Precise determination of δ⁸⁸Sr in rocks, minerals, and waters by double-spike TIMS: a powerful tool in the study of geological, hydrological and biological processes

Abstract

We present strontium isotopic (⁸⁸Sr/⁸⁶Sr and ⁸⁷Sr/⁸⁶Sr) results obtained by ⁸⁷Sr–⁸⁴Sr double spike thermal ionization mass-spectrometry (DS-TIMS) for several standards as well as natural water samples and mineral samples of abiogenic and biogenic origin. The detailed data reduction algorithm and a user-friendly Sr-specific stand-alone computer program used for the spike calibration and the data reduction are also presented. Accuracy and precision of our δ⁸⁸Sr measurements, calculated as permil (‰) deviations from the NIST SRM-987 standard, were evaluated by analyzing the NASS-6 seawater standard, which yielded δ⁸⁸Sr = 0.378 ± 0.009‰. The first DS-TIMS data for the NIST SRM-607 potassium feldspar standard and for several US Geological Survey carbonate, phosphate, and silicate standards (EN-1, MAPS-4, MAPS-5, G-3, BCR-2, and BHVO-2) are also reported. Data obtained during this work for Sr-bearing solids and natural waters show a range of δ⁸⁸Sr values of about 2.4‰, the widest observed so far in terrestrial materials. This range is easily resolvable analytically because the demonstrated external error (±SD, standard deviation) for measured δ⁸⁸Sr values is typically ≤0.02‰. It is shown that the “true” ⁸⁷Sr/⁸⁶Sr value obtained by the DS-TIMS or any other external normalization method combines radiogenic and mass-dependent mass-fractionation effects, which cannot be separated. Therefore, the “true” ⁸⁷Sr/⁸⁶Sr and the δ⁸⁷Sr parameter derived from it are not useful isotope tracers. Data presented in this paper for a wide range of naturally occurring sample types demonstrate the potential of the δ⁸⁸Sr isotope tracer in combination with the traditional radiogenic ⁸⁷Sr/⁸⁶Sr tracer for studying a variety of biological, hydrological, and geological processes.

---

1. Introduction

Variations in the radiogenic isotopic composition of Sr (⁸⁷Sr/⁸⁶Sr) are widely used as a tracer in a variety of biological, hydrological, and geological processes. Until recently, the stable Sr isotopic ratio (⁸⁸Sr/⁸⁶Sr) was used for internal normalization to correct for instrumental mass bias, thus masking natural mass-dependent Sr isotopic fractionation. The pioneering work of Patchett^1,2 demonstrated up to 1.5‰ amu⁻¹ mass-dependent Sr isotopic variation in the meteorite Allende. Subsequent studies based on newly developed MC-ICPMS and double-spike (DS) TIMS methods have begun to document ⁸⁸Sr/⁸⁶Sr variability in terrestrial samples.^3–10 These studies highlight the unique potential for this isotope system, especially when combined with measurements of radiogenic Sr (⁸⁷Sr/⁸⁶Sr). Namely, this area of study opens up an entirely new direction in the field of non-traditional stable isotope geochemistry because high-precision Sr isotope composition records information about both the source of Sr and processes causing mass-dependent isotope fractionation.

The natural processes responsible for strontium isotope fractionation currently are not well understood. The documented Sr isotope fractionation in carbonates is apparently controlled by temperature.³ Also, it was shown¹⁰ that the fractionation may increase at higher precipitation rates. First ICPMS measurements of igneous rocks lead to the estimation of the δ⁸⁸Sr† ∼0.27‰ value in bulk silicate Earth,¹¹ which is lower than δ⁸⁸Sr ∼ 0.39‰ in modern oceanic water, the highest δ⁸⁸Sr reported so far. Marine carbonates (both inorganic and biogenic) are variably depleted in ⁸⁸Sr compared to the water from which they precipitated.^3,4,10 The most negative rock δ⁸⁸Sr value measured to date, −0.42‰, was from a carbonate rock in South China and was ascribed to enhanced isotopic fractionation during precipitation from the originally ⁸⁸Sr-depleted seawater.¹² Knudson et al.⁸ reported even more negative δ⁸⁸Sr values measured by MC-ICPMS in biological samples and stated that different Sr isotopic signatures can be observed in different trophic levels as organisms preferentially incorporate the lighter isotope of Sr.

In this paper we present first ⁸⁸Sr/⁸⁶Sr ratio results obtained by ⁸⁷Sr–⁸⁴Sr double spike TIMS for several USGS standards as well as for natural water samples and mineral samples of biogenic and abiogenic origin. The double-spike calibration routine, detailed DS algorithm, and the DS data reduction method based on the stand-alone Sr-specific user-friendly computer program that corrects for Rb interference, calculates Sr concentrations and “true” ⁸⁸Sr/⁸⁶Sr, ⁸⁷Sr/⁸⁶Sr, and δ⁸⁸Sr values are also presented. We also discuss the lack of usefulness of the externally corrected for instrumental mass-fractionation “true” ⁸⁷Sr/⁸⁶Sr and δ⁸⁷Sr values as geochemical tracers.

2. Experimental methods

2.1. Sample preparation

During this study, we analyzed several different types of materials, including fossils (conodonts, Megalodon shark tooth, coral), modern fauna (dolphin tooth, acantharia, clam shell), abiogenic sulfate and carbonate minerals (celestite, strontianite, calcite), silicate whole-rocks (basalt and granite), and waters (groundwater and brine). Although the procedures used to process these materials vary and are presented individually, the procedure for the separation of Sr from all samples is essentially identical. Prior to spiking, small aliquots of water or dissolved solid samples were analyzed to determine the concentration of Sr in the solution using a Plasma Quad-III ICP-MS. Obtaining accurate Sr concentrations for the unknowns is crucial for optimizing the sample/spike ratio in the spiked aliquot using the double-spike method.

Conodonts (tooth-like microfossils of extinct marine chordates) were separated from the host rock using standard techniques described by Collinson¹³ and then better preserved fragments were handpicked for isotope analysis. Handpicking was performed dry with stainless steel tweezers. A selected number of conodont elements (normally one to six; enough for our desired Sr yield) were transferred to an aluminum weigh pan and weighed on a Cahn 4100 microbalance with a precision level of about ±0.000003 g, and then transferred into a pre-cleaned 7 ml PFA Teflon™ vial containing about 1 ml of 0.1 M HCl. HCl was used to pre-clean the conodonts, decanted three times prior to digestion with 1 M HNO₃, and then dried.

Samples of dentine and enamel from phosphatic fossil (Miocene/Pliocene) Megalodon shark tooth (samples ST-E and ST-D) were micro-drilled using a dental burr mounted in a hand-held rotary drill. A pre-powdered sample of bulk modern dolphin tooth (DT-1) was available because it is used in the USGS Denver stable isotope laboratory as an internal carbon and nitrogen isotope reference material. Similarly, a powdered sample of ∼120 ka-old Acropora coral (Acrop-1) was also available because it is used in the USGS Denver radiogenic isotope laboratory as an internal U-series dating reference material. All of these carbonate and phosphate samples were digested in a specific volume of 6 M HNO₃.

