Isotopic (δ¹³C, δ¹⁸O) Analysis of Small Amounts of Carbonate in Silicate Rocks by the Continuous Flow Isotope Ratio Mass Spectrometry Method

Abstract

An experimental study of the main factors affecting the accuracy of oxygen and carbon isotopic analysis in carbonates dispersed in silicate matrix is carried out. Artificial 1, 2, 5, and 10% mixtures of quartz with carbonates with different isotopic parameters (KH-2, Ko, MCA-8) were analyzed by continuous flow isotope ratio mass spectrometry (CF IRMS). It is established that, in addition to the influence of the instrumental nonlinearity, the results are affected by two factors: trace amounts of CO₂, constantly present in the system (the blank effect) and the presence of chemically neutral silicate particles (the matrix effect). The blank effect depends on the isotopic parameters of the sample and has very little influence on the estimated carbonate content in the rock. The matrix effect, on the contrary, strongly affects the estimated carbonate content, and produces the isotopic shift towards underestimated contents of heavy ¹³C and ¹⁸O isotopes. It is shown that this effect is related to the processes occurring near the CO₂–acid–quartz interface, which are accompanied by kinetic fractionation of carbon and oxygen isotopes. Both effects are dependent on the amount of silicate matrix in the system and most clearly manifested during analysis of carbonate-poor rocks. When the carbonate content in the rock is about 1–2%, deviations from the true δ¹³C and δ¹⁸O values can reach the first ppm, while carbonate content obtained by chromatographic peak calibration can be underestimated by 20–40%.

INTRODUCTION

Carbon and oxygen (δ¹³C, δ¹⁸O) isotopic analysis of carbonates decomposed in orthophosphoric acid is conventional for isotopic geochemistry and was developed more than 70 years ago (McCrea, 1950). However, the problems associated with the analysis of carbonates dispersed in silicate rocks are still poorly understood. This type of analysis is relevant to, e.g., igneous rocks that were contaminated, at some point of their history, by sedimentary matter (Zhao et al., 2001; Dubinina et al., 2010); products of metamorphism involving carbon dioxide; or rocks processed with aqueous carbonate fluid, e.g., during ore formation (Zheng et al., 2003, 2000; Dubinina et al., 2019). Analysis of silicate–carbonate material is also pertinent to studies of kimberlites (Giuliani et al., 2014; Galimov, 1991; etc.) and serpentinized ultramafic rocks of oceanic crust (Alt and Shanks III, 2006). The carbonate content in such rocks can vary from the first percent to hundredths of a percent; i.e., it is required to analyze samples where carbonates are surrounded by a large amount of silicate matrix. Despite such a wide range of applications, not much has been done to study limitations of the method, except for works devoted to selective acid decomposition of carbonates (Walters et al., 1972; Spotl and Wennemann, 2003; Rosenbaum and Sheppard, 1986; Liu et al., 2018; Du and Song, 2020; Sreenivasan et al., 2023 etc.).

Isotopic analysis of small carbonate contents can be performed using the modern method of continuous helium flow isotope ratio mass spectrometry (CF IRMS), which allows very small amounts of substance to be analyzed (Brand, 1996, 2004; Breitenbach and Bernasconi, 2011; Paul and Skrzypek, 2007; Skrzypek and Paul, 2006; Nelson, 2000; Revesz and Landwehr, 2002; Werner and Band, 2001). Application of the standard variant GasBenchII (Thermo, Germany) provides isotopic analysis of carbonate carbon and oxygen from 100- to 250-μg samples in terms of pure calcium carbonate (Finnigan, 2004); the improved version reduces that amount to 50 μg (Fiebig et al., 2005; Velivetskaya et al., 2009). An additional advantage of the CF IRMS method is the possibility of estimating the amount of analyzed gas (Zha et al., 2010).

Silicate rocks containing trace amounts of carbonate are analyzed in a bulk sample ground to a fine powder. To provide the necessary amount of carbonate substance, the sample weight is increased by tens and even hundreds of times. As a result, there are a large number of silicate matrix particles in the vicinity of the reaction occurring between carbonate and acid. The particles can affect the accuracy of both isotopic analysis and carbonate content determination. Obviously, the results of the analysis in this case are affected by several factors, studied to varying degrees. First of all, it is easily controlled instrumental nonlinearity of measurements of chromatographic peaks of different area and breadth (Spotl and Vennemann, 2003). The effect of blank, the residual amounts of CO₂ and water adsorbed on the vial and sample surface, is less studied (Zha et al., 2010; Nelson, 2000), and the effect of the silicate matrix, which is present directly in the reaction zone of carbonate with orthophosphoric acid, is almost completely unknown (Zha et al., 2017; Sreenivasan et al., 2023). The silicate matrix is inert with respect to orthophosphoric acid, but, since it is a highly dispersed system with a large surface area, it can play a special and very prominent role. Apart from the obvious fact that a large amount of matrix should lead to an increased blank, the matrix itself may exhibit specific effects and, while the effect of blank is obvious and can be considered as the presence of trace amounts of extraneous CO₂ gas in the analyzed sample, the role of chemically neutral matrix in the “silicate–CO₂–orthophosphoric acid” system is largely unexplored.

