3.2.1. The Problem of Obtaining a Durable Tablet for Multiple X-ray Measurements with the Use of Rigaku ZSX Primus II Spectrometer
After the implementation of the newly purchased sequential wavelength dispersive X-ray fluorescence spectrometer type Primus II (Rigaku, Japan) into laboratory practice, it seemed that the development of a method for determining the main chemical composition of solid waste with the use of the WDXRF technique with the preparation of samples for X-ray measurements by pressing with a binding agent using the new spectrometer would not be problematic, as it would not be a development of a new method but rather an adaptation, with some minor modifications and improvements, of the proven method successfully applied for several dozen years for Philips PW 1404 X-ray fluorescence spectrometer with wavelength dispersion and accredited by the Polish Centre for Accreditation. It turned out, however, that the Rigaku ZSX Primus II spectrometer, apart from many undoubted advantages, seems to have one disadvantage: the pressed sample can be measured practically only once, because every subsequent measurement gives higher results. This phenomenon is particularly pronounced for samples pressed with a binding agent. Following the suggestion of the manufacturer, that cellulose as a binding agent might not be the best choice, although it is the most versatile and best of all binding agents currently used in the WDXRF technique, especially in the analysis of solid wastes due to their great diversity in terms of chemical and mineralogical composition, other binding agents were also tested, including boric acid, starch and wax mixed with different tested wastes in different proportions with and without the addition of graphite, as were different pressing forces: 200 kN, 300 kN and even 400 kN, which also resulted in obtaining the same effect each time, i.e., a systematic increase in the intensity of the analytical lines. The results of these tests are not presented here in detail, as they are not the main subject of this paper, but to illustrate the scale of the problem, the results of the seven-fold measurement of one tablet of coal ash prepared for X-ray measurement according to the developed procedure used for both the quantitative calibration-based method and the semi-quantitative method, using the SQX analytical software supplied with the software controlling the operation of the spectrometer by the manufacturer (Rigaku), are presented in
Table 2. These results were compared with those obtained from a single measurement of seven tablets made from the same coal ash tested and prepared for X-ray measurements in an identical way (
Table 3). The results in
Table 3 show that both the tablet preparation method and the X-ray measurement itself are very precise, as evidenced by the small values of standard deviations ranging from 0.005% for TiO2 and 0.006% for Na2O at content levels of 1.10% and 0.84%, respectively, to 0.06% for Al2O3 and 0.13% for SiO2 at content levels of 23.92% and 50.00%, respectively, and the low coefficient of variation values ranging from 0.24% for MgO (3.02% content) to 0.74% for CaO (5.24% content).
From the analysis of the results contained in
Table 2 it can be seen that the highest absolute increase in the content concerns the components which occur in the examined coal ash in the highest concentrations, i.e., for SiO2, for which the content between the first and the seventh measurement increased from 50.24% to 56.70%, i.e., by 12.6% in relation to the result obtained in the first measurement, and for Al2O3, for which an increase was observed from 24.04% to 26.99%, i.e., by 12.3% of the first result. For the other determined oxides, the relative increases in content expressed as a percentage relative to the result of the first measurement are: 4.2% for CaO, 5.0% for MgO, 21.0% for Na
2O, 6.3% for K
2O, 6.8% for SO
3 and 15.2% for P
2O
5, respectively. Only in the case of two oxides, Fe
2O
3 and TiO
2, was there no increase in the content; on the contrary, the result of the first measurement was the highest.
An interesting observation is also that the highest increase in content always occurs between the first and second measurement, while after the fourth or fifth measurement the result stabilizes. It was also observed that when the previously tested (even several times) tablet is ground again in the mill and pressed, the results obtained in the first measurement on the spectrometer of this re-prepared tablet return to the initial state, i.e., are identical to those obtained at the beginning, and then in each subsequent measurement the determined content systematically increases. It has to be clearly stated, however, that in case of routine analysis of pressed samples this problem is not an issue, since the prepared tablet is used for the measurement only once, and even if it had to be used again it is not very time-consuming to crush the pellet and press it for the second time. Nevertheless, the prepared pressed standards can only be used once for calibration and are not applicable for re-calibration. Higher intensities of the analytical lines of the elements determined in the method, obtained in subsequent X-ray measurements made for the standard tablets, would result in lower determination results. In the laboratory practice this meant that the standard tablets carefully stored in a desiccator and used for years in case of the Philips spectrometer became useless, and it was necessary to develop the entire analytical method for the wavelength dispersive X-ray fluorescence spectrometer Rigaku ZSX Primus II from scratch with the use of newly purchased certified reference materials (CRMs) and standards (STDs).
