Standard-sample bracketing calibration method combined with Mg as an internal standard for silicon isotopic compositions using multi-collector inductively coupled plasma mass spectrometry

Silicon isotope analysis traditionally uses a standard-sample bracketing (SSB) method that relies upon greater instrument stability than can be consistently expected. The following proposed method reduces the level of instrumental stability required for the analysis process and provides a valid solution for high-precision and accurate studies of Si isotopic compositions. Rock samples were dissolved by using alkali fusion and acidification. Silicon isotopes were purified with an ion exchange resin. Interfering peaks for isotopes were separated by using a Nu Plasma 1700 multi-collector inductively coupled plasma mass spectrometry (MS) system in high-resolution mode (M/ΔM > 8000 RP). Two magnesium isotopes (25Mg and 26Mg) and three silicon isotopes (28Si, 29Si, and 30Si) were analyzed in the same data collection cycle. Mg isotopes were used as an internal standard to calibrate the mass discrimination effects in MS analysis of Si isotopes in combination with the SSB method in order to reduce the effects of MS interference and instrumental mass discrimination on the accuracy of measurements. The conventional SSB method without the Mg internal standard and the proposed SSB method with Mg calibration delivered consistent results within two standard deviations. When Mg was used as an internal standard for calibration, the analysis precision was better than 0.05 ‰ amu.


Introduction
Silicon is the second-most abundant element in Earth's crust; it makes up the skeleton of rocks and has stable chemical properties. Silicon has three stable isotopes: 28 Si, 29 Si, and 30 Si with relative abundances of 92.23 %, 4.67 %, and 3.1 % respectively (Cardinal et al. 2003;Georg et al. 2007). Researchers have conducted numerous studies on Si isotopes to better understand magmatism, meteorites, hydrothermal mineral deposits, clay minerals, the ocean silicon cycle, biological silicate, and fractionation of silicate melts and metallic melts (Brzezinski et al. 2003;Armytage et al. 2011;Opfergelt et al. 2011;Armytage et al. 2012;Opfergelt et al. 2013;Hin et al. 2014;Zhu et al. 2014). Studies on silicon isotopes have not only revealed Earth's evolutionary history Armytage et al. 2011;Ziegler et al. 2010;Savage and Moynier 2013;) but also are very important in explaining ore genesis (as it pertains to mineral resources) and in research on the climate and carbon cycle (Dugdale et al. 2004;Pringle et al. 2013;Hou et al. 2014).
Si isotopic composition is normally determined by using multi-collector inductively coupled plasma mass spectrometry (MC-ICP-MS), whose accuracy and precision are mainly affected by interfering mass spectrometry (MS) peaks for isobaric heterotopes, instrumental mass discrimination effects, and the stability of the sample injection system. Standard-sample bracketing (SSB) is normally used to calculate Si isotopic composition. To calibrate the instrumental mass discrimination, the SSB method requires identical instrumental conditions and excellent stability during analysis of the standard and actual samples. In practice, each sample needs to be measured more than three times, and the mean value of the measurements is calculated as the Si isotopic composition of the sample to obtain stable and reliable results. Fluctuations in instrumental conditions that affect the accuracy of the isotopic ratio analyses are mainly caused by changes in the sensitivity of the sample injection system or in the mass discrimination effects in the MS system. These are usually calibrated using two isotopes of elements with similar atomic weights (e.g., adding 203 Tl and 205 Tl for isotopic analysis of Pb). Because of their similar relative atomic masses to those of Si isotopes, the Mg isotopes 25 Mg and 26 Mg can be used to calibrate mass discrimination effects. Cardinal et al. (2003), Zambardi and Poitrasson (2011) added magnesium into silicon samples and standard solutions to calibrate the changes in the Si isotopic composition caused by changes in the mass discrimination effects from variations in the space charge effect or sample injection conditions. However, because of previously experienced hardware limitations, they analyzed Mg and Si isotopes in two different data collection cycles during the measurement process; simultaneous analysis of Mg and Si isotopes could not be achieved, and so the changes in the measured Si isotopic composition caused by variations in the instrumental conditions were not effectively calibrated.
In this study, interfering peaks were separated by using the high-resolution mode of the large dimension MC-ICP-MS system (Nu Plasma 1700). Mg was used as the internal standard, and the physical positions of the detectors at the high-and low-mass sides of the instrument were moved to the extremes to slightly extend the mass dispersion limit of the MC-ICP-MS system, allowing for the analysis of Mg ( 25 Mg and 26 Mg) and Si isotopes in the same data collection cycle, thus achieving simultaneous collection of Mg isotope and Si isotope signals. The Mg isotopes were used to calibrate the fractionation effect during the Si isotopic analysis to obtain accurate Si isotopic compositions.

