Application of bias correction methods to improve U 3 Si 2 sample preparation for quantitative analysis by WDXRF

The determination of silicon (Si), total uranium (U) and impurities in uranium-silicide (U3Si2) samples by wavelength dispersion X-ray fluorescence technique (WDXRF) has been already validated and is currently implemented at IPEN’s X-Ray Fluorescence Laboratory (IPEN-CNEN/SP) in São Paulo, Brazil. Sample preparation requires the use of approximately 3 g of H3BO3 as sample holder and 1.8 g of U3Si2. However, because boron is a neutron absorber, this procedure precludes the recovery of U3Si2 from the samples, preventing its use as nuclear fuel. Consequently, a significant amount of uranium is wasted in this process. An estimated average of 15 samples per month is expected to be analyzed by WDXRF, resulting in approx. 320 g of U3Si2 that wouldn’t return to the nuclear fuel cycle. The purpose of this paper is to present a new preparation method, replacing H3BO3 by cellulose acetate {[C6H7O2(OH)3-m(OOCCH3)m], m = 0~3}, thus enabling the recovery of the boron-free U3Si2 from the samples. The results demonstrate that the suggested sample preparation approach is statistically satisfactory, allowing the optimization of the procedure.


INTRODUCTION
The determination of Si, total U and inorganic impurities in low enriched uranium silicide (U 3 Si 2 , 19.9% of 235 U) powder samples by wavelength dispersion X-ray fluorescence (WDXRF) is carried out by a validated procedure at IPEN's X-Ray Fluorescence Laboratory (IPEN-CNEN/SP) in São Paulo, Brazil [1,2].WDXRF is able to perform non-destructive simultaneous multielement determinations with good precision and accuracy [3], thus preserving the original sample.Since routine analyses are to be required for the qualification of the U3Si2 fuel samples, a potential recovery could represent the reduction of radioactive solid wastes generation by the reincorporation of the compound to the fuel cycle.
IPEN's Nuclear Fuel Center (CCN-IPEN/SP) is responsible for the yearly production of 60 nuclear fuel elements for the Brazilian Multipurpose Reactor ("Reator Multipropósito", RMB) [4].The expected amount of U 3 Si 2 samples to undergo fluorescence analysis could then reach 324 g per year, once each reading is performed in triplicate to ensure the reliability of the results.
The current sample preparation method requires an amount of 1.8 g of U 3 Si 2 , which is supported by an approx.3 g of H 3 BO 3 , used as sample holder.This step is used to facilitate sample's handling [2].However, boron ( 10 B) is a neutron absorber (neutron poison) because of its high neutron capture cross section, thus disabling sample's recovery after the analysis, since boron contamination may impair the fuel's performance in the nuclear reactor.
Within this context, this study proposed a new preparation method for the determination of Si, total U and inorganic impurities in U 3 Si 2 powder samples by WDXRF, replacing boric acid (H 3 BO 3 ) by cellulose acetate {[C 6 H 7 O 2 (OH) 3 -m(OOCCH 3 )m], m = 0~3}.Systematic errors were evaluated in order to demonstrate that the proposed method presents no significant analytical impact.

Sample preparation
A candidate sample for reference material containing 12 g of U 3 Si 2 powder was supplied by the Nuclear Fuel Center (CCN) at IPEN (CNEN/SP).Sampling was performed in order to obtain 6 subfractions of 2.0 g each.3 of these sub-fractions were prepared using H 3 BO 3 as sample holder and the other 3 were prepared using cellulose acetate.For each single sample, the following procedure it was used: 1.8 g of U 3 Si 2 and 0.2 g of wax (Hoechst wax C micro powder, Merck Millipore, MA, USA) were transferred to a polyethylene flask (approx.5 cm 3 ) and homogenized in a mechanical mixer for 5 min (Spex CertiPrep, NJ, USA).The mixture was compacted in a hydraulic press (Herzog, Osnabruck, Germany) employing a 2 kN pressure.A pressed pellet of 25.01 ± 0.01 mm of diameter and 5.0 ± 0.2 mm of thickness was obtained for each sub-fraction.

