In situ calcium isotope analysis of Sr-rich carbonates using laser ablation multi-collector inductively coupled plasma mass spectrometry

Abstract

The in situ Ca isotopic composition of carbonates serves as a fundamental tool for tracing geological and biological processes. However, doubly charged Sr ions pose significant interference challenges in Ca isotope measurement using laser ablation multi-collector inductively coupled plasma mass spectrometry (LA-MC-ICP-MS). This study reports a method established for high-precision Ca isotope microanalysis in Sr-rich carbonates. Instrumental parameters including gas flow, torch position and laser settings were optimized to minimize the yield of doubly charged Sr ions. The two key factors involved in the correction strategy for Sr²⁺ interference are the true ⁸⁷Sr/⁸⁶Sr ratio and the mass fractionation coefficient of Sr²⁺. The accuracy required for the true Sr isotope ratios of carbonates for interference correction depends on the Sr/Ca ratio, e.g., a variation in ⁸⁷Sr/⁸⁶Sr of 0.005 (SD) can lead to a deviation in δ⁴⁴/⁴²Ca_915a of approximately 0.1‰ for samples with ⁸⁷Sr²⁺/⁴⁴Ca⁺ of 10⁻³. The fractionation coefficients for Sr²⁺ and Sr⁺ were found to differ, and adopting f⁺_Sr in the correction results in a deviation of δ^44/42Ca_915a up to 0.42‰ for calcite with a Sr/Ca ratio of 0.057. Utilizing the iteratively calculated Ca⁺ fractionation coefficient improved the accuracy and precision of Ca isotope microanalysis. The resulting in situ Ca isotopic compositions of dolomite and calcite with Sr/Ca ratios up to 0.057 were consistent with those obtained via SN-MC-ICP-MS, with precisions of δ⁴⁴/⁴²Ca_915a and δ⁴³/⁴²Ca_915a in the ranges of 0.10–0.19‰ and 0.09–0.12‰ (2SD). The method was further validated through microanalysis of calcite from the Miaoya carbonatite-associated REE-Nb deposit, revealing distinct isotopic signatures indicative of magmatic-hydrothermal evolution.

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1. Introduction

Calcium is an alkaline metal widely distributed in the Earth's lithosphere and hydrosphere, and it is the main rock-forming, fluid-active and biologically essential element. It has six stable isotopes, ⁴⁰Ca (96.941%), ⁴²Ca (0.647%), ⁴³Ca (0.135%), ⁴⁴Ca (2.086%), ⁴⁶Ca (0.004%) and ⁴⁸Ca (0.187%). The significant relative mass difference (Δm m⁻¹) of up to 10% between ⁴⁰Ca and ⁴⁴Ca contributes to notable fractionation of Ca isotopic composition (i.e., δ⁴⁴/⁴⁰Ca) with an amplitude of 4‰ in nature.¹ Variations in the Ca isotopic composition of rocks, minerals and biological samples highlight its potential as a tracer for earth-surface processes, global geochemical cycles, low- and high-temperature geochemistry, cosmochemistry, archaeometry and biochemistry.^1–4 Carbonates are among the most abundant calcium-bearing minerals, and the calcium isotopic composition of carbonates has been used to constrain a range of geological issues, including carbonate weathering mechanism,⁵ sedimentary stratigraphy tracing,^6–8 ocean acidification,⁹ origin and magmatic evolution of carbonatites,^10–12 mantle evolution,¹³ deep carbon cycle,^14,15 and bio-mineralization processes.¹⁶

High-precision calcium isotopic compositions are obtained through thermal ionization mass spectrometry (TIMS) and solution nebulization multi-collector inductively coupled plasma mass spectrometry (SN-MC-ICP-MS) analyses, and the external reproducibility for δ^44/40Ca and/or δ^44/42Ca achieved is exceptionally high with reported values as precise as 0.03‰ (2SD).¹⁷ The double-spike technique is adopted for TIMS analysis, where Ca isotopes are usually expressed as δ^44/40Ca or δ⁴⁴Ca.^18–24 Standard-sample bracketing (SSB) is adopted for mass fractionation correction using SN-MC-ICP-MS, and the ⁴⁴Ca/⁴²Ca ratio (expressed as δ^44/42Ca) is more commonly used due to ⁴⁰Ar⁺ interference.^25–34 These high-precision analytical methods effectively reveal the overall calcium isotopic composition of liquid or solid powder samples. In situ laser ablation (LA)-MC-ICP-MS offers a significant advantage by providing high spatial resolution Ca isotopic data and allowing for the investigation of inter- and intra-crystalline variability with reduced sample preparation.^35,36 The external reproducibility for δ^44/42Ca of samples with low Sr content obtained using LA-MC-ICP-MS can be as good as 0.10‰ (2SD),^35,36 which is adequate for geological studies with an isotopic variation amplitude of up to 4‰.¹

Calcium isotope analysis by MC-ICP-MS is now favored due to its higher sample throughput compared to TIMS. This method is challenged by spectral interferences from isobars, molecular ions and doubly charged species (Table 1). Among these, doubly charged Sr ion interferences, i.e., ⁸⁸Sr²⁺, ⁸⁶Sr²⁺ and ⁸⁴Sr²⁺ on ⁴⁴Ca⁺, ⁴³Ca⁺ and ⁴²Ca⁺, pose a significant challenge for accurate Ca isotope determination using MC-ICP-MS (Table 1). The resolution required to separate Sr²⁺ interferences at 16 447 cannot be mass resolved using the current generation of MC-ICP-MS instruments even in high resolution mode.³² To mitigate the impact of Sr²⁺ interference on Ca isotope measurement, it is crucial to maintain a very low Sr/Ca ratio in the analyzed sample in SN-MC-ICP-MS analyses. Sime et al.³⁷ suggested that the Sr/Ca ratio should be lower than 4 × 10⁻⁵ to ensure that the δ^44/42Ca deviation remains less than 0.1‰. Further studies have refined these requirements. Feng et al.³⁰ demonstrated that the deviation of δ^44/42Ca is less than 0.07‰ when the Sr/Ca ratio is below 2 × 10⁻⁵. Li et al.³¹ found that the interference becomes negligible when the Sr/Ca ratio is less than 10⁻⁵.

