O4SFCASFCA-ICa2SiO4FeOCFFCa2Fe2O5α‐SiO2Total calcium ferrites (SFCA + SFCA-I + CFF + Ca2Fe2O5)
Sample A44.1(1)15.5(1)19.5(3)8.6(2)6.3(2)1.7(1)2.5(2)0.1(1)1.6(1)30.71.811.01
Sample B37.0(1)18.9(1)20.7(3)11.0(3)7.9(5)1.2(1)1.6(2)n.d.1.7(1)33.31.891.03
Sample C33.0(1)23.0(1)21.8(4)9.3(3)8.5(6)1.8(1)1.5(2)n.d.1.2(1)

The Rietveld analysis provided mass fractions of not only the major mineral phases, such as α-Fe2O3, Fe3O4, SFCA, SFCA-I and Ca2SiO4, but also the less than 5 mass% minor mineral phases such as FeOx, CFF, and α-SiO2. The iron oxides, α-Fe2O3 and Fe3O4, accounted for more than about 50 mass% and the multi-component calcium ferrites SFCA and SFCA-I accounted for about 35 mass% in the sinter ore samples. Less than 10 mass% slags Ca2SiO4 and α-SiO2 were contained and little or no Ca2Fe2O5 was formed in the samples.

Here we verified the mass fractions determined by the Rietveld analysis by comparison of the chemical analysis results. Table 4 shows a comparison of the chemical compositions: the one obtained by chemical analysis, and the ones calculated by the mass fraction determined by the Rietveld analysis and the chemical compositions of initial structural models (denoted as “initial” in Table 4), and the ones calculated by the mass fraction determined by the Rietveld analysis results and the chemical compositions of multi-component calcium ferrites corrected by energy dispersive X-ray spectrometry measurements (“EDS,” see Section 3.3) in the sinter ore samples. The constituents Ca, Si, and Al are counted in the form of their oxides. The bottom row of Table 4 shows the average values of relative errors between the chemical analysis values and the chemical compositions calculated by the Rietveld analysis results using chemical compositions of the initial structural models or the multi-component calcium ferrites corrected by EDS.

Table 4. Chemical composition of samples A, B and C obtained by chemical and the Rietveld analysis. Rietveld (initial) and (EDS) shows the results for without and with consideration of deviation of chemical compositions from the reference ones.
SampleMethodChemical composition value (mass%)
Sample AChemical analysis58.189.725.491.28
Rietveld analysis (initial)
Rietveld analysis (EDS)58.910.05.81.2
Sample BChemical analysis56.5110.956.751.29
Rietveld analysis (initial)
Rietveld analysis (EDS)58.910.25.61.4
Sample CChemical analysis57.3910.336.011.45
Rietveld analysis (initial)58.410.35.21.7
Rietveld analysis (EDS)
Relative deviation of Rietveld analysis (initial)2.5%−7.3%−14.9%25.3%
Relative deviation of Rietveld analysis (EDS)3.1%−2.8%−5.6%−5.8%

The total iron content (shown as T.Fe) is slightly lower when measured by the Rietveld analysis than that when measured by chemical analysis; however, it can be quantified with a relative error of 2.5%. In contrast, the quantified values of Ca, Si, and Al contained in both the major mineral phases and the minor mineral phases have large relative errors. In particular, the relative error of Al is largest at 25.3%. The Al contents of the initial structure models of the SFCA and SFCA-I phases selected in the Rietveld analysis were probably higher than those in the Al content of the SFCA and SFCA-I phases actually formed in sinter. The cause of the relative error for the Si content is negative at −14.9%, which may be ascribed to the effect of amorphous slags contained in the sinter samples but not analyzed by the Rietveld method. It can be concluded that the mass fraction of major elements such as iron and calcium can be determined by the Rietveld analysis with an error less than a few %, whereas a much higher error is expected for the fractions of minor elements such as silicon and aluminum.

