Carbon Isotopes in Magmatic Systems: Measurements, Interpretations, and the Carbon Isotopic Signature of the Earth’s Mantle

Abstract

Carbon isotopes in magmatic systems serve as powerful tracers for understanding magma evolution, mantle processes, the deep carbon cycle, and the origin of Earth’s carbon. This review provides a comprehensive overview of carbon isotope measurements and behavior in magmatic systems, highlighting recent technological advancements and scientific insights. We begin by examining methods for measuring δ¹³C in volcanic gases, vesicles, glasses, melt, and fluid inclusions. We then explore the behavior of carbon isotopes in magmatic systems, especially during magmatic degassing. Finally, we evaluate what recent advances mean for our understanding of the carbon isotope signature of the Earth’s upper mantle.

1. Introduction

Magmatic processes have been instrumental in shaping Earth’s history, from planetary accretion and differentiation to whole-mantle convection, plate tectonics, and atmospheric degassing. Investigating the behavior of carbon isotopes in magmatic systems offers valuable insights into these fundamental processes. Carbon possesses two stable isotopes, ¹²C and ¹³C, with natural abundances of approximately 98.9% and 1.1%, respectively. The large relative mass difference of about 8% between these isotopes can be expected to result in measurable fractionation during magmatic processes, making carbon isotopes an effective tracer for studying the Earth’s interior and the carbon cycle.

Carbon isotope data are reported as δ¹³C values, which represent the deviations in parts per thousand (‰) of the ¹³C/¹²C ratio of a sample from that of the Pee Dee Belemnite (PDB) standard (from the Upper-Cretaceous Peedee Formation of South Carolina). The δ¹³C value is defined as follows:

$$\delta {}^{13}C\left({\displaystyle \frac{{\left(\frac{{}^{13}C}{{}^{12}C}\right)}_{Sample}}{{\left(\frac{{}^{13}C}{{}^{12}C}\right)}_{PDB}}}-1\right)\times 1000$$

(1)

A negative δ¹³C value indicates that the sample is depleted in ¹³C relative to the PDB standard. Conversely, a positive δ¹³C value signifies enrichment in ¹³C relative to the PDB standard. Early research on carbon isotopes in geological and biological materials [1] revealed a wide range of isotopic signatures, with δ¹³C values spanning from +10 to −36‰. This diversity was partly attributed to variable isotope fractionation by living matter (see Degens [2] for a review of early studies). Soon after, distinct patterns emerged, with marine limestones clustering around δ¹³C = ~0‰, organic sediments around δ¹³C = ~−27‰, and carbonatites and diamonds around δ¹³C = ~−5‰ (e.g., Degens [2] and references therein). This tri-partite view of the isotopic signature of the carbonate, organic, and mantle reservoirs of carbon will have a profound influence on subsequent views of carbon in magmatic systems with variable contribution of these three reservoirs becoming the default interpretation for observed variations in the carbon isotopic composition of volcanic gases (e.g., Refs. [3,4]; see also compilation of literature data in Figure 1 of Deines [5]).

This review aims to synthesize the current state of knowledge on carbon isotopes in magmatic systems, highlight recent developments, and identify key areas for future research. We first give an overview of methods used to measure carbon isotopes in magmatic systems in the gas phase and the melt. We then look at experimental and theoretical constraints on the behavior of carbon isotopes in magmatic systems. Finally, we look at current constraints on the carbon isotopic signature of the upper mantle.

2. Carbon Isotope Measurements in Magmatic Systems

2.1. Carbon Isotope Measurements in Volcanic Gases

The study of carbon isotopes in volcanic gases began in the mid-20th century, coinciding with the development of isotope ratio mass spectrometry (IRMS). One of the earliest studies was conducted by Craig [1], who measured carbon isotopes in geothermal gases from Yellowstone National Park. In the second half of the 20th century, advances in IRMS technology enabled more precise measurements of δ¹³C in volcanic gases, and such measurements started being performed on volcanoes across the globe such as at Mauna Loa [6], Kilauea [6,7], Usu [8], Satsuma-Iojima [8], Erta’ Ale [9], Asal rift [10], Merapi [11], Momotombo [11], Vulcano [12], White Island [13], and Etna [14] volcanoes.

Table 1. Early (1950s–1990s) C isotope measurements in high-temperature (>600 °C) volcanic gases.

Volcano	Location	Temperature (°C)	δ13C (‰ vs. PDB)	Reference
Mauna Loa	Hawaii	700–800	−13.1	[6]
Kilauea	Hawaii	905–935	−7.82	[7]
Usu	Japan	750	−4.4	[8]
Satsuma-Iojima	Japan	786	−5.5	[8]
Erta’ Ale	Afar	1130	−6.4	[9]
Asal rift	Afar	1070	−6	[10]
Merapi	Indonesia	850	−3.9	[11]
Momotombo	Nicaragua	880	−2.6	[11]
Etna	Italy	1090	−4.0	[14]

shows a compilation of δ¹³C values obtained on high-temperature (>600 °C) volcanic gases by early studies. We focus on high-temperature volcanic gases as they are the most faithful representation of true magmatic gases (e.g., Refs. [15,16,17,18]). It is clear from this non-exhaustive compilation alone that the carbon isotopic composition in magmatic gases can vary widely (from −2.6 to −13.1‰). We explore the reason behind these variations in the next section, and first present the methodology used to collect and analyze these gases.