Reagents
The experiments used AR-grade nitric acid and hydrochloric acid that were distilled twice with a PFA Savillex DST-1000 sub-boiling still (Minnetonka, USA). Ultrapure water was purified with Milli-Q Element (Elix-Millipore, USA) (18.2 MX/cm). The standard solutions were Alfa Si and Alfa Mg (Si: stock no. 38717; Mg: stock no. 14430, 2 % HNO 3 , plasma standard solution, Specpure, Alfa Aesar, Johnson Matthey Company). NaOH (LOT: 10165572, Alfa Aesar, Johnson Matthey Company) was used as the fluxing agent for the fusion test. A Bio-Rad polypropylene ion exchange column was used for the purification test with a Bio-Rad AG50-X12 cation exchange resin (Catalog # 142-1651, Bio-Rad Laboratories Inc., CA, USA).

Sample dissolution
Rock samples were fused by using NaOH as the fluxing agent and dissolved with HCl according to the method presented in a previous study (Georg et al. 2006). To avoid contamination during sample fusion in the Muffle furnace, 5 and 30 mL silver crucibles fabricated in the laboratory ( Fig. 1) were used as melting vessels in this study. The samples and crucibles in contact with the samples were kept inside a relatively clean and large crucible during the entire sample fusion process. The weighing of the sample, addition of the fluxing agent, and transfer of the small crucibles into the large crucible were performed with a class 100 clean bench to reduce the background level during the test process. The specific sample dissolution procedure was as follows: within the clean bench, 10 mg of powdery sample was evenly mixed with 200 mg powdery NaOH and placed into a 5 mL silver crucible. This crucible was then covered and transferred into a 30 mL crucible with a lid. The large crucible was placed into a Muffle furnace, where the sample was fused at 730°C for 10 min. Upon cooling, the 5 mL small silver crucible containing the melt was placed into a Teflon vial (30 mL, Savillex Corporation, Minnesota, USA), and 20 mL ultrapure water was added. The mixture was ultrasonicated for 15 min, allowed to settle for 24 h, and ultrasonicated for another 15 min. The solution inside the Teflon vial was diluted and acidified to pH 2.2 with hydrochloric acid (Fitoussi et al. 2009) and then heated at 40°C for 15 min to accelerate the dissolution of hydroxide.

Chemical separation
Si isotopes were purified by using 2 mL cation exchange resin (AG 50-X12). Because the active ion of the resin was - (Georg et al. 2006). Si could be directly eluted with the ultrapure water, and cations of substrate elements such as Na ? , K ? , Mg 2? , Al 3? etc. were adsorbed onto the resin; thus, Si was separated from the cations (Fig. 2). The recovery rate of Si isotopes was greater than 98 %, and the background level during the entire process was less than 20 ng. Table 1 presents the separation procedure.