A detailed study of artificial silicate–carbonate mixtures (Zha et al., 2010) showed that the accuracy of determining δ¹³C and δ¹⁸O drops in the presence of a significant amount of silicates; the measured values are systematically biased from the true ones. This conclusion was based on an analysis of mixtures prepared from the same carbonate standard with quartz (Zha et al., 2010). The authors established a threshold sample size (≈70 μg of pure CaCO₃) and identified bias in δ¹⁸O and δ¹³C values measured from lesser amounts of material for the influence of traces of CO₂ and moisture adsorbed on the sample surface.

Despite abundant evidence of the matrix effect manifested in analysis of multicomponent carbonate and silicate–carbonate mixtures (Walters et al., 1972; Liu et al., 2018; Zha et al., 2017; Al-Aasm et al., 1990), this factor has not been specifically studied. Experiments performed on artificial carbonate–silicate mixtures (Zha et al., 2010) did not isolate this effect because the mixtures were prepared from the same carbonate, making it impossible to distinguish the blank effect (impurities of residual CO₂) from the matrix effect (presence of “neutral” silicate or carbonate particles in the analytical space).

The aim of this work is to evaluate each factor influencing the results of analysis of carbonates in a silicate matrix. For this purpose, we have studied silicate–carbonate mixtures prepared from carbonates with different δ¹³C and δ¹⁸O values. Obviously, the blank effect should manifest itself in an isotope shift toward specific values of δ¹³C and δ¹⁸O, and this would be differently reflected in carbonates with different isotopic parameters. The matrix effect, being kinetic in nature, should not depend on the isotopic parameters of the mixtures. Thus, it is possible to distinguish between the blank effect and the matrix effect. The effect of instrumental nonlinearity associated with the measurement of small amounts of analyzed gas should also be independent of isotopic parameters, but this effect can be reliably calibrated and accounted for.

METHODOLOGY OF THE EXPERIMENT AND ANALYSIS OF CARBONATE–SILICATE MIXTURES

Experimental Mixtures

Laboratory standard quartz (Polaris, δ¹⁸O = 13.0‰) was used as a silicate matrix for the preparation of experimental mixtures. Carbonates were represented by three samples, which were previously often used as reference substances: KH-2 limestone and Ko and MSA-8 calcites. Their isotopic characteristics are summarized in Table 1. Each of these samples was used to prepare mixtures with 1, 2, 5, and 10 wt % carbonate content. The mixtures were homogenized by grinding under a layer of alcohol in a polished agate mortar to a fine powder. After grinding, the mixtures were dried in a drying oven at 105°С and stored in an desiccator. Prior to analysis, the prepared samples were additionally baked (105°С, 2 h) directly in borosilicate glass vials. The hot vials were hermetically sealed with standard rubber septa lids and placed in the measuring unit of the PAL autosampler, after which standard carbonate isotope analysis in continuous helium flow was performed using the GasBenchII option. The samples of pure carbonates used for preparing the silicate–carbonate mixtures were included in respective measurement series. The sample weights of pure carbonate were chosen as far as possible with regard to the expected range of the CO₂ amount, released from the silicate–carbonate mixtures. The data obtained for the pure carbonates were used to calibrate the area of the chromatographic peaks to calculate the amount CO₂ gas coming from the sample mixtures. The characteristics of the mixtures and analytical results are summarized in Table 2.

Table 1.   Oxygen- and carbon-isotopic composition in starting materials*

Table 2.   Results of analysis of artificial silicate–carbonate mixtures

Algorithm for Isotope Measurements

We used a set of equipment (Thermo, Germany), in which the GasBenchII device with a PAL autosampler is connected to a Delta V+ mass spectrometer via a ConFlo IV gas switch. Oxygen- and carbon-isotope analysis of carbonates by CF IRMS is based on their chemical decomposition with orthophosphoric acid:

$$3{\text{CaC}}{{{\text{O}}}_{3}} + 2{{{\text{H}}}_{{\text{3}}}}{\text{P}}{{{\text{O}}}_{4}}\, \to \,3{\text{C}}{{{\text{O}}}_{2}} + 3{{{\text{H}}}_{{\text{2}}}}{\text{O}} + {\text{C}}{{{\text{a}}}_{{\text{3}}}}{{\left( {{\text{P}}{{{\text{O}}}_{{\text{4}}}}} \right)}_{2}}.$$

(1)

