I. THE ANALYTICAL PROBLEM

Quicklime (“burnt lime”, CaO) is formed from lime-stone (CaCO₃) by calcination above 900 °C. At an industrial level there are various types of furnaces for producing different grades of quicklime, such as a lime kiln (Figure 1). They heat up the material to temperatures above 900 °C causing the decomposition of lime stone, CaCO₃ → CaO + CO₂.

Figure 1. (Color online) Lime kiln for quicklime production.

After the process some CO₂ and combined water remain in the product and degrade the desired (standardized) quality. For example, the Japanese Industrial Standard JIS R 9001:2006 defines material only as “special grade” if the remaining CO₂ is kept below 2 mass%.

Volatile light components are usually referred to as “loss on ignition” (LOI); in quicklime these are mainly CO₂ and combined water (labile hydroxy-compound). LOI is conventionally quantified by standardized weighing sequences before and after “ignition” at 1050 ± 50 °C, which is, however, laborious and time consuming.

The analytical challenge is to keep continuous control of total LOI as well as CO₂ during the calcination process by a quick (high throughput) and accurate method. Furthermore, impurities such as SiO₂, Al₂O₃, P₂O₅, MgO, and Fe₂O₃ influence the analytical data and require proper correction. The investigations and methodical development shown in this paper aim at demonstrating the superior ability of X-ray fluorescence analysis (XRF) for the determination of CO₂ and LOI in view of JIS R 9011:2006, which at the present time does not yet designate XRF a conforming method.

II. THE PROPOSED SOLUTION

Highlights are:

• • Compton intensity is used as prime analytical information for quantifying LOI. While the new developed method includes inter-element corrections for the influence of varying contents of CO₂ and trace elements, it is not solely a compensation tool for matrix effects.

• • For separating the CO₂ content from the total LOI, CKα radiation is measured with high accuracy by taking advantage of a synthetic multilayer crystal with optimized background shape and height characteristics (see Section V).

It is assumed (and confirmed by the employed reference materials) that in the present application no carbon is present (or negligible) except as CO₂, and the analyte material after the calcination process is basically a binary system, [CaO] + [LOI] + (impurities).

III. THE COMPTON SCATTERING APPROACH

Using Compton scattered radiation from oxides became popular by Reynold's (Reference Reynolds1963) observation that the total mass attenuation coefficient of a sample for the Compton energy is in good approximation proportional to the reciprocal Compton scattered intensity of that material:

$$\mu _{S\comma \, E_{{\rm Compton}} }=\sum\limits_j {W_j \cdot \mu _{\,j\comma \, E_{{\rm Compton}} } }=A \cdot \displaystyle{1 \over {n_{E_{{\rm Compton}} }^{{\rm Compton}} }}$$

This purely empirical model is the base of several methods for analyses of minerals (oxides) and does not require any theoretical modeling of Compton scattering. Applied to the present system of CaO + LOI this means that the inverse Compton intensity increases roughly in proportion to the concentration of CaO because of its dominating attenuation coefficient, or that the (direct) Compton intensity increases in reasonably good approximation linearly with LOI.

A more elaborate and accurate (however laborious) model was presented by Kataoka et al. (Reference Kataoka, Kawahara, Hara, Yamada, Matsuo and Mantler2006): Compton scattered intensities for arbitrary samples are computed by Monte Carlo methods, based entirely on a fundamental parameter approach; this requires

• • an accurate ray-tracing model for incident and scattered radiation paths (Figure 2) within the instrument,

• • and accurate numerical values of differential scattering cross-sections.

Figure 2. (Color online) Basic geometry and radiation paths.

Figure 3 shows Monte Carlo computed RhKα Compton scattering intensities from pure elements (Z < 10) based on a fundamental parameters approach. When the mass thickness is small, Compton scattering intensities are approximately constant among the elements except hydrogen and proportional to their scattering coefficients. For the bulk material they are increasingly sensitive to lighter elements and approximately proportional to the reciprocal mass attenuation coefficients. This correlation is of advantage in the present application.

Figure 3. (Color online) Computed Compton intensities from pure elements (Z < 10) for several mass thicknesses and bulk (9999 mg cm⁻²).

