Whole-rock trace element analyses via LA-ICP-MS in glasses produced by sodium borate flux fusion

Trace elements provide crucial information about the origin and evolution of the Earth. One common issue regarding their analyses is the reduced analyte recovery during hot plate acid digestion for some geological samples. To overcome this, alkali fluxes (e.g., Lithium borate) have been used to produce an homogeneous synthetic glass that can be used then for both X-ray fluorescence (XRF) and laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS). In this sense, we developed a method for LA-ICP-MS whole rock trace element analyses in glasses prepared by mixing high-purity sodium tetraborate and rock powders at high-temperature. We selected six international reference materials including peridotite ( JP-1), basalt (BRP-1), kimberlite (SARM-39), pyroxenite (NIM-P), diorite (DR-N) and andesite ( JA-1). Glasses were produced in a fully automatic fusion machine with step heating. Run products analyses were carried out on a Thermo® Element2 SF-ICP-MS coupled to a New Wave Research® Nd:YAG (213 nm) laser ablation system and on a Thermo® Element XR ICP-MS coupled to an Analyte G2 (193 nm) LA system. Results show that glasses are homogeneous and there is good agreement (generally > 90%) between our data and literature values for most trace elements, including large ion lithophile elements (LILE), high-field strength elements (HFSE) and rare-earth elements (REE).


INTRODUCTION
Despite their low abundance, trace elements provide crucial information about geochemical processes during the origin and evolution of the Earth and other planets (e.g., Kelemen et al. 1993, Münker 2010, White 2013. For example, trace elements have long been used to constrain tectonic settings and petrogenesis of a given geological unit (e.g., Pearce et al. 1984, Whalen et al. 1987, in mineral exploration and the origin of ore deposits (e.g., Pearce and Gale 1977, Hutchinson and McDonald 2008, Reich et al. 2016, or even to constrain large-scale planetary differentiation processes (e.g., Pfänder et al. 2007, Leitzke et al. 2017. For this reason, the high demand for trace elements analysis has led to a wide methodological/instrumental development in the last 10 to 20 years in geochemistry, promoting increasingly expressive analytical results in this area. For example, one of the most recent advances was to use laser ablation split stream analyses for measuring Sm-Nd, U-Pb or Hf isotopes together with trace elements content from the same ablated sample volume in a multi collector inductively coupled plasma mass spectrometer (ICP-MS) (e.g., Kylander-Clark et al. 2013, DesOrmeau et al. 2015, Fisher et al. 2020). However, one of the difficulties in the development of new techniques in multipurpose analytical facilities is, in particular, the issue of contamination, which can lead to a temporary or permanent damage to other analytical routines and procedural blanks in the geochemistry laboratory.
The analyses of trace elements in geological materials is mainly performed employing mass spectrometry, either with ionization through ICP-MS or emission of secondary ions, with the former being more cost effective than the latter (Jenner and Arevalo 2016). Sample introduction in the ICP-MS system can be via solution nebulization of a pre-dissolved rock powder or fused glass, or from a solid sample via laser ablation ( Jackson et al. 1992, Fryer et al. 1995, Russo et al. 2013. Solution nebulization ICP-MS (SN-ICP-MS) requires prior acid digestion of the samples (e.g., Taylor et al. 2002, Pinto et al. 2012) and has lower detection limits mainly due to the higher volume of material (mg level) and efficiency of ionization compared to laser ablation. However, reliability of SN-ICP-MS results is affected by incomplete digestion of samples that have minerals resistant to acid attack (e.g., zircon, monazite or rutile), as well as precipitation and adsorption during preparation, storage and data acquisition (Potts 1992, Eggins 2003. There are some alternatives to overcome these issues. The first is the use of analytical techniques that do not require sample digestion such as Spark Source Mass Spectrometry (SSMS), Secondary Ion Mass Spectrometry (SIMS) or instrumental neutron activation Whole-rock trace element analyses via LA-ICP-MS in glasses produced by sodium borate flux fusion analysis (INAA) (e.g., Korotev 1996, Jochum et al. 2001. The second is to use silicate glass beads produced by mixing rock powder and alkali salts, which lower the melting point of the system, as already done for X-ray fluorescence (XRF) measurements, and subsequently dissolving them with acid or alkaline solutions (Ingamells 1970, Panteeva et al. 2003. Another approach, recently developed by Peters and Pettke (2017), uses laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS) in nanoparticulate pressed rock powders to acquire trace element concentration. By applying this method, the authors were able to produce homogeneous pressed powders and quantify all groups of trace elements in six geological reference materials (RM) with accuracy similar to solution nebulization ICP-MS.
Still, except for the pressed rock powder technique (Peters and Pettke 2017), methods to acquire whole-rock trace element data are time and resource consuming. One simple, rapid and cost-effective technique is to analyze glass beads by laser ablation ICP-MS, which is a technique that can determine accurately and precisely more than 60 elements in geological samples in less than one minute (Eggins 2003, Jenner andO'Neill 2012). With this method, Eggins (2003) summarized the four main advantages LA-ICP-MS analyses of geological materials produced via alkali flux fusion: • possibility of coupling trace element analyses with XRF major element analyses; • less time and resource consuming compared to conventional solution nebulization; • simple spectral acquisition; • more reliable sample digestion and consequently less uncertainty on analyte recovery.