Next, we discuss the relationship between the mass formations of mineral phases and sintering conditions (Tables 1 and 3). The α-Fe2O3 and Fe3O4 mass fractions tended to decrease and increase, respectively, with the moving from the upper to the lower layers in the sinter cake. The SI test results showed that the SI of the sinter ore samples was highest for Sample C in the lower layer (Table 1). There was a positive correlation between the Fe3O4 mass fraction and the SI. Fe3O4 stably exists in the temperature region from 900 to 1600°C and readily forms as the temperature increases in the equilibrium condition. From this fact and from the results of the Rietveld analysis, it is inferred that the sintering reaction in the lower layer proceeded at higher temperature and longer time than those in the upper layer.

The total calcium ferrite mass fraction, considered to correspond with the melt volume, is almost equal among Samples, suggesting that the melt formation increases the mechanical strength. Calcium ferrites were fired at a higher temperature in the middle and lower layers, and the calcium ferrite melt volume consequently increased in these layers.

However, the melt volume of Sample B is larger than that of C, whereas the mechanical strength of Sample C is higher than that of B, suggesting that we may underestimate the melt volume in samples with high mechanical strength. This may be because we analyzed specimens after SI tests; small particles less than 5 mm in diameter were not detected. Thus, it is likely that sinters composed of small iron oxide surrounded by calcium ferrites melts are not detected, wherein the melt fraction is relatively high.

The above-mentioned discussion confirmed the mass fractions of the mineral phases in the sinter samples taken from the upper, middle, and lower layers of the sinter pot determined by the Rietveld method, and a correlation between the Fe3O4 mass fraction and the mechanical strength of sinter was observed. The Fe3O4 mass fraction is considered to have exhibited a high correlation with the mechanical strength of sinter by reflecting the histories of the sintering reaction temperature (900 to 1600°C) and oxygen partial pressure. In this test, the sintering temperature was higher in the lower layer. Furthermore, the oxygen gas concentration in the exhaust gas was 15% in the upper layer and 12% in the lower layer. From these results, it is inferred that combustion of coke was promoted more in the lower layer compared with the upper layer. Consequently, the sintering temperature increased in the lower layer, the formation of Fe3O4 increased with a decrease in the partial oxygen pressure, and strong sinter was produced. In addition to the mass fractions of the mineral phases, size and shape of the mineral phases, pores and other factors also contribute to the development of mechanical strength and other properties of sinter. The quantification of mineral phases by the Rietveld analysis was demonstrated to be an effective starting point for considering the effect of these factors.

3.3. Refinement of Crystal Structures of Mineral Phases and their Relationship with Sintering Conditions

Next, we discuss the details of the crystal structure parameters of calcium ferrites among the samples. The structure of calcium ferrite is considered to change with the amount of gangue contained because it is a multi-component, continuous solid solution containing gangue components such as silica and alumina.1,2,3,4,5,6) We attempted to determine the amounts of Ca, Si, and Al contents in calcium ferrites by the Rietveld analysis; however, these values could not be determined, because of the relatively low amounts of these phases in the samples. Thus, we experimentally determined these solid solution contents of Fe, Ca, Si, and Al in calcium ferrite phases including morphological observation of calcium ferrite phases by an electron microscope with energy dispersive X-ray spectrometry (EDS).

Figure 5 shows the backscattered electron micrographs of a high gangue calcium ferrite microstructure (a) and a low gangue calcium ferrite microstructure (b) in Sample B. The white dots in Fig. 5 indicate the EDS measurement points. The calcium ferrite microstructure with high Al and Si concentrations in Fig. 5(a) was regarded as the SFCA phase and the calcium ferrite microstructure with a high Fe concentration in Fig. 5(b) was regarded as the SFCA-I phase. Calcium ferrite compositions that reflect the average compositions of the EDS measurement points were obtained. As a result, the compositions of the SFCA and SFCA-I phases were determined as Ca2.3Fe10.3Al0.6Si0.8O20 and Ca3.6Fe15.1Al0.6Si0.7O28, respectively. The Al content of each phase was lower than that of the crystal structure models used in the present research. We modified the crystal structure models of the SFCA and SFCA-I phases according to the chemical compositions determined by the EDS analysis values (Tables 5-1 and 5-2). We assume that the atoms at the octahedral-coordinated cation sites in the SFCA and SFCA-I phases are substituted by Fe and Ca and the tetrahedral-coordinated cation sites in the SFCA and that SFCA-I phases are substituted by Fe, Al, and Si. In the case of the SFCA phase, the occupancies of cation sites were corrected to fit to the chemical composition by making the following assumptions (the changed site occupancies are shown in bold in Table 5). Ca preferentially substitutes sites with longer oxygen bond distances in SFCA. Therefore, the occupancy of Ca/Fe12 site was changed to fit the Ca composition. Next, Si in SFCA preferentially substitutes the tetrahedral site with the shortest oxygen bond distance. Therefore, the occupancy of Si/Al15 site was changed to fit the Si composition. Al prefers to distribute to the Si/Al15 sites and the Al/Fe6 sites with the next shortest oxygen bond distance, so the site occupancies of these sites were changed to fit the Al composition. In the case of the SFCA-I phase, it was assumed that Si statically distributed at the Al substituted the tetrahedral-coordinated cation sites because Si was not contained in the initial models.