Acantharia cysts (Acan-1) from the Bahamas were handpicked and processed similar to the conodonts, except that they were dissolved immediately after weighing to avoid chemical leaching of their extremely delicate structure. Acantharia are abundant oceanic protists, and are the only organisms known to form entire mineral skeletons of celestite (strontium sulfate, SrSO₄). They also have the capacity to completely change their morphology over the course of their life cycle in order to form cysts. The extreme Sr content of acantharia (∼47.5% by weight) is thought to produce enough Sr to outweigh any potential Sr surface contamination that was not eliminated due to a lack of surface leaching of the sample during processing.

Sulfate samples (acantharia Acan-1, celestite Cel-1, MAD-1, and OH-1) were dissolved in a mixture of 0.02 M hydroxylamine–HCl (NH₂OH–HCl) and 2 M nitric acid (HNO₃) after the methods by Puchelt and Setiobudi.¹⁴ Carbonate mineral samples (strontianite FI-1) were dissolved in 1 M HCl. Groundwater and brine samples were dried down and then chemically processed like solid samples.

Water standard NASS-6 was prepared in the same manner as the water/brine samples. Other standards, both carbonate and phosphate, were prepared in the same method as unknowns of the same chemical composition. The silicate standards SRM-607, BCR-2, G-3, and BHVO-2 were prepared in much the same manner except dissolution was achieved using concentrated ultrapure HF and HNO₃ in 7 ml PFA Teflon™ vials.

2.2. Chemical separation of Sr

Two aliquots of about 1 microgram of Sr per specimen were taken from each of the final solutions of known Sr concentration. One aliquot was spiked with about 100–200 microliters of a⁸⁴Sr–⁸⁷Sr double spike solution, and both separates were dried down on a hot plate. A few drops of concentrated HNO₃ and hydrogen peroxide (H₂O₂) were added to help breakdown of any remaining organic components, the samples were re-dried, and then dissolved in 6 M HNO₃ for Sr separation chemistry. Samples of Sr sulfates (acantharia, celestite) and carbonate (strontianite) were measured by TIMS with no further ion-exchange chemical separation of Sr.

Sr was separated from the major cations (e.g. Ca, Mg, Fe, etc.) in Ca-carbonate and silicate samples using a strontium-specific Eichrom Sr resin and a method that was slightly modified from De Muynck et al.¹⁵ The resin was pre-cleaned in deionized water (Milli-Q filtration) by five decantations. Small (0.25 ml volume), PFA Teflon™ columns were made in-house using 4 : 1 shrinkable tubing with FEP Teflon™ frits. These columns were filled with the Sr resin and the resin was cleaned with both deionized water and 6 M HCl prior to conditioning with 6 M HNO₃. About 0.4 ml of the dissolved sample were loaded onto each column and then washed with about 8 ml of 6 M HNO₃ and Sr was eluted with about 4 ml of 0.05 M HNO₃. The Sr separates were dried down and then a few drops each of concentrated HNO₃ and H₂O₂ were added to the residues of each separate and dried down again with 5 microliters of ultrapure phosphoric acid (H₃PO₄). The total blank for this process determined by ID-TIMS did not exceed 0.2 ng Sr, which was negligible considering the amount of Sr analyzed.

2.3. ⁸⁷Sr–⁸⁴Sr double spike preparation

Our double-spike (DS) preparation was similar to the one described by Krabbenhöft et al.⁶ Two powdered Sr-carbonates enriched in ⁸⁴Sr (1 mg from Oak Ridge National Laboratory, ORNL) and in ⁸⁷Sr (30 mg from ISOFLEX USA) were purchased in order to prepare a ⁸⁷Sr–⁸⁴Sr DS solution. The vendors-certified isotopic compositions of these spikes are given in Table 1. The certified abundance of Rb is 5 ppm in the ⁸⁴Sr carbonate, but was not reported for the ⁸⁷Sr carbonate, for which our ICP-MS analyses yielded a Rb concentration of 2 ppm. The latter value is lower than the ⁸⁷Rb content of <56 ppm reported by ref. 6 for ⁸⁷Sr-enriched spike from ORNL. Both of these Rb concentrations in the ⁸⁴Sr and ⁸⁷Sr spikes are negligible for samples analyzed without chemical separation of Sr and are irrelevant for samples passed through the Sr resin. The carbonate powders were dissolved in a specific volume of high-purity Seastar™ 6 M HNO₃. Based on the certified isotopic compositions we mixed the two ⁸⁴Sr- and ⁸⁷Sr-enriched solutions to reach the DS ⁸⁴Sr/⁸⁷Sr ratio of ∼1.2 recommended by Rudge et al.¹⁶ The spike calibration procedure is described in Section 3.1.

Table 1 Isotopic abundances (%) of the Oak Ridge National Laboratory (ORNL), ISOFLEX USA Sr carbonate standards, and USGS mixed double spike (DS)

Spike ID	^84Sr	^86Sr	^87Sr	^88Sr
a Errors are ± 2SD.
ORNL ^84Sr	99.64 ± 0.01	0.14 ± 0.01	0.03 ± 0.01	0.19 ± 0.01
Isoflex ^87Sr	<0.005	0.8	90.8 ± 0.02	8.4
USGS DS1a	52.2265 ± 0.0010^a	0.48830 ± 0.00009	43.2529 ± 0.0009	4.0323 ± 0.0007

---

2.4. TIMS analysis

Strontium isotope measurements were conducted at the USGS Denver radiogenic isotope laboratory, using the static mode on the TRITON (ThermoFisher Scientific) 9-collector mass spectrometer which operates in positive ion mode with a 10 kV acceleration voltage and 10¹¹ ohm resistors for the Faraday cups. Between 500 and 1000 ng of Sr were loaded on outgassed Re filaments with a Ta₂O₅ activator. All measurements were conducted in fully automatic mode with the targeted ⁸⁸Sr intensity of 8 V, which was commonly achieved at the filament temperature of about 1400 °C. Strontium sulfate and carbonate samples measured without chromatographic separation of Sr provided intense and stable ion beams, similar to chemically purified Sr separates. An ion beam of ⁸⁵Rb was monitored to correct for the interfering ⁸⁷Rb. Measured ⁸⁵Rb/⁸⁶Sr ratios in accepted analyses never exceeded a value of 1 × 10⁻⁵. A mass-spectrometric run comprised 14 blocks of data and each block consisted of 11 scans with an 8 seconds integration time and a 3 seconds idle time. Before each block the baseline (deflected beam) was measured for 80 s and the amplifier rotation was performed. Within-run uncertainties (2 SE, 2 standard errors) for conventionally fractionation-corrected isotope ratios using the accepted ⁸⁸Sr/⁸⁶Sr value of 8.375209 were typically ∼0.0008% for ⁸⁷Sr/⁸⁶Sr and 0.002–0.004% for ⁸⁴Sr/⁸⁶Sr in unspiked samples. Unspiked National Institute of Standards and Technology (NIST) SrCO₃ standard SRM-987 was run after each five unknowns and its average was used to determine a normalization factor for measured ⁸⁷Sr/⁸⁶Sr values as R = ⁸⁷Sr/⁸⁶Sr_{NIST average}/0.710248. This normalization factor was then applied to the ⁸⁷Sr/⁸⁶Sr ratio of all unknowns run in the same turret of 21 samples and the errors were propagated to include the uncertainty of the correction.