Most of the studies that perform LA-ICP-MS trace analyses on glasses produced via alkali fusion use Lithium borate as flux material (Nesbitt et al. 1997, Ødegård and Hamester 1997, Günther et al. 2001, Eggins 2003, since this is the standard procedure for XRF. Lithium borate is used instead of Na-borate in XRF analyses because the latter is an element of interest in whole-rock major element composition. Nevertheless, applications of Lithium isotope geochemistry have increased recently (Tomascak et al. 2012). Moreover,7 Li is one of the masses used for ICP-MS tuning, and there is a great interest in Li content of minerals and rocks for petrology and geochemistry, which makes the introduction of a large amount of Li into the ICP-MS system during laser ablation a problem in geochemical laboratories due to contamination and increase in background signals. One alternative is to produce these glasses employing sodium tetraborate (Na 2 B 4 O 7 ·10H 2 O), which is also less expensive than Lithium borate and readily available in most geochemistry laboratories. Therefore, this study aimed to present the evaluation of a rapid method for precisely and accurately determining whole-rock trace element content using LA-ICP-MS on glass beads produced by mixing high-purity sodium tetraborate and rock powders at high-temperature. Among the dataset of 27 trace elements chosen to be analyzed are the most relevant for geochemical applications, i.e., Sc, V, Cr, Ni, Cu, Zn, Rb, Sr, Y, Zr, Nb, Ba, La, Ce, Pr, Nd, Sm, Eu, Gd, Dy, Ho, Er, Yb, Lu, Hf, Ta, Th and U.

Sample selection and glass production
For this study, we selected a set of six standard RM including one andesite ( JA-1, Hakone Volcano, Geological Survey of Japan), one peridotite ( JP-1, Geological Survey of Japan), one pyroxenite (NIM-P, Bushveld Complex, Mintek South Africa), one kimberlite (SARM39, Kimberley Mine, Mintek South Africa), one diorite (DR-N, Rocher de Neuntelstein, Centre de Recherches Pétrographiques et Géochimiques (CRPG), Vandoeuvre-lès-Nancy, France), and one basalt (Ribeirão Preto, Instituto de Geociências, UNICAMP/Brazil). These certified RM comprise a large compositional range observed in nature, with SiO 2 contents from 33 to 65 wt.%, and all samples are well described in the literature and geochemical databases (e.g., GeoReM) ( Jochum et al. 2005b). This enables not only direct comparison and validation of the developed method but also the use of these samples as future matrix-match external RM for LA-ICP-MS analyses. Glasses were produced in a fully automatic PanAnalytical ® Eagon 2 fusion machine following a standard procedure used for XRF analyses, as described below. A 7:1 ratio of sodium tetraborate decahydrate (Na 2 B 4 O 7 .10H 2 O) flux (7 g) was mixed with the rock powder (1 g) and placed in a 95% Pt -5% Au crucible (melting point between 1,675 and 1,745°C) in the furnace. The true dilution ratio, after melting, however, is likely to lie around 3.79 to one, since almost half of the mass comprising water will evaporate during the glass production. The risk of using a flux that has almost half of it as water is that it such a large volume of gas can boil and blow out during the melting stage causing damage to the Pt ware or to the furnace. Because of that, we slowly heated the crucible from room temperature to the desired melting temperature (1,050°C), in order to release all water at a slow and constant rate and prevent that the mixture could be blown out of the crucible during glass production. The choice for 95% Pt -5% Au alloy is widely used for crucibles when producing silicate glasses via flux fusion for XRF analyses because the gold content reduces the wetting so that the glass can be easily removed after solidification without leaving residues. High-purity Merck ® sodium tetraborate decahydrate (> 99.5%) was chosen to avoid contamination of sample rock powders in the mixing stage. A droplet of Ammonium iodide was added to the mixture before each melting stage to additionally prevent that the glass would stick to the crucible wall. In order to test if the crucible has been previously contaminated by trace elements in prior fusion processes, one of our samples ( JA-1) was duplicated, by melting it with an "old" crucible, which was already in use routinely in the XRF laboratory and the other with a brand new one, which was the same used for the rest of our samples. Temperature was raised to 1,050°C and sample was stirred for 13 minutes. The choice of this temperature is because it is well below the point where trace elements of interest become volatile, with the exception of Rb and Zn (see Lodders 2003). After that, molten mixture was poured into a polished Pt plate with 32 mm diameter, forming a circular glass disc ca. 1.0 mm thick. Glasses were broken into small fragments and mounted in round 1" (25 mm ϕ) epoxy sections. Even though glasses already had a clean and plane surface, after mounting, they had to be re-polished to all be on the same height. Because of the hygroscopic characteristic of the sodium tetraborate glass, polishing was done with 0.3 micron alumina powder in ethanol and cleansed with kerosene due to the highly hygroscopic properties of the glass itself. Also, because the glass bead is highly hygroscopic, it is recommended that samples are kept in a desiccator to prevent formation of a white layer of hydrated borate on top of it (Fig. 1). Macroscopically, silicate glass beads were homogeneous and ranged in color from transparent to brown, green and black, while "blank" glass beads produced only from the Na 2 B 4 O 7 .10H 2 O are transparent immediately after quenching, but almost instantaneously acquire humidity from the atmosphere and have a whitish layer of hydrated borate on the surface (Fig. 1, right). The more iron rich the rock powder was, the darker the produced glass was. Compiled major element composition of the RM and exact proportion of rock powder to flux is given in Table 1. The proportion between flux and sample is crucial for the method development and data reduction, as well as for future application of LA-ICP-MS trace element analyses in tandem with XRF whole rock composition, in order to evaluate the original amount of Na in the sample and the amount added by the Na 2 B 4 O 7 .10H 2 O.

LASER ABLATION INDUCTIVELY COUPLED PLASMA MASS SPECTROMETRY
LA-ICP-MS data was acquired at two different laboratories, the first series at the Laboratório de Geologia Isotópica (LGI), Instituto de Geociências, Universidade Federal do Rio Grande do Sul (UFRGS), Brazil, and the second at the Institute für Mineralogie, University of Münster, Germany. The ICP-MS and laser operating conditions are given in Table 2.
