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The Rietveld method of quantitative analysis of amorphous materials has gained importance in the light of the BIS issuing specifications for composite cement.
Nowadays, many industries are looking for possibilities to reduce CO2 emissions, energy consumption and increase the reuse of waste materials, These demands are enforced by various regulations and international agreements, and in the long term, they will cause cost reductions. In the cement industry, this can be achieved by using modern techniques in production and by an optimisation of the burning process, by fuel substitutions, alternative clinker compositions or by the production of blended cements with different additives. A variety of completely or partly amorphous materials are used as additives, like slag, fly ash, silica, pozzolana and others. Controlling these additives quantitatively is essential in order to guarantee the cement norms.

Since the mineralogy strongly influences the reactivity of the cement as well as the physical properties of the hydrated product, the need for a direct mineralogical assessment by X-ray diffraction is more important than ever before. X-ray diffraction (phase analysis) opens enormous possibilities for process and quality control. Moreover, the recent development of ultra-high-speed X-ray detectors and of the software for quantitative X-ray diffraction analysis allows truly interactive process control. The quantitative Rietveld analysis is an important tool to control raw materials as well as industrial products, hence offering significant benefits in terms of cement production. Cluster analysis in combination with Automatic Program Selection increases the reliability of quantification results.

The examples presented in this paper will show how X-ray diffraction is being used to quantify blended cements with a complex mineralogy containing crystalline and amorphous phases.

Production and quality control using XRD
Nowadays X-ray fluorescence (XRD) and X-ray diffraction (XRF) analyses are standard tools for process and quality control in cement plants. XRD analysis in combination with Rietveld refinement is a reliable, precise and very reproducible way to quantify the relative phase abundances in building materials. The whole process from sample preparation, through measurement to Rietveld evaluation can be implemented in existing laboratory automation systems and takes approximately 10 minutes. Due to the completely automated operating principle, no additional staff are required and the results are user-independent. The Rietveld method is now being applied in industrial laboratories and also in various cement plants as the standard method for quantitative analyses of raw materials, Portland cement clinkers, Portland cements (OPC) and all types of blended cements.

For clinker, the Rietveld method is the only option to determine the phase content in an accurate and fast way, because the Bogue calculation is usually not correct due to the incorporation of higher amounts of minor and trace elements in the clinker phases, especially when alternative fuels are used. The quantitative mineralogical composition of the cement is directly linked to the hardening behavior and the compressive strength after 28 days. Blended cements are classified under different norms. In order to fulfill these norms and to guarantee the quality of the product, it is necessary to determine the exact amount of added blending materials which is only possible by Rietveld quantification.


Figure 1: Contribution of crystalline and amorphous phases to
an XRD pattern


Figure 2: Rietveld quantification of a pure fly ash, containing
mullite, quartz and around 45 per cent amorphous material..


Figure 3: Rietveld quantification of a fly ash
cement with separate


Figure 4: Cluster analysis of different slag cements with low
(blue), medium (grey) and high (green) amounts of slag
quantification of the fly ash components, including amorphous content

Application of Rietveld analysis for blended cements
The Rietveld analysis uses the whole XRD pattern for quantification and not only single peaks like the classical free lime determination. All peaks from the pattern are used for the refinement and the crystalline compounds are normalised to 100 wt.-%. The Rietveld analysis requires information on the structure data of all crystalline phases in the material and other crystallographic parameters. The quantification of amorphous material requires special procedures. Amorphous material doesn?t give clear diffraction peaks; the pattern may just show a higher background or a hump in a certain region. This hump is not always discernible, especially for low concentrations of the amorphous phases. The background noise strongly influences the quantification results for the amorphous material. Figure 1 illustrates the contribution of crystalline and amorphous phases to a XRD pattern.

Different approaches to determine the amorphous content are described in the literature. The addition of an internal standard is a common method for the determination of the amorphous content.

A defined amount of a standard (like corundum or rutile) is added to the material, and the amorphous content can be calculated from the obtained standard amount from the Rietveld quantification. Influences on the quantification resulting from mixing of the sample with the standard, from possible amorphous content in the standard (Whitfield & Mitchell, 2003) or from crystallographic parameters (De La Torre et al., 2001) were studied. Westphal et al. (2009) showed that the calculation of the amorphous content via Rietveld analysis using an internal standard follows a nonlinear function. For an industrial application, especially for automated systems, the internal standard method is not suitable.


Figure 5: Cluster analysis of different limestones rich in quartz, dolomite
or mica. Outlier in red was a damaged sample.
Figure 6: Working scheme of the Automatic Program Selection
based on Cluster Analysis.

For industrial applications, other methods for quantification of the amorphous material were developed. One possibility is the external standard method. In this case a crystalline standard material is prepared only once and measured separately on a weekly basis. Via mathematical procedures the data obtained from this scan are used for the determination of the amorphous content in the cement. The advantage of this method is that no mixing of standard material and cement sample is necessary. Another possibility is to calculate the area or the intensity of the amorphous contribution to the powder diffraction pattern. This approach is known as the ?HKL? method. The amorphous part is considered as an additional phase and included in the Rietveld calculation. The final result including all crystalline and amorphous phases is again normalised to 100 wt.-%.

Table 1 shows typical ranges of reproducibility and repeatability for different slag cements containing slag from 8 wt.% to 65 wt.%. Table 2 shows typical ranges of reproducibility and repeatability for different fly ash cements with fly ash contents from 10 wt.% to 30 wt.%. For the reproducibility sets of 10 separately prepared samples of the same material were measured. The variation of the results is mainly caused by sample inhomogenities and preparation effects. For the repeatability values one prepared sample was measured 10 times.

