1 Introduction

With the rapid development of the cement industry, how to reduce the energy consumption and CO2 emission is still an important issue to be addressed (Popescu et al., 2003; Liu et al., 2011; Wang and Liu, 2011). Belite cement (BC), which contains more than 50% (in weight) of Ca2SiO4 (C2S), has such advantages as lower calcination temperature, less calcium content, and lower heat of hydration. Therefore, it draws wide attention of many researchers (Chatterjee, 1996; Fukuda and Ito., 1999; Morsli et al., 2007; García-Díaz et al., 2011). However, BC has a chief disadvantage of low mechanical strength at its early age. This is mainly due to the low activity of β-C2S which is the key phase in BC. In order to improve the activity of β-C2S, many researchers focused on monomineral preparation and modification of β-C2S (Chen and Wang, 2000; Fukuda et al., 2001; Li et al., 2006). One of the monomineral preparation methods for pure β-C2S is calcining the sample repeatedly to obtain pure γ-C2S and then the β-C2S is prepared through phase conversion. Yet γ-C2S at the most stable phase at room temperature cannot be converted into β form completely during the heating and cooling period. Hence, it is significant to quantify the γ-C2S conversion rate, which has aroused great concern (Zhang, 1995). In the past, traditional quantitative X-ray diffraction analysis (QXDA) (such as internal standard, external standard, and K value method) as a direct measurement was used to quantify the γ-C2S phase conversion rate. However, it only can be applied to a single peak analysis, and polymorphs of β-C2S and γ-C2S have a strong peak overlap. Thus, errors will appear if the traditional QXDA method is used. Besides, it is difficult to prepare completely pure β-C2S to establish a correct phase-analysis calibration curve. Therefore, both of the above factors may lead to serious errors. The recent development of the Rietveld QXDA technique can eliminate or minimize the errors by minimizing the differences between the experimental pattern and calculated pattern (Rietveld, 1969; De la Torre et al., 2003; 2008; Scrivener et al., 2004; Le Saoût et al., 2011). With the primary purpose of assuring that the laboratory X-ray powder diffraction (LXRD) pattern is effective for the Rietveld QXDA technique in quantifying the conversion rate of γ-C2S into β-C2S, synchrotron X-ray diffraction images and integrated diffraction patterns are analyzed in this study.

2 Experimental

2.1 Synthesis of β-C2S and α-Al2O3

A mixture of stoichiometric proportion of CaCO3 and SiO2 (99.99%, Sinopharm Chemical Reagent Co., Ltd. (SCRC)) was prepared to get C2S. The mixture was ground in an agate ball mill at 200 r/min for 30 min, pelletized, heated at 1623 K for 10 h and cooled by turning off the furnace. The resulting solid sample underwent a change, through the above process to decrease the free lime (f-CaO) content to less than 1%, which could ensure pure γ-C2S would be obtained. After that, the sample was ground and heated twice in a Pt crucible at 1473 K for 1 h. The cooling system for this phase conversion was first adopted as air-cooling and then water-cooling was applied (when the calcining process is finished, a sample in the platinum crucible was rapidly taken out and immersed into water, the height of which was lower than the platinum crucible to avoid contacting with C2S) as the second approach.

α-Al2O3 was synthesized by γ-Al2O3 according to the following procedure (De la Torre et al., 2003). The powder of γ-Al2O3 was ground in an agate ball mill at 200 r/min for 30 min, heated at 1373 K for 4 h and cooled by turning off the furnace. Then the product was ground and heated at 1423 K for 6 h through a second-round thermal treatment.

2.2 Experimental test

The content of f-CaO in samples was determined by the glycerol-ethanol method. LXRD patterns were recorded by Rigaku X-ray diffracto-meter (D/max2550VB3+/PC, Rigaku International Corporation, Japan). The instrument settings for LXRD are described in Table 1. All Rietveld refine-ments were carried out through the GSAS software (Larson and Von Dreele, 2004). 2D synchrotron X-ray diffraction (SXRD-2D) experiments were performed at the beamline BL14B1 of Shanghai Synchrotron Radiation Facility in China. SXRD-2D images were recorded using a 3072×3072 charge-coupled device (CCD) detector and processed by the FIT2D software (Hammersley, 1998). Experimental parameters for SXRD-2D are listed in Table 2.

