The ED-XRF (Xepos HE, Spectro, Kleve, Germany) in this study uses a tungsten anode X-ray generator with a maximum tube voltage of 50 kV, and can selectively quantify the concentration of the elements using 8 secondary targets. The detector used was a silicon drift detector type of a peltier cooling module and the peak resolution is 155 eV at Mn-K_α. The X-ray path is in two perpendicular planes and the scatter noise from the generator tubes was minimized using polarization. The fluorescent x-rays were measured using cartesian geometry among the secondary targets, samples, and the detector. For the ED-XRF measurement, the geochemistry trace powder method provided by the manufacturer for environmental/mineral sample measurement was applied, and the ED-XRF measurement was repeated 7 times each for a total of 30 minutes using secondary targets made up of cobalt, molybdenum, aluminum oxide, and zinc. The correction of the mass attenuation effect on the sample medium, a modified algorithm for peak overlap, and a revised algorithm for Compton peak sizes were applied to the method used for this analysis. Table 2 presents analytical conditions, such as the secondary targets used according to target elements, the tube voltage (kV) and electrical current (mA) for X-ray tubes, and measurement times. When analyzing most samples—including raw material and by-product samples—using ED-XRF, the matrix effect produced depending on the components, background spectrum, elemental content, and peak overlap that could arise depending on the composition could be considered as uncertainty factors in the results.

In order to minimize these inteferences, the geochemical method employed in this study used a fundamental parameter method that applied basic physical parameters to modify the background spectrum by repeatedly recalculating the spectral peaks that occurred due to various electronic transitions of an element initially obtained from the spectrum. In addition, the geochemical method reproduced spectrum by modifying errors caused by peak overlap and absorption edge. In order to modify the changes in matrix and equipment stabilization, an algorithm was applied that modifies the coefficient of the total spectrum with regard to the intensity of Compton peaks. Moreover, to offset the matrix effect, the ratio of Compton scattering and Rayleigh scattering was analyzed for standard samples of approximately 25 species to calculate and apply the mass attenuation coefficient. Regarding the influence of peak overlap for characteristic energy, rubidium and strontium were quantified for uranium, while iron, rubidium, and strontirum were quantified for thorium for each characteristic peak. Peak separation was conducted by subtracting the corresponding area from the uranium peak. Such X-ray acquisition, correction, and analysis were automatically conducted using the X-LapPro program. The calibration curve of uranium, thorium, and component elements were prepared using various types of standard materials, such as soil and rock samples. For uranium and thorium, the determination coefficient (R²) of the calibration curve from sub-ppm to % of concentration range was 0.9981 and 0.9946, respectively. As shown in Figure 1A, the concentrations of uranium and thorium were analyzed using the molybdenum secondary target and the L_α characteristic X-ray of 13.612 keV and 12.967 keV, respectively. Meanwhile, during metallic element analysis using ED-XRF, the analytical result (or concentration level) was greatly influenced by adjacent peaks. As shown in Figure 1B, for uranium (L_α, 13.612 keV), if the concentration of rubidium is relatively high due to peak overlap caused by the adjacent rubidium (K_α, 13.390 keV) line, the analytical results could be overestimated or the detection limit could be higher.

For the analysis of trace elements in the raw material and by-product samples that used ED-XRF—especially that of uranium and thorium—method validation for the entire analysis process including sample preparation, estimation, and result management is an important provision for determining the reliability of the analytical results. The accuracy (or relative error) is determined by the difference of the measurement for the certified value of the certified reference material. The relative standard deviation (RSD, standard deviation/mean of experimental value, %) of the measurements denotes the precision of the analytical values. Both are used as criteria to determine the validity of the analysis method and process. In addition, U-test (an index that evaluates the trueness of the analytical value regarding the ceritifed value through statistical methods other than relative error and RSD) results are specified in Table 3. The results were calculated by dividing the difference between the analytical value and the certified value and the sum of the uncertainty of the certified value and the measured value. Systematic bias of the measured values did not appear in the 95% or 99% confidence levels if the U-score did not exceed 1.95 or 2.58, and the results could be considered statistically reliable [19, 20].

In this study, ED-XRF was used to analyze uranium and thorium in various certified reference materials from various raw material mediums (e.g. soil, rock, coal ash, bauxite, and zircon) and by-product mediums. The analysis was conducted in accordance with the conditions outlined in Table 2. The results of the analysis are organized in Table 3. According to Table 3, all analytical results showed a relative error of less than 10%, except for uranium (37.6%) in the coal ash medium SRM 1633c and thorium (18.6%) in the medium CNRS Bx-N. Relative standard deviation, which shows analytical precision, in the all results showed less than 10%, except for cases in which the concentrations of uranium and thorium were less than 10 mg·kg⁻¹.

Moreover, as presented in Table 3, accuracy evaluation for all analytical results shows that values were statistically reliable, as U-test results were all less than 1.96, except for the results of the SRM 1633c and SRM 694 uranium analysis. For SRM 1633c (4.4), the U-test result exceeded 2.0 and the relative error was relatively high at 37.6%. These results reflect the influence of peak overlap caused by the rubidium within the medium. However, based on the result that the confidence interval of the relative standard deviation of the experimental values was low, the modifying algorithm for the peak overlap must be supplemented. In addition, the U experimental value for SRM 694 showed a 2.0 U-test result, but this result is due to the extremely low relative expanded uncertainty of the certified value of the standard material (approximately 0.425%). Even in this case, however, although the relative error of the analytical results in this study was approximately 10.3%, the relative standard deviation was 2.28%. Thus, one may declare the analytical results of the phosphate rock medium is considered reliable with very precise measurement.