For the analyses at the LGI-UFRGS, a Thermo Fisher ® Element 2 Sector Field ICP-MS was coupled to a New Wave Research ® Nd:YAG deep UV (213 nm) laser ablation system (Fig. 2). Helium (compressed, 99.5 -100% pure, White Martins/Praxair Inc., Rio de Janeiro, Brazil) flow was increased slowly to a constant rate of 0.5 L min -1 flushing into the laser sample cell to minimize surface re-condensation and maximize transport (Eggins et al. 1998, Eggins 2003). An auxiliary flow of Ar (Argon Pure Liquid 99.9%, Air Products, Guaíba, Brazil) fixed at 0.86 L min -1 was combined with He as carrier Figure 1. Glass beads produced in this study; sodium borate + rock powders (left) and only sodium borate, which was as necessary to control blank measurement and possible contamination from the flux (right). gas prior to reaching the ICP-MS. Preliminary tests showed that line scans (raster) worked more effectively and were less time-consuming than spots in regard to homogeneity of the ICP-MS laser signal on the glasses. Sensitivity was monitored by ablation of the NIST-612 glass and maximized to always keep oxygen production rate below 0.1%, monitored by the formation of ThO +. Line scans were performed with 100 μm diameter, 20 Hz and 5 μm s -1 . Signal stability under these conditions was ca. 5% RSD or less over a period of 2 to 3 minutes. A take-up ablation time of 5 seconds on the sample/standard before starting the analysis in the ICP-MS was used to ensure that all the system is purged with the ablation gas and set with the mixture of sample and sample gas, guaranteeing that there is no "gap" time in the analysis. In total, ten points in each sample and blank were done and results are an average of them, and each line scan lasted for around 2 minutes. The analysis protocol at the LGI-UFRGS involved measuring the NIST SRM 612 glass before and after each sample assuming linear drift of the machine, as well as subtraction of "gas" background (laser turned off) from all count rates Albeit not all of them yielded meaningful results, no correction for interfering isobaric or molecular species (e.g., 11 B 40 Ar or 7 B 36 Ar) was done, and we chose to use only isotopes that are not prone to significant interferences (see Tab. 3 for selected masses) and keep oxygen production rate as low as possible (e.g., Eggins 2003). As seen from the list of analytes, special attention was given to refractory lithophile elements (Lodders 2003, Palme andO'Neill 2014), such as the large ion lithophile elements (LILE -e.g., Ba, Sr), high-field strength elements (HFSEe.g., Zr, Hf, Ti), and rare-earth elements (REE -e.g., La, Ce, Eu, Lu), because they are not prone to volatilization to the atmosphere or diffusion to the crucible during rock powder melting. Data reduction was performed employing in-house spreadsheets which apply the method described in Longerich et al. (1996) and are detailed in section "Calibration strategy and data reduction". Both NIST-610 and NIST-612 glasses were used as external standards in this study, and 43 Ca as internal standard. The rationale of using two external standards was to check for measurement accuracy by using at each time either one or another as external standard and unknown and viceversa. When this was done, values obtained for both NIST-610/612 do not deviate more than 5% of the preferred values reported by Jochum et al. (2011).
In order to verify the accuracy and precision of our results at the LGI-UFRGS, trace element concentrations of the glass pellets were also determined via LA-ICP-MS at the Institut für Mineralogie in Münster, Germany. Sample ablation was performed with a pulsed 193 nm ArF excimer laser (Analyte G2, Photon Machines). A spot size of 35 μm, repetition rate of 5 Hz and energy of ∼3-4 J/cm 2 were chosen and elemental analysis carried out with an Element XR mass spectrometer (ThermoFisher Scientific). Forward power was 1300 W and reflected power < 1 W, gas flow rates were about 1 L/min for He (carrier gas of ablated material), 0.8 and 1 L/min for the Ar-auxiliary and sample gas, respectively. Before starting analysis, the system has been tuned on a NIST-612 reference glass measuring 139 La, 232 Th and 232 Th 16 O to get stable signals and high sensitivity, as well as low oxide production rates ( 232 Th 16 O/ 232 Th < 0.1%). A total of 32 masses were monitored, including 7 Li, 29  Th and 238 U. External and internal standard were the NIST-612 and 43 Ca, respectively. Overall time of a single analysis was 75 s (20 s for background, 40 s for peak after switching on the laser, and 15 s of washout time). Concentrations of measured elements were calculated using the Glitter software (Griffin et al. 2008, Van Achterbergh et al. 2001. Standard reference glasses BHVO2-G and BIR1-G were analyzed as monitor for precision and accuracy. Obtained results match the published range of concentrations given in the GeoReM database and do not deviate more than 5% from the preferred values ( Jochum et al. 2005b).
Limits of detection and sensitivity on LA-ICP-MS analyses are individual for each analyte mass, being a function of ionization efficiency, mass, concentration and amount of material extracted from the sample and introduced in the mass spectrometer (Longerich et al. 1996). Sensitivity can be monitored via NIST SRM 612 average measurements (Tab. 3 and Fig. 3). In order to quantify the limit of detection for each mass, it is necessary to measure several samples with no analyte, which is normally done by acquiring data only with the gas flow to the ICP-MS, without firing the laser, i.e., equivalent to the machine background (e.g., Longerich 2008). In addition, in the case of our study, we need to add the count rates measured on only borate discs that were produced without mixing with rock powders. Machine background is normally extremely low in LA-ICP-MS, especially for heavy analytes, with only a few counts per second. Therefore, to avoid dealing with the non-gaussian distribution of the background values when there are only a few measurements, Poisson counting statistics are applied, and the detection limit (DL) for each analyte (x) is determined by the Equation 1 (Golitko 2016): (1) , it is necessary to measure several samples with no analyte, which is ne by acquiring data only with the gas flow to the ICP-MS, without firing the quivalent to the machine background (e.g., Longerich 2008). In addition, in f our study, we need to add the count rates measured on only borate discs roduced without mixing with rock powders. Machine background is normally ow in LA-ICP-MS, especially for heavy analytes, with only a few counts per herefore, to avoid dealing with the non-gaussian distribution of the values when there are only a few measurements, Poisson counting e applied and the detection limit (DL) for each analyte (x) is determined by g equation (Golitko 2016 (1) is mean value in counts per second of all background measurements, ll time, is the number of background measurements and is the i.e., the signal detected per unit of concentration. In our case, we have two values that need to be removed, and, hence, two possible "detection first is the one calculated based solely on the Ar and He gas flow, and the sed on our measurement of eleven borate discs that were melted without ture. The sum of both is the real analytical background when applying our applying equation (1), we obtain detection limit values ranging from the e of 0.0009 μg/g for Ho to the highest of 2.8 μg/g for V (Table 3 and Figure at for some elements (Ni, Cu, Zn, V, Ba and Th) the background measured the sodium tetraborate discs, instead of only gas, increases, resulting in es of detection limit (Table 3), which indicates that these elements are impurities in the powder, possibly contaminating the sample by a significant is exacerbates the importance of producing and analyzing systematically h only flux and no sample, given that these values have to be subtracted unt rates of the samples to provide a precise and accurate result.
