Determination of Rare Earth Elements by Inductively Coupled Plasma–Tandem Quadrupole Mass Spectrometry With Nitrous Oxide as the Reaction Gas

Nitrous oxide (N2O) was investigated as the reaction gas for the determination of rare earth elements (REEs) by inductively coupled plasma–tandem quadrupole mass spectrometry (ICP-QMS/QMS). The use of N2O as the reaction gas apparently improved the yields of m M16O+ for Eu and Yb in the reaction cell. As a result, the sensitivities for measurement of Eu and Yb were apparently improved in comparison to those obtained with O2 as the reaction gas. A high sensitivity measurement of the whole set of REEs was achieved, providing a typical sensitivity of 300,000 CPS mL/ng for REEs measured with an isotope having isotopic abundance close to 100%. The use of N2O as the reaction gas helped suppress Ba-related spectral interferences with the measurement of Eu, permitting the measurement of Eu in a natural sample without mathematic correction of spectral interferences. The detection limits (unit, pg/mL) for 14 REEs (except for Pm) from La to Lu were 0.028, 0.018, 0.006, 0.026, 0.006, 0.010, 0.017, 0.006, 0.016, 0.010, 0.016, 0.004, 0.023, and 0.012, respectively. The validity of the present method was confirmed by determining REEs in river water-certified reference materials, namely, SLRS-3 and SLRS-4.


INTRODUCTION
Rare earth elements (REEs) are a group of 17 transition metals, including Sc, Y, and 15 lanthanides, in the periodic table of chemical elements (Balaram, 2019). Nevertheless, the lanthanides are more often referred to as REEs in many research works, while Pm is usually not investigated due to the lack of a natural and stable isotope. In the present work, REEs stand for the lanthanides except for Pm.
Due to the specific physicochemical properties of REEs, they are usually studied as a group of tracers for geological, hydrological, environmental, and fossil fuel research (Zuma et al., 2020;Wysocka, 2021). Acknowledging the capabilities for multi-elemental analysis, lower detection limits at ng/kg or even pg/kg levels, and commercial availability in common chemical analysis laboratories, inductively coupled plasma mass spectrometry (ICP-MS) is becoming a dominant approach for quantitative analysis of REEs in various samples (Bandura et al., 2006).
The extremely high temperature of the argon plasma provides an ionization efficiency for all REEs close to 100%, permitting the high sensitivity measurements by ICP-MS. At the same time, polyatomic spectral interferences such as oxide and hydroxide are usually problematic for accurate quantitation of REEs in natural samples, for example, 137  There are majorly three ways to solve the problem caused by spectral interferences. One is the mathematic correction based on the ratio of the signal intensity of an interfering polyatomic ion (for example, 137 Ba 16 O + ) to that of an interferent ion (for example, 137 Ba + ) (Seregina et al., 2018;Zhao et al., 2019;Carvalho et al., 2020;Kunzetsova et al., 2021). Mathematic correction is a straightforward way of canceling spectral interferences in the measurements by ICP-MS. However, the accuracy and the precision of an analytical result may be greatly deteriorated in case of a relatively large portion (for example, over 30%) of spectral interference being corrected due to the variance in the signal intensity of the interfering spectrum. The second one is suppressing the formation of an interfering polyatomic ion by removing an interferent element (for example, Ba) from REEs through chemical separation (Watanabe et al., 2018;Ito et al., 2019;Barrat et al., 2020;Bradley et al., 2020) or by using a desolvating device to remove water contents introduced into the argon plasma (to suppress the formation of solvent related ions, for example, O + , H + , and OH + ) (Giardi et al., 2018;Gatiboni et al., 2020;Shen et al., 2022). The third one is separating an interfering polyatomic ion from an REE of interest by high-resolution ICP-MS (Giardi et al., 2018;Barrat et al., 2020;Bradley et al., 2020;Kiruba et al., 2021), collision/reaction cell ICP-MS (Gueguen et al., 2009;Arslan et al., 2018;Rojano et al., 2019;Trommetter et al., 2020;Baghaliannejad et al., 2021), and tandem quadrupole ICP-MS with a reaction cell (ICP-QMS/QMS) (Galusha et al., 2018;Zhang et al., 2019;Zhu, 2020;. A previous work by the present author showed that ICP-QMS/ QMS provides the best separation of interfering polyatomic ion from an REE of interest by measuring at a so-called mass-shift mode with oxygen as the reaction gas (Zhu, 2020). In ICP-QMS/ QMS, an octopole reaction cell is sandwiched by using two quadrupole analyzers. For the measurement of REEs at the mass-shift mode, the parameters for the first quadrupole (QMS1) were set to permit the pass of an ion of interest, for example, mass to charge ratio (m/z) = 139 for 139 La + (along with 138 Ba 1 H + ), and to block ions with m/z ≠ 139. After entering the reaction cell, 139 La + reacted with O 2 to form 139 La 16 O + , while 138 Ba 1 H + did not form 138 Ba 1 H 16 O + . These product ions were introduced to the second quadrupole (QMS2) whose parameters were set to permit the pass of an ion with m/z = 155. As a result, the 139 La 16 O + ions passed through and arrived at the detector, while the product ions of 138 Ba 1 H + were blocked by the second quadrupole.
The mass-shift mode by ICP-QMS/QMS with oxygen as the reaction gas was effective for separating spectral interferences in the measurement of REEs. However, since reactions for the formation of EuO + and YbO + are endothermic, the transference ratio from M + to MO + for Eu + and Yb + was significantly lower than that for other REEs, resulting in relatively lower sensitivities. Optimization of the octopole bias voltage helped to improve the formation of EuO + and YbO + .
Nevertheless, the transference ratio from M + to MO + for Eu + and Yb + was still apparently lower than that for other REEs .
In addition to the commonly equipped reaction cell gases, namely, He, H 2 , O 2 , and NH 3 , N 2 O had been used in collision/ reaction cell ICP-MS and ICP-QMS/QMS to improve the formation of oxide ions (Bandura et al., 2006;Harouaka et al., 2021). In the present work, N 2 O was investigated as the reaction cell gas for ICP-QMS/QMS to improve the formation of EuO + and YbO + to achieve the highest sensitivities for the measurement of all REEs. The optimized conditions were applied to the measurement of REEs in two natural water-certified reference materials, namely, SLRS-3 and SLRS-4.