Table 1 Potential isobaric interferences on ⁴²Ca, ⁴³Ca, and ⁴⁴Ca during in situ Ca isotope measurements of carbonate samples

Isotope	^42Ca(0.647%)	^43Ca(0.135%)	^44Ca(2.086%)
Polyatomic ion interference	^26Mg^16O^+	^14N2^15N^+	^26Mg^18O^+
	^24Mg^18O^+		^12C^16O^2+
	^40Ar^1H^2+		^14N2^16O^+
	^14N3^+
Doubly charged ion interference	^84Sr^2+(0.56%)	^86Sr^2+(9.86%)	^88Sr^2+(82.58%)
	^84Kr^2+(57%)	^86Kr^2+(17.3%)

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Reference materials used for calcium isotopic analysis typically have Sr/Ca ratios ranging from 0.00008 to 0.03.^30,31 This amount of Sr can introduce a significant offset in Ca isotopic determination when using both dry and wet plasma MC-ICP-MS. Chemical separation techniques are commonly employed for SN-MC-ICP-MS analyses, such as the use of Sr-specific columns in conjunction with cation-exchange or extraction resins (Table 2).^27–29,38 Recently, He et al.³² reported a novel method for direct Ca isotope measurement of calcium carbonates using SN-MC-ICP-MS without any matrix separation, achieving a precision of 0.08‰ (2SD). This method involves measuring signal levels of ⁸⁸Sr²⁺, ⁸⁷Sr²⁺, ⁸⁶Sr²⁺ and ⁸⁴Sr²⁺ using the NIST SRM 987 Sr isotope standard solution prior to each sample measurement, which allows for the calculation of the ^88/87Sr²⁺, ^86/87Sr²⁺, and ^84/87Sr²⁺ ratios necessary for Sr²⁺ interference correction. This analytical and correction scheme is effective for carbonate samples with Sr/Ca ratios < 0.1.

Table 2 A summary of Ca stable isotope ratio measurements established using different MC-ICP-MS systems

University	References	Chemical separation methods	MC-ICP-MS model	Rf power	Mass resolution^a	Carbonates measured	Tolerated Sr/Ca ratio	External reproducibility (δ^44/42Ca) (‰) (2SD)
a Res represents resolution.
Université de Paris	Dai et al., 2022 (ref. 38)	Two columns: DGA + Sr spec	Nu Sapphire	1300 W	Low resolution	NIST SRM 915b standard	< 0.0001	< 0.1 (δ^44/40Ca)
Chinese Academy of Sciences	Gao et al., 2022 (ref. 65)	One column: AG50	Nu Sapphire	1300 W	Low resolution	NIST SRM 915b	< 0.0001	< 0.05
China University of Geosciences (Beijing)	Li and Han, 2021 (ref. 33)	One column: AG50	Nu Plasma 3	1300 W	High resolution	NIST SRM 915a standard and NIST SRM 915b	< 0.00002	0.05 (n = 20)
University of Oviedo	Valencia et al., 2021 (ref. 34)	One column: AG50	Neptune	1100 W	Medium resolution	—	—	—
China University of Geosciences (Wuhan)	He et al., 2019 (ref. 32)	Dissolution without columns	Nu Plasma II	1300 W	Low resolution	Natural calcium carbonate samples	< 0.1	0.08 (n = 32)
China University of Geosciences (Wuhan)	Feng et al., 2018 (ref. 30)	One column: DGA	Neptune Plus	1250 W	Medium resolution	NIST SRM 915a and NIST SRM 915b	< 0.00002	0.06 (n = 28)
China University of Geosciences (Wuhan)	Li et al., 2018 (ref. 31)	One column: DGA	Nu Plasma 1700	1200 W	2500 Res	NIST SRM 915b	< 0.00001	0.05 (n = 67)
Arizona State University	Romaniello et al., 2015 (ref. 66)	The prepFAST MC and the supplied 1 mL Sr–Ca column	Neptune	—	Medium resolution	—	< 0.0001	0.06
CNRS	Tacail et al., 2014 (ref. 29)	Three columns: AG50 + AG1 + Sr spec	Neptune Plus	1200 W	Medium resolution	NIST SRM 915b	—	< 0.1
University of Copenhagen	Schiller et al., 2012 (ref. 28)	Four columns: AG50 + AG1 + Sr spec + DGA	Neptune	—	High resolution	NIST SRM 915a standard and NIST SRM 915b	—	< 0.04 (δ^42/44Ca)
Arizona State University	Morgan et al., 2011 (ref. 27)	Two columns: AG50 + Sr spec	Neptune	1200 W	High resolution	NIST SRM 915a standard and NIST SRM 915b standard	< 0.0001	0.12 (n = 188)
	Wieser et al., 2004 (ref. 26)	One column: AG50	Neptune	1200 W	Medium resolution	NIST SRM 915a and biogenic and non-biogenic marine carbonates	—	0.11 (n = 54)
Leibniz-Institut für Meereswissenschaften,	Fietzke et al., 2004 (ref. 67)	Dissolution without columns	AXIOM	400 W	430 Res	NIST SRM 915a standard and O. universa calcite	—	0.14 (δ^44/40Ca) (RSD) (n = 83)
University of Oxford	Halicz et al., 1999 (ref. 25)	Dissolution without columns	Nu Plasma	1400 W	300 Res	NIST SRM 915a standard and carbonates from continental, marine and metamorphic sources	< 0.005	0.16 (n = 9)

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Chemical purification is not feasible in laser ablation analyses, making Sr²⁺ interference correction crucial for Ca isotope analysis using LA-MC-ICP-MS. Tacail et al.³⁵ employed a fixed ⁸⁷Sr/⁸⁶Sr ratio of 0.7103 and an estimated fractionation factor of Sr²⁺ for interference deduction in Ca isotope analysis using LA-MC-ICP-MS. The fractionation factor was estimated by optimizing the corrected ⁴⁴Ca/⁴²Ca ratio of the HAPp2-SPS standard with the highest Sr level (⁸⁷Sr²⁺/⁴⁴Ca⁺ ≅ 3.8 × 10⁻³) to match the purified value obtained by SN-MC-ICP-MS. Zhang et al.³⁶ proposed an interference correction strategy for samples with low Sr content, measuring Sr isotopes prior to Ca isotope analysis. They utilized the fractionation factor of Sr single-charged ions determined using the exponential law along with an ⁸⁷Sr/⁸⁶Sr ratio accuracy of 1‰ for interference deduction. This method is primarily suitable for samples with low Sr content, up to 2249 μg g⁻¹.