2.5. Double spike algorithm and the data reduction program

The measured Sr isotope ratios of natural samples are affected by three isotopic fractionation processes, of which the first is natural and the second and third occur during chemical separation of Sr using the ion-exchange resin^4,17 and the evaporation of Sr in the ion source of the mass spectrometer.¹⁸ The magnitude of mass-dependent isotope fractionation introduced in the laboratory may be comparable to, or even significantly larger than, the natural fractionation. The DS method (internal standard) was developed^19–28 to correct for the bias (mass discrimination) introduced by chemical separation and TIMS analysis. This method relies on the laws describing mass-dependent isotope effects occurring during evaporation of atoms (molecules) in the ion source of the mass spectrometer. In its simplest form, the DS method consists of adding to an unknown sample two isotopes of the analyte (Sr in our case), which are absent in the sample.^19,29 The ratio of these added isotopes should be precisely known. If the fractionation law is the same for all isotopes of the analyzed element, it is possible to calculate the “true” isotope ratios of the sample from the known spike compositions and measured isotope ratios in unspiked and double-spiked sample aliquots. Because pure artificial isotopes are not always available, in the general case of double isotope dilution, the isotopic analysis is possible for elements with at least four stable isotopes, which is the case for Sr.

Various mathematical models have been proposed to describe the mass discrimination in the ion source.^23,30,31 The exponential model of Wasserburg et al.³¹ is considered to be the most accurate. According to this model, the “true” isotope ratios of Sr (X_N, Y_N, and Z_N) in the sample are related to their measured values (X^*_N, Y^*_N, and Z^*_N) by

In eqn (1)h is a fractionation factor in the unspiked run, m₈₄, m₈₆, m₈₇, and m₈₈ are the atomic masses of corresponding Sr isotopes, and , , and . Similarly, the ratios measured in the spiked run are

Indices N and M in eqn (1) and (2) correspond to unspiked and spiked runs, respectively, and g is a fractionation factor in the spiked run.

Combining eqn (1) and (2) with isotope dilution equations,³² namely,

we obtain the following equations for disbalances (W_x, W_Y and W_Z) in different isotope ratios, which should be equal to zero

In eqn (4)h, g and λ are the unknowns, the subscript T denotes a spike (tracer), and λ is the mixing ratio between the sample and the spike. The algorithm for solving eqn (4) was constructed following the recommendations of Rudge et al.¹⁶ and is given in Appendix A.

A stand-alone Windows-based computer program written in Turbo Pascal on the basis of this algorithm uses two input files in *.csv format for each sample analyzed and does not require any additional software to run (i.e. Excel or Matlab). The input files consist of baseline-corrected intensities of isotopes in each spectrum for spiked (n spectra) and unspiked (m spectra) runs so that n is not necessarily equal to m. The program also corrects mass 87 for ⁸⁷Rb interference using the beam intensity at mass 85. The raw isotope ratios are calculated for each spectrum and then the isotopic ratios of each spectrum from the spiked and unspiked runs are used for calculations of the “true” ⁸⁸Sr/⁸⁶Sr and ⁸⁷Sr/⁸⁶Sr isotopic ratios, which are corrected for instrumental mass fractionation. The data processing consists of two steps: (i) the solutions are obtained using the linear model of mass discrimination (see Appendix A) and (ii) the values of mass-bias coefficients (α and β) and λ from the linear model are used as starting values for iterations in the second stage of calculations, which use the exponential mass-fractionation model. The iterations in the second stage converge rapidly and the time it takes to process an array of 154 × 154 spectra is typically less than a second. After rejection of outliers beyond a user-defined 2 or 3σ thresholds, the calculated mean values and their standard deviations as well as standard errors are reported for “true” ⁸⁸Sr/⁸⁶Sr_N, δ⁸⁸Sr, and “true” ⁸⁷Sr/⁸⁶Sr_N in the sample. These “true” ratios are calculated using fractionation factors in the unspiked and spiked runs and the mixing ratio between the sample and the spike as it is described in Appendix A. The “true” ⁸⁷Sr/⁸⁶Sr_N ratio is not equivalent to the traditional ⁸⁸Sr/⁸⁶Sr-normalized ⁸⁷Sr/⁸⁶Sr ratio reported by studies of radiogenic Sr isotope ratios because it includes the “combination” of the radiogenic effect and the natural mass-dependent fractionation.

The program also calculates the Sr concentration in the sample, plots a histogram of calculated δ⁸⁸Sr values, and uses the Monte Carlo method^33,34 to calculate the predicted minimum standard deviation of δ⁸⁸Sr based on the precision of the mass-spectrometric analysis and on the measured ⁸⁴Sr/⁸⁶Sr in the sample/spike mixture. The program also has an additional mode for the DS calibration using the same exponential model of mass-fractionation. In the DS calibration mode two *.csv input files are used (i) measured raw intensities of masses 84, 85, 86, 87, and 88 for the pure spike isotope composition run and (ii) the raw intensities data for a SRM-987 + DS mixture run. This Windows-based stand-alone program is available upon request from N. Mel'nikov (E-mail: nickm46@mail.ru).

3. Results

3.1. Spike calibration

The double spike calibration was conducted in two steps. First, a DS aliquot containing a large amount of ⁸⁴Sr (about 200 ng) was used to conduct a single mass-spectrometric analysis of pure spike to obtain preliminary estimates of its isotopic composition. The raw fractionation-uncorrected data for a pure spike run and the raw data for a series of DS + SRM-987 mixtures were used to calculate fractionation-corrected values of isotope abundances of ⁸⁴Sr, ⁸⁶Sr, ⁸⁷Sr, and ⁸⁸Sr in the DS (Table 1) using the program described in the previous section. The SRM-987 solution used in the mixtures had a known concentration, so the analyses of the mixture were also used to evaluate the total Sr concentration in the DS spike (0.028 μmol Sr per g). The mixtures were prepared with targeted ⁸⁴Sr/⁸⁶Sr values in the range from 1 to 5. The optimal ⁸⁴Sr/⁸⁶Sr ratio in a DS + sample mixture of ∼5 was estimated based on predicted standard deviations of δ⁸⁸Sr values for our DS compositions (Fig. 1A), but lower values are preferred in order to conserve the DS. For a typical ⁸⁴Sr/⁸⁶Sr error of ∼0.002% in an unspiked run, a decrease of ⁸⁴Sr/⁸⁶Sr in a spiked run from the optimal value of 5 to 1 causes only a slight decrease in the anticipated precision of the δ⁸⁸Sr (SD value increases from 0.03 to 0.04‰; Fig. 1B). For a ⁸⁴Sr/⁸⁶Sr error of ∼0.001% and optimal spiking, the within-run δ⁸⁸Sr SD can be further reduced to 0.016‰, but it can only be achieved in practice by higher signal to noise ratios that would require about four times larger ion beam intensities than those typical of our runs.

