A high-sensitivity loading method using tantalum (Ta) gel for high-precision Ca isotope measurement by TIMS

Abstract

This study proposed a new loading technique using a tantalum (Ta) gel activator for high-precision Ca isotope (δ^44/40Ca) measurement by double-spike thermal ionization mass spectrometry (DS-TIMS). This method significantly reduces the required sample size of an individual analysis to 25–50 ng and yields a similar level of analytical precision, using double rhenium (Re) filaments, compared with conventional high-precision Ca isotope measurements, which consume microgram-level samples (3–5 µg) using TIMS. We show that the assistance of the Ta gel significantly enhances thermal ionization to a total ion efficiency of up to ∼0.8% compared with the typical rates of ∼0.01–0.05% reported in previous studies, representing an order of magnitude improvement in sensitivity. With a greatly reduced sample size, the potential domain-mixing effect would be avoided, and the mass fractionation is shown to fit well with the exponential law typically observed for TIMS. The δ^44/40Ca values of a suite of standards and geologic reference materials are reported to validate the accuracy and precision of this new method. Repeated measurements of primary standard NIST SRM 915a yielded an external reproducibility better than 0.06‰ (2SD, n = 9, 50 ng sample size). The analyses of USGS standards BHVO-2, BCR-2, and AGV-2 (25–50 ng Ca for each individual measurement) yielded mean δ^44/40Ca values of 0.82 ± 0.09 (2SD, n = 7), 0.79 ± 0.07 (2SD, n = 6), and 0.76 ± 0.05 (2SD, n = 4), respectively. These results suggest the utility of the Ta gel activator in Ca isotope measurements of small samples for potential sample-limited applications in geochemistry and cosmochemistry.

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1. Introduction

Calcium (Ca) has five stable isotopes, ⁴⁰Ca, ⁴²Ca, ⁴³Ca, ⁴⁴Ca, and ⁴⁶Ca, and a radioactive isotope, ⁴⁸Ca, with a very long half-life of 4.4 × 10¹⁹ years.^1–4 Naturally occurring Ca is overwhelmingly dominated by ⁴⁰Ca (96.941% atomic abundance), with minor contributions from other isotopes: ⁴⁴Ca (2.086%), ⁴²Ca (0.647%), ⁴⁸Ca (0.187%), ⁴³Ca (0.135%), and ⁴⁶Ca (0.004%).^5,6 This creates a 24 000-fold abundance disparity between ⁴⁰Ca and ⁴⁶Ca, an extreme natural abundance ratio among all elements with measurable isotope variations. Despite the significant relative mass differences (Δm/m up to 20%), natural mass-dependent fractionation of Ca isotopes is less than 4‰ per atomic mass unit (amu).⁷ Consequently, resolving subtle natural variations requires high-precision analytical methods capable of achieving external reproducibility better than 0.2‰ (2SD) for δ^44/40Ca values.^5,7

Ca ranks as the sixth most abundant element in the bulk silicate Earth (BSE), which plays a fundamental role in geological processes.^5,8 In cosmochemistry, Ca is one of the most refractory major elements in the solar nebula, with a half-condensation temperature of 1517 K,⁹ thereby governing the accretion dynamics of early condensates.¹⁰ To decode these planetary-scale processes, the stable Ca isotope variations (δ^44/40Ca) have emerged as a powerful tracer. Applications now span from geochemical investigations of magmatic differentiation, paleographic and paleoclimate reconstructions, archaeological provenance studies, to the fields of nutritional and biomedical studies and ocean chemistry.^11–13

High-precision Ca isotope measurements were first achieved by Russell et al.¹⁴ using a ⁴²Ca–⁴⁸Ca double-spike technique on TIMS (Thermal Ionization Mass Spectrometry). Currently, most high-precision Ca isotopic analyses employ the double-spike TIMS technique. Following chromatography, purified Ca samples are loaded onto Re or Ta filaments as nitrate, chloride, or phosphate salts, frequently with activators such as Ta₂O₅ or Ta-phosphate. Isotopic analyses utilize single-, double-, or triple-filament assemblies depending on the instrument configuration.^6,15 In the available Ca isotope datasets, the size of Ca loaded on the filaments typically ranges from 3 to 5 µg.⁶ During measurements using TIMS, the ⁴⁰Ca⁺ ion beam signal typically ranges from ca. 4 to 20 V over 100–1000 cycles with ∼4 s integration (Tables 1 and 2). However, excessive Ca loaded on a single filament may lead to domain-mixing and memory effects.^16,17 The mass bias produced by the domain-mixing effect may deviate from the exponential mass fractionation typically assumed for sector field mass spectrometry and thus cause inaccuracy and uncertainty in the final result. Hart and Zindler¹⁷ first documented this effect, and Zhu et al.¹⁸ found that the mass fractionation deviating from the exponential law during the TIMS measurement could cause inaccuracy up to 1‰. Additionally, prolonged excess of unionized Ca atoms may deposit on the lens stack and the isolation parts in the ion source. The residues may also be re-ionized during subsequent sample analysis, creating a memory effect, affecting ion focusing, and potentially causing cross-contamination.^16,19

Table 1 Summary of different double spike-TIMS measurement protocols established over two decades that have been used for Ca stable isotope ratio measurements