2.1.1. Traditional Technique (Direct Sampling + IRMS)

The so-called “direct sampling” method for collecting volcanic gases was first developed by Charles Joseph Sainte-Claire Deville and Felix Leblanc [19,20] during their pioneering studies on Vesuvius, the Phlegraean Fields, Mount Etna, and the Aeolian Islands. Their approach involved using custom-made, pre-evacuated glass tubes, which they filled with volcanic gases by breaking the tubes open at the sampling site. After sealing the tubes, they transported them back to the laboratory for analysis. This foundational concept—filling a pre-evacuated container with volcanic gases—remains a cornerstone of volcanic gas sampling to this day.

In modern practice, the method has been refined but retains the same basic principle. A tube, typically made of titanium, stainless steel, or quartz, is inserted into a volcanic vent (such as a fumarole or skylight) to ensure that the sampled gases are uncontaminated by atmospheric air (Figure 1A). The volcanic gases are then flushed through the tube for approximately 10 min to purge any atmospheric gases from the sampling line. At the end of the tube, the gas is directed into a pre-evacuated sampling flask, usually made of glass or, for helium analysis, lead glass [21]. Once the flask is filled, it is sealed and transported to the laboratory for further analysis.

Before conducting isotope ratio mass spectrometry (IRMS) analysis, the volcanic gases must be purified to isolate CO₂ for isotopic measurement. This purification is typically achieved using a vacuum extraction line, where CO₂ is separated from other gases through cryogenic trapping and release. The purified CO₂ is then analyzed for its carbon isotope ratio (δ¹³C) using IRMS, which remains the gold standard for high precision δ¹³C measurements.

2.1.2. Novel Approach (Dilute Samples + IRIS)

The traditional method of direct sampling involves collecting gas sampled directly from the volcanic vent. While this approach is effective, it poses significant risks due to the high concentration of volcanic hazards near the active vent. Several tragic incidents have highlighted these dangers, including the 14 January 1993 eruption of Galeras volcano, where six volcanologists on a gas sampling expedition and three tourists lost their lives [23]. Another limitation of the traditional method is that collection of gases free of any atmospheric contamination is not always feasible. In environments such as lava lakes or gas-filled craters, atmospheric dilution of the volcanic gases is inevitable.

In recent years, a novel approach using dilute gas sampling has emerged, reducing the need for close-proximity sampling and expanding the range of volcanoes suitable for carbon isotope measurements. This method employs the Keeling-plot technique [24], where volcanic gas samples, collected with variable amount of atmospheric air dilution, define a mixing line on a δ¹³C vs. 1/CO₂ plot between pure ambient air CO₂ and pure volcanic CO₂ (Figure 1). The isotopic composition of the volcanic CO₂ is then determined by the y-intercept of a linear best-fit through the data. When paired with isotope ratio infrared spectroscopy (IRIS), which saw the development of field-deployable instruments in the early 2000s, this approach can deliver real-time measurements. The technique was first successfully applied to high-temperature volcanic gases at Mt. Etna [22,25,26] and quickly gained popularity with measurements performed at Isluga [27], Lastarria [27], Turrialba [28], Aso [29], and Stromboli [30] volcanoes and during fissure eruptions in Iceland [31,32], in addition to systems emitting lower temperature volcanic gases [27,33,34].

A limitation of the Keeling-plot technique is that while it always provides a value for the δ¹³C of pure volcanic CO₂, the reliability of this value is based on an extrapolation. Consequently, it is heavily influenced by the degree of dilution in the analyzed volcanic gas samples. Proper error propagation in the extrapolation is crucial, but it can result in such high uncertainties that the measurement becomes uninformative. For example, a study at Manam volcano reported a volcanic gas δ¹³C value of −4‰ ± 9.5‰, illustrating this issue [35]. Another limitation is the potential for contamination from sources other than background atmospheric CO₂. Studies have reported contamination from car [26] and helicopter [33] exhaust as well as from CO₂ emitted from local fires [31]. Additionally, CO₂ produced by humans, animals, or plants in the vicinity can introduce contamination.

2.2. Carbon Isotope Measurements in Vesicles

Another approach to measuring the carbon isotopic composition of volcanic gases involves analyzing vesicles; gas bubbles trapped within solidified lava. This method, developed by Pineau et al. [36], involves crushing lava fragments containing gas inclusions under vacuum. In the original design, lava fragments were placed in stainless steel tubes. After evacuating the tubes, they were compressed using a press, and the released gases were collected in a vacuum line. The CO₂ was purified in the same manner as described in the previous section for volcanic gas samples and then analyzed by IRMS. In subsequent work, the crushing procedure was refined. Lava fragments have been crushed using an electromagnetically operated piston [37] (which allows for progressive crushing) or a ball mill [38] while connected to a vacuum line. A cryogenic trap immediately collects the CO₂ released, avoiding adsorption problems when the powder becomes very fine grained. An alternative approach to crushing for releasing and analyzing CO₂ trapped in vesicles is via step-heating extraction, as described in the next section.

The study of carbon isotope in CO₂ from vesicles has mostly focused on submarine and subglacial lavas as subaerial equivalents rarely retain entrapped gases. Measurements have been made at volcanoes in arc [38,39,40,41] and hotspot [42,43,44,45] contexts as well as mid-ocean ridges [36,37,46,47,48,49,50,51,52,53,54,55,56,57,58]. Measured δ¹³C_vesicle values range from −1 to −27‰ with a median of −6‰, an average of −7‰, and large overlaps between geodynamic contexts (

Table 2. Population statistics for δ¹³C measurements in natural vesicles and glasses. Vesicle data compiled from Refs. [36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58]. Glass data compiled from Refs. [37,40,43,44,50,51,55,56,57,59,60,61,62,63,64,65,66].