Apparatus and data processing
Instrumental analysis was performed with a high-resolution Nu Plasma 1700 MC-ICP-MS system (Nu Instruments, UK) installed in the State Key Laboratory of Continental Dynamics, Northwest University, Xi'an, China. The Nu Plasma 1700 system was equipped with three ion-counting multipliers and 16 Faraday cups. The high-and low-mass sides each had three independently movable Faraday cups and two independently movable slits before each Faraday cup to achieve separate resolution of the interfering peaks on the high-and low-mass sides (Fig. 3). The highest RP (edge 5, 95%) of the MS system was greater than 20,000. In this study, the outermost Faraday cups H8 and L7 were moved to the extreme positions, and the slits before the Faraday cup were moved to the two sides to receive 30 Si and 25 Mg signals simultaneously. Table 2 presents the detectors for the other isotopes. In this study, the resolution was in the range of 8000-10,000 RP, and data were collected in static mode. The ratios of Si/Mg in the solution were about 1 and the sensitivity of Si was about 2 V/ppm. During the Si isotope test, the background noise (\50 mV) was deducted as the on-peak zero (OPZ). Samples were injected in the wet state (Zambardi and Poitrasson 2011). Table 2 presents the instrument parameters.
For data calibration purposes, the fractionation factor was calculated from the measured ratio between a pair of DSM3 Mg standard isotopes ( 25 Mg-26 Mg) and the reference isotopic ratio by using the power index method. The Si isotopic ratios 29 Si/ 28 Si and 30 Si/ 28 Si were calibrated through fractionation. The Si isotopic compositions of the samples {d 29 Si = [( 29 Si/ 28 Si) sample /( 29 Si/ 28 Si) standard -1] 9 1000; d 30 Si = [( 30 Si/ 28 Si) sample /( 30 Si/ 28 Si) standard -1] 9 1000} were calculated by using the SSB method. The If there is a simple linear relationship between the fractionation factors of Mg and Si, then where a is calculated from the slope S of the plot of ln ( 29 Si/ 28 Si) measure versus ln ( 26 Mg/ 25 Mg) measure : The isotopic ratios of Si and Mg measured in the same analysis cycle in a mixed solution are plotted in Fig. 4. The slope of the plot is 0.882, and a was calculated to be 0.9833. Within the same analysis cycle, inserting a into Eq. 3 obtained the fractionation factor of Si. Inserting a into Eq. 4 obtained the Si isotopic composition of the samples. Differences in instrumental conditions, especially due to instrumental repair such as the replacement of a cone or torch, usually cause considerable changes in the absolute values of Si and Mg isotopic ratios; the variation in S can reach 25 % (Cardinal et al. 2003). Therefore, calculations should only be based on ln ( 29 Si/ 28 Si) measure and ln ( 26 Mg/ 25 Mg) measure with data obtained within the same analysis section under identical instrumental analysis conditions.
3 Mass spectrometry resolution and results

Resolution and interfering peaks in mass spectrometry spectra
The MC-ICP-MS analysis of the three silicon isotopes was subjected to the following interferences: (  . These interfering peaks cannot be effectively separated in conventional low-resolution mode (\1000 RP) and are at the high-mass side of the Si isotopes. Thus, a magnetic field deviating from the peak center is normally used for measurements on a narrow platform without interference (Fig. 3a)  ). However, slight disturbances in the testing conditions result in a shift of mass spectral peaks, which can affect the accuracy of the analysis results. In this study, the resolution of the MS system was increased to above 8000 RP, and the ion lens, focusing lens, and collector slits were adjusted. This resulted in complete separation of the mass spectral peaks for 28 Si ? , 29 Si ? , 30 Si ? , 25 Mg ? , and 26 Mg ? with good peak shapes from interfering peaks (Fig. 3b), thus ensuring the reliability of the Si isotopic analysis results.

Measurement results
NBS-28 and IRMM-018a are commonly used international reference standards in Si isotope studies (Reynolds et al. 2007). In addition, the Si isotopic composition of the BHVO-2 standard rock sample has been reported (Zambardi and Poitrasson 2011). In this study, the Mg internal standard plus SSB calibration method and the SSB calibration method without an internal standard were used to determine the Si isotopic compositions of IRMM-018a and BHVO-2, respectively ( Table 3).
The results indicate that the Mg isotopic compositions obtained by SSB calibration plus the Mg internal standard and by SSB calibration without the internal standard were consistent within the error range and agreed with the reported values. This indicates that both methods delivered an accurate Si isotopic composition. Overall, the Mg internal standard plus SSB method resulted in more stable relative errors than the SSB method without an