Fig. 5.

Electron micrographs of calcium ferrites and chemical compositions in Sample B determined by EDS. (a) calcium ferrite with high gangue (Ca2.3Fe10.3Al0.6Si0.8O20), (b) calcium ferrite with low gangue (Ca3.6Fe15.1Al0.6Si0.7O28).

Table 5-1. Structural model of SFCA3) based on EDS analysis. *Bold numbers show the changed occupancy rates (see text).
(a) SFCA3)
AtomCoodinate numberAtomic coodinatesOccupancy
xyzRef3)This study
Table 5-2. Structural model of SFCA-I4) based on EDS analysis. *Bold numbers show the changed occupancy rates (see text).
(b) SFCA-I4)
AtomCoodinate numberAtomic coodinatesOccupancy
xyzRef3)This study

The mass fractions of the mineral phases determined by the Rietveld analysis using the refined crystal structure models of calcium ferrites are shown in Table 6. The crystal structure factors of the SFCA and SFCA-I phases and the atomic coordinates and other parameters of the SFCA phase in the samples are shown in Tables 7 and 8, respectively. Comparison of the atomic coordinates in Tables 5-1 and 8 revealed differences between the initial models and refined models, particularly at the Al/Fe6 and Ca/Fe12 sites wherein the occupancy rates were corrected by the EDS analysis values. The deformation (distortion) of cation-oxygen coordination (polyhedral) by substitution of cation sites is generally explained as a change in the atomic distances with substitution. The effective ionic radii of Fe3+ and Al3+ at the tetrahedral Al/Fe6 sites are 0.039 and 0.049 nm, respectively. The effective ionic radii of Fe3+ and Ca2+ at the octahedral Al/Fe12 sites are 0.055 and 0.100 nm, respectively, and are significantly different from each other. Therefore, it is considered reasonable to have obtained such results because the coordination structure of the surrounding oxygen changed (polyhedra were distorted) and the atomic positions of cations in the SFCA phase were different between the initial model and the correction model by EDS. Figure 6(b) shows the crystal structure of the (111) plane in the SFCA phase. The sites arranged on the same plane as the Ca/Fe12 site are Fe2, Al/Fe6, Fe7, Fe8, Fe9, Fe10, and Fe11. It is highly probable that the change in the site occupancy of the Ca/Fe12 affects the atomic coordinates of these adjacent sites.