TIMS mode name	Filament type	Sample size	Loading acid	Activator	^40Ca^+ signal	Spike	Mean (2SD)	Reference
Triton XT	Double Re (zone-refine)	400 ng	10% HNO3	Ta gel	16–17 V	^42–43Ca	0.01 ± 0.06 (n = 3)	This study
		200 ng			9–10 V		−0.01 ± 0.08 (n = 3)
		100 ng			10–11 V		−0.01 ± 0.06 (n = 4)
		50 ng			10–17 V		0.02 ± 0.05 (n = 9)
		25 ng			8–14 V		0.01 ± 0.08 (n = 6)
Triton	Single Ta	∼5 µg	10% HNO3	H3PO4	15 V	^42–43Ca	0.01 ± 0.11 (n = 233)	Zhu et al.^20
	Single Ta	3–4 µg	10% HNO3	H3PO4	—	^42–43Ca	−0.03 ± 0.12 (n = 19)	Liu et al.^21
	Single Ta	∼5 µg	—	H3PO4	15 V	^42–43Ca	0.00 ± 0.11 (n = 29)	Liu et al.^22
	Single Ta	∼5 µg	10% HNO3	H3PO4	—	^42–43Ca	0.02 ± 0.13 (n = 61)	Kang et al.^23
	Double Re	1 µg	H3PO4	H3PO4	—	^42–48Ca	0.01 ± 0.08 (n = 15)	Retzmann et al.^24
	Double Re–Ta	2–3 µg	5% HNO3	Ta2O5	6–10 V	^43–48Ca	0.01 ± 0.07 (n = 9)	Mondal and Chakrabarti^25
	Double Re	3 µg	HNO3	—	—	^42–48Ca	0.01 ± 0.13 (n = 9)	Simon et al.^26
	Double Re	3 µg	—	H3PO4	15 V	^42–48Ca	−0.02 ± 0.12 (n = 5)	Ren et al.^27
	Double Re	3 µg	3 mol per L HNO3	—	9–10 V	^42–48Ca	−0.01 ± 0.13 (n = 137)	Feng et al.^28
	Double Re	3 µg	—	—	9–10 V	^42–48Ca	0.00 ± 0.15 (n = 50)	Feng et al.^28
	Single Ta	—	0.25 N HNO3	—	—	^42–43Ca	0.01 ± 0.05 (n = 14)	Schmitt et al.^29
	Double Re	—	3 mol per L HNO3	—	—	^42–48Ca	−0.01 ± 0.13 (n = 137)	Chen et al.^30
	Single Re	300–400 ng	—	—	10 V	^42–43Ca	0 ± 0.23 (n = 50)	Bermingham et al.^31
	Single Re	300 ng	2.2 mol per L HCl	Ta	4 V	^43–48Ca	0 ± 0.13 (n = 143)	Amini et al.^32
	Single Ta	5–8 µg	0.2 mol per L HNO3	—	10–20 V	^42–43Ca	0 ± 0.10	Amini et al.^32
IsoProbeT	Triple Re	5 µg	HNO3	—	—	^43–48Ca	−0.02 ± 0.03 (n = 43)	Huang and Jacobsen^33
	Triple Re	5 µg	—	—	—	^43–48Ca	0.04 ± 0.13 (n = 45)	Huang et al.^34
	Triple Re	5 µg	—	—	—	^43–48Ca	0.04 ± 0.15 (n = 55)	Huang et al.^35
Triton plus	Double Re–Ta	2.5 µg	0.8 M HNO3	Ta2O5	10 V	^43–48Ca	−0.01 ± 0.08 (n = 11)	Banerjee and Chakrabarti^36
	Double Re–Ta	2.5 µg	0.8 M HNO3	Ta2O5	—	^43–48Ca	−0.02 ± 0.05 (n = 4)	Banerjee et al.^37
	Double Re	5 µg	3% HNO3	—	8–30 V	^43–48Ca	−0.01 ± 0.14 (n = 286)	He et al.^38

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Table 2 Summary of different SSB-MC-ICPMS protocols established over two decades for Ca stable isotope ratio measurements

MC-ICPMS model name	Cones	Sample size	^44Ca^+ signal	Mean (2SD)	Reference
Neptune plus	Jet-sampler, X-skimmer	2 µg	7 V	0.84 ± 0.04 (n = 5)	Feng et al.^39
Neptune plus	Jet-sampler, X-skimmer	0.5 µg	∼1.5 V	0.88 ± 0.08 (n = 27)	Bao et al.^3
Neptune plus	Ni-sampler, H-skimmer	10 µg	—	0.77 ± 0.10 (n = 8)	Gu et al.^40
Neptune plus	—	—	2–8 V	0.87 ± 0.04 (n = 2)	Valdes et al.^41
Neptune	Jet-sampler, H-skimmer	—	∼3.3 V	0.82 ± 0.05 (n = 3)	Ionov et al.^42
Nu plasma 1700	—	—	—	0.77 ± 0.09 (n = 11)	Dai et al.^43
Nu plasma 1700	—	∼2 µg	5–8 V	0.71 ± 0.10 (n = 12)	Chen et al.^44
Nu plasma 1700	Standard sampling, skimmer	∼2 µg	5–8 V	0.79 ± 0.06 (n = 41)	Li et al.^2
Nu sapphire	Ni	0.5 µg	15 V	0.70 ± 0.11 (n = 11)	Dai et al.^45
Nu sapphire	—	1 µg	—	0.87 ± 0.05 (n = 3)	Eriksen et al.^46
Nu sapphire	—	1 µg	6 V	0.86 ± 0.07 (n = 5)	Eriksen and Jacobsen^47
Nu sapphire	Ni	0.6 µg	∼3 V	0.82 ± 0.05 (n = 6)	Gao et al.^48

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High-precision stable Ca isotope (δ^44/40Ca) measurements using TIMS would need to overcome the following difficulties: (i) the extreme differences in the natural abundance of Ca isotopes,⁴⁹ (ii) mass fractionation during thermal ionization,¹⁴ and (iii) isobaric interferences such as ⁴⁰K⁺, ⁴⁸Ti⁺, ⁸⁸Sr²⁺, ²⁴Mg¹⁶O⁺, and ²⁷Al¹⁶O⁺.^49–52 Therefore, it necessitates a large Ca ion beam in order for the measured minor isotopes to have sufficient signal-to-noise ratios and counting statistics, which typically requires a few micrograms of sample for an individual measurement. This, in turn, would have a sample size limit for high-precision δ^44/40Ca measurements of small samples, such as extraterrestrial materials, single mineral grains, and low-Ca geological samples. Here, we present a high-sensitivity method using a tantalum gel (Ta) activator to measure as low as 25 ng of Ca sample with a high precision of ≤0.08‰ for δ^44/40Ca (e.g., 2SD of repeated measurements of NIST SRM 915a) using double-spike TIMS. With the new utility of the Ta gel and an optimized sample-loading protocol, we were able to reduce the Ca sample size by a factor of ∼100 compared to previous studies, with comparable precision. The primary Ca standard NIST SRM 915a and several different international reference materials were measured to further validate the precision and accuracy of our improved analytical routine.

2. Experimental methods

All experimental work was conducted at the Research Center for Planetary Science (RCPS), Chengdu University of Technology (CDUT). Sample preparation and purification of Ca were performed under a Class-100 laminar flow hood in a Class-1000 cleanroom to minimize procedural blanks and contamination risks.