In contrast to conventional techniques based on vacuum purification of substances and reaction volumes, methods exploiting a continuous helium flow utilize purging of analytical volumes with a carrier gas (Paul and Skrzypek, 2006). We used high-purity helium (grade 6.0) at a flow rate of 180 mL/min for 360 s, after which specially prepared 105% orthophosphoric acid prevacuumed for 48 h was introduced into the vials (Burman et al., 2005). The acid was introduced manually along the vial wall, avoiding vertical drops and sputtering the sample. The amount of acid ensured complete coverage of the sample. An amount of 0.05 mL was added to pure carbonates, 0.1 mL to mixtures weighing up to 3 mg, and 0.2 mL to samples above 3 mg. The reaction time was 2 h at 70°C. As the reaction progressed, the released CO₂ gas flowed through the acid–gas interface into the free space of the vial filled with helium. At the end of the reaction, a portion of helium containing CO₂ extracted from the sample was withdrawn by a special measuring needle (Thermo) and fed into a moisture removal system (Nafion trap) and, then, into a chromatographic column (PoraPlot Q) heated to 70°. After chromatographic purification, a portion of CO₂ is delivered with helium flow through a ConFlo IV gas switch to the measurement system of a Delta V+ mass spectrometer.

Analytical procedure included registration of background intensities, adjustment to the peak center, triple input of the standard CO₂ and triple input of the analyzed gas portions. The errors of repeatedly measured homogeneous carbonate standards (NBS 19, NBS 18) was ±0.05 and ±0.1‰ (1σ) for δ¹³C and δ¹⁸O, respectively. Calibration of the results against the international scales V-SMOW (δ¹⁸O values) and V-PDB (δ¹³C values) was carried out by three-point normalization (Paul et al., 2007) using the international standards NBS-18 and NBS-19 and internal standard ATS (repeatedly certified homogeneous natural calcite) in each measurement series.

We applied a three-stage blank control covering the quality of vial preparation, helium purge efficiency, acid and silicate matrix purity with respect to CO₂. The first stage was performed by analyzing empty vials with a standard portion of acid at the beginning and end of each measurement series. The second step (acid purity test) was performed by measuring empty vials with different amounts (0.2–1 mL) of acid. Third step was analyzing samples (1 to 5 mg) of silicate matrix (quartz) with appropriate amount of acid added. No chromatographic peaks of CO₂ were observed at any stage.

KH-2, Ko, and MSA-8 carbonates were tested for homogeneity with respect to carbon and oxygen isotopic composition in a special calibration series, where ten sample weighs of 250 μg were analyzed (Table 1). With respect to carbon isotopic composition, all three carbonates are homogeneous within the range of 0.04–0.05‰ (1σ); with respect to oxygen isotopic composition, their homogeneity is somewhat lower, about 0.1‰ (1σ). Other measurement series revealed lower homogeneity in oxygen-isotope composition of MSA-8 calcite and KH-2 limestone and in carbon of MCA-8 calcite; however, these variations were rather random and had the order of 0.0n‰. It should be noted that the appearance of these carbonates is consistent with the difference in homogeneity of their oxygen- and carbon-isotopic compositions. MSA-8 is characterized by the largest grain size (Fig. 1a), while the heterogeneity of KH-2 limestone could be related to both the presence of impurities and the irregular grain size (Fig. 1b). Ko calcite (Fig. 1c), which turned out to be the most homogeneous in terms of isotopic parameters, is characterized by the uniform grain sizes, significantly smaller than the grains of MSA-8.

Fig. 1.

Photos of starting materials: (a) calcite MSA-8 calcite, (b) KH-2 limestone, (c) Ko calcite, and (d) Polaris v.

RESULTS

Carbonate Content in Silicate–Carbonate Mixtures Estimated by Chromatographic Peak Area

To estimate the carbonate content in the mixture, the area of one of the chromatographic peaks of the sample was used. We chose the fourth peak of the chromatogram corresponding to the first pulse of the sample coming from the vial as a reference. In contrast to the calibration based on the ion current intensity generated by mass 44 (Zha et al., 2017), we used the integrated peak area (Area All in the Isodat 3.0 software). Calibration of the correspondence of peak areas to the determined amount of CO₂ in the analyzed gas was performed by analyzing different sample weights of pure carbonates of KH-2, Ko, and MCA-8. The smallest sample of pure carbonates was ≈50 μg, which is the technical limit for manual weighing and loading of the sample into a vial. Thus, the lower limit of the calibration lines that were used to calculate carbonate content was 0.5 µm CO₂ (Table 2, Figs. 2a–2c).

Fig. 2.

Area of the fourth chromatographic sample peak (S, Vs) and expected amount of analyzed gas CO₂(0), μmol, for a mixture based on (a) KH-2, (b) Ko, and (c) MSA-8. Trend lines plotted for the fourth peak of pure carbonate samples were used to calculate ${\text{CO}}_{2}^{*}$ in silicate–carbonate mixtures.