In which: rom the sample and introduced in the mass spectrometer . Sensitivity can be monitored via NIST SRM 612 average and Figure 3). In order to quantify the limit of detection for sary to measure several samples with no analyte, which is ing data only with the gas flow to the ICP-MS, without firing the the machine background (e.g., Longerich 2008 . (1) lue in counts per second of all background measurements, the number of background measurements and is the l detected per unit of concentration. In our case, we have two t need to be removed, and, hence, two possible "detection e calculated based solely on the Ar and He gas flow, and the easurement of eleven borate discs that were melted without m of both is the real analytical background when applying our uation (1), we obtain detection limit values ranging from the g/g for Ho to the highest of 2.8 μg/g for V (Table 3 and Figure lements (Ni, Cu, Zn, V, Ba and Th) the background measured tetraborate discs, instead of only gas, increases, resulting in ion limit (Table 3), which indicates that these elements are the powder, possibly contaminating the sample by a significant es the importance of producing and analyzing systematically nd no sample, given that these values have to be subtracted e samples to provide a precise and accurate result. (1) where is mean value in counts per second of all background measurements, is the dwell time, is the number of background measurements and is the sensitivity, i.e., the signal detected per unit of concentration. In our case, we have two background values that need to be removed, and, hence, two possible "detection limits". The first is the one calculated based solely on the Ar and He gas flow, and the second based on our measurement of eleven borate discs that were melted without sample mixture. The sum of both is the real analytical background when applying our method. By applying equation (1), we obtain detection limit values ranging from the lowest value of 0.0009 μg/g for Ho to the highest of 2.8 μg/g for V (Table 3 and Figure   3). Note that for some elements (Ni, Cu, Zn, V, Ba and Th) the background measured by ablating the sodium tetraborate discs, instead of only gas, increases, resulting in higher values of detection limit (Table 3), which indicates that these elements are present as impurities in the powder, possibly contaminating the sample by a significant amount. This exacerbates the importance of producing and analyzing systematically glasses with only flux and no sample, given that these values have to be subtracted from the count rates of the samples to provide a precise and accurate result. = the dwell time; statistics are applied and the detection limit (DL) for each analyte (x) is determined by the following equation (Golitko 2016 (1) where is mean value in counts per second of all background measurements, is the dwell time, is the number of background measurements and is the sensitivity, i.e., the signal detected per unit of concentration. In our case, we have two background values that need to be removed, and, hence, two possible "detection limits". The first is the one calculated based solely on the Ar and He gas flow, and the second based on our measurement of eleven borate discs that were melted without sample mixture. The sum of both is the real analytical background when applying our method. By applying equation (1), we obtain detection limit values ranging from the lowest value of 0.0009 μg/g for Ho to the highest of 2.8 μg/g for V (Table 3 and Figure   3). Note that for some elements (Ni, Cu, Zn, V, Ba and Th) the background measured by ablating the sodium tetraborate discs, instead of only gas, increases, resulting in higher values of detection limit (Table 3), which indicates that these elements are present as impurities in the powder, possibly contaminating the sample by a significant amount. This exacerbates the importance of producing and analyzing systematically glasses with only flux and no sample, given that these values have to be subtracted from the count rates of the samples to provide a precise and accurate result.
= the number of background measurements; statistics are applied and the detection limit (DL) for each analyte (x) is determined by the following equation (Golitko 2016 (1) where is mean value in counts per second of all background measurements, is the dwell time, is the number of background measurements and is the sensitivity, i.e., the signal detected per unit of concentration. In our case, we have two background values that need to be removed, and, hence, two possible "detection limits". The first is the one calculated based solely on the Ar and He gas flow, and the second based on our measurement of eleven borate discs that were melted without sample mixture. The sum of both is the real analytical background when applying our method. By applying equation (1), we obtain detection limit values ranging from the lowest value of 0.0009 μg/g for Ho to the highest of 2.8 μg/g for V (Table 3 and Figure   3). Note that for some elements (Ni, Cu, Zn, V, Ba and Th) the background measured by ablating the sodium tetraborate discs, instead of only gas, increases, resulting in higher values of detection limit (Table 3), which indicates that these elements are present as impurities in the powder, possibly contaminating the sample by a significant amount. This exacerbates the importance of producing and analyzing systematically glasses with only flux and no sample, given that these values have to be subtracted from the count rates of the samples to provide a precise and accurate result.
= the sensitivity, i.e., the signal detected per unit of concentration.
In our case, we have two background values that need to be removed, and, hence, two possible DL. The first is the one calculated based solely on the Ar and He gas flow, and the second based on our measurement of eleven borate discs that were melted without sample mixture. The sum of both is the real analytical background when applying our method. By applying Equation 1, we obtain DL values ranging from the lowest value of 0.0009 μg/g for Ho to the highest of 2.8 μg/g for V (Tab. 3 and Fig. 3). Note that for some elements (Ni, Cu, Zn, V, Ba and Th) the background measured by ablating the sodium tetraborate discs, instead of only gas, increases, resulting in higher values of DL (Tab. 3), which indicates that these elements are present as impurities in the powder,  Jochum et al. (2011). For laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS) settings and analytical parameters see text and Table 2. Sensitivity is based on observed count rates during analysis of NIST SRM 612 glass. Detection limit take into account the average countrate for 11 sodium borate discs produced in a similar fashion to the samples, i.e., the dilution factor of 7:1 (total approx. 8 g). BG: background, DL: detection limit. possibly contaminating the sample by a significant amount. This exacerbates the importance of producing and analyzing systematically glasses with only flux and no sample, given that these values have to be subtracted from the count rates of the samples to provide a precise and accurate result.