Instruments
Measurements of REEs in the present work were carried out with an ICP-QMS/QMS instrument (Agilent 8800, Agilent Technologies Japan, Ltd.), for which the typical operating conditions are summarized in Table 1. These operating conditions were optimized to obtain the best performance for measuring REEs with the highest sensitivity. A Millipore purification system (Nihon Millipore Kogyo) was used to provide deionized water for the present experiment. A chemical balance (model XS205DU) purchased from METTLER TOLEDO was used for making samples and calibrating solutions, while the chemical balance was calibrated yearly by the Japan Calibration Service System (JCSS).

Chemicals and Samples
The following chemicals were purchased from Kanto Chemical Co., Inc.: single-element standard solutions (1,000 mg/L) of REEs and barium; Ultrapur ® grade HNO 3 (60% in mass). Two river water CRMs (SLRS-3 and SLRS-4) were purchased from the National Research Council of Canada and analyzed to confirm the validity of the present method. The CRM samples were acidified to 0.3 mol/L of nitric acid by adding concentrated nitric acid, where this dilution factor was calculated and applied to the results to obtain the initial concentrations of REEs. Calibrating solutions for measurement by ICP-QMS/QMS were also prepared in 0.3 mol/L of nitric acid. Standard N 2 O gas (99.5%, 8 kg/m 2 , 5 L) was purchased from AS ONE Corp. and used as the reaction cell gas for ICP-QMS/QMS.

Calibrating Method
The concentrations of REEs in the present work were obtained based on a standard addition method (Zhu et al., 2018). Spiked and non-spiked sub-samples were made for each sample and subjected to the measurement by ICP-QMS/QMS. The natural content of yttrium in the sample was used as the internal standard. The concentrations of REEs in a spiked sub-sample for standard addition were over two folds of those in the initial sample to ensure the precision of calibration.