Fig. 1 (A) Predicted error (within-run standard deviations, SD) of the calculated delta ⁸⁸Sr value as a function of the measured ⁸⁴Sr/⁸⁶Sr ratio in the sample + double spike mixture. Numbers by the curves in italics are relative errors of mass-spectrometric analyses. (B) The effect of the decreased ⁸⁴Sr/⁸⁶Sr ratio in the spiked run from the optimal value of ∼5 to 1 on the predicted error of the delta ⁸⁸Sr value.

Because the DS isotope abundances estimated in the first step of the DS calibration are based on a single pure DS run, we consider these values to be preliminary estimates of the DS isotopic composition. The second step of the spike calibration was conducted using the DS + SRM-987 mixtures together with a series of unspiked SRM-987 runs to calculate more statistically representative δ⁸⁸Sr values in the SRM-987 measured with our spike. Preliminary estimates of the DS isotopic composition obtained from the pure DS runs were used for this DS calibration step. This DS calibration routine was repeated periodically and the running average δ⁸⁸Sr value of −0.024 ± 0.009‰ (2SE, n = 61) for about two years of SRM-987 measurements is given in Table 2. Because the expected value for δ⁸⁸Sr in SRM-987 is equal to zero, all results for unknowns were corrected for the −0.024‰ bias and the final error was propagated to include its 2SE uncertainty of 0.009‰ (Table 2).

Table 2 Radiogenic and stable Sr isotopic compositions of various terrestrial water, rock, and mineral samples determined by DS-TIMS

Sample ID	Sample type	Sampling location/source	Number of replicates	^87Sr/^86Sr^a	±2SE	δ ^87Sr^b ‰	±SD‰	δ ^88Sr‰	±SD‰	±2SE‰	δ ^87Sr/δ^88Sr
a Conventionally calculated values corrected for mass-fractionation using ^88Sr/^86Sr = 8.375209 and normalized for the instrumental bias using ^87Sr^86Sr = 0.710248 in NIST SRM-987. b This parameter is not a useful geochemical tracer (see text for discussion). c n.a. – not applicable. d Long-term average used to adjust δ^88Sr data for unknowns.
Standards
SRM-987	SrCO3, NIST Sr isotope standard	Spex Industries, Inc., Metuchen, NJ	61	n.a.^c	n.a.	n.a.	n.a.	−0.024^d	0.032	0.009	n.a.
SRM-607	Potassium feldspar (KFsp) NIST standard	Kingman Feldspar mine, Arizona	6	1.200680	6 × 10^−5	0.154	0.017	0.180	0.021	0.017	0.86
NASS-6	NRC Canada, sea water standard	Sandy Cove, Nova Scotia	8	0.709179	5 × 10^−6	0.164	0.007	0.378	0.013	0.009	0.43
EN-1	CaCO3, USGS standard, shell of giant clam Tridacna gigas	Bikini Atoll, Enewetak lagoon, S. Pacific	28	0.709176	3 × 10^−6	0.114	0.009	0.259	0.018	0.007	0.44
MAPS-4	USGS standard, synthetic Ca3(PO4)2, modern bone proxy	n.a.	8	0.7078	6 × 10^−6	0.030	0.006	0.071	0.011	0.008	0.42
MAPS-5	USGS standard, synthetic Ca3(PO4)2, fossilized bone proxy	n.a.	6	0.70791	5 × 10^−6	0.078	0.009	0.162	0.018	0.014	0.49
BCR-2	USGS standard, Columbia River basalt	Bridal Veil Flow Quarry, Oregon	3	0.705004	5 × 10^−6	0.146	0.005	0.277	0.009	0.010	0.53
BHVO-2	USGS standard, Hawaiian basalt	Halemaumau Crater, Hawaii	3	0.703469	5 × 10^−6	0.137	0.005	0.254	0.008	0.009	0.54
G-3	USGS standard, granite	Sullivan Quarry, Rhode Island	3	0.709970	5 × 10^−6	0.177	0.003	0.338	0.005	0.006	0.53
Biogenic samples
Acan-1	SrSO4, Acantharia cyst	Bahamas, N. Atlantic	8	0.709173	4 × 10^−6	0.088	0.013	0.165	0.026	0.018	0.53
Acrop-1	Aragonite CaCO3, ∼120 ka-old Acropora palmata coral	Haiti, Carribian	3	0.709167	9 × 10^−6	0.070	0.010	0.161	0.020	0.023	0.43
Cono-V77	Early Ordovician conodonts, apatite	Nevada	3	0.708931	6 × 10^−6	−0.526	0.010	−1.059	0.020	0.023	0.50
Cono-V4	Early Silurian conodonts, apatite	Nevada	3	0.708176	6 × 10^−6	−0.449	0.003	−0.859	0.007	0.008	0.52
SP-5A	Early Mississippian Lower crenulata conodonts, apatite	Bridger Range, Montana	4	0.708183	5 × 10^−6	−0.064	0.002	−0.130	0.004	0.004	0.49
PNR-1	Middle Devonian conodonts, apatite	Pinyon Range, Nevada	6	0.707951	5 × 10^−6	0.045	0.004	0.104	0.009	0.007	0.43
Cono-V109	Late Mississippian conodonts, apatite	Alaska	6	0.708008	5 × 10^−6	0.138	0.009	0.305	0.018	0.015	0.45
BCT-14	Conodont Early marginifera, apatite	Pahrangat Range, Nevada	6	0.708329	6 × 10^−6	−0.200	0.010	−0.348	0.019	0.016	0.57
ST-E	Miocene shark (megalodon) tooth, enamel, apatite	S. Carolina	2	0.709001	6 × 10^−6	0.044	0.009	0.095	0.018	0.025	0.46
ST-D	Miocene shark (megalodon) tooth, dentine, apatite	S. Carolina	4	0.709014	6 × 10^−6	0.115	0.004	0.250	0.007	0.007	0.46
DT-1	Dolphin tooth (bulk), apatite	Sarasota Bay, Florida	4	0.709091	9 × 10^−6	−0.157	0.007	−0.287	0.013	0.013	0.55
Water samples
Salsbury 24-35-1H	Produced formation water (brine) from shale	Bakken Formation, Montana	4	0.710789	6 × 10^−6	0.700	0.004	1.373	0.007	0.007	0.51
State 21-28H	Produced formation water (brine) from shale	Bakken Formation, N. Dakota	4	0.710805	6 × 10^−6	0.672	0.007	1.301	0.014	0.014	0.52
PW1	Produced formation water (brine) from limestone	Charles Formation, Montana	6	0.708002	6 × 10^−6	0.055	0.019	0.133	0.032	0.026	0.41
Average of 4 samples	Groundwater	Dunn County, N. Dakota	4	n.a.	n.a.	0.172	0.028	0.354	0.055	0.055	0.49
Rock and mineral samples
Cel-1	SrSO4, celestite	Kara-Kum Desert, Turkmenistan	8	0.707758	1 × 10^−5	0.475	0.009	0.928	0.018	0.012	0.51
MAD-1	SrSO4, celestite	Madagascar	4	0.708053	6 × 10^−6	−0.018	0.013	−0.034	0.026	0.026	0.54
MAD-2	SrSO4, celestite	Madagascar	4	0.708073	6 × 10^−6	−0.011	0.012	−0.022	0.023	0.023	0.48
OH-1	SrSO4, celestite	Ohio	6	0.708521	6 × 10^−6	0.053	0.012	0.126	0.020	0.016	0.42
FI-1	SrCO3, strontianite	Fidalgo Island, Washington	6	0.704818	6 × 10^−6	0.034	0.016	0.063	0.030	0.025	0.53