Table 1 LXRD instrument settings
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Table 2 Experimental parameters for SXRD-2D
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3 Results and discussion

The LXRD patterns of γ-C2S are shown in Fig. 1. A1 and A2 were the mixture of CaCO3 and SiO2 heated once and twice, respectively. The content of f-CaO in A2 was determined as 0.2%, which was decreased significantly from A1 that was about 2.4%. Also, as seen from the LXRD pattern, the general trend of f-CaO was as expected. The characteristic peaks of f-CaO (2θ=32.2°, d=0.27774 nm and 2θ=37.3°, d=0.24059 nm) disappeared in A2. The indexing result showed that the LXRD pattern of A2 matched well with the standard powder diffraction file card (No. 49-1672).

Fig. 1
figure 1

LXRD patterns of γ-C 2S

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The calcination system of phase conversion was adopted as previously described. The LXRD patterns of β-C2S cooled at the first and second times are shown in Fig. 2 (continuous scanning) and Fig. 3 (step scanning), respectively. After the sample was calcinated for the second time and cooled in water, the intensity of γ-C2S unique distinguishing peaks at 2θ=29.6° and 47.5° decreased significantly, which indicated that only a small quantity of γ-C2S existed in the sample (Fig. 3).

Fig. 2
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LXRD pattern of β-C 2 S air-cooled at the first time

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Fig. 3
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LXRD pattern of β-C 2 S water-cooled at the second time

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Before calculating the quantity of γ-C2S and β-C2S by the Rietveld method, it is essential to ensure the high quality and reproducibility of the X-ray diffraction data. The key issue for the point detector data is that the diffracting particles in all directions are sufficient and randomly distributed. Thus, after being fine-ground, the sample whose LXRD pattern would be refined by the GSAS software was taken for SXRD-2D analysis at room temperature. SXRD-2D patterns were recorded using a flat CCD detector, mounted perpendicular to the incident beam behind the sample. The sample was adhered between two pieces of polyimide tape (Fig. 4). To obtain factual diffraction data of the sample, the same polyimide tape without powder was also immediately exposed at the incident beam for 30 s after finishing the test of the former sample. Synchrotron X-ray diffraction data were processed with the FIT2D software and transmission X-ray diffraction images of the sample with and without polyimide tape are depicted in Fig. 5. Debye-Scherrer cones of C2S powder diffraction (Fig. 5b) were continuous and individual grains were rarely visible. This indicated that the particles of C2S were ideal in size and were fulfilled by random distribution, which would reduce the irreproducibility error against poor analysis during the Rietveld refinement.

Fig. 4
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Experimental station at BL14B1 (y-axis: ray direction, Shanghai Synchrotron Radiation Facility (SSRF), China)

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Fig. 5
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Synchrotron X-ray diffraction images of C 2 S sample with (a) and without (b) polyimide tape (Fig. 5b is obtained through subtracting the transmission X-ray diffraction images of polyimide tape from Fig. 5a)

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In the SXRD-2D experiment, lanthanum hex-aboride as a standard was used to calibrate the Sample-to-detector distance and refine the instrumental parameters. An integrated 1D diffraction pattern of C2S (Fig. 6) was obtained from a 2D synchrotron diffraction image. As it was integrated from the whole 2D image data, the integrated diffraction pattern revealed more accurately the relative diffraction peak intensities at different values of dspacing. To some extent, it can be a preliminary criterion to analyze the reliability of the laboratory Bragg-Brentano geometry X-ray diffraction data. The comparison between Fig. 6 and Fig. 3 shows a good corresponding relationship which indicates the fine-ground powder of C2S heated for a second time and cooled in water had a good reproducibility to be refined by the Rietveld method.

Fig. 6
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Integrated diffraction pattern of C2S converted from synchrotron diffraction image (Fig. 5b)

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Rietveld QXRD pattern of β-C2S air-cooled at the first time and water-cooled at the second time are respectively shown in Fig. 7 and Fig. 8. As seen from the above two figures, the refinements were stable and the fits were satisfactory as indicated by the smoothness of the Yobs-Ycalc (Yobs−Ycalc means the differences between observed (Yobs) and calculated (Ycalc) pattern) curve and the R-factors, which illustrated that the quantification of the γ-C2S conversion rate was reliable. The quantity of γ-C2S and β-C2S obtained at the end of the refinement process and the least square R-factors like R F, R WP, and R P are displayed in Table 3. The Rietveld weight fractions of β-C2S and γ-C2S in the air-cooled sample were 69.0% and 31.0%, respectively. After the sample was calcined and water-cooled for the second time, the Rietveld weight fraction of β-C2S in the sample reached 92.7%, which indicated that most of the β-C2S had been prepared through the γ-C2S conversion.