There was a regular difference between the expected amount of CO₂ and the amount calculated from the peak area using the calibration line for all mixtures studied. In general, the analyte deficit ranged from 0.03 to 0.5 µm. We calculated the loss of analyzed gas as a percentage of the mass of the expected CO₂ amount using the following formula:

$$\Delta {\text{C}}{{{\text{O}}}_{2}},~\% = 100\left( {{\text{C}}{{{\text{O}}}_{2}}{\kern 1pt} \left( 0 \right) - {\text{CO}}_{2}^{*}} \right){\kern 1pt} {\text{/C}}{{{\text{O}}}_{2}}{\kern 1pt} \left( 0 \right),$$

(2)

where ${\text{C}}{{{\text{O}}}_{2}}{\kern 1pt} \left( 0 \right)~$ and ${\text{CO}}_{2}^{*}$ are the expected and real amounts of analyzed gas, respectively. The value of ΔCO₂ grows with decreasing carbonate content in the mixtures (Table 2). Maximum gas deficit was observed in 1 and 2% mixtures (12–43.6%); the values of ΔCO₂ in the mixtures with 2 to 10% carbonate content varied in smaller range (7–28%, Fig. 3), while CO₂ discrepancy in silicate–carbonate mixtures with higher carbonate contents (25 and 50%), as was shown by preliminary tests, were insignificant.

Fig. 3.

Losses of analyzed gaseous CO₂ as a function of carbonate content in silicate–carbonate mixtures: (a) absolute and (b) relative. Relative losses were calculated using Eq. (2).

Oxygen and Carbon Isotopic Composition of Silicate–Carbonate Mixtures

As expected, the values of δ¹³C and δ¹⁸O become distorted as the amount of CO₂ decreases. A lighter isotopic composition of carbon was observed for mixtures prepared using KH-2 and Ko carbonates, while the mixtures based on MSA-8 displayed heavier carbon compositions. Deviations in oxygen-isotopic composition for all mixtures are directed one way, towards a decrease of δ¹⁸O values, reaching 3.6‰ (Table 2). Small deviations in the isotopic composition (up to ≈0.7‰) were also observed for small samples (≈50 μg) of pure carbonates. The magnitude of deviations in the isotopic composition of a sample relative to its original composition can be expressed by analogy with the isotopic fractionation factor: α: 10³Lnα(C–C⁰) (≈δ¹³С_MEAS– δ¹³С_INI) and 10³Lnα(О–О⁰) (≈δ¹⁸О_MEAS – δ¹⁸О_INI), where С, О and С⁰, О⁰ are the carbon- and oxygen-isotopic compositions of the carbonate in the mixture and of the original pure carbonate, respectively (Table 2) and indices MEAS and INI refer to measured and initial parameters, respectively. The values of 10³Lnα(C–C⁰) and 10³Lnα(О–О⁰) relative to the amount of gas measured $\left( {{\text{CO}}_{2}^{*}} \right)$ are given in Fig. 4. Apparently, the experimental points obtained for mixtures prepared from the same carbonate form common trends, no matter whether the ${\text{CO}}_{2}^{*}$ value is lowered by decreasing the sample or by decreasing the carbonate concentration in the mixture.

Fig. 4.

Deviation of (a) δ¹³C and (b) δ¹⁸O measured in silicate–carbonate mixtures from the true values depending on the amount of analyzed gas. Dotted line is confidence interval (2σ).

Analysis of distorted isotopic parameters shows that, in the region of low ${\text{CO}}_{2}^{*}$ values, they are influenced by the CO₂ source common for all mixtures, with an approximately constant isotopic composition of carbon and oxygen. The δ¹³C values in this source (blank) are significantly higher than the values in MSA-8 (–31.30‰) and lower than those in KH-2 (+2.0‰). Since the minimum carbon isotopic shifts in the low ${\text{CO}}_{2}^{*}$ region are observed for Ko-based mixtures, it can be concluded that the value of δ¹³C blank is close to δ¹³C(Ko) = –8.5‰. As for the oxygen-isotopic composition, with an isotopic shift revealed in all mixtures directed towards decreasing values of 10³Lnα(О–О⁰), but manifested to different degrees, it can be assumed that the δ¹⁸O value of the total blank component is close to the δ¹⁸O values of the MSA-8 and Ko carbonates (19.48 and 16.50‰), but differs significantly from the oxygen isotopic composition of the KH-2 carbonate (27.73‰) (Fig. 4b).

The data obtained can be compared with experiments of Zha et al. (2010), for which, instead of ${\text{CO}}_{2}^{*}$ values, we use conversion to the absolute amount of CaCO₃ (mg) contained in the sample. This is necessary because the cited work does not provide data on the areas of the chromatographic peaks, and the approximate calibration of the amount of gas was carried out by the intensity of the ion current of the mass 44. Nevertheless, the deviations obtained for the δ¹³C and δ¹⁸O as a function of the absolute amount of carbonate in the vial are similar in magnitude (Figs. 5a, 5b). Zha et al. (2010) only reported one-way deviation of the measured values from the true ones, because they used the same carbonate with constant isotopic parameters (δ¹³C = +1.61‰ and δ¹⁸O = +18.96‰) in the experiment. The values of δ¹³C in the KH-2 carbonate and δ¹⁸O in the Ko carbonate are close to the composition of this carbonate. The deviations given by (Zha et al., 2010) and shown in Fig. 5 point in the same direction and are close to the deviations obtained for these mixtures. The carbonates with other isotopic parameters may show more or less strong deviations, or even change sign, depending on the isotopic parameters of the blank. As the amount of gas analyzed increases, the role of the blank gradually levels off from the strong influence at ${\text{CO}}_{2}^{*}$ < 0.5 µm to almost complete absence at ${\text{CO}}_{2}^{*}$ < 1.5 μmol.