	Vesicle [CO2] (ppm)	Vesicle δ13C (‰)	Glass [CO2] (ppm)	Glass δ13C (‰)
All data
Average	288	−7	170	−10
1-sigma	682	4	93	5
Min	0	−27	0	−34
Max	5452	−1	800	−1
N	432	411	2474	341
Arc
Average	102	−7	103	−12
1-sigma	75	2	74	7
Min	4	−13	0	−34
Max	279	−2	362	−3
N	24	28	157	78
Hotspot
Average	265	−9	87	−12
1-sigma	707	6	101	6
Min	1	−27	0	−28
Max	5452	−1	800	−3
N	147	146	372	75
Mid-Ocean Ridges
Average	319	−5	191	−9
1-sigma	695	2	81	3
Min	0	−11	0	−24
Max	4539	−1	674	−1
N	261	237	1945	188

).

2.3. Carbon Isotope Measurements in Glasses and Melt Inclusions

2.3.1. Traditional Technique (Fusion-Extraction + IRMS)

Measuring the isotopic signature of carbon dissolved in silicate melts/glasses has proved a challenging endeavor. Early (1950s to 1980s) studies on carbon extraction from basalts all used a bulk heating/melting techniques whereby the entire sample was fused and the carbon released analyzed [1,47]. These studies systematically found low δ¹³C values that were later understood to be due to contamination. In 1984, the step-heating technique was introduced [48,59], revealing that previous bulk fusion methods had analyzed mixtures of three distinct carbon sources: surface contamination, vesicles, and dissolved carbon in the silicate glass. Since then, the step-heating technic has become the standard.

In this technique, a phenocryst-free glass fragment is weighted, cleaned (typically in dichloromethane but it should be noted that this substance is carcinogenic), and loaded onto the extraction part of a vacuum line typically made of fused quartz glass or any other material with a fusion point higher than that of the sample of interest. The system is then evacuated, and the sample is heated using an external resistance furnace. The heating is carried out in steps; no strict convention exists, but the sample will typically be heated to 400–600 °C first and then incrementally in ~100 °C steps until complete fusion (~1200 °C) (Figure 2). At each step, the CO₂ released by the sample is extracted in the vacuum line. The gases released are first oxidized (via interaction with O₂ produced by a copper oxide furnace), trapped in a liquid nitrogen trap, then transferred to a variable temperature trap, permitting CO₂ to be released in isolation from all of the other gas species, its quantity measured (using manometry), and finally trapped in a sealed container that can be transferred to a mass spectrometer for isotopic analysis by IRMS.

The step-heating technique allows for the various sources of carbon that may be present in a sample to be released and analyzed independently. It was found that carbon released around 400 to 600 °C would typically be from organic carbon present as a contaminant on the sample surface. Organic carbon is so prevalent that it can be introduced at any point from the time a sample erupts until it undergoes analysis [48,50,59,67]. The subsequent heating steps from 700 to 900 °C, if they release significant amounts of CO₂, are typically taken to represent the carbon present in vesicles [40,44,48,61]. The final heating steps, from 1000 to 1200 °C, release the dissolved carbon component (Figure 2).

The incremental step-heating technique has been highly successful, and until recently, was the sole source of data on the isotopic composition of carbon dissolved in silicate melts. Despite its effectiveness, the technique is time-consuming and resource intensive. Only three laboratories worldwide have developed extraction lines capable of performing these measurements in basaltic glasses: Royal Holloway University of London, Scripps Institution of Oceanography, and the Paris Institute of Planetary Physics (IPGP). Of these, only the line at IPGP remains functional to date.

2.3.2. Novel Approach (SIMS)

One of the most significant limitations of the fusion-extraction procedure is its destructive and bulk nature, despite being applicable to relatively small samples, just a few millimeters in diameter. This technique is also primarily limited to submarine or subglacial basalts, constraining our understanding of the carbon isotopic system in mafic melts to depths of up to 4000 m below sea level. This depth restriction is problematic because at such low pressures (around 40 MPa), most of the CO₂ has already exsolved from the melt. Consequently, the δ¹³C values preserved in the glass and vesicles significantly deviate from those in equilibrium with the mantle, as discussed in Section 3.

Secondary Ion Mass Spectrometry (SIMS) is an in situ microanalytical technique that provides micron-scale spatial resolution, enabling analysts to avoid visibly altered or crystallized areas and assess sample homogeneity. The high sensitivity of SIMS makes it ideal for determining the concentrations and isotopic compositions of volatile elements such as hydrogen [68], oxygen [69], and sulfur [70] in silicate glasses. For carbon however, the low natural abundance of ¹³C and low abundance of CO₂ in silicate glasses in general, together with difficulties in maintaining a low background signal have made its isotopic analyses particularly challenging.

The appeal of an in situ approach for measuring δ¹³C in glasses and melt inclusions that can preserve melts trapped at much greater depths is clear. Several secondary ion mass spectrometry laboratories have attempted to develop this technique. However, early efforts resulted in measurements with a very high uncertainty [71]. The development and characterization of a large set of standards together with the optimization of analytical conditions have recently led to a breakthrough in δ¹³C analyses in silicate glasses by SIMS [72]. The technique has now been applied to both melt inclusions [32,73] and natural glasses [74]. Natural glasses with CO₂ contents as low as 67 ppm have been characterized with better than 0.8‰ precision (1σ) [74]. Natural melt inclusions with CO₂ contents as low as 390 ppm have been characterized with better than 0.5‰ precision (1σ) [32].