Natural carbonates exhibit a wide range of Sr contents. For instance, marine carbonates can contain up to 2000 μg g⁻¹ Sr, while magmatic carbonates may have Sr levels reaching tens of thousands of μg g⁻¹.^39–43 These variations in Sr content lead to Sr/Ca ratios spanning from 10⁻⁶ to 10⁻¹, with most carbonates displaying a > 10% variation amplitude as influenced by environmental, biological, and sub-diagenetic processes.^40,44,45 Thus, analyzing Ca isotopes for natural carbonates, particularly those enriched in Sr, remains challenging using LA-MC-ICP-MS. In this study, we aim to establish a high-precision in situ analytical method for determining calcium isotopes in carbonates with enriched Sr content using LA-MC-ICP-MS. We have refined the gas flow rate, torch position, and laser settings to reduce the yield of doubly charged Sr ions and improved the interference correction strategy by employing an iteratively calculated Ca⁺ fractionation coefficient. The resulting experimental analyses show that the Ca isotopic composition of carbonate samples with Sr content up to 20 468 μg g⁻¹ measured by LA-MC-ICP-MS is consistent with the SN values. The proposed strategy not only improves the accuracy of Ca isotope analysis of Sr-rich carbonates but also enhances analytical precision as indicated by a reduced 2SD (standard deviation).

2. Experimental

2.1 Instrumental settings and samples

In situ calcium isotope ratio measurements were performed on a Nu Plasma II multi-collector (MC) ICP-MS (Nu Instruments, U.K.) connected with a RESOlution (Australian Scientific Instruments, Canberra, Australia) 193 nm ArF excimer laser ablation system at the State Key Laboratory of Geological Processes and Mineral Resources (GPMR), China University of Geosciences, Wuhan. The RESOlution-LR ablation system is equipped with a Laurin Technic S155 laser ablation cell, uniquely designed as a dual-volume sample cell with the advantages of (1) ‘smooth’ aerosol extraction helping to minimize the flicker- and fixed-frequency components of the signal uncertainty; (2) absence of position effects; (3) fast washout; (4) efficient removal of the residual atmosphere; (5) a high level of automation and convenient navigation. This setup eliminates position effects during measurement. The Nu Plasma II is equipped with 16 fixed Faraday cups and 5 ion counting channels, enabling the simultaneous measurement of a wide range of isotopes. To ensure consistent performance, it is recommended to stabilize the Nu Plasma II MC-ICP-MS for 2–3 hours following startup or after a prolonged standby. Samples were ablated and transported by a helium carrier gas and then combined with argon gas before entering the plasma torch. A 319–645 sample cone with a 1.15 mm orifice and a Ni HS1-7 skimmer cone with a 0.6 mm orifice were employed to enhance measurement accuracy and precision. Various laser settings and gas flow rates were tested to assess their effects on potential interferences in low resolution mode. Calcite CAL7 was used as the standard for routine tuning to obtain the maximum sensitivity and the optimal peak shape, with the ⁴⁴Ca⁺ signal reaching 9 V using a laser spot size of 33 μm, a repetition rate of 10 Hz and an energy density of 3 J cm⁻². The ion signals for ⁴²Ca⁺, ⁴³Ca⁺, ⁸⁷Sr²⁺ and ⁴⁴Ca⁺ were measured simultaneously on the Faraday cups of L5, L4, L3, and L2, respectively. Each laser analysis comprised 30 s of background acquisition, 40 s of sample ablation signal acquisition and 30 s of cleaning. The detailed instrumental setup and operating parameters are shown in Table 3. Calcite and dolomite standards (CAL7 and DOL9) were used to correct the instrument mass bias and drifting, employing the standard-sample bracketing (SSB) method. The Ca isotope ratios of the samples are reported in δ notation relative to the NIST SRM 915a carbonate standard using the following equation:where 4x represents 44 or 43.

Table 3 Operating conditions for the MC-ICP-MS and laser ablation systems

Instruments	Operating conditions
MC-ICP-MS (Nu Plasma II)
Cup configuration	L5	L4	L3	L2
	^42Ca	^43Ca	^87Sr^2+	^44Ca
RF power	1300 W
Cool gas flow	13.5 L min^−1
Auxiliary gas flow	0.88 L min^−1
Argon make-up gas flow	0.70–1.04 L min^−1
Helium carrier gas flow	0.15–0.65 L min^−1
Nitrogen gas flow	0–4 mL min^−1
Sample cone	319–645 (1.15 mm orifice)
Skimmer cone	Ni HS1-7 (0.6 mm orifice)
Mass resolution	Low
Block number	1
Cycles of each block	400
Integration time (s)	0.2 s
Laser ablation system (resolution, Australian Scientific Instruments)
Laser type	ArF excimer laser
Wavelength	193 nm
Pulse length	20 ns
Energy density	1–5 J cm^−2
Spot size	33–130 μm
Ablation mode	Spot/raster scan
Laser frequency	2–14Hz

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The carbonates adopted for calcium isotope analysis in this study include two low-Sr calcites (calcium carbonate, CAL7 and CAL10) as investigated by Zhang et al.³⁶ and high-Sr magmatic calcites (OKA153, SXD8 and SXD2) with well-characterized chemical and Sr isotopic compositions.^41–43,46 Additionally, three dolomites (DOL9, DOL8 and DOL3)^47,48 with extensively studied chemical, C and Mg isotopic compositions were included as well. The detailed chemical (Ca, Sr, and Mg) and Sr isotopic compositions for the investigated carbonate samples are listed in Table 4.