---

3.2. Data for standards and unknowns

In addition to the NIST SRM-987 Sr isotope standard, we analyzed several other standards as well as unknown water and mineral samples. The results of these analyses are presented in Table 2 and in Fig. 2. A typical run with an optimal sample/spike ratio shows a symmetrical distribution of individual δ⁸⁸Sr values (Fig. 3) with a standard deviation of ∼0.05–0.06‰. The standard error of the mean, calculated by our program and by the DS-toolbox,¹⁶ SE = SD/√n, where n is a total number of individual within-run δ⁸⁸Sr values, is not the best representation of the precision for our analyses. Weighted averages for replicate analyses that used within-run 2SE as a weighing factor were calculated using the Isoplot program.³⁷ Theoretically, if the scatter of the replicate analyses is caused by random within-run errors, the mean square of weighted deviates (MSWD) value should be equal to one. For our measurements MSWD is ≫1 in all cases, thus indicating the presence of a substantial external error. For example, δ⁸⁸Sr values for eight replicate unspiked runs of the NASS-6 standard calculated with data for a single spiked DS + NASS-6 run gave an MSWD value of 188 (probability of fit = 0) (Fig. 4A). An even larger value of MSWD = 586 (probability of fit = 0) was obtained when the δ⁸⁸Sr values for a single unspiked run were calculated with nine separate spiked runs (Fig. 4B). However, the MSWD value is <1 and the probability of the fit is >0 when the 2SE error of ±0.03‰ was ascribed to individual δ⁸⁸Sr values (Fig. 4C). The external SD values calculated for several replicate analyses of the same unknown samples were ≤0.02‰ in most cases (Table 2). The 2SE value of ±0.03‰ is our preferred parameter to represent the precision of the δ⁸⁸Sr data calculated from typical runs, for which no replicate analyses were conducted.

Fig. 2 A comparison of delta ⁸⁸Sr values obtained during this work by double-spike thermal ionization mass-spectrometry (DS-TIMS) with published results obtained by DS-TIMS and multi-collector inductively coupled plasma mass-spectrometry (MC-ICPMS). Two standard error (2SE) error bars are shown where they exceed symbol sizes. GW – ground water.

Fig. 3 A histogram of calculated delta ⁸⁸Sr values for a typical sample run. SE – standard error, SD – standard deviation, and n – total number of calculated delta values.

Fig. 4 Weighted averages of delta ⁸⁸Sr values for the NASS-6 seawater standard. (A) Delta ⁸⁸Sr values calculated for eight replicate analyses of the unspiked sample with a single analysis of the sample + double spike mixture. (B) Delta ⁸⁸Sr values calculated for nine replicate analyses of sample + double spike mixtures with a single unspiked sample analysis. For both (A) and (B) calculated within-run standard errors (SE) were used as a weighting parameter. (C) The same data as in (A), but an internal 2SE of ±0.03 permil was used as a weighing factor.

Our mean δ⁸⁸Sr value of 0.378 ± 0.009‰ (2SE, n = 8) for the seawater standard NASS-6 (Table 2 and Fig. 2) is within the error of the 0.381 ± 0.010‰ value reported for the IAPSO seawater standard by Fietzke and Eisenhauer,³ 0.370 ± 0.026‰ by Liu et al.,³⁵ and 0.386 ± 0.005‰ given for this standard by Krabbenhöft et al.⁶ The NASS-6 results are also within the error of the average δ⁸⁸Sr = 0.382 ± 0.011‰ of the seawater standard IAPSO and samples from different marine environments (shallow brackish Baltic Sea, N- and E-Atlantic, Mediterranean Sea) reported by Liebetrau et al.³⁸ Comparison of our data for seawater with previous studies shows that the DS-TIMS method and the data reduction routine presented here produce accurate δ⁸⁸Sr values.

In addition to the seawater standard, we conducted a series of replicate analyses of the USGS carbonate standard EN-1 and of two synthetic phosphate standards MAPS-4 and MAPS-5 that mimic the chemical compositions of live and fossilized bones, respectively. We also analyzed three USGS silicate standards BCR-2 (Columbia River basalt), BHVO-2 (Hawaiian basalt), and G-3 (granite). Data for the modern giant clam shell EN-1 standard (δ⁸⁸Sr = 0.259 ± 0.010‰, Table 2) show a 0.12‰ δ⁸⁸Sr offset from the modern seawater value. The synthetic standards MAPS-4 and MAPS-5 yielded lower δ⁸⁸Sr values of 0.067 ± 0.008 and 0.162 ± 0.013‰, respectively. The silicate standards BCR-2, BHVO-2, and G-3 yielded δ⁸⁸Sr values of 0.277 ± 0.014, 0.254 ± 0.013, and 0.338 ± 0.011‰, respectively (Table 2 and Fig. 2). Our DS-TIMS δ⁸⁸Sr results for these materials are within the error of published yet less precise ICP-MS data for BCR-2, BHVO-2, and G-2 USGS silicate standards.^11,39,40 Our δ⁸⁸Sr value of 0.180 ± 0.017 for the NIST SRM-607 potassium feldspar standard (Table 2 and Fig. 2) is appreciably larger than the δ⁸⁸Sr value of −0.07 ± 0.06 determined for this material by MC-ICPMS.³⁹

Several Sr minerals (celestite and strontianite) showed a wide range of δ⁸⁸Sr values from 0.928 ± 0.012 to −0.014 ± 0.017‰. Biogenic SrSO₄ from acantharia (δ⁸⁸Sr = 0.165 ± 0.023‰) shows a strong 0.23‰ offset from the modern seawater value. The variability of δ⁸⁸Sr values observed in abiogenic celestite samples indicates that the stable Sr isotope fractionation may depend not only on the mineral chemistry, but also on other parameters such as parent water Sr isotopic composition and, probably, precipitation rates, as demonstrated for synthetic calcite.¹⁰ The highest δ⁸⁸Sr value of 1.373 ± 0.007‰ was measured in a brine sample from the oil-producing Bakken Formation black shale. A brine sample from a carbonate host rock has a much lower δ⁸⁸Sr value of 0.133 ± 0.030‰. These brines are thought to be potential groundwater contaminants by produced waters. Although the origin of this large range of δ⁸⁸Sr values in brines is unknown, the observed difference between the brines and regional groundwaters (which gave a mean δ⁸⁸Sr value of 0.354 ± 0.055‰; Table 2) makes this parameter a promising tool in addition to more commonly used ⁸⁷Sr/⁸⁶Sr and elemental tracers of groundwater/brine mixing and also may help to better understand the origin of deep-seated continental brines.