2.1 Reagents and materials

For wet chemistry work, ultrapure water with a resistivity of 18.2 MΩ cm (i.e., MQ water, purified with a Milli-Q system, Millipore, USA) was used for all dilution and cleaning procedures. All the acids used in this study, including nitric acid (HNO₃), hydrochloric acid (HCl), and hydrofluoric acid (HF), were double-distilled from trace-metal grade acids using a Savillex DST-1000 system. All labware, including columns and PFA containers, was cleaned with sub-boiled acids and fluxed with distilled 6 M HCl prior to use. One mL of AG MP-50 resin (100–200 mesh) was packed in a Savillex microcolumn (0.64 cm ID × 9.9 cm height; 30 mL reservoir) for Ca separation and purification. A ⁴²Ca–⁴³Ca double spike was used in this study.^{14,15,20–23}

For TIMS measurements, zone-refined rhenium (Re) filaments (>99.999%, H. Cross, USA) were degassed at 3.5 A for 60 minutes, and stored in the atmosphere at room temperature for at least 7 days prior to use. Sample materials used in this study include NIST SRM 915a, BHVO-2, BCR-2, and AGV-2. The SRM 915a samples measured in this study were diluted from a CDUT stock solution (2000 µg g⁻¹) in 10% (m/m) HNO₃.²² The international reference materials BHVO-2, BCR-2, and AGV-2 are natural rock powders from the United States Geological Survey (USGS).

2.2 Sample decomposition and spiking

For silicate samples, 20–50 mg of rock powders (containing ≥50 µg Ca) were dissolved in 2 mL of an acid mixture of 3 : 1 concentrated HF : HNO₃ at 130 °C for 7 days on a hotplate. After the solutions were evaporated to dryness at 100 °C, the samples were then heated in 2 mL of aqua regia for 12 hours to ensure the efficient digestion of Ca. Once the sample solutions were dried, they were treated with 0.5 mL concentrated HNO₃ twice, followed by 0.5 mL concentrated HCl, and taken to dryness after each acid addition. Five mL of 6 M HCl was then added and heated at 100 °C overnight for complete dissolution. At this point, the concentrations of the sample solutions were checked using an iCAP-Q ICP-MS (Thermo Scientific) and aliquots containing 50 µg Ca were spiked with a mixed ⁴²Ca–⁴³Ca tracer to a target ⁴⁰Ca_sample : ⁴²Ca_spike ratio of 7 : 1.²² The spiked samples were heated at 120 °C overnight in HCl to ensure complete equilibration.

2.3 Column separation

The spiked samples were loaded onto pre-cleaned columns packed with 1 mL of Bio-Rad AG MP-50 (100–200 mesh) resin. The separation and purification of Ca followed the protocols of Liu et al.²² The samples were rinsed with 17 mL of 1.6 mol per L HCl to remove the matrix elements of Al, Na, K, Ti and Fe. Calcium was then collected using 27 mL of 1.6 mol per L HCl. The eluted samples were evaporated to dryness on a hotplate and treated with concentrated HNO₃ three times prior to TIMS analysis. The typical total-procedure blank was 30 ng,^53,54 which is insignificant compared with the total amount of samples (50 µg) used for the column chemistry.

2.4 Activator

Since the analytical precision is directly dependent on the size of the ion beam, efficient emission of ions is a prerequisite for the analysis of small quantities of Ca. In order to improve the ionization efficiency of Ca (i.e., sensitivity) using TIMS, different types of activators (e.g., H₃PO₄, Ta₂O₅, and a tantalum gel) were tested to optimize the sensitivity.

H₃PO₄ was prepared from ≥99.999% ultra-pure phosphoric acid crystals (o-phosphoric acid, Merck, Art. No: 466123) dissolved in double-distilled MQ water. The H₃PO₄ was diluted to 0.1% using double-distilled MQ water.

The Ta₂O₅ activator was prepared from TaCl₅ powder (Sigma-Aldrich, 99.999%). Approximately 0.5 g of TaCl₅ powder was weighed into ∼10 mL of double-distilled MQ water in a 30 mL FEP bottle to form a suspension containing white Ta₂O₅ solid. The solution was then added with ∼0.3 mL concentrated HF, ∼0.3 mL concentrated H₃PO₄, and ∼5 mL concentrated HNO₃. The Ta₂O₅–HF–H₃PO₄–HNO₃ mixture was then diluted with additional ∼10 mL of double-distilled MQ water and sonicated prior to use.

Tantalum (Ta) gel was prepared from TaCl₅ powder (Sigma-Aldrich, 99.999% trace metals basis) after the recipe of R. Creaser (Boise State University Isotope Geology Laboratory labshare, https://www.boisestate.edu/earth-isotope/labshare/).⁵⁵ An aliquot of 0.5 g TaCl₅ powder was weighed and dissolved in 10 mL of ∼50% ethanol (anhydrous ethanol mixed with an equivalent volume of double-distilled MQ water) in a 15 mL PFA vial. The dissolved Ta was purified using a cation-exchange column (AG MP-50 resin, 100–200 mesh) to remove Ca and K contaminants. Prior to use, the resin was cleaned with 6 mol per L HCl and double-distilled MQ water. A column packed with 2 mL of this cleaned resin was used to further purify the Ta solution. The column was pre-cleaned with 30 mL of 6 mol per L HCl to ensure a negligible Ca background, followed by conditioning with 10 mL of double-distilled MQ water. At this point, an aliquot of the Ta solution was loaded onto the column. Since Ta does not bind to the cation-exchange resin, the unretained eluate was collected. The purified collection was then placed at room temperature for 5 days, loosely covered with a home-made FEP cover to let the ethanol evaporate. At this point, the remaining tantalum was turned into a gel. The Ta gel was then mixed with an equivalent amount of double-distilled MQ water, and diluted 500-fold by volume using 0.1% H₃PO₄. The Ta gel was sonicated for 60 minutes prior to use.

2.5 TIMS determination

A double filament assembly with zone-refined Re ribbon was used for Ca isotopic measurements.^34–37 Given that our method used a substantially reduced sample size than conventional techniques, a specialized loading protocol was developed. Based on the established methods for small samples, such as the total evaporation protocol for K isotopes described by Amelin and Merle⁵⁶ and U–Pb measurements,⁵⁷ the use of H₃PO₄ is essential to retain the loaded sample in a small drop of liquid on the filament. Therefore, 1 µL of H₃PO₄ was loaded and allowed to evaporate to a very small drop, and then 1 µL of the sample was loaded into this remaining liquid in four increments. Once dried, 1 µL of the Ta gel activator was loaded last, also in 3–4 increments, to cover the sample spot on the filament. In addition to this “sandwich-type” loading sequence (stabilizer–sample–activator), we have also tried to pre-mix Ta gel with the sample solution in a beaker or load the Ta gel first, but both tests did not yield Ca signals as stable as those from the “sandwich-type” method.