Table 4 Chemical composition, Sr isotopic and Ca isotopic composition of all carbonate samples

Descriptions	Sample	δ ^44/42Ca915a^a (‰)	δ ^43/42Ca915a^a (‰)	^87Sr/^86Sr	Ca (μg g^−1)	Sr (μg g^−1)	Sr/Ca	Mg (μg g^−1)
a Ca isotopic composition of carbonates measured by SN-MC-ICP-MS. b The reported value from Zhang et al.^36 c The value estimated based on the average Ca content of natural calcite. d The reported value from Chen and Simonetti.^46 e The reported value from Chen and Simonetti.^41 f The reported value from Chen et al.^43 g The reported value from Chen et al.^42 h The reported value from Lu et al.^47
Calcite	CAL7	0.58	0.29	0.70801^b	—	223^b	6.0 × 10^−4 c	—
	CAL10	0.40	0.20	—	—	29^b	7.7 × 10^−5^c	—
	OKA153	0.36	0.18	0.70338^d	385 505^e	10 620^e	0.028	180^e
	SXD8	0.35	0.17	0.70320^f	378 500^g	15 950^f	0.042	1620^g
	SXD2	0.34	0.17	0.70329^f	360 111^f	20 468^f	0.057	—
Dolomite	DOL9	0.47	0.21	—	157 143^h	165^h	—	73 200^h
	DOL8	0.50	0.21	—	163 571^h	36^h	—	70 800^h
	DOL3	0.23	0.06	—	160 714^h	42^h	—	64 800^h

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2.2 Ca isotope analysis by SN-MC-ICP-MS

To better quantitatively evaluate the accuracy and precision of our method for in situ Ca isotope measurement, the Ca isotopic compositions of carbonate samples were determined using SN-MC-ICP-MS at the Chinese Academy of Geological Sciences (CAGS, Beijing) and China University of Geosciences, Wuhan.

The Ca isotopic compositions of magmatic calcites (OKA153, SXD8 and SXD2) were measured using the HR Nu Instruments MC-ICP-MS at CAGS following the protocol reported by Sun et al.⁴⁹ Geological reference materials and calcite samples were ground to ∼200 mesh. Calcite samples were digested with dilute HNO₃ or HCl. The COQ-1 standard was digested with HCl and HF. The seawater standard underwent treatment with reverse aqua regia, and the NIST 915b standard was treated with HCl. Solutions were evaporated and re-dissolved in 2 M HCl. A Ca–Sr separation protocol using AG 50W-X12 resin was developed: approximately 150 μg Ca samples were loaded, matrix elements were eluted with 19 mL 2 M HCl, and Ca was collected with 18 mL 2 M HCl, followed by trace Ca elution with 2 mL of 3 M HCl. The collected solutions were dried, re-dissolved in HNO₃, evaporated to dryness three times, and dissolved in 0.3 M HNO₃ for isotope analysis, achieving over 98% Ca recovery. Ca isotope ratios were determined at low mass resolution, with mass discrimination corrected using the standard-sample bracketing method. Sr and other interferences were corrected using Ca-free solutions and a desolvating nebulizer. The accuracy and precision were verified using NIST 915b and geological reference materials, yielding values consistent with published results and those from high-precision DS-TIMS methods, with a long-term external precision for δ^44/42Ca of 0.05‰ (2SD).

The Ca isotopic compositions of dolomites were measured following the method described by Li et al.³¹ The carbonate powder was dissolved in 1.5 mL concentrated HNO₃ and 1.5 mL concentrated HF at 120 °C for 48 h. The solution was then re-dissolved twice in 1 mL concentrated HNO₃ to remove HF, followed by the addition of 0.5 mL concentrated HNO₃ and 1.5 mL concentrated HCl, and heated at 120 °C for 24 hours. To convert the solution to its nitrate form, it was dried and re-dissolved twice in 0.5 mL concentrated HNO₃ and then in 5 mL of 4 mol L⁻¹ HNO₃. Ca separation utilized the DGA resin. A 40 μg Ca solution was dried, dissolved in 400 μL 4 mol L⁻¹ HNO₃, and loaded onto the column. Matrix elements were eluted with 6 mL 4 mol L⁻¹ HNO₃, and Ca was collected with 3 mL deionized water. The purified sample was dried and re-dissolved in 2 mL 0.35 mol L⁻¹ HNO₃ for MC-ICP-MS analysis, achieving high Ca recovery with an approximately 10 ng Ca blank. Ca isotope measurements were performed using a Nu Plasma 1700 MC-ICP-MS, with standard sampling and skimmer cones used at a mass resolution of 2500 to resolve polyatomic interferences. Solutions with 5 μg g⁻¹ Ca were introduced using a Micromist nebulizer with ESI Apex-Q and CETAC Aridus II systems, yielding a 5–8 V signal for ⁴⁴Ca⁺. The Alfa Aesar 13 852 standard was used as the bracketing standard. Repeated measurement of NIST 915b, seawater, COQ-1, and BHVO-2 yielded δ^4x/42Ca_915a values consistent with those reported, with reproducibility (2SD) better than 0.10‰ and 0.08‰, respectively.

2.3 Correction models for deducting doubly charged Sr interference

The correction of doubly charged Sr interference in MC-ICP-MS measurement typically assumes that Sr isotope fractionation follows the mass-dependent exponential law.^27,29,35,36 The mass fractionation coefficient (f) is calculated using the following formula:where (A/B)_meas is the ratio of the measured isotopes, (A/B)_true represents the natural ratio of these isotopes, and M(X) denotes the absolute atomic mass of the isotopes.

The Sr²⁺ interference correction using f⁺_Sr has been successfully adopted for carbonates with limited Sr content by Zhang et al.³⁶ The correction process involves several key steps. Firstly, the fractionation coefficient of Sr single-charged ions (f⁺_Sr) is obtained by measuring ⁸⁶Sr/⁸⁸Sr of an external standard and normalizing it to the natural value of 0.1194 following eqn (2). Secondly, the Sr²⁺ interference signal is then calculated, including the superimposition on masses 42, 43 and 44, and mass bias corrected adopting the natural ⁸⁸Sr/⁸⁶Sr and ⁸⁴Sr/⁸⁶Sr ratios of 8.375209 and 0.05654 along with the ⁸⁶Sr/⁸⁷Sr ratio of the samples and previously determined f⁺_Sr. The corrected ^4xCa/⁴²Ca ratios are then calculated using the following equations:

where (^8xSr/⁸⁶Sr)_true represents the true Sr isotope ratio in nature, and (⁸⁶Sr/⁸⁷Sr)_sam represents the true radioactive Sr isotopic composition of the measured samples (where Sr isotope analysis is performed before Ca isotope measurements). I_x is the signal of the m/z beam, and M(^8xSr) represents the absolute atomic mass of the Sr isotopes.