3.2.3. Selection and Measurement of Standards to Obtain Calibration Curves
The assumption was to use for calibration all high-quality standards and CRMs at the laboratory disposal. In total, 22 such standards and 2 blends of two standards mixed in a weight ratio of 1:1 were selected. The standards represented all the objects tested in the laboratory: bottom coal ashes, fly coal ashes, soils, rocks, cements, sediments and ores. In spite of diversified chemical compositions of these standards, it was not possible to obtain for all determined oxides a wide range of calibration curve fully covering the range of variability of occurrence of these oxides in solid samples provided to the laboratory for testing, in particular for wastes. Such standards are also not available on the market, and therefore, it was decided to create such standards using natural waste samples provided to the laboratory for testing. Twenty-two such samples were selected, and their main chemical compositions (oxide contents) were determined using the accredited WDXRF method with sample preparation for X-ray measurements by fusion into a borate bead [
13] and the ICP-AES method. In total, the calibration curves for all 10 oxides determined in the research study presented in this paper were based on 42 standards. These selected standards were prepared for X-ray measurements as presented in
Section 3.2.2, and the resulting standard tablets were then measured with the use of the spectrometer to obtain intensities for the calibration curves. Experimentally determined optimum instrumental measurement conditions for all 10 oxides are given in
Table 4.
The α-empirical correction coefficients were applied to correct matrix effects at the stage of creating the final calibration curves. All calibration curves, shown in
Figure 1, are linear despite the wide content range and have high correlation coefficients from 0.9995 for SiO
2 and TiO
2 to 0.9999 for SO
3 and P
2O
5.
The blue colour represents the position of the measurement points relative to the statistically determined curve after correction of matrix effects, and the white colour represents those before correction. The interval between these colours for each measurement point can be taken as a measure of the matrix effect. Observation of the attached calibration curves shows that the matrix effects are largest for the lightest of the oxides determined, that is, Na
2O, and for the heaviest, TiO
2 and Fe
2O
3. It is also an interesting observation that the standards prepared in the laboratory do not differ in quality from the purchased international standards and certified reference materials. On the basis of the deviation of the measuring points from the determined calibration curve it cannot be stated whether a point represents the laboratory-made or an international standard, since the observed deviations are comparable for both types of standards and are generally small for all 10 tested oxides considering that the method is based on very different standards with sample preparation for X-ray measurements by pressing with a binding agent. Assuming that the declared contents of all oxides in the certificate and determined in the laboratory are close to the actual contents and that the tablet preparation error is small, as will be shown later in this paper, the deviations obtained are a measure of matrix effects. Based on previous experience, it may be stated that the matrix effects associated with the absorption and enhancement of the X-ray fluorescence emitted from the sample by a given element by the other matrix-forming elements present in the sample have only a small effect on the value of this deviation, since they are effectively minimized by α-empirical or theoretical matrix effects correction factors. In this study, α-empirical coefficients were applied because α-theoretical coefficients could not be used, taking into account their one major limitation, consisting of the fact that they can only be used if the sum of all the components determined in a given analytical application is above 99%. Not all standards applied in calibration met the above criterion. A much larger share of the observed deviations of standard points from the calibration curve constitute matrix errors associated with differences in the mineralogical composition of the standards applied in calibration, and unfortunately mineralogical effects, as mentioned in
Section 2, cannot be corrected by means of correction factors α. As a result, in the WDXRF technique, the determination accuracy of the main components in methods with sample preparation for measurement by pressing with a binding agent is always worse than for samples fused into a borate bead. In light of the above statement, an attempt to investigate the applicability of the SQX software for semi-quantitative analysis by comparing the results received from this software with those obtained in the calibration method and in the reference to certified values becomes even more justified.