For the comparative experiments using the Ta₂O₅ activator, we also used the “sandwich-type” loading sequence. In the last step of adding the activator, 1 µL of white Ta₂O₅ “slurry” was added to cover the sample. We have also noticed that slow drying of the Ta₂O₅ (Fig. S1a and b) or Ta gel (Fig. 1 and S1c, d) is very important to make a smooth surface on the filament. In our experiment, drying at 1.2 A would result in a relatively coarse surface (Fig. S1a and c). Filaments with this type of sample loads generally exhaust quickly. In contrast, drying the sample very slowly at 0.8 A would yield a very smooth surface (Fig. 1b and S1d). To achieve a good result, the entire loading process for a single filament typically takes ∼60 minutes.

Fig. 1 The appearance of the Ca sample (nitrate) and Ta gel mixture loaded on a Re filament. (a) Sample loaded with undiluted Ta gel. (b) Sample loaded with 500× diluted Ta gel.

The Triton XT TIMS (Thermo Scientific, Germany) at the RCPS of CDUT is equipped with a large Faraday cup at the low-mass side (L5) used for ⁴⁰Ca. All Faraday collectors were connected to amplifiers with 10¹¹ Ω resistors. Ca isotopes and ⁴¹K were measured simultaneously using the cup configuration given in Table 3. The isobaric interference of ⁴⁰K⁺ was monitored using ⁴¹K, and typically no correction is needed. The behaviour of instrumental fractionation on TIMS generally follows the exponential law,^14,58,59 which can be corrected by the ⁴²Ca–⁴³Ca double-spike technique through an iterative algorithm described by Heuser et al.⁶⁰ and Liu et al.⁵⁴ The detailed data reduction procedure is given in the SI. At RCPS, the instrumental fractionation is corrected by an internal normalization to a given ratio (⁴²Ca/⁴⁴Ca = 0.31221).⁵ After normalization, the unspiked NIST SRM 915a yields a long-term ⁴⁰Ca/⁴⁴Ca value of 47.1632 ± 0.0024 (2SE).⁶¹ Detailed analytical parameters are given in Table 3. The Ca isotopic compositions are expressed in δ^44/40Ca, defined by δ^44/40Ca = [(⁴⁴Ca/⁴⁰Ca)_sample/(⁴⁴Ca/⁴⁰Ca)_reference − 1] × 1000. These values can be converted to the δ^44/42Ca scale using a factor of ∼2.0483, assuming negligible radiogenic contributions to ⁴⁰Ca.^62,63

Table 3 Double spike-TIMS operating conditions

Instrument parameter	Setting
Cup configuration	^40Ca(L5), ^41K(L4), ^42Ca(L2), ^43Ca(L1), ^44Ca(C), ^46Ca(H2)
Resistors	10^11 Ω for all amplifiers
Ionization filament	3300–3600 mA (∼1600 °C)
Evaporation filament	1500–1800 mA
Intensity	^40Ca ≥ 10 V
Integration time	4.193 s
Number of blocks	10
Cycles in each block	50
Baseline	Beginning of each block
Peak center	Every 5 blocks
Len focus	Every 5 blocks

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3. Results and discussion

3.1 Loading blank

The loading blank of Ca most likely originated from the H₃PO₄ loading acid and Ta gel activator, which was tested with a ⁴²Ca spike. A load of ∼30 ng ⁴²Ca yielded an average ⁴⁰Ca/⁴²Ca of 0.0011, corresponding to a total loading blank of <35 pg. Compared with a typical sample size of 25–50 ng, the loading blank is insignificant for the determination of Ca isotopic compositions.

3.2 The duration and stability of the Ca ion beam emitted using Ta gel

Ca exhibits an extreme difference in isotopic abundance that necessitates a large ion beam for precise isotope measurements. In the sample loading protocol developed by Mondal and Chakrabarti,²⁵ a double-filament assembly was employed using Re and Ta filaments. Ca nitrate was loaded onto an evaporation filament of Ta, followed by the addition of a Ta₂O₅ activator, while Re (zone-refined) was used for the ionization filament. This protocol generated an ion beam with ⁴⁰Ca⁺ intensities of 6–10 V lasting 5 hours for a sample load of 2.5–3 µg, corresponding to a total ion yield >0.03%.^64–67 This method is more sensitive than the one using a single Ta filament,³² yet, it is not sufficient to generate a long-lasting and stable Ca ion beam for a sample size smaller than ∼100 ng.

With the aim of determining Ca isotopic compositions at high precision using <100 ng of sample, we present a comparative sample loading experiment using double filaments. It is observed that 500 ng of Ca loaded with the Ta₂O₅ activator using a double filament assembly produced a fluctuating ion beam which decayed rapidly. The total duration of the ⁴⁰Ca⁺ beam for a sample size of 500 ng is ca. 120 minutes, corresponding to an estimated ion yield of ∼0.05% (Fig. 2a), which is broadly consistent with the ion yield reported by Mondal and Chakrabarti²⁵ using the setup above. In comparison, our experiments using the Ta gel activator with 1/5 of the sample size yielded a long-lasting beam for more than 5 hours, with an average ⁴⁰Ca⁺ signal of ∼9 V. With the assistance of the Ta gel activator, the total ionization efficiency is >0.8% (Fig. 2b), an order of magnitude higher than the typical efficiency of 0.01–0.05% using double Re filament or single Ta filament protocols.^24,28 Our initial loading tests using the concentrated Ta gel did not yield a smooth sample spot on the filament (Fig. 1a), which resulted in inconsistent ion yields. Diluting the Ta gel activator by 500 times with 0.1% H₃PO₄ produced a satisfactory sample spot with a smooth surface and relatively uniform thickness on the filament within a small area (∼1 × 1 mm), and is reproducible between different loads (Fig. 1b).

Fig. 2 The stability and duration of the ion beam represented by the ⁴⁰Ca⁺ signal of NIST SRM 915a. (a) A 500 ng sample loaded with Ta₂O₅ lasts for ∼120 minutes with an average ⁴⁰Ca⁺ intensity of 8 V. (b) 100 ng of sample loaded with Ta gel. With the Ta gel activator, the signal lasts for ∼300 minutes with an average ⁴⁰Ca⁺ intensity of 9 V.

Loading with the dilute Ta gel also helped to reduce the loading blank. However, we found that the 500-fold dilution of Ta gel maximized ion yield for sample sizes of 25–100 ng, but may be insufficient for smaller sample sizes or loads >100 ng, suggesting further adjustments of the concentration of Ta gel for sample sizes beyond this range (Fig. 3a–e). The best results were achieved when the evaporation filament was heated very slowly until the ion beam reached the desired intensity, and inter-block heating was activated to keep the ion beam intensity in the ±20% window.