To further improve the accuracy of the Ca isotope analysis and effectively correct Sr²⁺ interference for Sr-rich carbonates, this study proposes an iterative method to refine the Ca isotope fractionation coefficient, which offers significant advantages for correcting isobaric interferences as shown in Nd and Ce isotope analyses.^50,51 The method effectively addresses both mass discrimination and doubly charged Sr ion interference. The method begins by setting the initial fractionation coefficient for singly charged Ca ions to zero , enabling the calculation of initial stable Ca isotope ratios with Sr²⁺ interference corrected using eqn (5) and (6):

The fractionation coefficient for is iteratively recalculated using eqn (2) until the relative deviation between consecutive iterations approaches zero, indicating convergence. Once convergence is achieved, the final Ca stable isotope ratios are computed using the stabilized .

2.4 Uncertainty budget

In this study, matrix matched CAL7 and DOL9 were used as the bracketing standards for calcite and dolomite. By measuring the isotope ratios of the standard before and after the sample, the δ value of the sample can then be calculated using the SSB method.where r_smp is the measured calcium isotope ratio in the sample and is the average value of the measured calcium isotope ratio in the two adjacent standards, calculated using eqn (8):where r_stdbef and r_stdaft are the measured calcium isotope ratios for the standard bracketing before and after the sample, respectively.

δ^4/x42Ca_915a = δ^4x/42Ca_smp/std + δ^4x/42Ca_std/915a (9)

The uncertainty propagation of δ^4x/42Ca_915a for each sample analysis can be estimated using the Monte Carlo simulation technique. This method is particularly effective in handling complex uncertainty propagation scenarios that involve relationships between the input parameters and the resulting value that are difficult to present as a deterministic function.

The simulation process involves the following steps: (1) estimation of the uncertainties of the individual input parameters and determination of the uncertainties of all variables involved, including r_smp, r̄_std and δ_std/915a. Each variable is assigned a probability distribution, typically a normal distribution centered around the measured value with a standard deviation equal to the reported uncertainty. (2) Generation of random samples. A random number generator is used to draw random samples from the defined probability distributions of the input variables. (3) Computation of the δ^4x/42Ca_915a value through iteration, followed by 10 000 simulated analyses to build a probability density function (PDF) for the δ^4x/42Ca_915a values. The uncertainty is calculated as the standard deviation of the simulated δ^4x/42Ca_915a values from the PDF. The precision for each sample analysis was determined by doubling the standard error of the mean result (2 s), with the assumption of 180 data cycles as actual measurements.

3. Results and discussion

3.1 Optimization of instrument parameters for interference deduction

3.1.1 Effect of gas flow rate and torch position on spectral interference. Ca isotope measurements by MC-ICP-MS are particularly sensitive to polyatomic and doubly charged isobaric interferences originating from the plasma.^26,32 The main isobaric interferences on ⁴²Ca, ⁴³Ca, and ⁴⁴Ca in the Ca isotope measurement of carbonates by LA-MC-ICP-MS are shown in Table 1. Introducing samples into the plasma using a laser ablation system means operating under “dry aerosol” conditions, thus greatly reducing the formation of hydroxide ions, e.g., interference from ⁴⁰Ar¹H₂⁺ measured at ∼0.012 V can be effectively corrected during background subtraction. No significant polyatomic interferences (neither ¹²C¹⁶O₂⁺ nor ¹⁴N₂¹⁶O⁺) were observed at 44 u. Nevertheless, interference from doubly charged and oxide ions remains crucial and was rigorously assessed in this study.^26,29,31,36

Adding N₂ to the sample gas is believed to enhance instrument sensitivity and suppress the oxides, because oxygen readily combines with nitrogen in the ICP, forming NO_x⁺ species and leaving less oxygen to react with other elements.^52,53 However, the use of N₂ also has significant implications for doubly charged species interference. In this study, the addition of N₂ into the plasma was found to increase the ⁴⁴Ca⁺ signal of calcite SXD2 by 1.1 times at 2.5 ml min⁻¹ and 1.4 times at 4 ml min⁻¹ (Fig. 1a). However, it also led to a rise in the yield of doubly charged Sr ions, with the ⁸⁷Sr²⁺/⁴⁴Ca⁺ ratio increasing by 2.2 times at 2.5 ml min⁻¹ and 3.7 at 4 ml min⁻¹ (Fig. 1b). Compared to the minimum value of ⁴⁰Ar¹⁶O⁺ (i.e. approximately 0.15 V) optimized by Zhang et al.,³⁶ which has a limited effect on the accurate Ca isotope measurement, a lower signal intensity was observed in the current instrumental settings both with and without N₂ addition (i.e., less than 0.1 V; Fig. 1c and f), indicating negligible oxide ion interference for Ca isotope analysis. Despite the expected benefits of increased signal intensity, the internal precision of calcium isotope ratios in carbonate samples was actually better without the addition of N₂, where the ⁴⁴Ca⁺ signal was lower (Fig. 2). In general, the internal precision of ⁴⁴Ca/⁴²Ca and ⁴³Ca/⁴²Ca was better than 0.05‰ and 0.07‰ (2SE) when the signal intensity of ⁴⁴Ca⁺ was higher than 9 V (Fig. 2). This improved precision is attributed to the reduced yield of doubly charged Sr ions and the potential interference from N₃⁺ and N₂O⁺ ions that may impact Ca isotope measurements but becomes negligible without N₂. The trade-off between increased signal intensity and increased interferences suggests that Ca isotope analysis may be more effectively conducted without the addition of N₂.

Fig. 1 Effects of the gas flow rate ((a–c), helium flow; (d–f), mixed gas flow) and the addition of N₂ on the yield of doubly charged Sr and polyatomic ions. The vertical line represents the gas flow rate corresponding to the maximum ⁴⁴Ca⁺ signal intensity with and without the addition of N₂.