3.2.4. The Principle of Semi-Quantitative Analysis and Optimization of the Method of Performing the Determination in Terms of the Correctness of the Obtained Results
Any determination of elemental composition with the use of the WDXRF technique is based on calibration. In standard calibration methods, the user prepares standards for X-ray measurements, develops an analytical application, optimizes instrumental measurement conditions, makes calibration measurements and finally develops calibration curves without or with correction of matrix effects. WDXRF spectrometry ensures high accuracy of the results provided that the standards applied to calibrate the method and the unknown samples determined in this method represent the same object (and thus differ only slightly in mineralogical and chemical compositions) and are prepared for X-ray measurements in an identical way. It is a valuable and useful research tool because of the ease of sample preparation and short analysis time. However, X-ray analysis applied to a sample that differs significantly from the standards employed in calibration may lead to unsatisfactory results even after applying a correction for matrix effects. Therefore, every leading manufacturer of X-ray fluorescence spectrometers also provides analytical software for semi-quantitative determination of the content of elements in any unknown sample as a part of the computer operational software accompanying the spectrometer. This software is also based on calibration, but the difference is that it is prepared by the manufacturer. In this case, calibration is based on a series of synthetic standards covering a wide range of elemental content over a large range of matrix variation; hence, this method is commonly referred to as a standardless analysis. This analytical software takes into account various factors at the stage of calculating the elemental content of the sample, such as coincidence of spectral lines, matrix effects, geometry of the optical system of the spectrometer, characteristics of the detectors and how the sample was prepared for X-ray measurement. It enables the determination of elements ranging from sodium to uranium and in the content range from 0.01% to 100%. Rigaku bases the calibration of the standardless software on six standards designated DSC 1–DSC 6. The most important advantage of this software seems to be that the sample does not have to be analysed itself, but it can be mixed and pressed with a binding agent before X-ray measurement. After the analysis, at the stage of calculating the results, the type of a binding material, its chemical formula and the weight ratio in which the binding agent was mixed with the tested sample are specified, and the software recounts the obtained results into percentages of the initial sample. The analysis of a completely unknown sample by means of the SQX program is possible because the spectrometer is equipped with a set of analysing crystals allowing the determination of elements ranging from boron to uranium, and thus also oxygen and carbon, as important elements in waste analysis. This is especially important since the software summarises the contents of all detected elements to 100% with the possibility of converting them to oxides. In this situation, the only potential source of additional error is the inability to determine the hydrogen content, which may be, however, overcome in two ways. The first is to analyse dry samples to eliminate hydrogen present in the water. The second is to determine the hydrogen content by elemental analysis, if the laboratory is equipped with a suitable analyser, and enter the determined hydrogen into the program as a fixed value during the calculation of final results. The same can be done with carbon and nitrogen because, as very light elements, they will always be determined in WDXRF with high error. No corrections were applied in testing the SQX software, and the samples analysed were dried at 105 °C. The analysis of the chemical composition of the tested sample using the SQX software may be performed optionally in three time variants: short, standard and long. In all analyses performed for the purpose of this study, the “long” option was used. The time of full analysis is only a few minutes longer, but due to the use of a larger number of measuring points at the stage of scanning the spectral range, the spectrometer is able to detect elements that, due to their low content, are not detectable in the standard option. Depending on the chemical composition of the analysed sample, the software itself automatically selects the optimum measuring conditions for each of the determined elements by choosing the appropriate analysing crystal and changing the current parameters of the X-ray tube. In order to obtain the lowest possible limits of detection in our tests, the measured surface was always the maximum surface, a circle of 35 mm diameter.
3.2.5. The Effect of the Type and Amount of Binding Agent on the Result of the SQX Software Analysis
The first test was to verify how the SQX software handles the conversion of the results obtained from the measurement of the tablet, which is a mixture of the test sample and the binding agent, to the content of determined elements in the initial sample. In order to carry out the test, the test samples previously mentioned in
Section 3.1.1 were used, i.e., a soil sample and a coal ash sample. For both test samples, seven tablets were prepared according to the adopted procedure presented in
Section 3.2.2, by mixing the samples with different binding agents and in different weight ratios (
Table 5).
The tablets were then analysed using the SQX software. The results obtained after conversion by the software into the contents of 10 main oxides in the initial soil and coal ash samples along with statistical calculations are presented in
Table 6.