The precision of isotopic measurements is fundamentally related to the number of counts (or ions) detected. The theoretical relationship can be understood through counting statistics, which are governed by Poisson statistics. The standard deviation (σ) of a Poisson distribution is the square root of the mean number of counts (N). Therefore, σ = √N. The relative standard deviation, which is our measure of precision, is given by the standard deviation divided by the mean number of counts: RSD = σ/N = 1/√N. If one wants to achieve a precision of ±0.5‰ on a δ¹³C analysis, a total of 4 million counts are needed on ¹³C (the number of count and precision on ¹²C will be far greater so the error on the ratio is dominated by the error on the ¹³C measurements). The results from Lee et al. [72] aligned well with these statistical expectation. Achieving the required number of counts for the desired precision can be accomplished through several methods. These include increasing the primary beam current, widening the field aperture, extending the counting time, or increasing the number of cycles. However, it is important to be aware that adjusting these parameters can have other consequences that may compromise the quality of the analysis. Increasing the beam current results in a larger crater size. Widening the aperture degrades signal quality by increasing background noise and reducing spatial resolution and exacerbating border effects as secondary ions near the sides of the crater are being collected. Additionally, an excessive counting time and number of cycles can exacerbate edge effects as the crater deepens.

The accuracy of isotopic measurements by SIMS is directly related to two key factors: (i) the characterization of reference materials, and (ii) the characterization of instrumental mass fractionation (IMF). IMF refers to the systematic bias or discrimination that occurs during the measurement of isotopic ratios due to instrumental and analytical conditions. This bias arises from variations in ionization and transmission efficiencies between isotopes, detector response, and matrix effects. Because IMF is dependent on analytical conditions, it must be characterized under the exact same conditions used to analyze unknown samples. Since the precision of an analysis is a function of the count rate, which is related to the CO₂ content, reference materials should have CO₂ contents similar to those of the unknown samples to ensure consistent analytical conditions. The study of Lee et al. [72] provided that; 31 reference silicate glasses of basaltic and basanitic compositions covering a wide range of CO₂ concentrations (380–12,000 ppm) and δ¹³C values (−28.1 ± 0.2 to −1.1 ± 0.2‰, ±1σ) that were made available to the community.

A third critical factor is the background level during analysis. Characterizing the isotopic signature of the background signal is challenging, but assuming an organic signature around −25‰, measuring a silicate glass with 1000 ppm CO₂ and a true δ¹³C value of −4‰ in an ion probe instrument with a background level equivalent to 50 ppm CO₂ would yield a measured δ¹³C value of −5‰ for the sample. Therefore, ion probe instruments routinely analyzing C-rich phases or samples mounted in epoxy mounts should not be used for carbon isotope analyses in silicate glasses. With optimal instrumental conditions, background levels as low as 1 ppm equivalent can be achieved [74]. Finally, it is essential to ensure that no drift in IMF occurs over time to maintain measurement accuracy (Figure 3B).

2.4. Carbon Isotope Measurements in Fluid Inclusions

2.4.1. Traditional Technique (Crushing-Extraction + IRMS)

Fluid inclusions are microscopic pockets of fluids trapped within minerals. The first carbon isotope measurements in fluid inclusions were conducted in the 1970s and 1980s, with studies primarily focusing on quartz [75,76,77], where fluid inclusions can be relatively large. The traditional method for CO₂ extraction and isotopic analysis of fluid inclusions is similar to that used for vesicles and glass analyses. Both crushing and heating approaches have been employed. The heating approach for fluid inclusions differs slightly from glass analysis in that the required temperatures are generally lower. This method can be performed at a single temperature increment or in steps [78,79]. Similar to glass analyses, the lower temperature steps often reveal organic carbon contamination [80,81]. The crushing approach for fluid inclusions is identical to that described for vesicles. Minerals can be crushed using various methods including a manual crusher [81], a ball mill [79], an automated piston crusher [82], or other vacuum crushing systems [83]. All of these approaches can be applied to mineral separates or single crystals, but they remain bulk and destructive methods. Even within a single crystal, multiple populations of fluid inclusions may exist [84,85,86], complicating the interpretation of carbon isotope data obtained from bulk extraction.

2.4.2. Novel Approach (Raman Spectroscopy)

Measuring the isotopic composition of individual fluid inclusions without destroying the sample is possible using Raman spectroscopy, which can distinguish between peaks for ¹²CO₂ and ¹³CO₂ [87]. While the theoretical basis for such measurements is straightforward [88], it was only recently, in 2023, that the first successful measurements in natural fluid inclusions hosted in corundum [89], pyroxene [90], and olivine [90,91] were achieved.

However, carbon isotopic measurements in fluid inclusions remain challenging. Even when the areas under the ¹²CO₂ and ¹³CO₂ peaks can be accurately resolved, calibrating these area or intensity ratios is complex. This calibration depends on the pressure [92], temperature [93], and the isotopic composition itself [93]. Controlling temperature is particularly difficult, as the laser used in Raman spectroscopy can locally heat the inclusions, requiring additional corrections to ensure accurate measurements [91].

3. Carbon Isotope Behavior in Magmatic Systems

The temptation to look at the carbon isotopic signature of volcanic gases and compare it directly to that of the mantle or even to subducted carbon components for arc volcanoes has been a constant in the last 30 years [3,4]. Such an approach, however, blissfully ignores the multiple isotopic fractionation episodes that can occur as carbon changes forms on its journey in and out of the deep Earth.

3.1. Carbon Isotopic Fractionation During Degassing

3.1.1. Isotopic Fractionation Between CO₂ Gas and Dissolved Carbon in Silicate Melts; The Javoy-Mattey Conundrum and Its Resolution

Differences in the δ¹³C values of coexisting vesicles and glass in submarine basalts provide direct evidence of local carbon isotope fractionation between the vapor and melt phases (e.g., [37,48,50,58,64]). Even before this realization, Javoy et al. (1978) [94] conducted an experimental study to determine the isotopic fractionation between dissolved carbon and CO₂ gas in basaltic melts, reporting a fractionation (1000lnα_gas-melt ≈ △¹³C_eq = δ¹³C_gas − δ¹³C_melt) between 4.0 and 4.6‰. Twelve years later, similar experimental studies by Mattey et al. in sodamelilite and MORB compositions reported a much smaller fractionation coefficient, ranging from 1.8 to 2.7‰ [95,96].