Fig. 3 (a–e) ⁴⁰Ca⁺ intensity vs. scan number. (f–j) ln(⁴⁰Ca/⁴⁴Ca)_Mvs. ln(⁴²Ca/⁴⁴Ca)_M of representative measurements. Isotope ratios (^40/44Ca and ^42/44Ca) uncorrected for mass bias are plotted to verify if the mass fractionation follows the exponential law. Final results after the correction for mass fractionation and double spike are expressed as δ values. A good fit to the exponential law (slope = 2.0483) suggests an ideal mass fractionation behavior during evaporation.

The process of thermal ion emission from Ta gel, in general, is not fully understood, but some speculations could be drawn.^30,35–39 According to the Saha–Langmuir equilibrium equation for surface ionization,⁶⁷ filament materials with high work functions have higher ionization capabilities than those of low work-function materials. Tantalum has a work function for positive ion emission of 4.25 eV,⁶⁸ and rhenium has a higher work function of 5–5.5 eV.⁶⁹ Oxidation would increase the work function of Re and Ta.⁷⁰ The uniform distribution of Ta nano-particles in the Ta gel possibly facilitates a more effective interaction at the interface, resulting in a greater sample-metal contact and thus a likely boost in ion yield. We also found that the current of the evaporation filament is higher than normal when using the Ta gel activator.²⁸ We speculate that the use of Ta gel helps immobilize the samples on the filament and slows down the evaporation.⁵⁷

3.3 Mass fractionation

Instrumental mass fractionation occurs during thermal ionization due to preferential evaporation of lighter isotopes.⁷¹ Previous studies evaluating different fractionation laws for the measurement of Ca isotopes suggest that the exponential law best describes the mass fractionation of Ca in TIMS.¹⁴ However, mixing different sample domains on the same filament whose evaporative stages are different would compromise the mass fractionation behavior. In other words, the Ca compounds loaded on the filament may be dispersed into several different deposits rather than a single small spot (Fig. 1a). In practice, the former situation is more likely to occur for large sample loads of a few micrograms. The mixing between two or more domains at different stages of fractionation would cause the measured isotopic ratio to depart from the ideal exponential mass fractionation, which is the so-called domain-mixing effect.⁷² If the exponential law is still applied to the mass bias correction, the results would deviate from the true values. We avoided the domain-mixing effect by significantly reducing the sample size loaded on a filament to 25–50 ng (compared to 3–5 µg) with very careful loading. This confines the sample within a very small spot (1 × 1 mm) on the filament, thus preventing the domain-mixing effect during analysis (Fig. 1b and S1d).

The mass dependency during thermal ionization may differ when different activators are used. For example, for K isotope measurements, the samples loaded with silica gel generally followed the exponential mass fractionation law, but samples loaded with Ta activators tend to follow the Rayleigh fractionation.^56,65 To validate the mass fractionation of Ca isotopes during our measurement using the Ta gel, the slopes of ln(⁴²Ca/⁴⁴Ca) − ln(⁴⁰Ca/⁴⁴Ca) were monitored for different sample sizes.¹⁸ As demonstrated in Fig. 3, all sample loads between 25 and 400 ng follow the exponential mass fractionation (ln(⁴⁰Ca/⁴⁴Ca)/ln(⁴²Ca/⁴⁴Ca) = 2.0483). Since the exponential mass fractionation has long been demonstrated to reflect the kinetic process of TIMS, the consistency shown by the data reflects ideal sample evaporation behavior with the Ta gel activator on the filament.⁷² It is, however, necessary to stress the importance of achieving sample exhaustion on the filament if there is any indication that the instrumental mass fractionation does not follow the utilized mass fractionation law. Exhaustion of the sample on the filament (i.e., total evaporation) provides a form of symmetrical mis-correction during the entire process of sample evaporation, canceling out the offsets generated by the mass fractionation correction. Our results show that all samples on the filament followed the exponential fractionation law from start to finish (Fig. 3e and f).

3.4 The precision of different sample sizes of Ca

Current methodologies for Ca isotope ratio determination (summarized in Tables 1 and 2) reveal two divergent trends: (i) recent advancements in TIMS have reduced sample size requirements from ∼10 µg to ∼1 µg over the last 20 years through both instrumental improvements and reduced total-procedural blanks (<50 ng); (ii) to avoid the ⁴⁰Ar interference, measurements by standard-sample bracketing (SSB)-MC-ICP-MS still necessitate 1–10 µg of purified Ca samples due to its reliance on minor isotopes (e.g.⁴²Ca and ⁴³Ca), requiring larger samples for comparable precision. To date, a relatively large sample size is needed in order to obtain high analytical precision for Ca isotope composition for both SSB-MC-ICP-MS and DS-TIMS measurements (Tables 1 and 2). Our proposed Ta gel method significantly enhances ionization efficiency on the filament on account of the presence of Ta nano-particles in the Ta gel, which substantially reduces the sample size required for high precision Ca isotope measurement using TIMS (Fig. 2b).

The test runs of NIST SRM 915a with different sample sizes are summarized in Table 4. The δ^44/40Ca values are 0.01 ± 0.06 (2SD, n = 3), −0.01 ± 0.08 (2SD, n = 3), −0.01 ± 0.06 (2SD, n = 4), 0.02 ± 0.06 (2SD, n = 9), and 0.01 ± 0.08 (2SD, n = 6) for SRM 915a of 400 ng, 200 ng, 100 ng, 50 ng, and 25 ng, respectively (Fig. 4 and 5). The results of all SRM 915a measurements agree with each other. For 50 ng loads of SRM 915a, the in-run precision is better than 0.028‰ (2SE) when all 50 nanograms of samples are exhausted on the filament. The external precision of repeated measurements of SRM 915a (i.e., reproducibility) is better than 0.06‰ (2SD, n = 9) for the 50 ng loads. The external precision of the 50 ng loads is slightly better than that of the 25 ng loads, and therefore the preferred sample size is 50 ng for our routine Ca isotope analysis (Fig. 4 and 5).