Fig. 5.

Deviation of (a) δ¹³C and (b) δ¹⁸O measured in silicate–carbonate mixtures from the true values depending on the absolute content of CaCO₃ in the silicate–carbonate mixture. Data from the present work and experimental results from (Zha et al., 2010) are presented. Vertical dashed line is amount of CaCO₃ (70 µg) recommended by Zha et al. (2010) as a threshold amount for isotopic analysis of silicate–carbonate mixtures.

DISCUSSION

Taking into Account Nonlinearity Related to the Amount of Analyzed Gas

This parameter can be minimized using mass-spectrometer ion-source settings and estimated by measuring portions of the same CO₂ gas, differing in peak area. Test measurements were performed in the course of the prolonged experiment when isotopic ratios were measured in 43 portions of gas from the same vial filled with a 0.3% mixture of He with CO₂. As the amount of CO₂ in the vial was gradually decreased, the sample peaks had an increasingly smaller area and reach background levels at the end of the test. The results of such a test for δ¹³C values are shown in Fig. 6 in comparison with the data obtained by measuring silicate–carbonate mixtures prepared on the basis of KH-2 and MSA-8. It can be seen that the nonlinearity effect with the used instrument settings leads to a slight overestimation of the measured values of δ¹³C by 0.2–0.4‰ in the region of low peak areas and that this effect is small compared to the variations obtained when analyzing silicate–carbonate mixtures. Similar results were obtained for δ¹⁸O values, except that their overestimation was slightly stronger, up to 0.6–0.7‰ in the region of extremely low peak areas. The effect of instrumental nonlinearity is manifested uniformly for the values δ¹³C and δ¹⁸O and does not depend on the isotopic parameters of the measured gas, which allows it to be taken into account. In our case, the effect of nonlinearity is manifested in the region of peak areas of the first Vs and the corresponding correction averages 0.2–0.4‰ for all carbonate mixtures, which is extremely small compared to the effects caused by other factors.

Fig. 6.

Deviations of ¹³C values from the true value as a function of peak area: (1) instrumental nonlinearity determined by the prolonged experiment; (2, 3) data for silicate–carbonate mixtures prepared on the basis of KH-2 and MCA-8, respectively.

Blank Effect

This factor is clearly manifested at decreasing absolute amount of analyzed gas, CO₂(*), when differences in sign and absolute value of the parameters 10³Lnα(C–C⁰) and 10³Lnα(О–О⁰) begin to show (Table 2, Fig. 4). The data in Fig. 4 suggest that the effect of the blank on δ¹³C and δ¹⁸O is evident at ${\text{CO}}_{2}^{*}$ < 1.0 μmol and at ${\text{CO}}_{2}^{*}$ < 2 m, respectively, which corresponds to 100 and 200 μg of pure carbonate. In the case of carbon, our estimates are close to the threshold value of 70 μg established by (Zha et al., 2010). In the case of oxygen, we believe that the threshold amount should be increased to 200 μg if the standard GasBenchII option is used. The fact that the oxygen-isotope system appears to be more sensitive to the blank effect than the carbon-isotope system has been attributed to the presence of trace amounts of water (Zha et al., 2010), including that condensed on the vial walls above the acid surface (Wachter and Hayes, 1985). Otherwise, carbon-dioxide particles adsorbed by the vial walls and sample surface are responsible for the blank effect. Considering that the influence of adsorption on the vial walls can be neglected, since it is a constant value for all experiments, it can be assumed that the blank contribution must be proportional to the mass of the solid sample in the vial:

$${\text{C}}{{{\text{O}}}_{2}}\left( {{\text{blank}}} \right)\sim {{\gamma }}{\kern 1pt} \left( {\text{b}} \right){\kern 1pt} M,$$

(3)

where γ(b) is a constant coefficient equal to the content of adsorbed CO₂ gas in 1 mg of the mixture and M is the mass of the sample.

Despite purging with high-purity helium and a high-quality preparation of vials and starting materials (Paul and Skrzypek, 2006; Nelson, 2000) CO₂ blank is extremely difficult to remove from the reaction space. We estimate that the blank contribution may be about 1–3% of the total amount of gas analyzed, corresponding to a value of γ(b) ≈ 0.005 μmol CO₂. At ultralow (less than 1%) carbonate contents, the measured isotopic parameters of the sample can be significantly distorted because increasing the mass of the suspension, according to relation (3), raises the blank contribution.