The discrepancy between these two sets of experimental results has led to significant confusion in the literature on carbon isotopes in magmas over the past decades. Knowing the isotopic fractionation factor is crucial for interpreting δ¹³C measurements in volcanic gases or glasses, as discussed in the next section. Consequently, studies reporting such measurements have had to choose which fractionation coefficient to use. Some studies adopted values close to those determined by Javoy et al., around 4.3 to 4.5‰ [37,44,47], while others used values closer to those reported by Mattey et al., around 2.3 to 2.5‰ [40,43,65]. Some studies considered both estimates [45,64], and others used intermediate values around 3.3 to 3.5‰, based either on observed differences between vesicles and glass in natural samples [58] or on the experimentally determined fractionation coefficient between CO₂ gas and carbonate melts [54,55,56,57,97]. A few studies even used entirely different values such as 1.5‰ [42].

In 2024, a new experimental study [98] measured the gas-melt carbon isotopic fractionation coefficient in silicate melts, but this time across a range of compositions, providing a clearer picture that reconciled almost all pre-existing experimental data within a single framework (Figure 4). The study found that the isotopic fractionation coefficient is strongly influenced by the melt composition, particularly the degree of polymerization (NBO/T, the ratio of non-bridging oxygens per tetrahedral cations). In highly polymerized melts (NBO/T ≈ 0), the isotope fractionation coefficient is 0‰, consistent with previous experiments in rhyolites [99]. In contrast, in depolymerized melts (NBO/T > 1), the fractionation coefficient is around 3 to 3.5‰, aligning with previous experiments in nephelinite [100] and natrocarbonatite [97]. For NBO/T values between 0 and 1, the experimental data define a trend consistent with the Mattey [95,96] experiments, best fitted by the equation 1000lnαg-m = 3.251 × NBO/T + 0.026, or alternatively, expressed using simply SiO₂ and Al₂O₃, the two most abundant network forming cations, the equation becomes 1000lnαg-m = −0.087 × (SiO₂ + Al₂O₃)wt% + 7.968 [98].

The mechanism proposed by Lee et al. [98] to explain the transition in the isotope fractionation coefficient over a specific structural/compositional range has to do with carbon speciation in silicate melts. Carbon in silicate melts can exist as molecular CO₂ or CO₃²⁻ (carbonate ion). Spectroscopic studies in glasses have long shown that CO₂ exists exclusively as molecular CO₂ in rhyolite glasses and as CO₃²⁻ in basaltic glasses and glasses of other silica-undersaturated magmas [101,102,103,104,105,106,107]. Multiple lines of evidence, however, from annealing experiments [108], molecular dynamics simulation studies [109,110], and in situ spectroscopy studies [111] have shown that in the melt (not the quenched glass), molecular CO₂ is present even in basaltic and carbonated melt compositions. The CO₃²⁻/CO₂ ratios in silicate melts is a function of polymerization, decreasing with increasing degree of polymerization. In a highly polymerized melt (NBO/T ≈ 0), all the carbon will be as molecular CO₂, and the isotope fractionation coefficient between molecular CO₂ in the melt and CO₂ gas appears to be negligible, close to 0‰. In a depolymerized melt (NBO/T > 1), most (not quite all) of the carbon will be as CO₃²⁻, and the isotope fractionation coefficient between CO₃²⁻ and CO₂ gas appears close to ~3‰. In detail, CO₃²⁻ first converts to molecular CO₂ in the melt prior to going into the gas phase, and it is that first conversion which causes the heavy isotope (¹³C) to be preferentially converted to molecular CO₂ and depleted in the CO₃²⁻ remaining in the melt [98]. In the transition region (NBO/T values between 0 and 1), the isotope fractionation coefficient is hence simply a linear combination of the relative proportion of molecular CO₂ in the melt going to CO₂ gas and CO₃²⁻ in the melt going to CO₂ gas. An interesting implication of this theoretical framework is that the observed bulk isotopic fractionation coefficient should be indicative of the CO₃²⁻/CO₂ ratio in the melt, potentially offering a novel approach to estimate this ratio.

Here, an alternative parametrization of the isotope fractionation coefficient as a function of melt polymerization is proposed to the one of Lee et al. [98]. The available experimental data were fitted with an error function of the form $f\left(x\right)=a\times erf(b\times (x-c\left)\right)+d$. An error function is appropriate to model the observed behavior in line with the theoretical expectation of a shift in reaction mechanisms (and reactant) as the melt composition changes. The best fit, obtained by minimizing the mean square error on 35 experimental data points, is shown in Figure 4, has a R² of 0.82 and a standard deviation of ±0.4‰ (Figure S1), making it slightly better than the previous parametrization (which had a R² of 0.74) and allowing for fitting of the entire compositional spectra with a single equation. Best fit parameters were $a=1.529$, $b=2.880$, $c=0.506$, and $d=1.470$. Several other functions could fit the experimental data just as well. The best fit of a sigmoidal function of the form $f\left(x\right)={\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\left(A+{exp}^{\left(B+C\times x\right)}\right)$}\right.},$ similarly obtained by minimizing the mean square error on the 35 experimental data points, is shown in Figure 4, has a similar R² of 0.82, and a similar standard deviation of ±0.4‰. Best fit parameters were $A=0.340$, $B=2.626$, and $C=-7.264$.

