Experimental

2.1.2.1 Instrumentation

RESOlution M-50 ablation system (ASI, Australia) combined with an Element 2 sector field ICP-MS (ThermoScientific, USA) were used in this study. A ‘squid’ smooth device was used to improve the signal precision (Müller et al., 2009). Helium was employed as ablation environment gas to enhance the sensitivity (Eggins et al., 1998; Günther and Heinrich, 1999).

The instrument conditions were optimized by continuous ablating NIST 612 in raster mode to achieve the highest ¹³⁹La intensity while keeping the U/Th around 1, oxide (ThO⁺/Th⁺) and secondary ion production (Ca²⁺/Ca⁺) lower than 0.5%. The detailed instrument conditions and measurement parameters of LA-ICP-MS are summarized in Table 1.

Table1 Operation conditions of LA-ICP-MS system

12 2.1.2.2 Samples and Data Acquisition

A series of glass reference materials that include NIST, MPI-DING, USGS, and CGSG were investigated in this study (Table 2). These glasses are mostly acceptable as LA-ICP-MS calibration materials and well characterized in previous studies. Reference values of USGS glass were cited from GeoReM database (http://georem.mpch-mainz.gwdg.de/). Reference values of CGSG-1 and CGSG-5 glass were obtained from Prof. Dr. Zhan Xiuchun (National Research Center for Geoanalysis, China). All others were cited from Jochum’s literature (Jochum and Enzweiler, 2014; Jochum et al., 2006; Jochum et al., 2011), except Nb and Ta in NIST610, which were collected from Hu et al. (2008) (see Table 2).The glasses were firstly embedded in epoxy and then polished to a flat surface. Ultrasonic cleaning in water medium was performed before LA-ICP-MS analysis. Analysis sequence started with a calibration group that includes NIST610, StHs6/80-G, and GSD-1G, followed by three, five or ten repetitions of one glass reference material (treated as unknown), and then again calibration group. The analysis sequence consisting of a number of spot analyses was run in the automatic mode. A total of 15 sequences were run over three years (Appendix S1).

The aerosol from ablation may produce deposits across the sample surface so that a pre-ablation procedure (two laser pulses) was performed to avoid the potential influence caused by aerosol deposits and any other form of surface contamination. Element 2 produces a flat-top peak at low resolution with the flatness comprising about 20% of the entire peak.

The central 5% of the peak (one point) were sampled to achieve short sweep time. Element 2 was adjusted to the fast speed mode. The sweep time from the lowest (7) to highest (238) mass was optimized by carefully adjusting magnetite setting time without deteriorating the counting efficiency. Each individual analysis incorporated a background acquisition of 20 s (gas blank) followed by a 35 s ablation data acquisition, which consists of a total 55 sweeps.

The ICP-MS method is shown in Appendix S2. The detailed information of scanned isotopes, oxide and oxide coefficient are shown in Appendix S3.

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Table 2 Detailed information of the investigated glass reference materials in this study

Sample Supplier Category Matrix Source of reference values

NIST610 NIST CRM Synthetic silicate Jochum et al. 2011 and Hu et al.2008a NIST612 NIST CRM Synthetic silicate Jochum et al. 2011

NIST614 NIST CRM Synthetic silicate Jochum et al. 2011 StHs6/80-G MPI-Chemie CRM Natural andesite Jochum et al. 2006 ATHO-G MPI-Chemie CRM Natural rhyolite Jochum et al. 2006 T1-G MPI-Chemie CRM Natural quartz-diorite Jochum et al. 2006 ML3B-G MPI-Chemie CRM Natural basalt Jochum et al. 2006 KL2-G MPI-Chemie CRM Natural basalt Jochum et al. 2006 GOR128-G MPI-Chemie CRM Natural komatiite Jochum et al. 2006 GOR132-G MPI-Chemie CRM Natural komatiite Jochum et al. 2006

BCR-2G USGS RM Natural basalt GeoReM database

BHVO-2G USGS RM Natural basalt GeoReM database

BIR-1G USGS RM Natural basalt GeoReM database

GSD-1G USGS RM Synthetic basalt GeoReM database

CGSG-1 NRCG CRM Natural basalt X.Zhan per.comm

CGSG-2 NRCG CRM Natural nepheline syenite Jochum and Enzweiler 2014

CGSG-4 NRCG CRM Natrural soil Jochum and Enzweiler 2014

CGSG-5 NRCG CRM Natural andesite X.Zhan per.comm

NIST: National Institute of Standards and Technology, USA; MPI-Chemie: Max Plank Institute for Chemistry, Germany; USGS: United States Geological Survey, USGS; NRCG: National Research Center for Geoanalysis, China; CRM: Certified Reference Material; RM: Reference Materia

2.1.2.3 RSN Strategy and Iolite software

The quantification strategy consists of three parts, including Ratioing, Standardization, and Normalization (RSN).

Ratioing

Elemental intensities collected in each sweep were firstly normalized to the internal standard.