Table 6. Phase fractions of mineral phases in samples A, B, and C determined by the Rietveld analysis based on EDS analysis.
Sample namePhase fractions (mass%)Rwp (%)S
α‐Fe2O3Fe3O4SFCASFCA-ICa2SiO4FeOCFFCa2Fe2O5α‐SiO2Total calcium ferrites (SFCA + SFCA-I+ CFF + Ca2Fe2O5)
Sample A42.4(1)14.1(1)20.8(3)8.2(2)7.6(2)1.7(1)2.6(2)0.8(1)1.9(1)32.41.740.93
Sample B35.9(1)19.7(1)21.3(3)9.6(3)7.0(2)1.5(1)2.3(2)1.2(1)1.6(1)34.41.881.02
Sample C33.5(1)23.9(1)18.2(2)9.2(2)8.8(2)1.8(1)2.5(1)0.9(1)1.3(1)30.81.880.97
Table 7. Main parameters of crystal structures for SFCA and SFCA-I refined by the Rietveld method.
SampleCa2.3Fe10.3Al0.6Si0.8O20 (SFCA)Ca3.6Fe15.1Al0.6Si0.7O28 (SFCA-I)
Sample ASpace Group: P1,
a=0.9102(3) nm, b=1.0124(2) nm, c=1.0986(2) nm, α=60.30(2)°, β=73.42(2)°, γ=65.57(2)°, V=0.7966(5) nm3
Space Group: P1,
a=1.0364(6) nm, b=1.0483(5) nm, c=1.1780(6) nm, α=94.16(2)°, β=111.50(3)°, γ=110.09(2)°, V=1.0891(6) nm3
Sample BSpace Group: P1,
a=0.9109(2) nm, b=1.0122(4) nm, c=1.0984(4) nm, α=60.21(2)°, β=73.32(2)°, γ=65.48(2)°, V=0.7955(5) nm3
Space Group: P1,
a=1.0406(5) nm, b=1.0541(5) nm, c=1.1733(6) nm, α=94.63(4)°, β=110.82(4)°, γ=110.05(4)°, V=1.0993(4) nm3
Sample CSpace Group: P1,
a=0.9110(3) nm, b=1.0110(3) nm, c=1.0983(3) nm, α=60.23(2)°, β=73.39(2)°, γ=65.48(2)°, V=0.7948(4) nm3
Space Group: P1,
a=1.0373(4) nm, b=1.0540(5) nm, c=1.1720(6) nm, α=94.25(3)°, β=111.51(3)°, γ=109.99(3)°, V=1.0959(8) nm3
Table 8. Atomic coordinates of SFCA phases in (a) Sample A, (b) B and (c) C determined by the Rietveld analysis based on the refined crystal structure model (Table 5-1).
(a) Sample A(b) Sample B(c) Sample C
Fig. 6.

Polyhedral representation of the SFCA3) structure. (a) shows stacking of the spinel and the pyroxene modules and (b) shows the projection along (111). S: Spinel module (M4T2O8), P: Pyroxene module (Ca2M2T4O12) T: Tetrahedral site, M: Octahedral site.

As described before, however, the refinement was performed by assuming the sites to be substituted by Al and Ca and by fixing the oxygen positions. This may cause possible fitting errors in determining the atomic coordination (x,y,z) of these sites in the unit cell. To resolve this possible error, it is necessary to perform further research, including identification of the sites in which the Si or other atoms substitute preferentially and optimization of oxygen positions in the multi-component calcium ferrites.

This report independently confirms that fixing the atomic coordinates of oxygen atoms did not significantly affect the mass fractions and lattice constants of the mineral phases. The Rwp values calculated from the EDS analysis values were better than those calculated from the reference values of Table 3. The changes of mass fractions of the total calcium ferrites were insufficiently large to change the magnitude relationship of the mass fractions of the major mineral phases between the samples. Thus, it is considered the Rietveld analysis makes possible the quantitative evaluation of the SFCA and SFCA-I phases. The relative errors from the chemical analysis values related to the gangue are greatly improved by crystal structure models that reflect the EDS analysis values (Table 4).

3.4. Lattice Constants of Mineral Phases and their Relationship with Sintering Conditions

In Section 3.3, the Rietveld analysis of the samples was conducted using the initial crystal structure models (Table 5) with the solid solution components of calcium ferrites corrected by the EDS analysis values. This section discusses the lattice constant results of the mineral phases. The lattice constants of the mineral phases in samples, as determined by the Rietveld method, are shown together with those reported in the references in Fig. 7.

Fig. 7.

Comparison of lattice constants refined by the Rietveld analysis of major mineral phases in samples A, B and C, and the ones reported in ICDD.

The lattice constants of the mineral phases in the samples as refined by the Rietveld analysis using the EDS compositions of Fig. 5 were compared with the references in the ICDD database. The lattice constants of α-Fe2O3 (a), Fe3O4 (b), and Ca2SiO4 (e) slightly varied among the samples and were not significantly different from the reported lattice constants. This indicates that the crystal structures of these mineral phases are almost identical among the samples.