3.1.2. Degassing Styles and Carbon Isotope Evolution During Degassing

With a clear understanding of the carbon isotope fractionation coefficient, we can now calculate the evolution of the isotopic composition of both the melt and gas phases during degassing. CO₂ degassing can occur in four distinct modes, depending on two key factors: (1) System behavior, whether the gas phase remains within the system or escapes (closed vs. open system degassing), and (2) diffusion dynamics, whether the diffusion of CO₂ from the melt into the gas bubble is time-limited (equilibrium vs. kinetic degassing).

Closed system equilibrium degassing (batch degassing). In this scenario, the evolution of the melt’s δ¹³C is described by:

δ¹³C_melt = δ¹³C_initial − (1 − F) 1000lnα_gas−melt

(2)

where δ¹³C_melt is the δ¹³C of C dissolved in the melt, δ¹³C_initial is the initial δ¹³C of C in the melt before degassing, F is the fraction of C remaining in the melt, and 1000lnα_gas−melt is the carbon isotopic fractionation coefficient at equilibrium. The evolution of the gas δ¹³C can be calculated using:

δ¹³C_gas = 1000 lnα_gas−melt + δ¹³C_melt

(3)

Open system equilibrium degassing (Rayleigh distillation). For open system equilibrium degassing, also known as fractional equilibrium degassing, the evolution of the melt’s δ¹³C is given by:

δ¹³C_melt = δ¹³C_initial − 1000 (1 − F^α−1)

(4)

The evolution of the gas δ¹³C at any point can still be calculated with Equation (3).

Kinetic degassing. For both closed-system and open-system kinetic degassing, the evolution of the melt’s δ¹³C follows the same formulas as Equation (2) and Equation (4), respectively, and the evolution of the gas’ δ¹³C follows the same formula as Equation (3). However, the isotopic fractionation factor 1000 lnα_gas−melt is replaced by the kinetic isotopic fractionation coefficient 1000lnα_kinetic. According to Graham’s law of diffusion, this coefficient can be calculated as the square root of the inverse ratio of the molar masses of the diffusing species. This results in a kinetic isotopic fractionation coefficient of −8.2‰, if the diffusing species considered is CO₃²⁻, or −11.1‰, if the diffusing species considered is molecular CO₂. It is important to note that although kinetic isotopic fractionation coefficients have been widely used to model observed degassing trajectories [32,37,56,66], they have yet to be experimentally validated.

Magmas can hence follow four main degassing paths, each with distinct isotopic evolutions (Figure 5). The specific path a degassing magma follows depends on several parameters including the magma ascent/decompression rate, bubble ascent rate, bubble number density, melt composition, volatile content, and temperature. As these parameters can change during magma ascent, the degassing path may consist of multiple stages with different degassing styles. For example, open-system degassing can occur after a stage of closed-system degassing, and kinetic degassing may follow a stage of equilibrium degassing. Most natural systems indeed show evidence of such complex, multi-stage, degassing [66].

3.2. Isotopic Fractionation in Subduction and Mantle Processes

3.2.1. Isotopic Fractionation During Mantle Partial Melting

Isotopic fractionation during degassing has been a focal point of numerous studies because it is often an incomplete process, leading to significant isotopic variations in both the melt and gas phases (Figure 5). In contrast, any phase change reaction that runs to completion should not result in isotopic fractionation. Partial melting, at least batch melting, of the mantle is often considered such a reaction.

Carbon is present in the upper mantle primarily as carbonate minerals and elemental carbon (graphite or diamond) [112,113,114] as it enters the structure of common mantle silicate minerals in only extremely small quantities [115]. During partial melting, carbonate minerals are the first to melt, producing carbon-rich and silica-poor melts, even at very low degrees of partial melting [116,117,118,119,120,121]. Under the oxidized conditions of the upper mantle, diamond and graphite are unstable and will also melt entirely to form a carbonated melt [122,123,124]. Therefore, no isotopic fractionation is expected from the partial melting of the upper mantle, as all carbon is expected to transition into the melt phase.

Until recently, direct evidence of this absence of fractionation had been lacking. CO₂-undersaturated melts, which have never reached saturation and thus never degassed CO₂, are rare at the Earth’s surface [125,126,127,128]. One such series of melts (preserved as melt inclusions) from the Southwest Indian Mid-Ocean Ridge shows evidence of generation from varying degrees of partial melting [128]. Carbon isotopic measurements on these inclusions revealed no correlation between their δ¹³C values and major, trace, or volatile element abundances, nor with the degree of partial melting [73]. Both theoretical considerations and available empirical evidence thus indicate that there is no carbon isotopic fractionation during mantle partial melting.

3.2.2. Isotopic Fractionation During Slab Release and Diamond Formation

Subduction zones introduce carbon into the Earth’s mantle through various carbonate-bearing lithologies including pelagic marine sediments, variably altered oceanic crust, and hydrated subcrustal ultramafic rocks. The conditions under which these lithologies decarbonate and release their carbon into fluids that may migrate into the mantle wedge have been explored in numerous theoretical [129,130,131,132] and experimental [133,134,135] studies. However, the isotopic fractionation of carbon during this decarbonation process has not been investigated, either experimentally or theoretically. If decarbonation proceeds to completion, no fractionation is expected to occur. Rare field studies have documented instances where the δ¹³C of metasediments changes with metamorphic grade. A study of the δ¹³C of carbonaceous matter (metamorphosed organic matter) in metapelites from the Western Alps showed a strong increases (from around—24‰ to values as high as—10‰) with metamorphic grade, potentially reflecting partial loss of carbon to metamorphic fluids as methane [136,137]. Notwithstanding this field evidence, the extent to which isotopic fractionation occurs during slab fluid release remains poorly known. In addition to isotopic fractionation, we should consider that some subducted lithologies will decarbonate at lower pressure-temperature conditions than others, potentially changing the bulk δ¹³C of the downgoing slab and releasing fluids/melts with variable δ¹³C at different depths (Figure 6). Exactly which lithology decarbonates when is a complex function of pressure, temperature, and fluid infiltration [138,139,140,141].