Instrumental parameters
The experiments were carried out using a WDXRF spectrometer (RIGAKU Co., Tokyo, Japan), model RIX 3000, comprising the following primary devices: one 3 kW (Rh target) X-ray tube, 6 positions sample, 8 crystal analyzers and 2 detectors (scintillation and flow-proportional counters).

Systematic error coefficient (SEC)
Systematic errors, which affect the accuracy of the results, have identifiable causes and can be eliminated [6].In X-ray fluorescence spectrometry, systematic errors are usually related to sample preparation.For instance, metallic samples require surface treatment using abrasives.Abrasive change, or even the employment of a new batch, may lead to systematically divergent results (above or under the results obtained for the original abrasive).Considering pressed pellets, the substitution of the binder or support base, as described in this study, may also conduct to systematically divergent results.
Because of this, X-ray fluorescence spectrometers' manufacturers provide mathematical tools, enabling the correction of the systematic errors through the calculation of these coefficients.This is a very valuable tool, since these coefficients allow the analysis of samples prepared by different procedures using a calibration curve obtained by a determined procedure.In this study, Eq. 1, available in the software Simultix 14 of the Rigaku spectrometer, was employed [7]. ( where Ai = correction coefficient; Wis = standard value; Wi = analyzed value.

Methodology evaluation
Samples were divided into 2 sub-groups: "Group A", prepared using the cellulose acetate as holder, and "Group B", using H 3 BO 3 .Each sample was randomly analyzed 3 times under the established instrumental conditions, resulting in a set of 18 measurements for each element and the data were evaluated statistically [2].The Fisher-Snedecor F-test was applied to compare the variances of groups A and B at a 95% confidence level.When the calculated values of F were below their critical value (0.05), the hypothesis of different variances was accepted.The Student t-test was applied to compare the average values (means), assuming different variances for a 95% confidence level.
For calculated values of "t" below their critical value (2.13), the difference between the mean values can be assumed as statistically insignificant.Both tests were performed using the Software Microsoft Excel (2013 version).

RESULTS AND DISCUSSION
The results for "Group A" and "Group B" are presented in Tab. 2 comprising elemental contents and standard deviations ( ±), followed by the relative standard deviations (RSD), calculated values of F and t, both for a 95% confidence level, and systematic error coefficients (SEC) calculated according Eq. 1.The results showed that all elements were quantified for both procedures.The calculated values of F were lower than the critical value (F-critical = 0.05) for all elements, demonstrating that the difference between the variances of Groups "A" and "B" are statistically insignificant, except for Si (1.69) and U (0.62).The relative standard deviation (RSD) values were significantly lower for the samples of "Group A" (0.2 %) compared to those of "Group B" (1.5 %).Thus, the repeatability of the overall results for the samples prepared with cellulose acetate was more satisfactory than for the samples prepared with H 3 BO 3 .
The calculated values for the "t" Student test ("t-test") for all the elements were lower than the critical values (2.13), demonstrating that there are no statistically significant difference between the samples of "Group A" and "Group B".
For Si and U, the systematic error coefficients (SEC) showed that the influence of the major constituents were lower (0.0002±0.0001) when compared to the other elements (0.014±0.004).However, the SEC values can be disregarded for all the elements, when the correction is applied, because the variation in the concentration values is smaller than the standard deviation.Thus, the hypothesis can be accepted, that there are no statistically significant differences between both methods.
It was visually evident that the 3 samples prepared with cellulose acetate were easily removable from its base after the analysis (Fig. 1), thus ensuring boron-free U 3 Si 2 pellets.The probable hypothesis for this is that the cellulose acetate had undergone some sort of decomposition after the irradiation in the spectrometer, favoring the detachment of the sample from its base.Source: author

CONCLUSION
The results allowed concluding that the substitution of boric acid for cellulose acetate in the preparation of pressed pellets for elemental analysis by WDXRF can be applied, since statistically equivalent results are achieved in both cases.Indeed, the cellulose acetate proved to be more suitable than the H 3 BO 3 , because it allowed an effortless recovery of the sample.Thus, the aim of this study was achieved, as an effective alternative preparation procedure for U 3 Si 2 analysis by WDXRF was proposed.In addition, using cellulose acetate as support base allows a simple and complete recovery of the U 3 Si 2 samples.

Table 2 :
WDXRF analysis results for "Group A" and "Group B" samples