Fig. 2 Effects of nitrogen on the internal precision of ^4xCa/⁴²Ca repeatedly measured in carbonate samples. Data presented are uncorrected for interference deduction and mass discrimination (excluding samples with high Sr content). The black dashed lines indicate the 2SE values of 0.05‰ (a) and 0.07‰ (b).

In LA-MC-ICP-MS, the He gas flow in conjunction with the mixed gas flow and sampling position significantly affects the transport, particle mobilization and ionization efficiency of different elements within the plasma.^52,54–56 Roudushkin et al.⁵⁴ pointed out that different combinations of He and Ar gas flows have varying effects on element signal intensities, a phenomenon also observed in calcium isotope measurements in this study (Fig. 1). The ⁸⁷Sr²⁺/⁸⁷Sr⁺ ratio stays stable during analysis, as observed by Li et al.³¹ and Zhang et al.³⁶ Without the addition of N₂, the impact of the He gas flow on the ⁸⁷Sr²⁺/⁴⁴Ca⁺ ratio is minimal at a low flow rate of <450 ml min⁻¹ (Fig. 1b). Of note, when the He flow rate surpasses 450 ml min⁻¹, the ⁸⁷Sr²⁺/⁴⁴Ca⁺ ratio increases notably. In contrast, the effect of varying mixed gas flow on the change of the ⁸⁷Sr²⁺/⁴⁴Ca⁺ ratio is insignificant (<0.003; Fig. 1e), suggesting that the He gas flow rate has a more pronounced impact on particle mobilization efficiency compared to the Ar gas flow rate.

The torch position, or sampling position, also significantly influences the yield of doubly charged Sr ions. Fig. 3 exhibits a more marked decrease of Sr²⁺ yield compared to Ca⁺ when the sampling is conducted further from the sampling zone (i.e., smaller in/out position). The more significant decrease of ⁸⁷Sr²⁺ than ⁴⁴Ca⁺ fits the ‘zone model’ proposed by Vanhaecke and Dams⁵⁷ and Andren et al.⁵⁵ The model suggests that for ions with a higher mass number, the maximum density in the plasma occurs closer to the sampling cone. The torch position is set to balance the ⁸⁷Sr²⁺ yield and ⁴⁴Ca⁺ intensity, with an optimal setting at 6.5 in this analytical session when the ⁸⁷Sr²⁺/⁴⁴Ca⁺ ratio becomes stable.

Fig. 3 Effects of the torch position on the Sr²⁺ yield. The In/Out position indicates the distance between the torch and the sample cone with the greater values representing a shorter distance. I_norm represents the signals normalized to the maximum intensity (triangles for ⁴⁴Ca⁺ and diamonds for ⁸⁷Sr²⁺). (⁸⁷Sr²⁺/⁴⁴Ca⁺)_norm refers to the ratios normalized to the minimum value (circles).

3.1.2 Effect of laser parameters on Sr²⁺ yield and Ca isotope measurement. Calibration of laser parameters is essential, as they can significantly influence the material sampled, which may lead to calcium isotopic fractionation.⁵⁸ As shown in Fig. 4, conditional experiments were conducted on CAL7 with low Sr content and SXD2 with the highest Sr/Ca ratios by varying the beam spot size (33–130 μm), frequency (2–14 Hz) and energy density (1–5 J cm⁻²). A smaller laser beam spot size (e.g., 33 μm) resulted in substantially poor external precision (2SD) for δ^44/42Ca_915a, reaching up to 0.28‰ for SXD2 and 0.64‰ for CAL7 (Fig. 4a). This may be attributed to the insufficient signal intensity of ⁴⁴Ca⁺ (e.g., 1 V) at smaller spot sizes. Laser frequency affects both the accuracy and precision of Ca isotopic compositions (δ^44/42Ca_915a) in Sr-depleted and Sr-enriched calcites. The deviation is more pronounced at frequencies less than 6 Hz, and maximum deviations of 0.26‰ for CAL7 and 0.23‰ for SXD2 are identified at a frequency of 2 Hz (Fig. 4b). Lower laser frequencies result in less efficient sample ablation, generating larger aerosol particles that are less fully ionized, leading to isotopic fractionation.⁵⁹ Kuhn et al.⁵⁹ observed that larger particles were associated with heavier isotopic signatures in copper analysis of chalcopyrite. This has also been identified by Lv et al.,⁶⁰ where deviations of δ⁶⁵Cu (up to 0.09‰) were observed for chalcopyrite at laser frequencies smaller than 4 Hz. The laser frequency of 10 Hz was chosen to minimize laser-induced isotope fractionation and to achieve the best external reproducibility. In this study, an energy density range of 1–5 J cm⁻² was used for detailed analysis. The results show that, in contrast to spot size and frequency, energy density has an insignificant effect on the accuracy and precision of Ca isotope measurements (Fig. 4c), suggesting that energy density does not substantially impact Ca isotope analysis within the adopted range.

Fig. 4 Effects of spot size (a), frequency (b) and energy density (c) on Ca isotope measurement. Each data point represents at least 10 analyses, with error bars indicating twice the standard deviation (2SD). All data have been corrected using values measured under standard conditions of a 90 μm spot size, 10 Hz frequency, and 3 J cm⁻² energy density. The solid lines denote the SN-MC-ICP-MS values, while the shaded areas between the dashed lines represent twice the standard deviation (2SD) measured by SN-MC-ICP-MS.

3.1.3 Characterization of the in-house standards. The matrix effect caused by the diversity of physical and chemical properties in carbonates requires the use of matrix-matched standards to correct for matrix-induced fractionation in the Ca isotope determination using LA-MC-ICP-MS. To evaluate the isotopic uniformity of carbonate samples used in this study, in situ analyses were performed on carbonate samples CAL7 and DOL9 with low Sr content and relatively homogeneous chemical compositions.^36,47,48 All the measured points are evenly distributed across each sample in a cross pattern. The external reproducibility of δ^44/42Ca_915a and δ^43/42Ca_915a was better than 0.09‰ for both CAL7 and DOL9 (2SD; Fig. 5). This level of reproducibility indicates excellent micro-homogeneity for both carbonate samples. Given their demonstrated homogeneity and low Sr content, CAL7 and DOL9 were adopted as standards for in situ calcium isotope measurements of calcites and dolomites in this study.