Upon release, slab fluids can migrate into the mantle wedge. Partial melting of the mantle wedge is not expected to result in isotopic fractionation, as previously discussed for the partial melting of the mid-ocean ridge mantle [73], although direct evidence for this is still lacking. As magma migrates to the surface and undergoes partial to near-complete degassing of its initial CO₂ concentrations, significant isotopic fractionation occurs, as outlined in the previous section. Additional processes, such as contamination of the melt through the assimilation of carbon-rich crustal components, may further modify its isotopic signature. Consequently, the carbon isotopic signatures of erupted products, including glasses (ranging from −34 to −3‰; Table 1) and gases (ranging from −14‰ [142] to +2‰ [143], with a mean of −5 ± 3‰ based on compiled literature data from 33 arc volcanoes) at arc volcanoes, are never a direct reflection of their source isotopic composition. This will remain the case until CO₂-undersaturated melts can be identified in arc settings, which has yet to occur.

Slab fluids released deeper in the mantle, can potentially become trapped as diamonds through redox freezing. Understanding isotopic fractionation during this process is crucial for interpreting the isotopic composition of carbon in diamonds. Detailed examinations of the isotopic composition of carbon in diamonds have revealed zonation in δ¹³C values [144], either increasing [145,146,147] or decreasing [148] from core to rim. An increase in δ¹³C from core to rim is typically attributed to diamond formation from oxidized carbon sources, such as CO₂ or carbonate, whereas a decrease suggests formation from reduced carbon sources like methane [149]. The isotopic fractionation coefficient in each scenario has been determined through both theoretical considerations [145,150,151,152,153,154] and experimental [155,156,157,158,159,160,161,162,163] studies and in the temperature range of diamond formation varies between.

1000lnα_{diamond−CO2} ≈ −4‰ and 1000lnα_{diamond−CH4} ≈ 2‰. Additionally, Rayleigh distillation processes, driven by fluid depletion and growth rate evolution, can significantly influence the isotopic composition of diamonds [164,165,166]. These processes highlight the complex interplay between carbon sources and fractionation mechanisms in the formation and isotopic signature of diamonds.

4. Carbon Isotope Signature of Earth’s Upper Mantle

4.1. Review of Available Evidence

Constraining the average carbon isotopic value of Earth’s convecting upper mantle, its variability, and its potential evolution through time is critical to understand carbon’s origin and its deep cycling. Multiple sample types can be used toward that aim including diamonds, kimberlites, carbonatites, popping rocks, CO₂-undersaturated melts, and fluid and melt inclusions.

Diamonds have by far been the most studied sample type for carbon isotopes [1,167,168,169,170,171]. Their bulk δ¹³C signature ranges from −41.4‰ [172] to 2.7‰ [173]. A recent review compiled 4308 diamond δ¹³C analyses [165] and found, in line with previous studies [149], that peridotitic diamonds (n = 1906) formed a narrow distribution centered at −4.9 ± 1.9‰ [165]. This mode in the carbon population at −5‰ (Figure 7) has long been recognized and held as representing the carbon isotopic signature of the mantle [5,174].

Carbonatite and kimberlite melt can retain most of their initial CO₂ contents until shallow depths [107,175]. As such, their δ¹³C signature may remain partly or entirely unchanged during ascent. A recent compilation of kimberlite δ¹³C measurements [176] shows a range from −8.9‰ to −3.4‰ with a mean at −5.5 ± 1.2‰. For carbonatites, data compiled from the GEOROC database (https://georoc.eu/; accessed on 17 March 2025) reveal δ¹³C signatures ranging from −12.1‰ to 3.5‰, with a mean of −4.2 ± 2.1‰ (Figure 7).

Mid-ocean ridge basalts are typically highly degassed by the time they reach the seafloor, resulting in carbon isotopic signatures ranging from −24‰ to −1‰ (Table 2), significantly modified by degassing. However, some MORB samples have either retained all of their exsolved CO₂ in vesicles (known as “popping rock” samples [55,177,178]) or have never degassed any of their initial CO₂ content [125,126,127,128]. Both sample types should hence retain the δ¹³C signatures they had at equilibrium with the mantle. While the two ‘popping rock’ samples analyzed record δ¹³C values close to −4‰ [55,177], the twelve CO₂-undersaturated MORBs analyzed to date record a much larger range, from −10.5‰ to −3.6‰ [73,74]. Taken together, these data currently show a bi-modal distribution with the mode centered around −4‰ comprising all samples from the Mid-Atlantic Ridge, while the mode around −8‰ is representative of samples from the Indian, Arctic, and Pacific ridges [74].

Melt inclusion δ¹³C studies are still very few in number. Besides the ones on CO₂-undersaturated MORBs [73,74], only a single study on the 2021 Fagradalsfjall eruption (Iceland) reported δ¹³C measurements in melt inclusions [32]. Because these melts are not CO₂-undersaturated, however, the isotopic signature they had at mantle depth can only be estimated assuming a given initial CO₂ concentration and degassing path (in this study, the δ¹³C signature of the Icelandic mantle was estimated to be −6.5 ± 2.5‰). Fluid inclusion δ¹³C studies will suffer from the same limitation, with the added caveat that most such studies to date are bulk, measuring all fluid inclusions in a crystal or batch of crystals at once. Most fluid inclusion studies in magmatic systems have focused on mantle xenolith. A compilation of recent fluid inclusions in xenolith studies from Stromboli [179], Fogo [180], La Palma [181], El Hierro [90,182], Piton de la Fournaise [183], and the Ethiopian Plateau [90] reveals a very wide range from −8.9‰ to 7.5‰, and a possible bi-modal distribution with modes around −7‰ and −2‰ (Figure 7,

Table 3. Population statistics for δ¹³C measurements in natural diamonds, kimberlites, carbonatites, CO₂-undersaturated MORBs and popping rocks, and fluid inclusions in magmatic xenoliths.