A. Matrix corrections for Compton intensities

The analyte materials contain up to 2 mass% impurities, such as MgO, SiO₂, Al₂O₃, Fe₂O₃, and others. While their absolute concentrations are low (<0.5%), their relative amounts vary greatly and require accounting for their individual influence on the measured Compton counts rates. A simple equation similar to popular forerunners was found suitable:

$$W_{{\rm LOI}}=\lpar {A \cdot I_{\rm C}+B} \rpar \cdot \left({1+\sum\limits_j {\alpha_j \cdot W_j } } \right)$$

where W _LOI and W _j are weight fractions of LOI and matrix components; I _C the Compton photon count rate; α _j the matrix influence coefficients; A and B are calibration constants. The matrix influence coefficient for Fe₂O₃ was the highest among the investigated impurities (Table I). The overall influence of the matrix is shown in Figure 4. Here the accuracy is defined as root-mean-square error of the data points from the calibration line. It includes CO₂ as a correcting component in addition to impurities and thereby allows accounting for changes of the CO₂/H₂O ratio due to loss on ignition conditions during calibration. Its contribution is, however, comparably very small.

Figure 4. (Color online) Calibration curve for LOI with matrix correction.

Table I. Values of matrix influence coefficients.

IV. SAMPLES AND SAMPLE PREPARATION

The raw sample material was taken from the production site, broken to small pieces by a jaw crusher, and ground by a cross-beater mill until more than 90% of the material reached a target grain size of less than 100 μm. Immediately thereafter the material was temporarily filled into air-tight containers in order to avoid reaction with moisture in the ambient air. Just before the measurement (recommended: within 1 min) the samples were taken from the container and pressed at 250 kN in aluminum rings of 43 mm diameter. No binder was used in order to avoid possible interferences by carbon.

A. Standard samples

For CO₂: 50 samples were made from quicklime products with CO₂ reference concentrations up to 7.3 mass%; for LOI: 60 samples were made from quicklime products with LOI reference concentrations up to 6.3 mass%; they were measured by the capacitance method and weight loss by ignition at 1050 °C, respectively, as defined by JIS R9011:2006 (Table II).

Table II. Concentration ranges of the reference materials for LOI analysis.

The reference samples were collected from materials with a wide range of concentrations, including non-conforming products, for the purpose of studying calibration curves for LOI and CO₂.

V. MEASUREMENTS AND INSTRUMENTATION

All measurements have been carried out with a wavelength dispersive spectrometer Rigaku ZSX Primus II with “tube above” geometry. This design is an advantage for pressed powder materials as in the present application because loose particles cannot drop to the window of the tube or contaminate the X-ray path. The settings are shown in Table III.

Table III. Instrumentation.

The measurements of CKα aimed at achieving highest reasonably possible intensities and sensitivity: advantage was taken of the reduced background height (particularly at the high-energy side of the peak) as well as shape, of the new RX61F multilayer analyzer in comparison with the standard version, RX61 (Figure 5). An important improvement is that the background shape is not a function of the CO₂ concentration.

Figure 5. (Color online) CKα peak and BG shapes with RX61F and RX61 multilayer analyzers.

VI. SYSTEM CALIBRATION AND PERFORMANCE

The system was calibrated using the reference materials mentioned above for LOI (by Compton scattering) as well as for CO₂ (by CKα).

The calibrations were made using both, computed intensities with a fundamental parameter method and measured intensities of RhKα Compton scattering (Figure 6). The calibration curve of measured intensities shows good accuracy and is almost identical to that of computed intensities, demonstrating that this approach is effective for the determination of LOI. With respect to sample treatment this includes the successful protection of the ground samples from contact with air and moisture.

Figure 6. (Color online) Computed and measured calibration curves for LOI.

Calibration curves for CO₂ have been obtained experimentally for three different kinds of furnaces (A, B, and C) and evaluated individually as well as jointly by combining all data to one set. The accuracy for furnace B was worse than the others possibly because of the raw limestone, which was a mixture of several sources. The results show that the individual evaluations deliver clearly better accuracies than the total average (Figure 7); this confirms that the methodical accuracy was satisfactory for the intended application since it was comparable with that of the capacitance method, typically 0.1 mass%. With respect to sample composition it verifies the assumption that practically all of the carbon in quicklime is bound to CO₂.

Figure 7. (Color online) Calibration curves for CO₂ for three different furnaces and for all measurements.