Fig. 5 In situ Ca isotopic homogeneity test for DOL9 (a) and CAL7 (b). The black dots represent the values measured by SN-MC-ICP-MS. The black horizontal solid lines indicate the average values of repeated measurement for each sample, and the error bars represent the uncertainty (internal precision) of each analysis.

3.2 Doubly charged Sr interference correction

The variation in the ⁸⁷Sr/⁸⁶Sr ratio can significantly affect the accurate measurement of calcium isotopes using LA-MC-ICP-MS, necessitating careful consideration in the interference correction of doubly charged Sr ions.^35,36 The ⁸⁷Sr²⁺/⁴⁴Ca⁺ ratio is highly dependent on the Sr/Ca ratio, which shows a positive linear correlation in Fig. 6, and a similar phenomenon has also been observed by Zhang et al.³⁶ In this study, calcites with varying Sr/Ca ratios (from 0.000077 to 0.057) were evaluated to assess the effect of ⁸⁷Sr/⁸⁶Sr variation in the range of 0.70301 to 0.70801 on the deviation of Ca isotopic composition (Fig. 7). The results demonstrate that the impact of ⁸⁷Sr/⁸⁶Sr variation on calcium isotope measurement intensifies with increasing Sr content within calcite. Numerical simulations indicate that when the Sr²⁺ yield, represented by the ⁸⁷Sr²⁺/⁴⁴Ca⁺ ratio, reaches 10⁻³, a variation in ⁸⁷Sr/⁸⁶Sr of ± 0.005 (SD) can cause a deviation in δ⁴⁴/⁴²Ca_915a of approximately 0.1‰ (Fig. 7a). The deviation in δ⁴³/⁴²Ca_915a follows a similar trend but is approximately twice as high due to the abundance ratio of ⁸⁶Sr/⁴³Ca at 73.037 being 1.84 times greater than that of ⁸⁸Sr/⁴⁴Ca at 39.588 (Fig. 7b). The required accuracy of the true Sr isotope ratios for interference correction depends on the Sr/Ca ratio of the carbonate sample.

Fig. 6 Relationship between the Sr/Ca ratio and Sr²⁺ yield (⁸⁷Sr²⁺/⁴⁴Ca⁺) obtained using LA-MC-ICP-MS in adjacent sessions of this study.

Fig. 7 Influence of ⁸⁷Sr/⁸⁶Sr variation on δ^44/42Ca (a) and δ^43/42Ca (b). Δ-δ^4x/42Ca refers to the discrepancies of δ^4x/42Ca_915a when corrected using inaccurate ⁸⁷Sr/⁸⁶Sr ratios. The green slash marks the Sr²⁺ yield when the Ca isotope deviation is 0.1‰, calculated at the critical ⁸⁷Sr/⁸⁶Sr value of the sample.

Another significant factor involved in the interference correction is the mass fractionation coefficient of Sr²⁺. The first correction strategy adopted in the study estimates f²⁺_Sr using f⁺_Sr similar to that adopted by Zhang et al.³⁶ Of note, the mass fractionation coefficient of Sr⁺ (f⁺_Sr) varies significantly across different analytical sessions (e.g., from 1.45 to 1.62 for CAL7) and among carbonates with distinct compositions. Generally, f⁺_Sr is lower in Sr-enriched carbonates (e.g., 1.45 for CAL7 and 1.36 for SXD2). A similar phenomenon has been observed in in situ Hf and Fe isotope analysis, where the absolute values for f_Yb and f_Cr decrease with the increase of their intensities in the sample.^61,62 Thus, f⁺_Sr for carbonate with low and high Sr contents (represented by CAL7 and SXD2) was used for the doubly charged Sr ion correction (Fig. 8a–d). Regardless of the coefficients adopted, the resulting Ca isotopic compositions (δ^4x/42Ca_915a) of the carbonates with low Sr content (i.e., CAL10) are generally consistent with the SN obtained values, with reproducibility (2SD) better than 0.13‰ and 0.10‰, respectively. However, for Sr-enriched carbonates (i.e., OKA153, SXD8, and SXD2), the Ca isotopic compositions all deviate from the SN values, e.g., by 0.42‰ and 0.63‰ for SXD2 (Fig. 8c–d). This deviation likely arises from differences in the fractionation behavior of Sr²⁺ compared to Sr⁺ during Ca isotope measurements, as observed by He et al.³² This difference is particularly relevant due to the space-charge effect, where electrostatic repulsion within the ion beam results in distinct fractionation behaviors for ions with different charge states. Specifically, the larger Coulomb force acting on the Sr²⁺ ions induces distinct fractionation patterns relative to Sr⁺ ions, contributing to the observed deviation in Sr-enriched carbonates when using f⁺_Sr for correction.⁶³

Fig. 8 δ ^4x/42Ca values with Sr²⁺ interference correction using f⁺_Sr from CAL7 (a and b) and SXD2 (c and d) and iteratively calculated f⁺_Ca (e and f). Values are compared to those obtained via SN-MC-ICP-MS. Data points represent the average of at least 15 analyses (n ≥ 15), with error bars indicating twice the standard deviation (2SD). The black solid line represents the 1 : 1 correlation.

The second correction strategy estimates f²⁺_Sr using f⁺_Ca achieved through an iterative method. The resulting Ca isotopic compositions of all calcite samples are consistent with the SN determined values with the Sr²⁺ interference correction using the iteratively calculated Ca mass fractionation coefficient (Fig. 8e–f). Furthermore, the external precision for δ^4x/42Ca_915a analysis in carbonates with high Sr content is also improved; e.g., for SXD2 calcite with Sr/Ca = 0.057, the external reproducibility of δ^4x/42Ca_915a improved from 0.16‰ to 0.14‰ and from 0.17‰ to 0.14‰, respectively. Tacail et al.³⁵ estimated f²⁺_Sr by minimizing the ⁴⁴Ca/⁴²Ca ratio measured in LA mode to match that without interference in SN mode, which also results in accurate correction, ignoring that different mass fractionation may occur in wet and dry plasma. The successful application of our strategy is attributed to the convincing similar fractionation behavior observed between Ca⁺ ions and Sr²⁺ ions. Notably, both Tacail et al.³⁵ and Zhang et al.³⁶ required additional analysis before conducting in situ Ca isotope measurement. This necessitates optimal instrument conditions and overlooks the fact that the instrument may drift over time. The proposed new iterative correction strategy can monitor and address this limitation effectively.