Dependence of Relative Signal Intensities of La, Eu, and Yb on the Octopole Bias of ICP-QMS/QMS
Measurement of REEs by ICP-QMS/QMS at the mass-shift mode ( m M + → m M 16 O + ) with O 2 as the reaction gas was effective for separating spectral interferences. However, the production ratios of EuO + and YbO + were significantly lower than those of other REEs because the reactions for the formation of EuO + and YbO + were endothermic, while those for other REEs were exothermic. A relatively stronger negative voltage applied to the octopole bias resulted in limited improvement of signal intensities for the measurement of Eu and Yb . In the present work, N 2 O was used as the reaction gas for ICP-QMS/QMS to improve the production ratios of oxide ions of Eu + and Yb + , while La + was investigated as a representative of other REEs. The dependence of signal intensities of La, Eu, and Yb on the octopole bias of ICP-QMS/QMS was investigated with O 2 and N 2 O, respectively, as the reaction gases. The results are plotted in Figure 1. The default value of the octopole bias (suggested for mass-shift measurement with O 2 as the reaction gas) was −5 V, and the range for octopole bias investigated in the present work was from −25 V to −5 V with a footstep of 5 V.
A preliminary test in the present work was performed to check the major product ions from an REE ion m M + when O 2 and N 2 O were, respectively, used as the reaction gases. The results showed that the major product ions were m M + , m M 16 O + , and m M 16 O 2 + and m M + , m M 16 O + , and m M 14 N + , respectively. Therefore, a study on the dependence of relative signal intensities on octopole bias was focused on these ions. Figures 1A-C  was not varied apparently. These results indicated that a stronger negative voltage of the octopole bias improved the relative yields of m M 16 O + ions whose producing reactions are endothermic, which can be attributed to the increase of the velocity and the resulting collision energy of the precursor ion entering the reaction cell. However, such an increase in the velocity also results in a shorter retention time in the reaction cell and a lower reaction rate of an exothermic reaction. This contributed to the decrease in the relative signal intensity of 139 La 16 O + and the increase in that of 139 La + when the octopole bias changed from −5 V to a stronger negative voltage until −25 V, as shown in Figure 1D. By contrast, the maximum values of relative signal intensities of 153 Eu 16 O + and 172 Yb 16 O + ( Figures 1E,F) were obtained at an octopole bias of −15 V, which can be attributed to the increased yields of these ions due to the elevated collision energy in comparison to the octopole bias of −5 V. Moreover, the decrease in the sum of relative signal intensities of product ions (black plots, Figures 1D-F) may indicate the decrease in transmittance of the ions when a stronger negative voltage was applied to the octopole bias. Based on these results, an octopole bias of −15 V was selected as the compromised optimum condition for measuring the whole set of REEs at relatively higher sensitivities.
The results obtained with N 2 O as the reaction gas are plotted in Figures  It can be seen from Figure 1G that the major product ion from 139 La + was 139 La 16 O + when N 2 O was used as the reaction gas, with a portion comparable to that obtained with O 2 as the reaction gas ( Figure 1A). By contrast, instead of the dominating production ions as 153 Eu + ( Figure 1B) and 172 Yb + ( Figure 1C) obtained with O 2 as the reaction gas, 153 Eu 16 O + ( Figure 1H) and 172 Yb 16 O + ( Figure 1I) accounted for the dominating portions when N 2 O was used as the reaction gas. This can be attributed to the decrease in reaction energy for producing 153 (Harouaka et al., 2021).
As can be seen in Figures 1J-L