Analyzing carbonate–silicate mixtures different in isotopic parameters, we evaluated the isotopic parameters of the blank, which turned out to be close to the composition of Ko carbonate, deviating by about 0.5‰ in both carbon and oxygen towards lighter isotopic compositions (Fig. 4). To a first approximation, the δ¹³C and δ¹⁸O values of the blank are about –9 ± 1 and +16 ± 1‰, respectively. The carbon-isotopic composition of the blank is close to the δ¹³C values of atmospheric carbon dioxide (Gruber et al., 1999; NOAA ESRL GMD). The magnitude of δ¹⁸O in blank CO₂ is probably controlled to some extent by equilibrium with atmospheric moisture, but this cannot be established precisely because moisture composition can vary significantly in the ground-level atmosphere and is only partially determined by the mean isotopic composition of precipitation and air temperature (Jacob and Sonntag, 1991, Bastrikov et al., 2014).

Effect of Silicate Matrix

Laboratory standard quartz (Polaris) prepared from a large fragment of vein quartz from the Zhelannoe deposit (Polar Urals) was used as a matrix in our experiments. The quartz has a homogeneous oxygen-isotope composition (δ¹⁸O = 13.05 ± 0.05‰) and a minimal number of inclusions. Figure 1d shows a photo of Polaris quartz grinded in an agate mortar, taken during preparation of the mixtures, i.e. exactly as the matrix present in the analytical space. Very few particles exceed the size of 20 µm, predominant size being 5–10 µm, which, apparently, is responsible for the matrix effect, clearly manifested in losses of the analyzed gas (Table 2) in the most carbonate-poor mixtures.

In contrast to the blank effect, expressed as an additional, albeit very small, contribution of extraneous gas to the sample, the matrix effect is manifested in the opposite way, i.e., by partial retention of CO₂ in the part of the vial that is occupied by the mixture of the sample with orthophosphoric acid. The total effect associated with the action of the blank and matrix can be expressed as a balance equation for the amount of ${\text{CO}}_{2}^{*}$ measured in the sample:

$${\text{CO}}_{2}^{*} = {\text{C}}{{{\text{O}}}_{{\text{2}}}}\left( 0 \right) + {\text{C}}{{{\text{O}}}_{2}}\left( {\text{b}} \right) - {\text{C}}{{{\text{O}}}_{2}}\left( {\text{m}} \right),$$

(4)

where CO₂ (b) and CO₂ (m) are the amount of CO₂ added to the sample due to the blank and removed from the sample due to the matrix effect, respectively. By analogy with Eq. (3), the following should be true for the matrix effect:

$${\text{C}}{{{\text{O}}}_{2}}{\kern 1pt} \left( {\text{m}} \right)\sim {{\gamma }}{\kern 1pt} \left( {\text{m}} \right){\kern 1pt} M,$$

(5)

where γ(m) is a constant coefficient equal to the amount of CO₂ removed from the reaction space when a sample has a mass of 1 mg. The balance equation, taking into account the isotopic shift produced by both entry of the blank into the sample and the loss of the sample material due to the matrix effect, can be written as follows:

$$\begin{gathered} \left( {{{\delta }^{{\text{m}}}}} \right)\left( {{\text{C}}{{{\text{O}}}_{{\text{2}}}}\left( {\text{m}} \right)} \right) = \left( {{{\delta }^{0}}} \right)\left( {{\text{C}}{{{\text{O}}}_{{\text{2}}}}\left( {\text{0}} \right)} \right) \\ + \,\,\left( {{{\delta }^{{\text{b}}}}} \right)\left( {{\text{C}}{{{\text{O}}}_{{\text{2}}}}\left( {\text{b}} \right)} \right) - \left( {{{\delta }^{*}}} \right)\left( {{\text{CO}}_{2}^{*}} \right), \\ \end{gathered} $$

(6)

where the values δ⁰, δ^b, δ*, and δ^m are the carbon- or oxygen-isotopic composition of CO₂ of the initial carbonate, blank, analyzed gas, and gas lost due to matrix effect, respectively. The combination of Eqs. (3)–(5) leads to the following important relation:

$$\frac{{{\text{CO}}_{2}^{*}}}{M} = {{\gamma }}{\kern 1pt} \left( 0 \right) + {{\gamma }}{\kern 1pt} \left( {\text{b}} \right) - {{\gamma }}{\kern 1pt} \left( {\text{m}} \right),$$

(7)

where γ(0) is the amount of CO₂ that theoretically should be extracted from 1 mg of the sample. Relationship (7) allows parameter γ(m) to be found in the case in which parameter γ(b) is known or assumed. Assuming that γ(b) is approximately constant for all experimental mixtures and is 0.005 µm CO₂ and using the blank isotopic parameters given above (see Section 3.2), we calculated the isotopic parameters of the gas removed due to the matrix effect using Eq. (6). The nonlinearity effect was taken into account in the calculations according to the calibration carried out in the prolonged testing experiment.