Sample Type	Reference	Observations (n)	Minimum	Maximum	Mean	Std. Deviation
Diamonds (all)	[165]	4308	−41.4	2.5	−6.9	5.5
Diamonds (peridotitic)	[165]	1906	−34.5	2.3	−4.9	1.9
Kimberlites	[176]	65	−8.9	−3.4	−5.5	1.2
Carbonatites	GEOROC	1035	−12.1	3.5	−4.2	2.1
CO2-Undersaturated MORBs, seamounts, and popping rocks	[73,74]	14	−10.5	−3.6	−7.5	2.2
Fluid inclusions in magmatic xenoliths	[90,180,181,182,183]	165	−8.9	7.472	−3.4	3.3

).

Figure 7. Distribution in the carbon isotope composition (δ¹³C) of diamonds [165], kimberlites [176], carbonatites (GEOROC), CO₂-undersaturated MORBs and popping rocks [74], and fluid inclusions in magmatic xenoliths. Histograms have a 1‰ binning interval, red curves show the kernel density estimation using Gaussian function and a bandwidth of 1.

Figure 7. Distribution in the carbon isotope composition (δ¹³C) of diamonds [165], kimberlites [176], carbonatites (GEOROC), CO₂-undersaturated MORBs and popping rocks [74], and fluid inclusions in magmatic xenoliths. Histograms have a 1‰ binning interval, red curves show the kernel density estimation using Gaussian function and a bandwidth of 1.

4.2. Carbon Isotope Signature of Earth’s Upper Mantle, Spatial, and Temporal Variability

From our review of available samples, it is evident that we cannot assign a single δ¹³C value to the Earth’s convecting mantle, particularly for the modern convecting mantle. The variability in diamond δ¹³C values has long been attributed to plate tectonics and the recycling of sedimentary carbon [171,184,185]. Multiple lines of evidence now indicate that the mantle is heterogeneous in its carbon isotopic signature; studies of fluid inclusions in xenoliths from active volcanic systems provide clear evidence of heavy δ¹³C values, interpreted as mantle contamination by recycled carbonates [179,181,182]. Zoned diamonds, which trap inclusions from both lower and upper mantle assemblages, record δ¹³C values ranging from −10.4‰ to 3.8‰ [186], indicating vertical heterogeneity in mantle δ¹³C values. Additionally, CO₂-undersaturated melts and popping rocks from mid-ocean ridges worldwide exhibit δ¹³C values ranging from −10.5‰ to −3.6‰ [74], suggesting lateral heterogeneity in mantle δ¹³C values.

Has the Earth’s mantle always been heterogeneous in δ¹³C? If this heterogeneity is linked to plate tectonics and the recycling of sedimentary carbon, one might expect it to increase over time. This hypothesis has been suggested based on the age distribution of kimberlite δ¹³C values [176], but based on a skewed sample size distribution over time. While diamond formation ages remain unknown at many localities, compiling the available diamond δ¹³C isochron age data reveals that both the existence of variability in diamond δ¹³C values and the presence of a strong mode around −5‰ are features that have persisted over the last 3.5 Ga (Figure 8, see also Figure 7 in Howell et al. [187]). This brings into question the assumption that all heterogeneity in mantle δ¹³C values is due to subduction processes. In fact, Moussallam et al. [74] found that the carbon isotopic signature of CO₂-undersatutated MORBs was uncorrelated with geochemical markers of contamination from subduction materials. The possibility of primordial heterogeneity in the mantle carbon isotopic signature should hence not be discarded.

5. Future Studies

The recent development of carbon isotopic analyses in individual melt inclusions by SIMS [32,72,73,74] and individual fluid inclusions by Raman spectroscopy [89,90,91] opens the door to a golden age for research on carbon isotopes in magmatic systems. These types of studies will greatly enhance the interpretation of carbon isotopic measurements in volcanic gases, which can now be made operationally from the main plume of active volcanoes. By tracking the degassing process, they will also improve our understanding of the styles of degassing taking place during magma ascent and their potential relation to eruption dynamics. Additionally, such studies will bring new constraints on the carbon isotopic composition of the mantle source of magmatic systems worldwide, from which a much clearer image of the isotopic composition and distribution of carbon in the modern upper mantle should emerge.

A number of critical questions remain that warrant further investigation to advance our understanding of carbon isotopes in magmatic systems. While the carbon isotopic fractionation factors during equilibrium degassing and diamond formation are now well-understood, the fractionation occurring during carbon release from the subducting slab remains poorly constrained. Additionally, the kinetic isotopic fractionation during magmatic degassing is currently only theoretically constrained and requires experimental validation. Further research is needed to determine the extent of the mantle’s heterogeneity in its carbon isotopic signature and to explore the temporal evolution of this heterogeneity over geological time. This investigation will help ascertain whether the observed heterogeneity is primarily or solely a result of subduction processes or if it reflects, in part, primordial variations in the mantle’s carbon isotopic signature. Finally, if we want to compare the carbon isotopic signature of the early Earth to that of other solar system bodies (meteorites, comets, planets, and the Sun) in an attempt to elucidate the provenance of carbon on Earth, we need to understand the carbon isotopic fractionation that occurred during planetary accretion, core formation, and the giant impact.