The intensity ratios were treated as the basic unit for the quantification algorithms. The intensity ratios, instead of absolute intensity, could improve the analytical precision since mass spectrometry measure precisely for the relative value rather than absolute one.

𝑖_𝑒𝑙 𝑖_𝑖𝑠 , ^𝑐_𝑐^𝑒𝑙

𝑖𝑠

14 Standardization

The standardization algorithm is used for the calculation of the elemental concentration ratios, which is based on a certified reference material as a calibration standard. The standardization algorithm is shown in Eq.1 (modified from Longerich et al. (1996)).

𝑐𝑒𝑙 the change of ablation mass for each analysis and give the constraint to calculate the absolute concentration.

∑ ^{𝑐𝑒𝑙𝑛}

𝑐𝑖𝑠|_𝑆𝐴𝑀∗ 𝑓_𝑒𝑙

𝑁𝑛=1 =^{100 %𝑚/𝑚 −𝜖}

𝑐𝑖𝑠 (2)

Combining the Eq.1 and Eq.2 obtains Eq.3, as shown below.

𝑐_𝑒𝑙^𝑐𝑜𝑟_{|𝑆𝐴𝑀}=^𝑖𝑒𝑙 represent the targeted element and internal standard; SAM and RM represent target samples and reference material; f represents the corresponding oxide coefficient; 𝜖 is the missed components.

Iolite provides a powerful framework for transient data processing and interpretation, especially for LA-ICP-MS (Paton et al., 2011). The RSN strategy was accomplished in Iolite3.4 software and a data reduction scheme (modified from “Trace element”, see Appendix S2) was compiled to realize the quantification algorithms. The initial five and last

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three sweeps were excluded from the data integration to avoid the influence of unstable intensity. In practical, the reduction procedure is shown as follows.

The intensity was firstly subtracted from the gas blank and then normalized to the internal standard to make intensity ratio. The instrumental drift was corrected by using a linear interpolation based on the variations of NIST 610 intensity ratios. An arbitrary value (such as 40 %m/m) was given to the internal standard. The internal standardization (calibrated with an external reference material) was carried out to produce the raw element concentration data.

These raw data were converted to oxide concentration by multiplying oxide coefficient, and then the sum of oxide was scaled to 100 %m/m to calculate the internal standard concentration. The factor (ratio of an arbitrary value and the calculated concentration of internal standard) was used to correct the raw data to final data.

The crucial uncertainties in RSN strategy are related to the normalization part (bulk normalization as 100 %m/m), which include (1) the state of multivalent elements, (2) the missed components, and (3) the accuracy of single point calibration. The first two have been discussed in previous works by Guillong et al. (2005), Gagnon et al., (2008), and Liu et al., (2008). Generally, an assumption of a multivalent state of high abundance element may lead an uncertainty for the bulk normalization as 100 %m/m. Iron is the only multivalent element as a major component occurring in silicate rocks. Here, four assumptions of iron valence were evaluated (Fig.1). As shown in Fig.1, the maximum uncertainty was only 1% with an assumption of Fe²⁺/Fe_t as 0.5 for FeO_t (total Fe content expressed as FeO) up to 15 % m/m.

This 1 % uncertainty is ignorable considering around 10% analytical uncertainty for trace element analysis with LA-ICP-MS technique.

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Fig. 1 Uncertainties caused by the assumption of iron valence.

The missed components that include H, C, N, F, Cl, Br and I (those parts could not be measured or accurately measured by LA-ICP-MS) will introduce uncertainty for the bulk normalization as 100 %m/m (Liu et al., 2008). The percentage of the missed components could lead to the same degree uncertainty (Fig.1 in Appendix S4). A proper assumption of the missed components is a prerequisite for the accurate quantification of hydrous or high halogen minerals (the missed components could be up to 10 % m/m). Here we calculated the sum of oxide (Fe²⁺/Fe_t as 0.5) for the investigated glass reference materials (Table 1 in Appendix S4). The missed components in the investigated glass samples are generally lower than 1% (except CGSG-5), which demonstrates that the assumption of oxide as 100 %m/m for the glass reference materials is appropriate.

In most cases, a single external reference material was used for LA-ICP-MS calibration, so that any uncertainty in single point calibration will propagate to the bulk normalization part, especially for the major elements. Fig.2 shows the calibration lines of the selected elements (covering from major to trace elements). The usage of NIST glasses to calibrate geological glass may result in imprecise values for some major elements (Mg, Fe, Ti, Mn and K) due to

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their low concentration (nearby the limit of detection), and thus would cause the uncertainty for bulk normalization as 100 %m/m. Meanwhile, reference materials with elements concentration lower than the detection limit (like Cs in BIR-1G, Th in GOR130-G and GOR128-G) are not suitable as the external calibration materials, especially for those elements calibration.

Fig. 2 Calibration line of selected elements including Mg, Fe, Cu, Tm, Cs and Th. Grey zone indicates the detection limits (calculated with three times of standard deviation of gas blank intensity). The intensity ratios used here are corrected from the effect of instrument drift.