Figure 2 presents the ED-XRF measurements of uranium and thorium regarding the certified reference materials. A linear regression analysis was conducted in order to identify the variability of the results according to the range of concentration levels. As a result, the regression coefficient—the deviation of the two variables regarding the mean—was 0.9914, and the variation coefficient—the dispersion of the deviation—was 0.9945, which shows a great linearity in a wide range of concentration from 3.0 to 350 mg·kg⁻¹. When the concentrations of ²³⁸U and ²³²Th were converted into mass concentrations in terms of the registration standards of the raw materials or by-products, the values were 80.4 mg·kg⁻¹ and 246 mg·kg⁻¹. The mass concentrations that correspond to the raw material standard of 0.1 Bq·g⁻¹ were 8.04 mg·kg⁻¹ and 24.6 mg·kg⁻¹, which magnified in detail the concentration range of raw material standards outlined in Figure 2. As shown in Figure 2, a linear relationship was also maintained in the low concentration range of below 30 mg·kg⁻¹.

The applicability of an analysis using ED-XRF is very good as a rapid screening method since it can rapidly measure the checmical composition of samples and at the same time, can directly infer the radioactivity concentrations of ²³⁸U and ²³²Th, the mother nuclides of naturally occurring radionuclides. Therefore, ED-XRF is considered the most effective analytical method in terms of on-site applicability and convenience since it can be applied to monitor the concentration levels of naturally occurring radionuclides for samples of the same medium during the processing phase and on site. However, because the ED-XRF analysis is highly dependent on the sample medium, the establishement of fundamental parameters (e.g. correction of the mass attenuation effect on the sample matrix, modifying algorithms for peak overlap, etc.) is essential in order to improve the accuracy of the analytical results [21–23]. Therefore, in order to identify the uncertainty of these mediums, the ED-XRF analytical results were intercompared to the ICP-MS analytical results of the raw material samples (e.g. zircon, bauxite) and by-product samples (e.g. coal ash) actually distributed in Korea. The ICP-MS analytical results were cited from references that verified the development and validity of the analytical method [24, 25].

Measurements using ED-XRF and ICP-MS were conducted 3 times. The natural isotopic abundance ratios (²³⁸U: 99.3%, ²³²Th: 100%) were applied to convert into the radioactivity concentration. The radioactivity concentration of ²³⁸U and ²³²Th in the 27 types of raw material and by-product samples analyzed using ED-XRF were presented in Table 1 and Figure 3. Based on the results, the mean radioactivity concentration of ²³⁸U and ²³²Th were 1.074 Bq·g⁻¹ (0.028–4.283 Bq·g⁻¹) and 0.471 Bq·g⁻¹ (0.005–4.408 Bq·g⁻¹), respectively. ²³⁸U showed the highest mean value of 2.370 Bq·g⁻¹ in the zircon matrix of the raw materials, and 75% of the samples were assessed to be over the registration standard of 1.0 Bq·g⁻¹, which was similar to the concentration range (²³⁸U: 1–4 Bq·g⁻¹, ²³²Th: 0.5–1 Bq·g⁻¹) found in world-wide commercial zircon in the previous study [26]. The ²³⁸U concentration of the zircon dust sample was also found at a high level of 0.892 Bq·g⁻¹ (0.354–1.604 Bq·g⁻¹). In the case of bauxite and ceramic ball, the concentration level was approximately 0.5 Bq·g⁻¹, while bentonite and coal ash showed a low concentration level of less than 0.1 Bq·g⁻¹. The concentration of ²³²Th was 4.408 Bq·g⁻¹ for the ceramic ball sample, which was about 4.4 times higher than the registration standard, and this sample was analyzed to be part of the alumina series with the following element distribution: SiO₂ 64.5%, Al₂O₃ 19%, Fe₂O₃ 7.2%, TiO₂ 0.8%. The radioactivity concentrations of ²³²Th appeared to be relatively high, similar to those of ²³⁸U in raw materials such as zircon and bauxite, but when compared to ²³⁸U in terms of radioactivity concentration, it was distributed in relatively low concentration levels.

In order to evaluate the applicability of ED-XRF in the radioactivity analysis of ²³⁸U and ²³²Th in raw materials and by-products, the analytical results of ED-XRF and ICP-MS were intercompared and presented in Figure 4. To be clear the analytical results of ICP-MS were set as the standard and the relative difference percent (RDP) between the methods was calculated and schematized. As shown in Figure 4, there was a high correlation between the analytical results from the two methods. The regression coefficients for ²³⁸U and ²³²Th were 0.916 and 1.055, respectively, and the variation coefficients were 0.954 and 0.992, respectively. However, the concentrations of ²³⁸U and ²³²Th show a relatively higher difference for a few zircon matrix samples and zircon process dust samples. As shown in Figure 4A, the 8 sets of data that deviated from the linear drift curve were all samples made up of zircon components. As shown by the RDP analytical results in Figure 4B, the concentration difference between the two screening methods for a certain medium appears frequently in the area of radioactivity concentration below 0.5 Bq·g⁻¹. It is considered that such analytical uncertainty was caused by the mass attenuation effect for sample mediums in the ED-XRF analysis. Therefore, in order to analyze the raw material and by-product samples of the zircon series, additionally building fundamental parameters is required. Moreover, it is considered that the concentration difference of more than 20% as shown in Figure 4 for vermiculite and coal ash samples is caused by the relative increase in measurement uncertainty in terms of the detection limit level (0.1- a few mg·kg⁻¹) of the ED-XRF equipment. Therefore, nevertheless it is difficult to quantify low levels of ²³⁸U and ²³²Th during analysis using ED-XRF, the method is considered excellent in terms of analytical accuracy and convenience for application as a rapid screening method for radioactivity concentration levels of more than 0.5 Bq·g⁻¹ regarding various medium samples.