Fig. 7
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Rietveld QXRD pattern of β-C 2 S air-cooled at the first time

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Fig. 8
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Rietveld QXRD pattern of β-C 2 S water-cooled at the second time

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Table 3 Rietveld QXRD results of C 2S
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To evaluate the accuracy of the Rietveld quantity phase analysis of C2S, an artificial mixture of β-C2S and α-Al2O3 were prepared in appropriate proportions (\(m_{{\text{C}}_{\text{2}} {\text{S}}} = 0.4964 {\text{g}}\) and \(m_{{\text{Al}}_{\text{2}} {\text{O}}_{\text{3}} } = 0.5036 {\text{g}}\)) and the LXRD pattern of the mixture would be refined by GSAS software again. Before that, the mixture was ground in an agate mortar about 15 min for the first time and another 30 min for the second time. They were separately exposed at the synchrotron X-ray incident beam and the original PGM format images of SXRD-2D are shown in Fig. 9. By comparing the two images, Debye-Scherrer cones in Fig. 9b were much smoother and had a better continuation, telling of a very fine and randomly oriented microstructure of the sample. This is mainly because with the grinding time increasing, the particles size in the mixture became smaller, forming a better random distributed sample. Figs. 10 and 11 are respectively a 1D diffraction pattern (converted from SXRD-2D images) and a Rietveld QXRD plot of the mixture. Their perfect consistency made this LXRD step scanning pattern available for the Rietveld refinement.

Fig. 9
figure 9

SXRD-2D images of β-C 2 S and α-Al 2 O 3 mixture ground for 15 min (a) and another 30 min (b) (partial crystal plane indexes have been pointed out)

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Fig. 10
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Integrated diffraction pattern of C 2 S and α-Al 2O3 mixture converted from synchrotron X-ray diffraction images (Fig. 9b)

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Fig. 11
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Rietveld QXRD pattern for C 2 S and α-Al 2O3 mixture

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The Rieveld quantification phase analysis results for a mixture of C2S and α-Al2O3 after refinement are shown in Table 4. The relatively smoothness of the Yobs−Ycalc curve and small value of the R-factors indicates that the fits are in good agreement. From Table 4, several conclusions can be drawn: (1) The relative error between the weighted fraction and Rietveld weight fraction of phases (C2S and α-Al2O3) is only 2.6%, which sufficiently shows an accurate result based on the Rietveld refinement method; (2) The Rietveld weight fraction of β-C2S is 96.3%, 3.6% more than that in the C2S without α-Al2O3. The reason for the absolute error is that the low content of γ-C2S in the mixture has an extremely weak X-ray diffraction intensity compared with other phases in the sample, especially the α-Al2O3. So the γ-C2S in this system might be slightly underestimated. However, these errors are acceptable and these results show that the Rietveld QXRD is an appropriate method to quantify the γ-C2S phase conversion.

Table 4 Rietveld QXRD results of mixture of C 2S and α-Al2O3
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4 Conclusions

  1. 1.

    The Rietveld quantification shows that the conversion rate of γ-C2S is higher than 92% after it was calcined at 1473 K of calcining temperature, 1 h of holding time and followed by water cooling.

  2. 2.

    The analysis of the 2D synchrotron diffraction image and the 1D integrated diffraction pattern can be used as an intuitive and effective method to check the randomly oriented distribution of sample and to evaluate reproducibility of the laboratory X-ray diffraction pattern which would be refined by the Rietveld method.

  3. 3.

    The relative error between the weighted fraction and the Rietveld weight fraction of the phases (sample of C2S and α-Al2O3) is 2.6%. The absolute error of the γ-C2S conversion rate between the two LXRD Rietveld refinements is 3.6%. The Rietveld QXDA analysis is an appropriate and accurate method to quantify the γ-C2S phase conversion.