The lowest δ⁸⁸Sr value of −1.059 ± 0.023‰ was measured in an Ordovician conodont sample (Table 2). This result combined with the brine data defines a total range of δ⁸⁸Sr values obtained during this work of >2.4‰, which is the widest range reported so far for terrestrial samples (Fig. 2). This range of δ⁸⁸Sr values is 80 times larger than the typical TIMS-DS external error of ≤0.03‰ demonstrated in previous studies^6,41 and in our measurements. A significant variability of stable Sr isotopes was observed in different conodont species (Table 2). A negative δ⁸⁸Sr value of −0.287 ± 0.013‰ was measured for a bulk dolphin tooth sample and a measurable difference of 0.14‰ between δ⁸⁸Sr was obtained for fossil shark tooth dentine and enamel. These “vital effects” may open the door for potential biological applications using precise stable Sr isotope data.

3.3. Are the “true” ⁸⁷Sr/⁸⁶Sr and δ⁸⁷Sr values useful geochemical tracers?

The “true” ⁸⁷Sr/⁸⁶Sr_N ratio is not equivalent to the traditional ⁸⁸Sr/⁸⁶Sr-normalized ⁸⁷Sr/⁸⁶Sr_{Sample CN} ratio reported by studies of radiogenic Sr isotope ratios because it includes the “combination” of the radiogenic effect and the natural mass-dependent fractionation. Ohno et al.¹² and Liu et al.³⁵ proposed to calculate the δ⁸⁷Sr value using a formula δ⁸⁷Sr = 1000 × {[(⁸⁷Sr/⁸⁶Sr)_N/(⁸⁷Sr/⁸⁶Sr)_SRM987 − 1] − [(⁸⁷Sr/⁸⁶Sr)_{Sample CN}/(⁸⁷Sr/⁸⁶Sr)_SRM987 − 1]}‰, which includes “true” ⁸⁷Sr/⁸⁶Sr_N in the sample, the conventionally normalized ratio (⁸⁷Sr/⁸⁶Sr)_{Sample CN} and supposedly separates the radiogenic and the natural mass-dependent fractionation effects. In its simplified form this formula transforms to δ⁸⁷Sr = 1000 × [(⁸⁷Sr/⁸⁶Sr)_N − (⁸⁷Sr/⁸⁶Sr)_{Sample CN}]/(⁸⁷Sr/⁸⁶Sr)_SRM987. This δ⁸⁷Sr value should not be confused with the δ⁸⁷Sr parameter defined in several publications (e.g.ref. 36) as deviation of conventionally normalized ⁸⁷Sr/⁸⁶Sr measured in a sample from the ⁸⁷Sr/⁸⁶Sr in the modern seawater.

The δ⁸⁸Sr and δ⁸⁷Sr values for all samples except the SRM-607 NIST standard show a very good linear correlation (Fig. 5) with an R² value of 0.9964. The regression line goes through the origin of the coordinates and has a slope of ∼0.5. According to Ohno et al.¹² and Liu et al.³⁵ this relationship should mean that the natural mass-fractionation effects are a factor of two smaller for ⁸⁷Sr/⁸⁶Sr than for ⁸⁸Sr/⁸⁶Sr, which is expected considering the mass differences of isotopes and should provide evidence for natural mass-dependent isotope fractionation for both ⁸⁷Sr and ⁸⁸Sr. However, as it is shown in Appendix B, δ⁸⁸Sr and δ⁸⁷Sr values are not independent and the way the δ⁸⁷Sr value is calculated makes it a function of the δ⁸⁸Sr value. The observed linear correlation and δ⁸⁷Sr ≈ 0.5 × δ⁸⁸Sr relationship are artifacts of the measured ⁸⁷Sr/⁸⁶Sr ratios of most samples being close to this ratio in the NIST SRM-987 standard. These relationships should not hold for samples with significantly more radiogenic Sr than in the NIST standard. Indeed, data for the NIST potassium feldspar standard SRM-607, which contains radiogenic Sr with ⁸⁷Sr/⁸⁶Sr ≈ 1.20 (Table 2), confirm this reasoning because its δ⁸⁷Sr ≈ 0.86 × δ⁸⁸Sr, but not ∼0.5 × δ⁸⁸Sr as it is for other samples, which have ⁸⁷Sr/⁸⁶Sr ratios of ∼0.7 (close to the ⁸⁷Sr/⁸⁶Sr in the NIST SRM-987 standard; Table 2). Our conclusion is that the natural mass-fractionation effect and the radiogenic effect cannot be separated for the “true” ⁸⁷Sr/⁸⁶Sr and, therefore, the δ⁸⁷Sr value calculated using the approach by Ohno et al.¹² and Liu et al.³⁵ does not bear any useful independent information. The “true” ⁸⁷Sr/⁸⁶Sr value obtained by the DS-TIMS or any other external normalization method combines both the radiogenic and mass-dependent fractionation effects, and thus, may be less useful as an isotope tracer compared to the conventional ⁸⁷Sr/⁸⁶Sr radiogenic tracer.

Fig. 5 The delta ⁸⁸Sr (δ⁸⁸Sr) versus delta ⁸⁷Sr (δ⁸⁷Sr) diagram for samples analyzed during this study (data from Table 2). δ⁸⁷Sr is calculated using a formula from Ohno et al.¹² and Liu et al.³⁵ (see Appendix B). R – correlation coefficient.

4. Conclusions

We used a ⁸⁷Sr–⁸⁴Sr double spike to eliminate the effects of isotope fractionation during ion chromatographic separation of Sr and TIMS analysis and precisely measure the δ⁸⁸Sr values of natural materials. A Sr-specific user-friendly computer program was developed for the double-spike data reduction. It was confirmed that a digestion routine using a mixture of 0.02 M hydroxylamine–HCl and 2 N nitric acid can be successfully applied to Sr sulfates, and the TIMS analysis of these Sr-rich minerals can be conducted without the chromatographic separation and purification of Sr. Our DS-TIMS δ⁸⁸Sr data for a variety of standards and unknowns show external reproducibility of better than 0.02‰ (1SD). Observed agreement of our seawater data with previous studies shows that the method presented here produces accurate results.