Table 4 Ca isotopic composition of reference materials obtained in this study and the literature

Sample	Simple size	^40Ca^+ signal	Cycles	δ ^44/40Ca (‰)	2SE	Mean	Reference
NIST SRM 915a	400 ng	16–17 V	208	0.00	0.069	0.01 ± 0.06 (2SD)	This study
			208	−0.01	0.069
			208	0.05	0.062
	200 ng	9–10 V	369	−0.04	0.064	−0.01 ± 0.08 (2SD)
			409	0.04	0.066
			208	−0.02	0.069
	100 ng	10–11 V	600	−0.03	0.040	−0.01 ± 0.06 (2SD)
			1828	0.03	0.028
			1000	−0.04	0.039
			1000	0.00	0.038
	50 ng	10–17 V	208	0.00	0.055	0.02 ± 0.06 (2SD)
			208	0.00	0.062
			750	0.04	0.046
			500	0.03	0.051
			208	0.04	0.073
			208	0.00	0.067
			700	0.03	0.048
			388	0.05	0.057
			190	−0.04	0.059
	25 ng	8–14 V	190	0.03	0.110	0.01 ± 0.08 (2SD)
			208	−0.03	0.074
			208	−0.01	0.076
			174	0.03	0.084
			490	−0.04	0.059
			200	0.07	0.094
BHVO-2	50 ng	9–11 V	500	0.76	0.059	0.82 ± 0.09 (2SD)/±0.04 (95% c.i)	This study
			500	0.85	0.059
			500	0.87	0.057
			1000	0.82	0.059
			500	0.88	0.054
			500	0.78	0.059
			500	0.81	0.061
	25 ng	9–10 V	500	0.77	0.063	0.82 ± 0.13 (2SD)/±0.07 (95% c.i)
			500	0.78	0.063
			450	0.80	0.061
			500	0.76	0.062
			500	0.86	0.064
			500	0.93	0.066
						0.79 ± 0.04 (n = 2, DS-TIMS)	Banerjee et al.^37
						0.82 ± 0.05 (n = 3, SSB-MC-ICPMS)	Ionov et al.^42
BCR-2	50 ng	10–12 V	500	0.81	0.055	0.79 ± 0.07 (2SD)/±0.04 (95% c.i)	This study
			500	0.77	0.056
			500	0.79	0.052
			500	0.80	0.054
			500	0.85	0.056
			499	0.74	0.057
	25 ng	9–10 V	500	0.80	0.062	0.81 ± 0.12 (2SD)/±0.06 (95% c.i)
			500	0.88	0.066
			500	0.74	0.058
			500	0.87	0.059
			500	0.78	0.060
			500	0.76	0.061
						0.87 ± 0.18 (n = 3, SSB-MC-ICPMS)	Valdes et al.^41
						0.8 ± 0.06 (n = 2, DS-TIMS)	Banerjee et al.^37
AGV-2	50 ng	9–11 V	444	0.78	0.063	0.76 ± 0.05 (2SD)/±0.04 (95% c.i)	This study
			350	0.74	0.073
			500	0.73	0.053
			500	0.78	0.056
						0.77 ± 0.10 (n = 3, SSB-MC-ICPMS)	Valdes et al.^41
						0.79 ± 0.09 (n = 9, DS-TIMS)	Feng et al.^73

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Fig. 4 δ ^44/40Ca values of NIST SRM 915a measurements with sample sizes between 25 and 400 ng. Sample loads are denoted as follows: (a) 400 ng, (b) 200 ng, (c) 100 ng, (d) 50 ng, and (e) 25 ng. The error bar represents two standard deviations (2SD).

Fig. 5 The mean δ^44/40Ca_915a 915a values of 25–400 ng measurements compared with literature data. The measurements of NIST SRM 915a with sample sizes as low as only 1% of typical sample loads yielded comparable, and even slightly better, precision. Symbols denote sample loads: yellow star (400 ng), red square (200 ng), purple triangle (100 ng), orange diamond (50 ng), blue circle (25 ng); gold circle indicates literature data.^{18,22,24–27,31,32,34,36,73} The error bar represents two standard deviations (2SD).

3.5 Ca isotopic compositions of geological reference materials

Ca isotope ratios for international reference materials (BHVO-2, BCR-2, and AGV-2) are presented in order to verify the accuracy of the small sample measurements using Ta gel (Table 4 and Fig. 6). For the 50 ng loads, the measured Ca isotopic compositions are 0.82 ± 0.09‰ (2SD)/± 0.04‰ (95% c.i) (n = 7) for BHVO-2, 0.79 ± 0.07‰ (2SD)/± 0.04‰ (95% c.i) (n = 6) for BCR-2, and 0.76 ± 0.05‰ (2SD)/± 0.04‰ (95% c.i) (n = 4) for AGV-2. At a reduced sample size of 25 ng, the uncertainty is slightly higher, with δ^44/40Ca values of 0.82 ± 0.13‰ (2SD)/± 0.07‰ (95% c.i) (n = 6) for BHVO-2 and 0.81 ± 0.12‰ (2SD)/±0.06‰ (95% c.i) (n = 6) for BCR-2.

Fig. 6 The δ^44/40Ca values for international geological reference materials of 25 ng and 50 ng measurements using Ta gel. The data of 50 ng samples are generally more consistent than the 25 ng samples. (a), (b), and (c) denote δ^44/40Ca for BHVO-2, BCR-2, and AGV-2, respectively; yellow and blue indicate 50 ng and 25 ng filament loads. The error bar represents two standard deviations (2SD).

In comparison with published results of these international reference materials, our results for 25 and 50 ng samples agree with reference values within error (Fig. 7). However, some of the previous results show relatively more scatter and larger uncertainties compared to our results. We suspect this may be due to imperfect mass fractionation correction when the domain-mixing effect existed for sample loads at the microgram level.

Fig. 7 The δ^44/40Ca values for 25 ng and 50 ng measurements of international geological reference materials and a comparison with literature data. The following reference materials are presented BHVO-2 (circles), BCR-2 (diamonds), and AGV-2 (stars). Open symbols indicate literature data.^{2,3,20,22,25–27,30,32,37,41–45,73–78} Error bars represent 95% c.i.

In summary, compared with previous Ca isotope results, our measurements with significantly reduced sample size (by a factor of up to ∼100) yielded data with comparable precision (Fig. 5, 7 and Table 4). This method opens a new window for Ca isotope analyses of sample-limited materials, for example, the returned extraterrestrial samples (e.g., Chang'e lunar samples, Ryugu and Tianwen asteroid samples) and low-Ca geological samples (e.g., single grain analysis of olivine).⁷⁹ For the analysis of Ca isotopic (nucleosynthetic) anomalies (i.e., ⁴⁸Ca anomaly in meteorites), previous analytical work required 10–100 µg Ca for each individual analysis. The large sample size may raise concerns about potential mass independent fractionation during measurement. Our high-sensitivity method using the Ta gel would consume only ∼1/100 samples compared to previous typical TIMS or MC-ICPMS measurements, making it possible to determine the ⁴⁸Ca anomaly of Ca-poor materials with high precision.^76,80

4. Conclusions

In conclusion, we present a new Ta gel activator for high-precision Ca isotope analysis using double-spike TIMS. The use of the Ta gel significantly boosted the ionization efficiency of Ca to ∼0.8%, corresponding to a ca. 20-fold increase in sensitivity. This method therefore substantially reduces the sample size requirement from the microgram level (1–3 µg) to the nanogram level (25–50 ng) for the high-precision determination of δ^44/40Ca values. The small sample load also helps to minimize the potential domain-mixing effect in TIMS. Using this new method, the external precision for 50 ng NIST SRM 915a is better than 0.06‰ (2SD, n = 9). The accuracy is validated by analyses of 25 and 50 ng of geologic reference materials (e.g., BHVO-2, BCR-2, and AGV-2).