Calibration strategy and data reduction
Differences in ablation yield a common issue with LA-ICP-MS analyses, i.e., the extent of material transported from the sample to the ICP-MS during the acquisition time. They can arise not only from changes in ablation conditions (e.g., spot size, frequency and energy) but also from distinct physicochemical properties of materials that can absorb a particular laser wavelength weakly or strongly causing extensive variation on the ablation yield (e.g., Jackson 2008). Moreover, differences in the ionization potential, melting and boiling point, and, in turn, volatility of the chemical elements, can cause elemental fractionation between vapor and the solid phase during ablation, despite otherwise ideal conditions (e.g., Fryer et al. 1995, Outridge et al. 1998, Chen 1999, Kuhn and Günther 2004. To overcome any issues with the changes in the amount of material that is ablated, transported and ionized at the ICP-MS, a correction factor is applied by using internal standardization. In this study, the calibration and quantification of the LA-ICP-MS data was performed by combining periodically (at the beginning and end) the ablation of an external standard (NIST-610/612 glasses) to an internal standard ( 43 Ca), which is an element of known concentration in BG: background, DL: detection limit. the sample and standard (e.g., Jackson 2008). This procedure has been recognized to provide accurate analyses for many trace elements ( Jackson et al. 1992, Perkins et al. 1993, Eggins 2003, Wu et al. 2018. The choice of 43 Ca as internal standard fulfils the requirements established by Jackson (2008), since this element is homogeneously distributed individually in the samples, it is present in sufficient concentration for both determination via LA-ICP-MS and an independent method (in our case, EPMA-WDS) and has the same fractionation behavior as the analytes. Moreover, by using 100 μm and 43 Ca as internal standard, we avoided laser induced element fractionation (LIEF) that could be exacerbated by using a smaller spot size. Regarding LIEF, Jenner and Arevalo (2016) have shown that the use of 29 Si (which would be another option for these glasses) produces LIEF offset to systematically higher values in reference silicate glasses such as BCR-2G, VG-2 and NIST-612, something that is not observed when using 43 Ca as internal standard. When 43 Ca is used as internal standard to obtain trace element content in reference silicate glasses, LIEF patterns between Ca and other elements are comparable, eliminating the need for a correction factor (see Fig. 2 in Jenner and Arevalo 2016). The choice of the NIST 610 and 612 glasses as external standards is justified because they have been used routinely to calibrate LA-ICP-MS trace element analyses of several geological materials successfully, from strongly UV-absorbing materials (e.g., titanite) to colorless, weakly UV-absorbing materials, such as fluorite or silicate glasses (see Jackson et al. 1992, Jackson 2008. Throughout the analysis run, blank (background) values were recorded by flushing the carrier gas (He) into the ICP-MS, without firing the laser, and these values were discounted from the laser signal values. Internal standard normalized count rates were converted to concentrations using the count rates of spots carried out on the NIST 610 and 612 glasses as the external standard, using preferred values of Jochum et al. (2011), and the methodology of Longerich et al. (1996), which is represented by the Equation 2: 1997; Chen 1999; Kuhn and Günther 2004). To overcome any issues with the changes in the amount of material that is ablated, transported and ionized at the ICP-MS, a correction factor is applied by using internal standardization. In this study, the calibration and quantification of the LA-ICP-MS data was performed by combining periodically (at the beginning and end) the ablation of an external standard (NIST-610/612 glasses) to an internal standard ( 43 Ca), which is an element of known concentration in the sample and standard (e.g., Jackson 2008). This procedure has been recognized to provide accurate analyses for many trace elements (Jackson et al. 1992;Perkins et al. 1993;Eggins 2003;Wu et al. 2018). The choice of 43 Ca as internal standard fulfils the requirements established by Jackson (2008), since this element is homogeneously distributed individually in the samples, it is present in sufficient concentration for both determination via LA-ICP-MS and an independent method (in our case, EPMA-WDS) and has the same fractionation behavior as the analytes.
Moreover, by using 100 um and 43 Ca as internal standard, we avoided laser induced element fractionation (LIEF) that could be exacerbated by using a smaller spot size.
Regarding LIEF, Jenner and Arevalo Jr. (2016) have shown that the use of 29 Si (which would be another option for these glasses) produces LIEF offset to systematically higher values in reference silicate glasses such as BCR-2G, VG-2 and NIST-612, something that is not observed when using 43 Ca as internal standard. When 43 Ca is used as internal standard to obtain trace element content in reference silicate glasses, LIEF patterns between Ca and other elements are comparable, eliminating the need for a correction factor (see Figure 2 in Jenner and Arevalo Jr. 2016). The choice of the NIST 610 and 612 glasses as external standards is justified because they have been used routinely to calibrate LA-ICP-MS trace element analyses of several geological materials successfully, from strongly UV-absorbing materials (e.g., titanite) to colorless, weakly UV-absorbing materials, such as fluorite or silicate glasses (see Jackson et al. 1992;Jackson 2008). Throughout the analysis run, blank (background) values were recorded by flushing the carrier gas (He) into the ICP-MS, without firing the laser, and these values were discounted from the laser signal values. Internal standard normalized count rates were converted to concentrations using the count rates of spots carried out on the NIST 610 and 612 glasses as the external standard, using preferred values of Jochum et al. (2011), and the methodology of Longerich et al. (1996), which is represented by the following equation: (2) (2) Where: [C] = concentration; S = sample; M = mass (analyte); (CR) = count rate; IS = internal standard (in our study 43 Ca); ES = external standard (in our study the NIST SRM 610 and 612 glasses).