In summary, accurate correction of Sr mass discrimination and isobaric Sr²⁺ interference relies on the true ⁸⁷Sr/⁸⁶Sr ratio of the sample and the estimation of Sr²⁺ fractionation using the iteratively calculated Ca⁺ fractionation coefficient. The iterative correction using f⁺_Ca consistently yielded accurate δ^44/42Ca values, even in Sr-rich samples, underscoring the necessity of addressing both Sr²⁺ interference and instrument-specific mass fractionation.

3.3 Results of Ca isotope analysis of carbonate samples

The calcite and dolomite samples, with δ^44/42Ca ranging from 0.23‰ to 0.58‰, were measured with CAL7 calcite and DOL9 dolomite as bracketing standards. After Sr²⁺ interference correction, the Ca isotope results of all calcite samples, especially the calcites with Sr/Ca ≥ 0.028, were all consistent with the SN determined values, as shown in Fig. 9. The analytical external precision of calcites was better than 0.14‰ for δ^44/42Ca_915a and 0.11‰ for δ^43/42Ca_915a. The results confirm that the proposed method is effective for Sr²⁺ interference correction in Sr-rich carbonates. For dolomite samples, the precision was better than 0.19‰ for δ^44/42Ca_915a and 0.12‰ for δ^43/42Ca_915a. The poorest external precision was recorded in DOL3, which exhibits chemical zonation and significant δ^26/24Mg variation across different zones (e.g., −2.08 ± 0.21‰ for the core and −2.78 ± 0.20‰ for the rim).⁴⁸

Fig. 9 δ ^44/42Ca (a) and δ^43/42Ca (b) values of all carbonate samples obtained using LA-MC-ICP-MS compared to SN-MC-ICP-MS values. Error bars denote twice the standard deviation (2SD), with the black solid line indicating the 1 : 1 correlation.

In order to further verify the feasibility of the proposed method, in situ Ca isotope analysis was performed on calcites documenting magmatic-hydrothermal evolution from the Miaoya carbonatite associated REE-Nb deposit.⁶⁴ Of note, Sun et al.⁴⁹ indicated that magmatic and hydrothermal carbonatites worldwide consist of distinct Ca isotopic compositions. The average δ^44/42Ca_915a value for magmatic carbonatites is 0.35‰, whereas that for hydrothermal carbonatites ranges from 0.26‰ to 0.44‰. The coarse-grained calcites investigated are characterized by more enriched REE signatures and less radiogenic Sr isotopic compositions compared to the fine-grained calcites, which indicate that the latter are more intensely affected by late-stage Mesozoic alteration.⁶⁴ The results in Fig. 10 show that the δ^4x/42Ca_915a values of the relatively primary coarse-grained calcites are 0.33 ± 0.10‰ (2SD, n = 4) and 0.17 ± 0.12‰ (2SD, n = 4), which are consistent with those identified worldwide.⁴⁹ The δ^4x/42Ca_915a values of hydrothermal fine-grained calcites are 0.47 ± 0.22‰ (2SD, n = 4) and 0.25 ± 0.12‰ (2SD, n = 4), and the elevated Ca isotopic compositions are dominated by Rayleigh fractionation as the hydrothermal calcites within the Miaoya carbonatites are characterized by heavier in situ C isotopic compositions.^49,64 The application of this method to Miaoya calcites revealed isotopic distinctions between primary magmatic and later hydrothermal phases, aligning with known geological models.⁴⁹ These findings demonstrate the applicability of the proposed in situ Ca isotope analytical method in tracing complex geological histories.

Fig. 10 High-resolution in situ Ca isotope analysis of fine-grained and coarse-grained calcites from the Miaoya carbonatite REE-Nb deposit. The data highlight variations in Ca isotopic compositions, reflecting magmatic-hydrothermal evolution stages.

4. Conclusion

We have developed a high-precision method for in situ Ca isotope analysis in Sr-rich carbonates using LA-MC-ICP-MS. The in situ δ^4x/42Ca_915a reproducibility of both DOL9 and CAL7 was better than 0.09‰ (2SD), and they were adopted as bracketing standards for in situ Ca isotope analysis of dolomite and calcite. The optimized gas flow rate, torch position, and laser parameters were employed without the addition of N₂ to minimize the yield of Sr doubly charged ions (⁸⁷Sr²⁺/⁴⁴Ca⁺ < 0.003 for SXD2), while ensuring that the ⁴⁴Ca⁺ signal intensity was large enough to generate good precision. Two key factors involved in the accurate correction of Sr doubly charged ions for the Ca isotope analysis are the true ⁸⁷Sr/⁸⁶Sr ratio of the sample and the mass fractionation coefficient of Sr²⁺. The latter is estimated using the iteratively calculated Ca⁺ fractionation coefficient, and the corrected δ^4x/42Ca_915a values for all carbonates (especially those with Sr/Ca > 0.02) are consistent with those obtained using SN-MC-ICP-MS. This method holds promise for broad applications in geochemical studies, particularly in resolving complex histories in carbonate systems.

Data availability

The datasets generated and analysed during this study are not publicly available because different instruments and conditions may have specific but similar phenomena, and the total raw data of up to 20 days are too large to share. However, it is available from the corresponding author on reasonable request.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

We thank three anonymous reviewers for their constructive comments, which improved the manuscript significantly. We are also grateful to editors Rebecca Garton and Ziva Whitelock for editorial handling of the manuscript. Constructive discussions and insightful contributions from Prof. Wen Zhang, Lanping Feng and Dr Ji Mao from the China University of Geosciences are deeply appreciated. And we would like to particularly thank Prof. Wen Zhang for providing the standard samples of calcite CAL7 and CAL10. This work is financially supported by the National Key R&D Program of China (Grant No. 2019YFA0708400) and the National Natural Science Foundation of China (No. 42321001).

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