Conflicts of interest

There are no conflicts to declare.

Data availability

All relevant data are within the manuscript and its additional files.

Supplementary information is available. See DOI: https://doi.org/10.1039/d5ja00331h.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (42473050 to X. L. and 42173022 to F. L.) and National Key Research and Development Program of China (2024YFF0807504 to D. W.). Fengyong Xia is acknowledged for the maintenance of the mass spectrometer.

References

1. W. M. Haynes, CRC Handbook of Chemistry and Physics, CRC press, 2016.
2. M. Li, Y. Lei, L. Feng, Z. Wang, N. S. Belshaw, Z. Hu, Y. Liu, L. Zhou, H. Chen and X. Chai, J. Anal. At. Spectrom., 2018, 33, 1707–1719.
3. Z. Bao, C. Zong, K. Chen, N. Lv and H. Yuan, Int. J. Mass Spectrom., 2020, 448, 116268.
4. N. E. Holden, CRC Handbook of Chemistry and Physics, 2014.
5. D. J. DePaolo, Rev. Mineral. Geochem., 2004, 55, 255–288.
6. R. Chakrabarti, S. Mondal, A. D. Jacobson, M. Mills, S. J. Romaniello and H. Vollstaedt, Chem. Geol., 2021, 581, 120398.
7. A. Heuser and A. Eisenhauer, Bone, 2010, 46, 889–896.
8. J. Frausto da Silva and R. J. P. Williams, The Biological Chemistry of the Elements: the Inorganic Chemistry of Life, Oxford University Press, 2001..
9. K. Lodders, Astrophys. J., 2003, 591, 1220.
10. L. Grossman, Geochim. Cosmochim. Acta, 1972, 36, 597–619.
11. J. Skulan, D. J. DePaolo and T. L. Owens, Geochim. Cosmochim. Acta, 1997, 61, 2505–2510.
12. N. Gussone, A.-D. Schmitt, A. Heuser, F. Wombacher, M. Dietzel, E. Tipper, M. Schiller, F. Bohm, Calcium Stable Isotope Geochemistry, Springer, 2016.
13. J. Skulan and D. J. DePaolo, Proc. Natl. Acad. Sci., 1999, 96, 13709–13713.
14. W. Russell, D. Papanastassiou and T. Tombrello, Geochim. Cosmochim. Acta, 1978, 42, 1075–1090.
15. L. Norris, R. C. Martindale, A. Satkoski, J. C. Lassiter and H. Fricke, Palaeogeogr., Palaeoclimatol., Palaeoecol., 2025, 113103.
16. A. Y. Kramchaninov, J. Anal. At. Spectrom., 2021, 76, 1549–1557.
17. S. R. Hart and A. Zindler, Int. J. Mass Spectrom., 1989, 89, 287–301.
18. H. L. Zhu, Z. F. Zhang, G. Q. Wang, Y. F. Liu, F. Liu, X. Li and W. D. Sun, Geostand. Geoanal. Res., 2016, 40, 185–194.
19. S. K. Aggarwal and C. You, Mass Spectrom. Rev., 2017, 36, 499–519.
20. H. Zhu, F. Liu, X. Li, Y. An, G. Wang and Z. Zhang, J. Anal. At. Spectrom., 2018, 33, 547–554.
21. F. Liu, X. Li, Y. J. An, J. Li and Z. F. Zhang, Geostand. Geoanal. Res., 2019, 43, 509–517.
22. F. Liu, X. Li, Z. Zhang, J. Bai and Y. An, Geostand. Geoanal. Res., 2022, 46, 307–319.
23. J.-T. Kang, D. A. Ionov, H.-L. Zhu, F. Liu, Z.-F. Zhang, Z. Liu and F. Huang, Chem. Geol., 2019, 524, 272–282.
24. A. Retzmann, D. Walls, K. A. Miller, J. Irrgeher, T. Prohaska and M. E. Wieser, Anal. Bioanal. Chem., 2022, 414, 675–689.
25. S. Mondal and R. Chakrabarti, J. Anal. At. Spectrom., 2018, 33, 141–150.
26. J. I. Simon, M. K. Jordan, M. J. Tappa, E. A. Schauble, I. E. Kohl and E. D. Young, Earth Planet. Sci. Lett., 2017, 472, 277–288.
27. H. Ren, M. Casalini, S. Conticelli, C. Chen, S. F. Foley, L. Feng and Y. Liu, Geochim. Cosmochim. Acta, 2024, 364, 100–113.
28. L. Feng, L. Zhou, L. Yang, S. Tong, Z. Hu and S. Gao, J. Anal. At. Spectrom., 2015, 30, 2403–2411.
29. A.-D. Schmitt, S. Gangloff, F. Cobert, D. Lemarchand, P. Stille and F. Chabaux, J. Anal. At. Spectrom., 2009, 24, 1089.
30. C. Chen, Y. Liu, L. Feng, S. F. Foley, L. Zhou, M. N. Ducea and Z. Hu, Geochim. Cosmochim. Acta, 2018, 238, 55–67.
31. K. R. Bermingham, N. Gussone, K. Mezger and J. Krause, Geochim. Cosmochim. Acta., 2018, 226, 206–223.
32. M. Amini, A. Eisenhauer, F. Böhm, C. Holmden, K. Kreissig, F. Hauff and K. P. Jochum, Geostand. Geoanal. Res., 2009, 33, 231–247.
33. S. Huang and S. B. Jacobsen, Geochim. Cosmochim. Acta, 2017, 201, 364–376.
34. S. Huang, J. Farkaš and S. B. Jacobsen, Earth Planet. Sci. Lett., 2010, 292, 337–344.
35. S. Huang, J. Farkaš, G. Yu, M. I. Petaev and S. B. Jacobsen, Geochim. Cosmochim. Acta, 2012, 77, 252–265.
36. A. Banerjee and R. Chakrabarti, Chem. Geol., 2018, 483, 295–303.
37. A. Banerjee, R. Chakrabarti and A. Simonetti, Geochim. Cosmochim. Acta, 2021, 307, 168–191.
38. Y. He, Y. Wang, C. Zhu, S. Huang and S. Li, Geostand. Geoanal. Res., 2017, 41, 283–302.