RESULTS AND COMPARISON WITH LITERATURE REFERENCE VALUES
LA-ICP-MS average whole-rock concentration and uncertainty obtained for twenty-seven trace elements in six RM determined at the LGI-UFRGS are given in Table 4, as well as lower and upper limits of the reported values for the same RM in the literature extracted from the "Geological and Environmental Reference Materials database -GeoReM" ( Jochum et al. 2005b) on its online version 27 (02/01/2020). Literature data on these RM was obtained by several other analytical methods, for example SIMS, isotope dilution thermal ionization mass spectrometry (ID-TIMS), and conventional acid digestion and SN-ICP-MS.
When our data are compared with minimum and maximum literature values, there is an overall agreement for V, Cr, LILE, REE, and HFSE, which are refractory lithophile elements under the conditions our glasses were produced (Fig. 4). Barium, Th, and V, although present in significant amount in the sodium tetraborate powder, which resulted in higher DL (Tab. 3), were correctly determined by subtracting procedural blanks. On the other hand, Ni, Cu, and Zn show values that are offset systematically to lower values when compared to the minimum reported in the literature (Fig. 3). This is expected, because nickel is well known to have a siderophile behavior, and it is likely that it diffused to the Pt-crucible during the melting process, depleting the sample in this element (e.g., Wang et al. 2020). This is also the case for Cu and Zn, which, despite of their chalcophile behavior, can also act as moderately siderophile elements (Siebert et al. 2011, Mahan et al. 2017, Wang et al. 2020. Relative standard deviation obtained in the analyses in this study is within those expected for LA-ICP-MS analyses in the literature (e.g., Eggins 2003), being around 5-10% for most materials, and reaching up to 25% for the basalt BRP-1 (Tab. 4). The exception is the peridotite JP-1, for which analyses were close to the detection limit and uncertainty rose up to ca. 50% of the mean value in some cases (e.g., Eu, Gd, Dy, Ta).
There are at least two ways to quantitatively check for data accuracy obtained in this study by comparing the variation of our data to those obtained in this study from literature reference values (RV), i.e., |X LA-ICP-MS -X RV | (Eggins 2003). A first and simple one described in Korotev (1996) considers the maximum uncertainty (σ max ) as the larger of the uncertainties of the RV (σ RV ) and the LA-ICP-MS analysis (σ LA-ICP-MS ). A second and more sophisticated approach is described in Eggins (2003) and makes a pooled uncertainty estimate taking into account both σ RV and σ LA-ICP-MS by applying the Equation 3: analysis (σLA-ICP-MS). A second, and more sophisticated approach is described in Eggins (2003) and makes a pooled uncertainty estimate taking into account both (σRV) and (σLA-ICP-MS) by applying the following equation: To facilitate data visualization, all literature reference values, average, minimum and maximum are also compiled in Table 4. According to Eggins (2003) To facilitate data visualization, all literature RV, average, minimum and maximum are also compiled in Table 4. According to Eggins (2003), the test for agreement at the 95% confidence level is if |X LA-ICP-MS -X RV | < 1.96 analysis (σLA-ICP-MS). A second, and more sophisticated approach is described Eggins (2003) and makes a pooled uncertainty estimate taking into account bo (σRV) and (σLA-ICP-MS) by applying the following equation: To facilitate data visualization, all literature reference values, average, minimu and maximum are also compiled in Table 4. According to Eggins (2003),  ( Jochum et al. 2005b), we used maximum and minimum literature values to obtain the uncertainty associated with the RV (Tab. 4). By applying Equation 3, trace element content of the andesite reference material JA-1 at the 95% confidence level are 92% within the RV, except for Cu, with our data at 22.8 ± 8.1 μg/g, while average RV range between 36.6 and 48 μg/g, and U, in which we measured 0.3 ± 0.02 μg/g and literature ranges from 0.31 to 0.39 μg/g. For the Peridotite ( JP-1) around 80% of the whole budget of trace elements are within literature values, but there are some significant variation in Cr, Pr, Yb, and Lu, besides Ni and Cu, which were already discussed above. Values of Chromium determined in this study for the peridotite sample is 5754 ± 471 μg/g, while the literature ranges from 15.7 to 3,300 μg/g. Literature RV for Chromium vary by more than two orders of magnitude ( Jochum et al. 2005a). Therefore, we can suggest that the presence of relict Fe-Cr-spinel microcrysts, which are highly refractory (melting point above 1,600°C) and common for this type of rock, did not react or melted entirely during the glass production process, generating an heterogeneity in the glass. Regarding Yb and Lu, measured values for the peridotite sample in this study are 0.045 ± 0.011 and 0.010 ± 0.003 μg/g, respectively, higher by a few ng/g when compared to literature, with values that range from 0.018 to 0.022 μg/g (Yb) and 0.001 to 0.006 μg/g (Lu). This indicates that data quality for the JP-1 peridotite was affected by measuring close to the detection limit for these elements. The Bushveld pyroxenite (NIM-P) has more than 95% of the values measured within the literature RV, with the only exception being Zn. Diorite (DR-N) and basalt (BRP-1) samples have more than 90% of the trace elements within literature RV, being the exception Ni, Cu and Zn. The Kimberlite SARM-39 sample also shows offset values for Ni, Cu and Zn, in addition to Cr and Yb, and an overall agreement of 81% when compared to the literature. Chromium content measured in the SARM-39 sample is 1,016 ± 56 while literature values range from 1,204 to 1,360, which could also be explained by areas that are enriched in Fe-Cr spinel microcrysts that did not react during glass production. Ytterbium literature RV for SARM-39 range from 0.86 to 1.04 μg/g, while in this study we measured 0.76 ± 0.05 μg/g, which is 10 ng/g below.
If we exclude from the accuracy evaluation (Eq. 3) the siderophile and chalcophile elements analysed in our study (i.e., Cu, Zn and Ni), i.e., elements that show consistent offset values linked to migration and diffusion to the crucible, and consider mostly litophile refractory elements such as LILE, REE and HFSE, we achieve an agreement with literature RV of more than 95% of trace elements being correctly determined for all RM measured in this study, including 100% agreement for samples NIM-P (Pyroxenite), DR-N (Diorite) and BRP-1 (Basalt). Moreover, the accuracy of our method is similar to the obtained by Eggins (2003) when performing a LA-ICP-MS study on trace elements but using lithium borosilicate glasses, showing that the method described here is accurate and precise to determine most of the trace elements of interest from a whole-rock powder.