Some blended cements have a very complex composition containing more than 20 crystalline phases and one or more amorphous components, introduced by the addition of materials like fly ash or other compounds. Fly ashes used in the cement industry contain usually 30 – 70 per cent amorphous material and as main crystalline phases quartz and mullite. Different feldspars, magnetite, hematite, anhydrite or other phases may also occur.

A Rietveld refinement of an example of a fly ash containing quartz, mullite and amorphous material is shown in Figure 2.

The described quantification methods including amorphous contents can easily be integrated into automation systems. The output file can be defined according to the needs, either all crystalline phases are shown separately (as depicted in Figure 3), or a total value for the amount of slag, fly ash, pozzolana or other added material is given.

A Rietveld refinement of a cement sample containing 20 per cent fly ash is shown in Figure 3.

Cluster Analysis
Statistical analysis techniques are necessary for the data interpretation.
Cluster analysis is a useful tool, as it greatly simplifies the analysis of large amounts of data. This application can be used for simple pass/fail analyses of raw materials, characterisation of blended cements, and automatic selection of control files for Rietveld analysis (APS).

Powder diffraction scans or other data sets are sorted automatically into separate clusters, with closely related scans in a cluster. The most representative as well as the most different scans or data sets can be identified. Outliers are clearly visible as they do not fit into any of the defined classes. Outliers represent deviations or problems in the production process, like changes in the composition, instabilities in a kiln or others. They can be also a result of problems with the sample itself, resulting from sample preparation or transport, like uneven surface or a broken sample. An example of cluster analysis of different slag cements is shown in Figure 4. In Figure 5 an example for an outlier produced by a damaged sample is given.

Automatic Process Control (APS)
The quality of the control files for the Rietveld quantification is decisive for the accuracy of the results and therefore also for the whole process control. A control file can work over a large range of compositions, e.g. from very low to very high amounts of slag in a cement, with good results. For smaller ranges, the control files can be designed with an optimised accuracy. Separate control files are also recommended if different fly ash types are used. Special designed refinement strategies, different background treatment and an optimised fitting for other parameters can be implemented to achieve higher accuracy for the quantification. The selection of a control file can be done automated by cluster analysis. After a measurement, the scan is compared with a pool of scans, the master scans. These scans define separate clusters, representing clinkers or cements with different compositions, like slag cements with low, mid, and high amounts of slag. The variability of each cluster, represented by the diameter of the spheres in the PCA (Principal Component Analysis) plot, is defined by the allowed range of composition for each material. Every measured scan is classified into an existing cluster, if it is within the allowed range, or rated as an outlier.

To each cluster, an optimised control file for the automated quantification is assigned. Each scan can then be processed by a special control file designed for this material. The results of the quantification can be handled by a LIMS (Laboratory Information Management Solution) system. Outliers have to be treated in a special way. The scan can be processed with the control file of the nearest cluster, accompanied by a warning message, that the quantification is of limited reliability. In any way, human interaction is necessary or recommended. The process scheme of the Automatic Program Selection is shown in Figure 6.

Conclusion
Phase analysis by X-ray diffraction opens enormous possibilities for process and quality control in the cement industry especially for blended cements. Moreover, the development of fast X-ray detectors allows fast quantitative X-ray diffraction analysis and truly interactive process control. The Rietveld method allows precise and reproducible quantitative analysis of all types of blended cements. It can be performed in an automated, stable and accurate way. Using an external standard or HKL fit, the determination of the amorphous content can be done directly on the cement sample. The result output includes the quantitative analysis of the crystalline and amorphous phases as well as the total amount of added cementitious material. Nowadays the Rietveld method is being applied in many cement plants worldwide as the standard method for quantitative phase analyses of all types of blended cements. The integration of the cluster analysis into the Rietveld quantification allows fully automated selection of an optimised control file for each material. This increases the accuracy of the quantification and allows an easy identification of outliers.

References
1.Rietveld, H. M. (1969): A profile refinement method for nuclear and magnetic structures, J. Appl. Cryst. 2, 65-71
2. Young, R. A. (1993): The Rietveld Method, Oxford University Press
3.De La Torre, A. G., Bruque, S., and Aranda, M. A. G. (2001): Rietveld quantitative amorphous content analysis, J. Appl. Crystallogr. 34, 196-202.
4.Westphal, T., F?llmann, T., and P?llmann, H. (2003): Rietveld quantification of amorphous portions with an internal standard-mathematical consequences of the experimental approach, Powder Diffr. 24, 239-243
5.Walenta, G., Gimenez, M., and F?llmann, T. (2008): Quantitative analyses of blended cements in industrial applications.- International Cement Review, July 2008, 67-71
6.Whitfield, P. S. and Mitchell, L. D. (2003): Quantitative Rietveld analysis of The amorphous content in cements and clinkers, J. Mater. Sci. 38, 4415-4421.
7.Westphal, T., F?llmann, T.: Quantifying Amorphous Portions in Blended Cements – A Comparative Study.
8.F?llmann, T., Meier, R., and Witzke, T.(2012): Use of X-ray techniques to optimize the efficiency of cement and concrete characterization.
Fuellmann, T., Witzke, T., van Weeren, H. PANalytical B.V., Lelyweg 1, 7602 EA Almelo, The Netherlands

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