The behavior of nitrogen during magmatic degassing and the potential kinetic fractionation between N and other volatile species (H, C, O, noble gases) are poorly known due to the paucity of N diffusion data in silicate melts. To better constrain N mobility during magmatic processes, we investigated N diffusion in silicate melts under reducing conditions. We developed uniaxial diffusion experiments at 1 atm, 1425 °C, and under nominally anhydrous reducing conditions (fO2 ≤ IW-5.1, where IW is oxygen fugacity, fO2, reported in log units relative to the iron-wüstite buffer), in which N was chemically dissolved in silicate melts as nitride (N3–). Although several experimental designs were tested (platinum, amorphous graphite, and compacted graphite crucibles), only N diffusion experiments at IW-8 in compacted graphite crucibles for simplified basaltic andesite melts were successful. Measured N diffusivity (DN) is on the order of 5.3 ± 1.5 × 10−12 m2 s−1, two orders of magnitude lower than N chemical diffusion in soda-lime silicate melts (Frischat et al. 1978). This difference suggests that nitride diffusivity increases with an increasing degree of melt depolymerization. The dependence of N 3– diffusion on melt composition is greater than that of Ar. Furthermore, N3– diffusion in basalticandesitic melts is significantly slower than that of Ar in similarly polymerized andesitic-tholeiitic melts at magmatic temperatures (1400–1450 °C; Nowak et al. 2004). This implies that N/Ar ratios can be fractionated during reducing magmatic processes, such as during early Earth's magma ocean stages.


Understanding the behavior of volatile elements (H, C, N, noble gases) in silicate melts is fundamental to better constrain their fate during the formation and evolution of Earth and other planetary bodies in the inner solar system (Marty et al. 2016; Piani et al. 2020). Because N, as molecular N2, is expected to behave like noble gases, particularly Ar, during magmatic processes (Marty 1995; Miyazaki et al. 1995, 2004), the N2/36Ar ratios of Earth's atmosphere and mantle are expected to be comparable. However, the N2/36Ar value of Earth's mantle (>106, estimated from mid-ocean-ridge basalt glasses) is two orders of magnitude higher than that of the atmosphere (~104) (Marty 1995; Marty et al. 1995; Marty and Humbert 1997), perhaps as a result of kinetic disequilibrium during the formation of Earth's atmosphere due to mantle degassing (Marty et al. 1995) or the distinct volatile histories of these two reservoirs (Marty and Humbert 1997). Diffusion strongly controls this ratio because it governs volatile transport and degassing during magmatic activity at all stages of planetary evolution (from magma ocean differentiation to volcanic eruptions). However, whereas the diffusion of H2O, CO2, and noble gases in silicate melts has been widely studied (e.g., Zhang and Stolper 1991; Baker et al. 2005; Zhang and Ni 2010; Lux 1987; Roselieb et al. 1995; Amalberti et al. 2018), N diffusion in silicate melts remains largely under-constrained.

Elemental speciation fundamentally controls the diffusion of redox-sensitive species such as nitrogen in silicate melts (Frischat et al. 1978; Zhang and Ni 2010). Depending on fO2 conditions, N is incorporated as free molecular N2 and NH3 or bonded N3–, CN, NH2–, and/or NH2 (Libourel et al. 2003; Li et al. 2015; Dalou et al. 2017, 2019; Mosenfelder et al. 2019; Boulliung et al. 2020; Grewal et al. 2020). At atmospheric pressure and under anhydrous conditions, N is either incorporated as molecular N2 under oxidizing conditions (fO2 > IW-1.5) or chemically dissolved as nitride (N3–) under reducing conditions [fO2 ≤ IW-1.5 (Libourel et al. 2003; Boulliung et al. 2020)]. To date, N diffusion in silicate melts has only been studied in soda-lime silicate melts at atmospheric pressure and high temperature (1000–1400 °C) for molecular N2 and nitride species (Frischat et al. 1978). In these melts, physical diffusion of N2 is significantly faster than chemical diffusion of nitride (Behrens 2010). However, N solubility not only depends on fO2 but also on melt composition and structure; when dissolved as N3–, N solubility increases with an increasing degree of melt depolymerization (Boulliung et al. 2020). These observations indicate that melt composition may affect N diffusion and, therefore, that N diffusivities determined for soda-lime silicate melts cannot be representative of those in natural silicate melts.

In this study, various experimental approaches were tested to determine uniaxial N diffusion in silicate melts of simplified basaltic andesite and highly depolymerized, magma ocean-like compositions to address the influence of melt composition on N diffusion under conditions in which N is chemically incorporated as nitride. Uniaxial diffusion experiments were conducted at 1425 °C, 1 atm, and IW-8 and IW-5.1. Nitrogen concentration profiles in the quenched run products were determined by in situ secondary ion mass spectrometry (SIMS). The results provide new insights into the N diffusion mechanism(s) in naturally occurring silicate melts, thereby improving our understanding of the behavior of N during reducing magmatic processes.