However, the lattice constants of Ca2.8Fe8.7Al1.2Si0.8O20 (SFCA) and Ca3.14Fe15.48Al1.34O28 (SFCA-I) differ between the samples and from the values reported in ICDD data. The differences between the value reported in ICDD data and the chemical compositions of calcium ferrites in Sample B were confirmed by the EDS observation (Fig. 5). These differences also appear in the differences of the lattice constants. As shown in Fig. 6(a), it is reported that SFCA has a crystal structure in which the pyroxene and the spinel modules are alternately stacked, and the charge balance and the relaxation of crystal distortion due to substitution determine the solid solution of gangue components and the substitution sites.2,6) It was confirmed that the lattice constant differences agree with the reported results.

In the value reported in ICDD data, the Fe/(Al + Si) atomic ratio of SFCA is 8.7/(0.8 + 1.2) = 4.4. In the crystal structure model of the Rietveld analysis based on the EDS results, Fe/(Al + Si) = 10.3/(0.6 + 0.8) = 7.4. The lattice constant of SFCA is predicted to increase as the solid solution contents of the gangue components Al and Si decrease6) due to the effective ionic radius of the atoms (Fig. 7(c)).

The lattice constant of Ca3.14Fe15.48Al1.34O28 (SFCA-I) tended to differ among the samples. Comparison of their Fe/(Al + Si) atomic ratios indicates that it is Fe/(Al + Si) = 15.48/(1.3 + 0) = 11.6 in the value reported in ICDD data and Fe/(Al + Si) = 15.1/(0.6 + 0.7) = 11.6 in the EDS analysis values, which are approximately equal to each other. Although the SFCA-I phase in the samples has solid solutions of gangue components in amounts equivalent to those of the value reported in ICDD data, it contains Si with a smaller effective ionic radius than that of Al. Therefore, it is considered that the lattice constant variations between the samples may be influenced by the different Si/Al ratio in SFCA-I phases. The present study used an initial crystal structure model of the SFCA-I phase that unreasonably assumed the solid solution of Si as the chemical composition of the SFCA-I in the sinter ore determined by EDS. Moreover, a diffraction peak derived from the long-range ordered structure of the SFCA-I phase was confirmed near 2θ = 11° of the XRD patterns (Fig. 3). We consider it necessary to refine the crystal structure models of SFCA-I in which Si is substituted for further analysis.

The above-mentioned discussion indicates that the Rietveld analysis can refine the lattice constants of the mineral phases. According to the results of the Rietveld analysis, the lattice constant of α-Fe2O3 or Fe3O4 was almost identical between the samples; however, the lattice constant of the calcium ferrites was different between the samples. It is considered that the difference in their lattice constants is influenced by the solid solution contents of calcium ferrites. It was demonstrated here that the quantification of crystal parameters of the mineral phases by the Rietveld analysis provides useful information for discussing these factors.

4. Conclusions

We successfully determined the mass fractions and crystal structural parameters for co-existing phases found in sinter samples made by sintering pot tests by the Rietveld analysis of XRD pattern. The sinter samples contained α-Fe2O3, Fe3O4, SFCA (Ca2.8Fe8.7Al1.2Si0.8O20), SFCA-I (Ca3.14Fe15.48Al1.34O28), and Ca2SiO4 as major mineral phases and FeOx, CFF, and α-SiO2 as minor mineral phases. We verified the accuracy of the determination of the mass fractions of these mineral phases that were quantified by the Rietveld analysis by comparing the findings with the chemical analysis values.

The SI of sinter samples taken from different positions in the sinter pot differed due to their different heating patterns. The mass fraction of the Fe3O4 phase may be a primary indicator directly related to the SI of sinter because of differences in the heating pattern. A clear correlation between the total calcium ferrite contents in the sinter ores and each layer position in the sintering pot was not observed in this study.

It was confirmed that the Rietveld analysis can refine the lattice constants and other crystal parameters of the mineral phases in sinter. The lattice constant of α-Fe2O3 and Fe3O4 was almost identical between the samples; however, the lattice constant of multi-component calcium ferrites was different among the samples. The latter difference is suggested to be related to the solid solution content of the gangue components.

The crystallographic knowledge revealed by the Rietveld analysis as well as the conventional microstructural information is expected to provide fundamental information that will contribute to designing high-quality sinter.

© 2018 by The Iron and Steel Institute of Japan