On the basis of the analysis of the results given in
Table 6, it may be concluded that the effect of the type of a binding agent applied on the results of the determination of the main chemical composition using the Rigaku SQX software for semi-quantitative analysis is not significant. As previously mentioned, all that is needed is to define the binding agent applied in the preparation of a tablet after the X-ray measurement, and the mathematical algorithm included in the software effectively converts the results obtained into the content of oxides in the initial sample. The effectiveness of the conversion algorithm is evidenced by the small differences between the results obtained for all the tested binding agents mixed with tested samples of coal ash and soil at different weight ratios, which is directly reflected in the low values of standard deviations and coefficients of variation. In case of the coal ash sample, the standard deviation values are the highest for SiO
2 (0.5888%) at its average determined content in ash of 46.59% and for Al
2O
3 (0.4202%) at its content of 24.52%, and the lowest is for Na
2O (0.0329%) at its average determined content of 0.84% and for P
2O
5 (0.0280%) at its average determined content of 1.05%. The coefficients of variation are also low and range from 1.26% for SiO
2 and 1.71% for Al
2O
3 to 5.51% for MgO and 6.50% for TiO
2. These trends are similar for the tested soil sample: the highest values of standard deviation were reported for SiO
2 (0.2675%) at its average determined content in soil equal to 91.96% and for Al
2O
3 (0.1798%), at 4.00%; the lowest were reported for SO
3 (0.0084%) at its average determined content of 0.10% and for P
2O
5 (0.0035%) at its average determined content of 0.06%. The coefficients of variation are also at similar levels to those of coal ash and range from 0.29% for SiO
2 and 2.37% for K
2O to 5.83% for P
2O
5 and 8.55% for SO
3.
3.2.7. Results Accuracy Estimation of the Determination of the Main Chemical Composition of Solid Samples with the Use of the SQX Software for Semi-Quantitative Analysis of the Rigaku ZSX Primus II Wavelength Dispersive X-ray Fluorescence Spectrometer
In order to estimate the accuracy of the results of determining the main composition of solid samples by means of the SQX software, 22 certified reference materials (CRMs) representing various objects under the study were used. These included waste, coal ash, construction materials (binders and aggregates), soils, rocks and biomass. In addition, two more samples were prepared, which were blends of two different CRMs mixed in a weight ratio of 1:1. Thus, the total number of samples for the study was 24, and these samples differed among themselves in mineralogical composition and were also characterized by a wide range of variation in the content of all 10 oxides determined (
Table 8).
Selected CRMs were then prepared for X-ray measurements according to the procedure adopted and presented in
Section 3.2.2., and the tablets were subjected to chemical analysis on a spectrometer, first by the method based on calibration and then using the SQX software. The results obtained by both methods for all 24 CRM samples tested were compared with the certified values, and relative errors of determinations were calculated (
Table 9).
Based on the data presented in
Table 9, one major conclusion may be drawn that the calibration method is more accurate than the semi-quantitative analysis using the SQX software because the results obtained by the calibration method are closer to the certified contents as evidenced by the lower values of relative determination errors compared to the corresponding errors calculated for the SQX method. The Fe
2O
3, and for some CRMs the relative error of determination in the method based on calibration, is larger than that with the use of the SQX software. It should be noted that the range of content of a few oxides in the 24 tested CRMs samples comprises even three orders of magnitude. For example, the SiO
2 content is in the range of 0.505% to 90.36%, while the Al
2O
3 content is in the range of 0.0419% to 54.50% (
Table 9), and the minimum and maximum CaO contents in the tested certified reference materials are 0.0180% and 61.87% (
Table 8), respectively. For the remaining seven oxides these ranges are narrower but also include two or even three orders of magnitude as, for example, SO
3, whose minimum content in the selected CRMs is 0.0022% and maximum is 2.64% (
Table 8). Thus, the calculation and adoption of a single mean determination error for the entire range would not be substantively justified and would contradict commonly applied statistical principles. Therefore, in the work presented in this paper the principle of dividing the full range of applicability of the semi-quantitative analysis, i.e., the range from 0.01% to 100%, into four sub-ranges and calculating the mean relative error of determination of a given oxide in a given sub-range was adopted. These four subranges hereinafter referred to as “Ranges” are:
- -
Range 1: below < 0.1%;
- -
Range 2: between 0.1% and 1.0%;
- -
Range 3: between 1% and 10%;
- -
Range 4: above 10%.
The calculated mean values of relative errors in relation to certified content obtained for the semi-quantitative method with the use of the SQX software and for comparison for the method based on calibration are presented in
Table 10.