The resulting δ¹³С(m) and δ¹⁸О(m) estimates in the CO₂ gas lost by the sample due to matrix effects are higher than the δ¹³С(0) and δ¹⁸О(0) values in the original carbonates. The degree of this increase is almost equal for the carbon- and oxygen-isotopic compositions, indicating kinetic fractionation of carbon and oxygen isotopes in the process of CO₂ capture by the matrix (Fig. 7).

Fig. 7

. Calculated deviation of δ¹³C and δ¹⁸O in the gas lost due to the matrix effect from the true values.

It is important that the direction of isotopic shifts 10³*Lnα(O(m)–O(0)) and 10³Lnα(C(m)–C(0)) does not depend on isotopic parameters of the analyzed gas, i.e. the matrix effect, unlike the blank effect, is directed towards retention of CO₂ molecules that are enriched in heavy ¹³C and ¹⁸O isotopes. This result can be explained in at least two ways. The first explanation was proposed by (Zha et al., 2010), who suggested that some of the CO₂ molecules do not have time to diffuse through the layer of viscous orthophosphoric acid and do not get into the free space to be taken for measurements. Indeed, kinetic fractionation during diffusion of CO₂ molecules through the acid layer can lead to enrichment of the gas remaining in the acid with CO₂ molecules with heavier isotopic composition. However, it should be borne in mind that the elevated temperature in the reaction zone (70°C) significantly reduces the viscosity of the acid and that the reaction time (2 h) is quite sufficient for effective gas yield even from its maximum volume (0.2 mL) used in our experiments. The second option is partial adsorption of CO₂ on the surface of solid particles wetted with orthophosphoric acid. This process can also lead to enrichment of adsorbed gas with heavy ¹³C and ¹⁸O isotopes.

To test the first option, we conducted an experiment with an additional batch of samples of pure KH-2 carbonate, which had different sample weights, from ≈100 to ≈250 μg in increments of about 50 μg. Three samples of each mass were prepared, a standard amount of orthophosphoric acid (0.05 mL) was added to two of them, and the maximum amount used in this work (0.2 mL) was added to the third. All other experimental parameters were identical to those we used for studying silicate–carbonate mixtures and performing peak area calibrations. The results of this experiment are shown in Fig. 8 as a dependence of the chromatographic peak area on the mass of the KH-2 carbonate sample. If the losses of the analyzed gas were due to diffusion in the acid, the experiments with a larger amount of acid would have produced weaker dependence than those obtained using a standard volume of acid (similar to the patterns shown in Figs. 2a–2c). However, it can be seen that, in the absence of the silicate matrix, we obtain the same amounts of analyzed gas from the same carbonate suspensions regardless of the volume of acid added. Consequently, the loss and distortion of isotopic parameters of the measured gas are neither related to the diffusion of CO₂ in the acid nor to its amount, as was suggested by Zha et al. (2010), but precisely to the presence of silicate matrix particles. This effect does not depend on the composition of the analyzed carbonates and is always expressed in the underestimation of the measured values of δ¹³C and δ¹⁸O, since the adsorbed gas is enriched in heavy isotopes of carbon and oxygen (Fig. 7).

Fig. 8.

Experimental results on the effect of the volume of orthophosphoric acid on the amount of gas released from pure carbonates: (1) peak areas of samples with 0.05 mL of acid added; (2) peak areas of samples with 0.2 mL of acid added.

The influence of matrix particles surrounded by acid has been repeatedly discussed in studies of the selective dissolution of mixtures of carbonate minerals, primarily calcite and dolomite (Walters et al., 1972; Spotl and Wennemann, 2003; Rosenbaum and Sheppard, 1986; Liu et al., 2018; Du and Song, 2020; Sreenivasan et al., 2023). The matrix in these experiments was dolomite or another carbonate with a lower dissolution rate than calcite. For example, it has been suggested that some of the CO₂ may form microscopic bubbles accumulating around the matrix particles in the viscous acid; therefore, microvibration of the autosampler platform could have prevented the effect (Sreenivasan et al., 2023). All of this work was carried out at reduced temperatures to allow dissolution of calcite without cross contamination by dolomite, where the acid is indeed viscous. Had the matrix effect been related to a bubble mechanism, however, there would need to be isotopic fractionation between the small and large CO₂ bubbles released during the reaction of calcite with acid, with the heavy isotopes ¹³C and ¹⁸O being concentrated in the small bubbles, which, in our opinion, is unlikely.

The matrix effect that we observed, in principle, corresponds to the idea of adsorption, in which kinetic effects are directed toward decreasing both δ¹³C and δ¹⁸O in the gas leaving the acid-covered matrix zone. The same isotopic shifts have been repeatedly documented in selective carbonate dissolution for the first portions of CO₂ produced by calcite dissolution when the matrix mass in the system was at its maximum (Walters et al., 1972; Liu et al., 2018; Du and Song, 2020; Al-Assam et al., 1990; Baudrand et al., 2012). This effect was independent of the isotopic composition of the calcite used to make the experimental mixtures. Taking into account that the matrix effect is accompanied by a significant absorption of the analyzed gas, we can conclude that the matrix–acid–gas interface plays a key role in the matrix effect. Further experiments, e.g., studying various matrix material, are required to investigate this interesting problem.