Comparison of Normalized Sensitivities for the Measurement of REEs by ICP-QMS/QMS
The sensitivity for measuring an element by ICP-QMS/QMS depends on the sample uptake rate, the ionization rate, the abundance of the isotope selected for measurement, the transmittance in the ion lens system, and the yield of the product ion in the reaction cell. In the case of measuring REEs, the parameters for all REEs are quite similar, except for the abundance of the isotope and the yield of the product ion.
Therefore, normalized sensitivities of REEs were obtained to cancel the effect of the abundance of the isotope and to elucidate the contribution of the improved yield of the product ion by using N 2 O as the reaction gas. A normalized sensitivity (S*) was calculated from the initial sensitivity (S 0 ) and the abundance of an isotope (A) based on Eq. 1. If the yields of product ions of interest were close to 100% for all REEs, the normalized sensitivities are expected to be close to one another.
The normalized sensitivities for REEs obtained in the present work are plotted in Figure 2, with O 2 and N 2 O, respectively, used as the reaction gases. The octopole bias was set to -15 V for both O 2 and N 2 O. As can be seen from Figure 2, the normalized sensitivities for all REEs were generally at a similar level when N 2 O was used as the reaction gas. The relatively lower normalized sensitivities of La and Ce might be attributed to the formation of m M 14 N + ions (over 10% of the product ions), as indicated in Figure 1G.
By contrast, the normalized sensitivities of Eu and Yb were apparently lower than those of other REEs, when O 2 was used as the reaction gas. Moreover, the relative sensitivities for all REEs obtained with N 2 O as the reaction gas were higher than those with O 2 as the reaction gas. These results indicated that the optimized operating condition with N 2 O as the reaction gas provided higher yields of m M 16 O + ions for all REEs and helped achieve higher sensitivities for measuring the whole set of REEs by ICP-QMS/QMS.

Ba-Related Spectral Interferences With the Measurement of Eu by ICP-QMS/QMS
Due to relatively smaller differences (one to two orders of magnitudes) among the concentrations of REEs in a natural sample, spectral interferences of oxide ions of lighter REEs (with a smaller atomic number) with the measurement of heavier REEs (with a larger atomic number) can be effectively suppressed by measuring at the mass-shift mode of ICP-QMS/QMS with O 2 as the reaction gas. However, the concentrations of Ba in natural samples are usually much higher (for example, over four orders of magnitudes) than those of Eu, whose both stable isotopes ( 151 Eu and 153 Eu) suffer from spectral interferences from oxides and hydroxides of Ba. As a result, mathematical correction of Ba-related spectral interferences is still required even for the measurement by ICP-QMS/QMS with O 2 as the reaction gas .
Ba-related spectral interferences with the measurement of 153 Eu + were further investigated in the present work, with O 2 and N 2 O as the reaction gases, respectively. The investigation was carried out by introducing 10 mg/L Ba standard solution to the ICP-QMS/QMS and measuring the product ions of 153 M + (m/z = 153 for QMS1) at the m/z range of 160-180 for QMS2, covering the spectra of 153 Eu 16 O + . The results are plotted in Figure 3.
As can be seen from Figure 3, the major product ions obtained with O 2 as the reaction gas were 168 M + and 169 M + , which can be attributed to 136

Analytical Figures of Merits for Measurement of REEs by ICP-QMS/QMS
Sensitivity, blank equivalent concentration (BEC), and detection limit (DL) are usually provided as analytical figures of merits for the measurement of the elements by ICP-MS. These parameters are evaluated and summarized in Table 2, respectively, with O 2 and N 2 O as the reaction gases.
The sensitivity was obtained as the signal intensity corresponding to each of 1.0 ng/mL REEs. A BEC value was obtained as the concentration equivalent to the average of five measurements of 0.3 mol/L HNO 3 solution, where each measurement contains 10 repetitions (1 s/repetition) for each REE. A DL value was obtained as the concentration corresponding to 3-fold of the maximum standard deviation obtained in five measurements of the 0.3 mol/L HNO 3 solution.
As can be seen from Table 2, the sensitivity, BEC, and DL values for each REE obtained with N 2 O as the reaction gas were generally superior to those obtained with O 2 , especially for Eu and Yb due to the improved yields of m M 16 O + ions in the reaction cell. It is notable that the sensitivities summarized in Table 2 were the initial values without normalization to the isotopic abundances. As a result, the sensitivity depended on the isotopic abundance of an isotope measured. When N 2 O was used as the reaction gas and an REE was measured at an isotope with an isotopic abundance of 100%, the typical sensitivity was around 300,000 CPS mL/ng. The BEC and DL values for each REE with N 2 O as the reaction gas were, respectively, lower than 0.01 pg/mL and 0.03 pg/mL, sufficiently low for the direct measurement of REEs in most natural water samples. The data for Eu and Yb with N2O as the reaction gas are shown in bold fonts in Table 2 to highlight the improved analytical performance.