As it can be seen, for various oxides, the ranges are represented by a different number of measurement points. This is mainly due to the range of variation in the occurrence of a given oxide in the selected objects. For example, in 24 tested standards, in none of them is the content of SiO
2 below 0.1%, and in the case of Al
2O
3 and CaO there is only one such standard. In contrast, Range 4 (content above 10%) is represented by as many as 15 standards for SiO
2 and 13 standards for Al
20
3, but Na
2O, K
2O, SO
3, TiO
2 and P
2O
5 are not represented in this range at all. Thus, the largest number of standards is located in the middle ranges (Ranges 2 and 3), and therefore, the calculated mean error of determination of a given oxide in these two ranges reflects the real state best and can actually be accepted as uncertainty of determination of this oxide in a given content range. This is also true for Range 4 but only for the oxides SiO
2, Al
20
3 and CaO, which are represented in this range by a larger number of standards: 15, 13 and 9, respectively. In general, the data included in
Table 10 only confirm the conclusion already quoted, that for all the determined oxides, except for Fe
2O
3, the calibration method is more accurate than the semi-quantitative SQX method, but even for the SQX method, the mean relative errors of determination do not have very high values and decrease with increasing content of the given oxide in the standard. The highest error value was reported for Al203 in Range 2, equal to 63.08%, but for the same oxide in Range 3 the mean error is only 15.51%. As for Range 2, the second highest mean error is 28.75% for SO
3, and the lowest is 10.10% for SiO
2. For Range 3, the mean error values are between 5.12% for Fe
2O
3 and 33.83% for CaO. The mean relative errors of determination in Range 1 are from 298.5% for SO
3 (the second highest is 84.14% for K
2O) to 16.61% for P
2O
5, and taking into consideration the fact that the contents of the determined oxides in this range are below 0.1%, these errors are also acceptable. Further analysis of the data presented in
Table 10 allows us to conclude that all 10 oxides are determined with comparable accuracy, which proves that the SQX software at the stage of calculating the content of individual oxides in the tested sample deals with matrix effects very well and is therefore universal and can be successfully applied in semi-quantitative determination of the main chemical composition of any unknown solid, bulk or powder sample with satisfactory accuracy. This last statement leads to another and better way of estimating the accuracy of this standardless semi-quantitative method.
Before starting the work we had at our disposal only 22 certified reference materials plus 2 extra samples prepared by us by mixing 2 different CRMs in a weight ratio of 1:1. Thus, the estimation of the accuracy of the determination of each oxide in the wide range of variation of its occurrence in the analysed CRMs (see
Table 9) by four ranges was based on 24 measurement points, and in the case of Na
2O, SO
3 and P
2O
5, on 23, because there was no certified content of these oxides in one of the standards. If the determination errors are on the same level for all 10 determined oxides and depend mostly on the content of the oxide in the standard, the accuracy of the method can be expressed as the mean determination error in each of four selected content ranges. The accuracy estimated in this way better characterises the validated method since it is calculated based on a much larger number of measurement points more evenly distributed over all four content ranges. In this case, since the method concerns the determination of 10 oxides, and 24 standard samples were at disposal, its accuracy was estimated on the basis of 237 measurement points (one certified content was missing for Na
2O, SO
3 and P
2O
5), which were distributed among the selected content ranges as follows: 39 results below 0.1% (Range 1), 77 results between 0.1% and 1% (Range 2), 80 results between 1% and 10% (Range 3) and 41 results above 10% (Range 4). Thus, the calculated average determination errors for all 10 determined oxides present in the selected CRMs in a given content range, which can be equated with measurement uncertainty, are presented in
Table 11. For a more complete illustration, they are compared with the average determination errors calculated in the same way in the calibration method.
The analysis of the data in
Table 11 shows that in both the semi-quantitative SQX method and the calibration method the accuracy of the determination increases with increasing oxide content in the sample as evidenced by the decreasing values of relative errors. The accuracy of the SQX method compared to the calibration-based method is more than two times lower for an oxide content of up to 10% and even three times lower for oxide contents above 10%. However, keeping in mind that it is, by design, a semi-quantitative method, the estimated accuracy is surprisingly high when one realises how diverse certified reference materials were applied to validate the method. Only in the lowest range (below 0.1%) is the estimated uncertainty 68.11%, but it increases significantly with increasing oxide content, reaching only 7.13% for contents above 10%.
In summary, the Rigaku software for semi-quantitative analysis supplied by the manufacturer with the wavelength dispersive X-ray fluorescence ZSX Primus II spectrometer is an ideal analytical tool for determining the chemical composition of unknown solid, bulk and powder samples with very satisfactory accuracy. The ease of sample preparation for X-ray measurements, the low cost of analysis and the short time leading to a result make the SQX program a valuable and necessary tool for any chemical laboratory equipped with a WDXRF spectrometer.