The Role of the Studied Effects in Distorting the Results of Analysis of Silicate–Carbonate Mixtures

The main sources of errors, as well as the values of isotopic shifts caused by the influence of each of the considered factors, are different. The smallest is the contribution of nonlinearity of instrument measurements in the region of small gas contents. It is constant for specific instrument settings and the specific state of the measuring system, and it is easy to calibrate and take into account.

The blank effect significantly distorts the isotopic parameters of the measured gas in the samples without affecting the accuracy of measured concentrations. It is most strongly manifested in the samples with low (1–5%) carbonate content, reaching the first ppm. In contrast, the matrix effect strongly affects measured carbonate contents in the mixture, with little effect on the results of isotopic determinations. Carbonate contents less than 10 and 5% are expected to be underestimated by 20 and 30–40%, respectively. The isotopic shift associated with the matrix effect is always directed towards the depletion of the analyzed gas in ¹³C and ¹⁸O isotopes, and the shift is not very significant due to the weak isotopic effect of adsorption. Sometimes, the matrix effect can be compensated by the blank effect if the latter works in the opposite direction. If the isotopic parameters (δ¹³C and δ¹⁸O) of the blank are significantly lower than those in the sample, the factors are added together and their mutual effect leads to a significantly lighter isotopic composition of the measured gas. Such a case is observed, e.g., for mixtures based on KH-2 (Figs. 4–7). Since this carbonate is close in isotopic composition to carbonates of marine sedimentary origin (Table 1), one can expect analytical errors to appeal when analyzing rocks containing carbonate material with sedimentary characteristics.

The importance of the effects can be shown by the example of calculated isotopic shifts accompanying the process of high-temperature decomposition of carbonate with typical sedimentary characteristics (Fig. 9). We calculated the shift of δ¹³С and δ¹⁸О values in the residual carbonate with KH-2 isotopic parameters (Table 1) as it decarbonizes at 600°C (Bottinga, 1986; Chacko and Deines, 2008). Along with the calculated curve, the values of δ¹³С* and δ¹⁸О* measured in the mixtures prepared with KH-2 are plotted in Fig. 9. The measured compositions almost exactly correspond to the calculated curve; i.e., these data can be erroneously interpreted as the result of high-temperature decomposition of sedimentary carbonate with CO₂ removal, with a process depth of up to 60%. In fact, we are dealing with an artifact due to blank and silicate matrix effects.

Fig. 9.

Calculated line of isotopic parameter alteration of KH-2 carbonate during its decomposition with CO₂ removal at 600°. The fractionation factors of carbon and oxygen isotopes in the CO₂–CaCO₃ system are taken from Bottinga (1968) and (Chacko and Deines, 2008). Numbers near the line are the fraction of remaining carbonate after partial decomposition (% of the initial amount). Dots are the measured carbon- and oxygen-isotopic compositions of samples of silicate–carbonate mixtures prepared on the basis of KH-2.

CONCLUSIONS

The results of experiments lead to the conclusion that the total error of isotopic analysis of carbonate-poor silicate rocks (up to 10 wt % in terms of CaCO₃) is composed of three main factors: instrumental nonlinearity of measurements of small amounts of gas, the blank effect, and the silicate-matrix effect. Each of these effects can be accounted for, but only to a certain extent. Minimizing the blank effect can be done by reducing the volume of the vials (Breitenbach and Bernasconi, 2011) or by changing the heating conditions of the samples. However, matrix effects can only be accounted for if the exact mechanism of interaction between the matrix surface and CO₂ is understood. Obviously, ignoring these effects can lead to significant distortion of the measured results and affect their interpretation. At the moment, silicate rocks with low carbonate content cannot be analyzed with the same accuracy as pure carbonates, at least by standard methods. The data-correction approach based on measuring variable portions of pure carbonate standards, as well as the use of very large sample weights, are not helpful because of the possible influence of matrix and blank. At carbonate contents of about 1–2%, deviation of δ¹³C and δ¹⁸O from the true values can reach the first ppm and the carbonate content obtained from the chromatographic peak area can be underestimated by up to 40%.

The analysis of silicate rocks with low carbonate content requires a special approach, such as mandatory assessment of the nonlinearity of instrumental measurements and measures to minimize the blank contribution—in addition to special requirements for clean utensils and reagents, sample baking prior to analysis is recommended; some other measures may also be taken. The matrix effect can be detected only if the carbonate content in the sample is known in advance, therefore one should keep in mind the possible manifestation of this effect and, hence, underestimated values of δ¹³C and δ¹⁸O in the case of, e.g., deficiency of the analyzed gas.