Results for the Recovery Test of Spiked REEs in River Water CRMs
Recovery tests of spiked REEs in river water CRMs were carried out by adding a mixed solution of REEs into river water CRMs, ( 2 ) The results of recovery tests are summarized in Table 3. It can be seen from Table 3 that each recovery value is close to 100%, indicating that the concentrations of REEs spiked to the river water CRMs can be accurately determined by ICP-QMS/QMS with O 2 or N 2 O as the reaction gas. It is notable that the standard deviation values for La, Ce, Pr, Tb, Ho, Tm, and Lu were around 1.0%, which can be attributed to the excellent sensitivities due to the isotopes measured having high isotopic abundance. The standard deviation values for other REEs were generally in the range of 1-2%, except for those of Yb (roughly 3%) measured with O 2 as the reaction gas. Such relatively lower standard deviation values of Yb were improved to a level similar to those of other REEs when N 2 O was used as the reaction gas, attributable to the improved yields of 172 Yb 16 O + in the reaction cell.

Analytical Results of REEs in River Water CRMs
The concentrations of REEs in two river water CRMs, namely, SLRS-3 and SLRS-4, were determined in the present work. The results are summarized in Table 4 along with reported data.  It can be seen from Table 4 that the results for each CRM obtained with O 2 and N 2 O, respectively, as the reaction gas agreed with each other considering the standard deviation of each value. However, it is notable that the measurement of Eu with O 2 as the reaction gas suffered approximately 10% of Barelated spectral interference, which was mathematically  corrected. By contrast, Ba-related spectral interference with the measurement of Eu was negligible when N 2 O was used as the reaction gas and did not require mathematic correction. The concentrations of Ba in both samples were approximately 15 ng/ mL, roughly four orders of magnitude higher than the concentration of Eu. The present results for REEs in SLRS-3 were generally close to those reported by Brenner et al. (1998), who applied mathematic corrections to the measurements of La, Ce, and Eu regarding Barelated spectral interferences. The DLs for REEs achieved by Brenner et al. (1998) were in the range from 0.02 pg/mL for Sm to 0.2 pg/mL for Nd, roughly 10-fold higher than those obtained in the present work. By contrast, the results by Halicz et al. (1999) showed slightly higher values for most REEs except for Sm, Eu, Tm, and Lu, perhaps indicating some spectral interferences, even mathematic correction applied to the measurements of 151 Eu + regarding the spectral interference by 135 Ba 16 O + . The DLs for REEs obtained by Halicz et al. (1999) were in the range from 0.005 pg/mL for Tm to 0.1 pg/mL for Nd. Brenner et al. (1998) and Halicz et al. (1999), respectively, used a Meinhard type pneumatic concentric nebulizer and an ultrasonic nebulization system to introduce the samples to their ICP-MS instruments. The present results for REEs in SLRS-4 obtained in the present work agreed with the compiled data based on multiple works .
These results for REEs in SLRS-3 and SLRS-4 showed that the present method is effective for the determination of REEs in river water samples.

CONCLUSION
The application of N 2 O as the reaction gas for ICP-QMS/QMS provided excellent analytical figures of merits for the determination of REEs. In comparison to O 2 that was usually used as the reaction gas, N 2 O improved the yields of m M 16 O + ions for Eu and Yb in the reaction cell and permitted measuring them at much higher sensitivities.
The application of N 2 O as the reaction gas also contributed to the suppression of Ba-related spectral interferences with 153 Eu + to 2.6% of that observed with O 2 as the reaction gas. This merit permitted the measurement of Eu without mathematic correction even with Ba concentrations over four orders of magnitude higher.
The analytical results for spiked REEs in SLRS-3 and SLRS-4 provided recovery values quite close to 100%. The concentrations of REEs in SLRS-3 and SLRS-4 determined by the present method were incidence with those reported, indicating the validity of the method.

DATA AVAILABILITY STATEMENT
The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.