39. L. Feng, L. Zhou, L. Ynag, W. Zhang, Q. Wang, S. Tong and Z. Hu, J. Anal. At. Spectrom., 2018, 33, 413–421.
40. H.-O. Gu, X. Liu, H. Sun, G. Sun, D. Li, F. Wang, C. Ge, Y. Fan and T. Zhou, Anal. Chem., 2024, 96, 6131–6138.
41. M. C. Valdes, M. Moreira, J. Foriel and F. Moynier, Earth Planet. Sci. Lett., 2014, 394, 135–145.
42. D. A. Ionov, Y.-H. Qi, J.-T. Kang, A. V. Golovin, O. B. Oleinikov, W. Zheng, A. D. Anbar, Z.-F. Zhang and F. Huang, Geochim. Cosmochim. Acta, 2019, 248, 1–13.
43. W. Dai, F. Moynier, M. Paquet, J. Moureau, B. Debret, J. Siebert, Y. Gerard and Y. Zhao, Chem. Geol., 2022, 590, 120688.
44. C. Chen, W. Dai, Z. Wang, Y. Liu, M. Li, H. Becker and S. F. Foley, Geochim. Cosmochim. Acta, 2019, 249, 121–137.
45. W. Dai, Z. Wang, Y. Liu, C. Chen, K. Zong, L. Zhou, G. Zhang, M. Li, F. Moynier and Z. Hu, Geochim. Cosmochim. Acta, 2020, 270, 144–159.
46. Z. T. Eriksen, S. B. Jacobsen, J. M. D. Day and W. M. White, Geochim. Cosmochim. Acta, 2024, 373, 326–341.
47. Z. T. Eriksen and S. B. Jacobsen, Earth Planet. Sci. Lett., 2022, 593, 117665.
48. B.-Y. Gao, B.-X. Su, W.-J. Li, M. Yuan, J. Sun, Y. Zhao and X. Liu, J. Anal. At. Spectrom., 2022, 37, 2111–2121.
49. M. S. Fantle and E. T. Tipper, Earth-Sci. Rev., 2014, 129, 148–177.
50. J. L. Morgan, G. W. Gordon, R. C. Arrua, J. L. Skulan, A. D. Anbar and T. D. Bullen, Anal. Chem., 2011, 83, 6956–6962.
51. L. Simpson, R. Hearn, S. Merson and T. Catterick, Talanta, 2005, 65, 900–906.
52. S. Stürup, L. Bendahl and B. Gammelgaard, J. Anal. At. Spectrom., 2006, 21, 297–304.
53. F. Liu, H. L. Zhu, X. Li, G. Q. Wang and Z. F. Zhang, Geostand. Geoanal. Res., 2017, 41, 675–688.
54. F. Liu, Z. Zhang, X. Li and Y. An, Int. J. Mass Spectrom., 2020, 450, 116307.
55. R. A. Creaser, H. Grütter, J. Carlson and B. Crawford, Lithos, 2004, 76, 399–414.
56. Y. Amelin and R. Merle, Chem. Geol., 2021, 559, 119976.
57. M. H. Huyskens, T. Iizuka and Y. Amelin, ,J. Anal. At. Spectrom., 2012, 27, 1439.
58. C. Holmden and N. Bélanger, Geochim. Cosmochim. Acta, 2010, 74, 995–1015.
59. C. Holmden, Saskat. Geol. Surv., 2005, 1, 7.
60. A. Heuser, A. Eisenhauer, N. Gussone, B. Bock, B. T. Hansen and T. F. Nägler, Int. J. Mass Spectrom., 2002, 220, 385–389.
61. M. Wang, Z. Wang, L. Guo, Z. Zou, F. Wu, W. Dai, J. Guo, K. Chen, L. Feng, H. Chen, M. Li and Y. Liu, Geochim. Cosmochim. Acta, 2025, 400, 248–264.
62. E. D. Young, A. Galy and H. Nagahara, Geochim. Cosmochim. Acta, 2002, 66, 1095–1104.
63. G. Jörg, Y. Amelin, K. Kossert, C. Lierse and V. Gostomski, Geochim. Cosmochim. Acta, 2012, 88, 51–65.
64. H. Gerstenberger and G. Haase, Chem. Geol., 1997, 136, 309–312.
65. D. Wielandt and M. Bizzarro, J. Anal. At. Spectrom., 2011, 26, 366–377.
66. Y. Amelin and W. J. Davis, J. Anal. At. Spectrom., 2006, 21, 1053–1061.
67. G. F. Kessinger and J. E. Delmore, Int. J. Mass Spectrom., 2002, 213, 63–80.
68. R. Wilson, J. Appl. Phys., 1966, 37, 3170–3172.
69. H. Kawano, Prog. Surf. Sci., 2008, 83, 1–65.
70. W. D. Davis, Environ. Sci. Technol., 1977, 11, 587–592.
71. M. S. Fantle and T. D. Bullen, Chem. Geol., 2009, 258, 50–64.
72. S. R. Hart and A. Zindler, Int. J. Mass Spectrom. Ion Processes., 1989, 89, 287–301.
73. L. Feng, L. Zhou, L. Yang, D. J. DePaolo, S. Tong, Y. Liu, T. L. Owens and S. Gao, Geostand. Geoanal. Res., 2017, 41, 93–106.
74. W.-N. Lu, Y. He, Y. Wang and S. Ke, Geochim. Cosmochim. Acta, 2020, 278, 392–404.
75. Y. Wang, Y. He, H. Wu, C. Zhu, S. Huang and J. Huang, Geochim. Cosmochim. Acta, 2019, 259, 37–52.
76. J. Lewis, T.-H. Luu, C. D. Coath, H. Wehrs, J. B. Schwieters and T. Elliott, Chem. Geol., 2022, 614, 121185.
77. W.-N. Lu, Y. He, S. Li, Y. Wang, Q. Shi, S. Ke and S.-J. Wang, Geochim. Cosmochim. Acta, 2025, 404, 41–52.
78. J. Sun, X.-K. Zhu, N. S. Belshaw, W. Chen, A. G. Doroshkevich, W.-L. Song, B.-B. Chen, Z.-G. Cheng, Z.-H. Li, Y. Wang, J. Kynicky and G. M. Henderson, Geochem. Persp. Let., 2021, 17, 11–15.
79. S. F. Foley, D. E. Jacob and H. S. C. O’Neill, Contrib Mineral Petrol., 2011, 162, 1–20.
80. Y. Masuda, M. Schiller, M. Bizzarro and T. Yokoyama, Geochim. Cosmochim. Acta, 2025, 388, 1–17.

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