In order to verify the accuracy and precision of the measurements performed at the LGI-UFRGS, borosilicate glass beads from the RM used in this study were also double-checked by  Table 4. LA-ICP-MS trace element contents obtained on standard reference materials in this study (LGI-UFRGS, Brazil) and comparison with literature data (all in μg/g)*.
*Literature data compiled from the GeoReM database (Jochum et al. 2005a). Values in red are the ones that have no lower limit detected at the database, for which we assumed the lowest possible considering the least significant digit. Concentration values and uncertainties are rounded to the least significant digit, for the exact value used in the RSD calculation see the online version of the table; LA-ICP-MS: laser ablation inductively coupled plasma mass spectrometry. RSD: relative standard deviation; SD: standard deviation.    measuring trace element contents via LA-ICP-MS at the Institut für Mineralogie at the University of Münster (Germany), and results are given in Table 5. When our data are compared with minimum and maximum literature values from the GeoReM, the same overall agreement for V, Cr, LILE, REE, and HFSE is observed, as well as the depletion in Cu, Ni and Zn for some of the RM (Fig. 5). Laser induced element fractionation is a common issue in LA-ICP-MS, already observed by the first published works that described this technique (e.g., Gray 1985, Fryer et al. 1995, Kroslakova and Günther 2007. For example, Fryer et al. (1995) showed that for chalcophile and volatile elements such as Cu, Zn, Cd, Ag, Sb, Tl and Pb, elemental fractionation relative to Ca occurs in the intensity of the signal as the ablation progresses deeper into the sample with time when measuring the NIST-610 RM. The factors responsible for the fractionation, however, are still not completely understood, being possible to be linked to the ablation process itself and aerosol transport, or during the vaporization, atomization, and ionization within the ICP (Kroslakova and Günther 2007). Regardless of the reason for the observed fractionation, it is widely accepted that it occurs due to the decrease in the laser pit size during progressive ablation (e.g., Eggins et al. 1998, Jenner andArevalo 2016) and it could also be responsible for the divergence of our data from reported values in some cases. Whenever this occurs, the countrates for different elements and their ratio can vary progressively with time during the analyses, being not representative of the sample itself (e.g. Fryer et al. 1995, Eggins et al. 1998, Jackson 2008, Jenner and O'Neill 2012. This fractionation is controlled by external parameters such as wavelength, pulse duration; carrier gas composition and flow rates, as well as internal, such as optical and physicochemical properties of the sample substrate, geochemical behavior, element electronegativity, first ionization potential and condensation temperature ( Jackson 2008, Russo et al. 2013, Arevalo 2014, Jenner and Arevalo 2016. Indeed, Jenner and Arevalo (2016) showed that there is an increase in element fractionation with decreasing volatility, and that siderophile and litophile elements are prone to negative fractionation when compared to 29 Si, for example, being necessary to apply a matrix correction to increase accuracy ( Jenner and O'Neill 2012). However, when 43 Ca is used as internal standard, as in this study, even for non-matrix matching external standards, laser induced element fractionation is not significant, and no correction needs to be applied ( Jenner and Arevalo 2016). In this sense, we can consider that even if element fractionation occurred during laser ablation of samples in this study, the choice of 43 Ca as internal standard was enough to account for its effect and provide reliable results, given that all analytes included here are classified as "routinely" analyzed in geological materials by LA-ICP-MS ( Jenner and Arevalo 2016). It is important to point out that this indicates that the differences observed for Cu, Ni and Zn are likely due to their loss during glass production and not due to LIEF.
Heterogeneities of siderophile/chalcophile elements, such as Cu, Zn and Ni were also observed in MPI-DING and NIST RM in the literature, and their high affinity to form alloys with Table 5. LA-ICP-MS trace element contents (μg/g)obtained on standard reference materials in this study (Institute für Mineralogie, University of Münster).  Pt is also an issue to be considered as an interference factor in the determination of their contents ( Jochum et al. 2005a, Kempenaers et al. 2003, Rocholl 1998. Copper, Zn and Ni can suffer fractionation due to their chalcophile/siderophile behavior, by preferential evaporation due the laser heat von Blanckenburg 2007, Jochum et al. 2014), and also incomplete vaporization of large particles in the plasma source, due to inefficient ablation (Gaboardi and Humayun 2009). Another issue related to the incomplete vaporization is the influence of sample mass loaded by LA, which can influence the ratio of volatile chalcophile/siderophile elements (Jochum et al. 2012). Eggins et al. (1998) noted a systematic volatile element enrichment at shallower levels of ablation and refractory enrichment as the pit deepens into the samples. These authors analyzed ablation pit morphology and surface condensate material to interpret that element fractionation behavior reflects a change in the ablation processes itself, from photothermal to plasma dominated mechanisms, and the presence of surface deposits is reduced when the ablation is done under He when compared to Ar (Eggins et al. 1998).