The mass-fractionation effect and the radiogenic ingrowth effect cannot be separated for ⁸⁷Sr/⁸⁶Sr and, therefore, the δ⁸⁷Sr based on the “true” ⁸⁷Sr/⁸⁶Sr determined using external correction for mass-dependent instrumental discrimination in DS-TIMS or MC-ICPMS does not bear any useful information about ⁸⁷Sr mass-fractionation in nature.

A total range of δ⁸⁸Sr values reported here is ∼2.4‰, which is the widest range observed so far in terrestrial samples. This range of δ⁸⁸Sr values is 80 times larger than the typical DS-TIMS external error thus demonstrating a potential of the δ⁸⁸Sr isotope tracer in combination with the traditional radiogenic ⁸⁷Sr/⁸⁶Sr tracer for studying a variety of biological, hydrological, and geological processes.

Appendix A

To solve eqn (4) in the main text, an initial estimate of values for the unknowns h, g (fractionation factors in the unspiked and spiked runs, respectively) and λ (the mixing ratio between the sample and the spike) is required. These estimated values are obtained using a linear model of mass-fractionation,⁴² which is based on a geometric representation of the DS problem.²⁵ According to the linear model the measured isotope ratios X^*_N = ⁸⁴Sr/⁸⁶Sr, Y^*_N = ⁸⁷Sr/⁸⁶Sr, and Z^*_N = ⁸⁸Sr/⁸⁶Sr are linked with the “true” isotope ratios X_N, Y_N, and Z_Nviaand

In eqn (A.1) and (A.2)α and β are fractionation factors in the unspiked and spiked runs, respectively. These equations define two straight lines in the XYZ isotope ratios space which intercept a third line defined by eqn (3) in the main text. The plane containing the line (A.1) and the point of the spike isotopic composition is defined by

PX + QY + RZ + S = 0. (A.3)

The coefficients P, Q, R, and S in the plane eqn (A.3) are calculated first and then the unknown α, β and λ values are obtained. Because both the DS isotopic composition and the line defined by eqn (A.1) belong to the (A.3) plane, the solution for the coefficients P, Q, R, and S is

The value of the coefficient β in eqn (A.2) is defined by the intersection of the line (A.2) with the plane (A.3) and is given by

The isotope ratios X_M, Y_M, and Z_M are calculated using formula (A.2), after which the isotope ratio X_N is defined by

where , , M = −Y^*_N/2X^*_N, and N = 3Y^*_N/2,

The values of α and λ are calculated via

Eqn (A.1) and (A.2) are used to calculate values of Z_N and Z_M, which then are used to redefine linear model mass-fractionation factors α and β in terms of the exponential model of mass-discrimination (exponential model mass-fractionation factors h and g) so that h = ln(Z^*_N/Z_N)/P_Z and g = ln(Z^*_M/Z_M)/P_Z.

Eqn (4) in the main text, which is repeated below

is solved by iterations using the Jacobian matrix composed of derivatives of functions W_x, W_Y and W_Z with respect to h, g and λ variables, namely,

For brevity, the elements of the Jacobian matrix are denoted by

The functions W_x, W_Y and W_Z are calculated using the starting values for the variables h, g, and λ from (A.5) and (A.7) based on the linear mass-fractionation model. If one or more of these values exceed a predefined threshold (e.g., 10⁻¹²), then the next iteration step starts. For each iteration step, the determinant Q of the matrix (A.8) is calculated using the current values of the h, g and λ. Then, the new values for h, g and λ, denoted by h′, g′ and λ′, are calculated from

where

Finally, the values of h, g and λ are recalculated again until the user-prescribed accuracy is achieved.

Appendix B

A “true” ⁸⁷Sr/⁸⁶Sr value determined by the DS-TIMS or external correction using bracketing by MC-ICPMS reflects both the radiogenic effect and the isotopic fractionation effect in nature. In order to separate these two effects the δ⁸⁷Sr parameter was introduced,^12,35 which is calculated using the formula δ⁸⁷Sr = [(⁸⁷Sr/⁸⁶Sr_Sample)/(⁸⁷Sr/⁸⁶Sr)_NIST − 1]_ext. × 1000 − [(⁸⁷Sr/⁸⁶Sr_Sample)/(⁸⁷Sr/⁸⁶Sr)_NIST − 1]_int. × 1000, where subscripts “ext.” and “int.” represent the externally corrected (“true”) and internally corrected (conventional) isotopic data, respectively. It was also stated that this δ⁸⁷Sr value, similar to δ⁸⁸Sr, shows the degree of natural mass-dependent isotopic fractionation. Ohno et al.¹² and Liu et al.³⁵ reported δ⁸⁷Sr ≈ 0.5 δ⁸⁸Sr for each sample from their datasets, and also present a linear correlation between the δ⁸⁷Sr and δ⁸⁸Sr values (Fig. 2b in Ohno et al.¹²), and interpret this correlation as representing mass-dependent isotopic fractionation of both ⁸⁷Sr and ⁸⁸Sr that occurred in those samples. We also observed similar correlation (Fig. 5), but question this interpretation because δ⁸⁷Sr and δ⁸⁸Sr values are not independent and are mathematically linked through the calculation process.

Using notations accepted in our paper (see Appendix A) the δ⁸⁷Sr formula from Ohno et al.¹² and Liu et al.³⁵ can be rewritten as

δ⁸⁷Sr = [(Y_N − Y_C)/Y_SRM987] × 1000, (B.1)

where Y_N and Y_C are “true” and conventionally corrected for instrumental discrimination ⁸⁷Sr/⁸⁷Sr ratios, respectively.

According to the exponential model of mass-fractionation,

where f is a conventional correction factor. This correction factor f = [−ln(Z_SRM987/Z^*_N)]/P_Z. The measured isotope ratios Y^*_N = ⁸⁷Sr/⁸⁶Sr and Z^*_N = ⁸⁸Sr/⁸⁶Sr are linked with the “true” isotope ratios Y_N, and Z_Nviaeqn (1) in the main text, which are repeated here for the reader's convenience

It can be shown that from the δ⁸⁷Sr definition given by (B.1)

where

For a set of samples with non-radiogenic Sr for which Y_N/Y_SRM987 ≈ 1, eqn (B.4) corresponds to a straight line passing through the origin of coordinates in the δ⁸⁸Sr–δ⁸⁷Sr plot with a slope of ½, because δ⁸⁸Sr ≪1000 and V ≈ 0.5 for realistic h and f values. Also, according to (B.4) the ratio δ⁸⁷Sr/δ⁸⁸Sr should be >0.5 in samples with more radiogenic Sr than in SRM-987 and <0.5 in samples that are less radiogenic than SRM-987. Therefore, the observation of δ⁸⁷Sr ≈ ½ δ⁸⁸Sr reported in our paper as well as in Ohno et al.¹² and Liu et al.³⁵ and the presence of good linear correlation between these values is just an artifact of small variations of ⁸⁷Sr/⁸⁶Sr values around the value of this ratio in the NIST standard SRM-987 and, therefore, cannot be interpreted as a proof of natural mass-dependent fractionation for the ⁸⁷Sr.

Acknowledgements

The authors are grateful to B.A. Galperin for his helpful suggestions on the mathematical aspects of the work. We also thank Z. Peterman and R. Bernstein for providing some samples for this study. A. Pietruszka and three anonymous JAAS reviewers provided detailed comments that helped to improve the manuscript. Any use of trade, product, or firm names in this publication is for descriptive purposes only and does not imply endorsement by the U.S. Government.

References

1. P. J. Patchett, Earth Planet. Sci. Lett., 1980, 50, 181–188.
2. P. J. Patchett, Nature, 1980, 283, 438–441.
3. J. Fietzke and A. Eisenhauer, Geochem., Geophys., Geosyst., 2006, 7(8).
4. T. Ohno and T. Hirata, Anal. Sci., 2007, 23, 1275–1280.
5. L. Halicz, I. Segal, N. Fruchter, M. Stein and B. Lazar, Earth Planet. Sci. Lett., 2008, 272, 406–411.
6. A. Krabbenhöft, J. Fietzke, A. Eisenhauer, V. Liebetrau, F. Böhm and H. Vollstaedt, J. Anal. At. Spectrom., 2009, 24, 1267–1271.
7. G. F. de Souza, B. C. Reynolds, M. Kiczka and B. Bourdon, Geochim. Cosmochim. Acta, 2010, 74, 2596–2614.
8. K. J. Knudson, H. P. Williams, J. E. Buikstra, P. D. Tomczak, G. W. Gordon and A. D. Anbar, J. Archaeol. Sci., 2010, 37, 2352–2364.
9. Y. Sawaki, T. Ohno, M. Tahata, T. Komiya, T. Hirata, S. Maruyama, B. F. Windley, J. Hand, D. Shud and L. Yong, Precambrian Res., 2010, 176, 46–64.
10. F. Böhm, A. Eisenhauer, J. Tang, M. Dietzel, A. Krabbenhöft, B. Kisakürek and C. Horn, Geochim. Cosmochim. Acta, 2012, 93, 300–314.
11. F. Moynier, A. Agranier, D. C. Hezel and A. Bouvier, Earth Planet. Sci. Lett., 2010, 300, 359–366.
12. T. Ohno, T. Komiya, Y. Ueno, T. Hirata and S. Maruyama, Gondwana Res., 2008, 14, 126–133.
13. C. Collinson, State of Illinois Geological Survey Circular, Department of Registration and Education, Urbana, State of Illinois, 1963, http://www.ideals.illinois.edu/bitstream/handle/2142/35164/collectionprepar343coll.pdf?sequence=2.
14. H. Puchelt, I. J. Setiobudi and Z. Fresenius, Anal. Chem., 1989, 335, 692–694.
15. D. De Muynck, G. Huelga-Suarez, L. Van Heghe, P. Degryse and F. Vanhaecke, J. Anal. At. Spectrom., 2009, 24, 1498–1510.
16. J. F. Rudge, B. C. Reynolds and B. Bourdon, Chem. Geol., 2009, 265, 420–431.
17. O. I. Takao, O. Hideki, H. Morikazu and K. Hidetake, Sep. Sci. Technol., 1992, 25, 631–643.
18. T. Suzuki, C. Kanaki, M. Nomura and Y. Fujii, Rev. Sci. Instrum., 2012, 83, 02B506.
19. L. A. Dietz, C. F. Pachucki and G. A. Land, Anal. Chem., 1962, 34, 709–710.
20. M. H. Dodson, J. Sci. Instrum., 1963, 40, 289–295.
21. M. H. Dodson, J. Sci. Instrum., 1969, 2, 490–498.
22. M. H. Dodson, Geochim. Cosmochim. Acta, 1970, 34, 1241–1244.
23. L. E. Long, Earth Planet. Sci. Lett., 1966, 1, 289–292.
24. W. Compston and V. M. Oversby, J. Geophys. Res., 1969, 74, 4338–4348.
25. M. J. Dallwitz, Chem. Geol., 1970, 11, 311–314.
26. N. H. Gale, Chem. Geol., 1970, 6, 305–310.
27. A. W. Hofmann, Earth Planet. Sci. Lett., 1971, 10, 397–403.
28. R. Russell, J. Geophys. Res., 1971, 76, 4949–4953.
29. W. Todt, R. A. Cliff, A. Hanser and A. W. Hofmann, in Earth Processes: Reading the Isotopic Code, ed. A. Basu and S. Hart, American Geophysical Union Geophysical Monograph, 1996, vol. 95, pp. 429–437.
30. W. A. Russell, D. A. Papanastassiou and T. A. Tombrello, Geochim. Cosmochim. Acta, 1978, 42, 1075–1090.
31. G. J. Wasserburg, S. B. Jacobsen, D. J. DePaolo, M. T. McCulloch and T. Wen, Geochim. Cosmochim. Acta, 1981, 45, 2311–2323.
32. R. K. Webster, in Methods in Geochemistry, ed. A. A. Smales and L. R. Wagner, Interscience, N-Y, 1960, pp. 202–246.
33. G. M. Anderson, Geochim. Cosmochim. Acta, 1976, 40, 1533–1538.
34. N. N. Mel'nikov, Geochem. Int., 2010, 48, 876–886.
35. H.-C. Liu, C.-F. You, K.-F. Huang and C.-H. Chung, Talanta, 2012, 88, 338–344.
36. L. A. Derry, L. S. Keto, S. B. Jacobsen, A. H. Knoll and K. Swett, Geochim. Cosmochim. Acta, 1989, 53, 2331–2339.
37. K. R. Ludwig, Berkeley Geochronological Center Special Publication, 2003, 4, 70.
38. V. Liebetrau, A. Eisenhauer, A. Krabbenhöft, J. Fietzke, F. Böhm, A. Rüggeberg and K. Gürs, Geochim. Cosmochim. Acta, 2009, 73, A762.
39. B. L. A. Charlier, G. M. Nowell, I. J. Parkinson, S. P. Kelley, D. G. Pearson and K. W. Burton, Earth Planet. Sci. Lett., 2012, 329–330, 31–40.
40. J.-L. Ma, G.-J. Wei, Y. Liu, Z. Y. Ren, Y.-G. Xu and Y.-H. Yang, Chin. Sci. Bull., 2013, 58, 3111–3118.
41. N. Shalev, I. Segal, B. Lazar, I. Gavrieli, J. Fietzke, A. Eisenhauer and L. Halicz, J. Anal. At. Spectrom., 2013, 28, 940–944.
42. N. N. Mel'nikov, Geochem. Int., 2005, 43, 1228–1234.

---

Footnote

† The δ⁸⁸Sr value in permil (‰) is calculated versus the accepted ⁸⁸Sr/⁸⁶Sr_SRM987 value of 8.375209 in NIST standard SRM-987 via formula δ⁸⁸Sr = [(⁸⁸Sr/⁸⁶Sr)_N/(⁸⁸Sr/⁸⁶Sr)_SRM987 − 1] × 1000‰.

---