In another study, Steenstra et al. (2019) summarized the main causes of elemental and isotopic fractionation during ablation and sample heating, ranging from sub-solidus reaction with phases formed close to the ablation pit (Kosler et al. 2005); non-congruent evaporation of volatile elements from the ablation pit (Hergenröder 2006); fractional condensation of the sample plume vapor during cooling after ablation (Eggins et al. 1998); and differential transport according the particle size and composition from the ablation cell to the ICP torch (Koch et al. 2002). In the same study, Steenstra et al. (2019) also pointed out that incomplete vaporization can result in higher count rates of more volatile elements (Guillong et al. 2003) and high loading of laser aerosols and their effect on plasma conditions can reduce signal intensities for volatile elements compared to refractory elements (Kroslakova andGünther 2007, Steenstra et al. 2019). Steenstra et al. (2019) found also that Cu and Zn behave relatively volatile than refractory during LA-ICP-MS and that matrix effects on laser fractionation are more significant for volatile elements than refractory ones, resulting in substantial inter-laboratory offsets on the analyses of these elements. Regarding element mobility and diffusion to the Pt-Au crucible, Wang et al. (2020) performed high temperature and pressure experiments on elemental diffusion from silicate glass to Pt metal and noted that elements like Ni, Cu and Zn are lost at different proportions from the sample through diffusion from the silicate glass to the Pt metal, forming alloys under graphite-buffered conditions (Wang et al. 2020). At relatively more oxidizing conditions (FMQ + 2), Cu and Ni are still loss to a great extent, while Zn is not, and at FMQ + 5 only Cu is observed to be lost (Wang et al. 2020). Because we did not control fO 2 conditions during glass production in our study, and given that our crucible was not pure Pt, but a PtAu alloy, we can only speculate that these diffusion and migration processes may have also occurred, an assumption that remains to be tested. Anyhow, all these fractionation and migration or volatilization effects, when associated, can likely lead to a result divergent than the ones found in literature for elements like Cu, Ni, and Zn, in a similar fashion to the observed in this study, and it is a complex task to individualize each of their effects one by one. It is likely, however, for the reasons stated above, that the depletion observed in Cu, Ni, and Zn was caused either during glass production, by migration or volatilization (e.g., Steenstra et al. 2019, Wang et al. 2020 rather than due to LIEF ( Jenner and Arevalo 2016).
A different approach, instead of considering average, minimum and maximum literature values for the RM as guidelines for method precision and accuracy, is to compare our data with "preferred" values. Preferred values are reported for some RM at the GeoReM, especially those that are widely used in geochemistry laboratories and go through a thorough revision on their trace element content (e.g., Jochum et al. 2005a, Jochum et al. 2016. For example, Jochum et al. (2016) published "preferred" values for the most accessed rock RM samples of the GeoReM database. These authors determined RV and their uncertainties at the 95% confidence level following ISO guidelines and the Certification Protocol of the International Association of Geoanalysts (Kane et al. 2003(Kane et al. , 2007, and include data obtained by techniques that have different levels of metrological confidence reported in the literature. Given that several methods exist to acquire trace element contents in geological materials, and each one has its own degree of precision and accuracy, Jochum et al. (2016) grouped all analytical data for the RM by their metrological properties in decreasing order of confidence, being the primary or definitive values those obtained by isotope dilution using TIMS, MC-ICP-MS and ICP-MS. The authors state that ID-MS data has the highest degree of confidence because operations can be completely described and understood, and for which a complete uncertainty statement can be written (CCQM 1988, Jochum et al. 2016. The second and third group divided by Jochum et al. (2016) are methods that also have a high-level of confidence, including on the second solution methods such as SN-ICP-MS, ICP-AES and AAS, and on the third XRF, INAA and SSMS, being the difference that the first either uses certified standard solutions of matrix matching RM while in the latter calibration is done mainly on non-certified RM ( Jochum et al. 2016). Glass beads (such as this study) or pressed powder pellets (e.g., Peters and Pettke 2017) are grouped in a fourth category by Jochum et al. (2016), having the lowest degree of confidence because of possible inhomogeneities and matrix effects (e.g., Hervig et al. 2006, Jochum et al. 2014. By collecting data reported for RM from all these methods and carefully analyzing analytical procedures and applying Horwitz function, Jochum et al. (2016) assigned a more reliable set of RV to nineteen rock standard RM, including the JA-1 andesite we used in our study.
In our study, two samples have preferred values reported in the GeoReM, the JA-1 ( Jochum et al. 2016) and the BRP-1 (Cotta and Enzweiler 2008). This allows us to do a more thorough comparison and evaluate quality of our data. In Figure 6, there are average values measured in our study normalized to the preferred values for the JA-1 and BRP-1. When the average value from the data acquired in our study is compared to the preferred values for the BRP-1 basalt and the JA-1 andesite, three elements (Ni, Cu and Zn) have values that deviate more than 15% of the preferred values. This means that all the rest 24 trace elements have average values that lie within ± 15% of the preferred ones (Cotta andEnzweiler 2008, Jochum et al. 2016). In any case, the offset of 15% is higher than the standard deviation for several of our analyses and much higher than the standard deviation of the preferred value itself, which normally do not exceed 5%. This is probably due to the generally low precision of the LA-ICP-MS technique when compared to other methods, especially isotope dilution (e.g., Jochum et al. 2016). Nevertheless, the precision and accuracy obtained in this study is similar to other studies dealing with LA-ICP-MS (Eggins 2003).

CONCLUSIONS
We presented a method for determining precisely and accurately whole-rock trace element contents using LA-ICP-MS on glass beads produced by mixing high-purity sodium borate and rock powders at high-temperature. By applying this method, values for twenty four refractory litophile trace elements (including LILE, HFSE and REE) in the range of ppb to ppm obtained in six RM in our study are mostly within error from the reported minimum and maximum values in the literature, with an overall agreement of more than 90%. This method has also shown that, in the absence of a matrix-matching standard, the NIST SRM 612 glass can be used as external standards to obtain trace element concentration in silicate materials with an average to good reproducibility. Measured values of Ni, Cu, and Zn were compromised probably due to their siderophile/ chalcophile nature or even through their volatile behavior and laser induced element fractionation. This issue will also be observed if we apply this method to analyze trace elements that tend to be volatile, chalcophile or siderophile at magmatic temperatures, such as Ga, Ge, Mo, W, and Pb. Even though in our study laser induced element fractionation seems to not have impact negatively in the results for refractory elements, the use of femtosecond lasers could potentially produce a more robust dataset (e.g., Jochum et al. 2014). Moreover, one alternative for the current method would be to analyse via LA-ICP-MS pressed rock powders, which has been proved recently to also be an efficient and clean procedure for the measurement of several trace elements in bulk rock, including those that cannot be measured by the flux melting technique (e.g, Peters and Pettke 2017).