Experimental and analytical methods

Two starting materials of different simplified iron-free compositions were synthesized and their bulk compositions determined by electron microprobe analysis at Université de Lorraine (Service Commun de Microscopie Electronique et de Microanalyses X, Nancy, France): (1) a basaltic andesite composition (AND1: 53.6 wt% SiO2, 20.7 wt% Al2O3, 9.9 wt% MgO, 15.0 wt% CaO, 0.45 wt% Na2O, 0.16 wt% K2O) and (2) a mafic composition (MO2: 47.4 wt% SiO2, 4.6 wt% Al2O3, 19.8 wt% MgO, 26.1 wt% CaO). These starting glass materials are characterized by extreme NBO/T values (the number of non-bridging oxygen atoms per tetrahedrally coordinated cations) of 0.5 (AND1) and 2.1 (MO2); the latter is comparable to that estimated for the terrestrial magma ocean (Ringwood 1966; Dasgupta and Grewal 2019). To prepare these starting materials, oxide and carbonate powders were dried and decarbonated at 1000 °C in a muffle furnace for 12 h. After mixing in appropriate proportions, they were fused in a platinum crucible at 1400 °C in a muffle furnace for 4 h and quenched in air. The fused starting glasses AND1 and MO2 were ground for 1 h for use in the different experiments.

Different experimental supports were tested to study uniaxial N diffusion. Compacted graphite (15 mm long, 6 mm outer diameter, 1.5 mm wall thickness) and vitreous graphite (12 mm long, 7 mm outer diameter, 1 mm wall thickness) cylinders were used for experiments at IW-8, whereas Pt cylinders (13 mm long, 3 mm outer diameter, 0.2 mm wall thickness) were used for experiments at IW-5.1 (Table 1). To obtain bubble-free glass prior to the diffusion experiments, the starting powder was incrementally filled into the cylinders and melted for 30 min under a CO2 flux (300 cm3 min−1) at 1600 °C for Pt crucibles (as described by Amalberti et al. 2018) and under Ar flux (300 cm3 min−1) at 1450 °C for graphite cylinders to minimize potential atmospheric nitrogen contamination. The filled cylinders were subjected to a final melting step at 1550 °C for Pt crucibles and 1450 °C for graphite crucibles during ~15 h under the same Ar and CO2 fluxes to ensure the complete removal of bubbles.

Uniaxial N diffusion experiments were performed in a Gero vertical furnace at atmospheric pressure, 1425 ± 1 °C, and under a controlled N2-CO(-CO2) atmosphere at log fO2 = −17.4 and −14.5 (IW-8 and IW-5.1, respectively; Table 1). Diffusion at such low oxygen fugacities is expected to result in discernable and measurable N concentration gradients, whereas low N solubilities in silicate melts under more oxidizing conditions (log fO2 > IW-1.5) limit N contents to a few parts per million (Libourel et al. 2003; Boulliung et al. 2020). The gas flux was maintained at 300 cm3 min−1 by TYLAN mass flow controllers. The graphite cylinders were placed into an alumina crucible, whereas the platinum cylinders were held in place using Pt wire (0.3 mm). Diffusion experiments using compacted graphite and vitreous graphite cylinders lasted 3 h, but were restricted to 1 h with Pt crucibles to minimize Pt loss by evaporation at high temperature under reducing conditions (Darling et al. 1970) (Table 1). Regardless of melt composition, these experimental durations are too short to reach gas-melt equilibrium; based on experiments using 2–5 mm diameter silicate melt spherules in graphite crucibles, equilibrium is expected to be achieved in 24 h (Humbert 1998; Boulliung et al. 2020). After quenching in air, run products were fixed onto a flat ceramic support using CrystalbondTM adhesive and cut in half along the direction of diffusion. The obtained glass half-cylinders were then mounted in high-purity indium, polished, and gold coated.

N concentrations were quantified by in situ measurements of 14N16O secondary ions using the CAMECA 1280 HR2 SIMS at the Centre de Recherches Pétrographiques et Géochimiques (Nancy, France) operating with a 10 kV Cs+ primary ion beam, a current of ~10 nA, and a nominal mass resolution of ~13 000 (for details, see Füri et al. 2018). N contents were measured along profiles from each exterior edge of the glass cylinders toward their center (Fig. 1). Uncertainties on N contents (2σ) are ≤4% for N contents >100 ppm, ≤30% between 10 and 100 ppm, and 50–100% below 10 ppm. Carbon (CO2) and water (H2O) contents were measured in one sample (along profile A of AND1; Fig. 1) using the CAMECA IMS-1270 E7 ion microprobe (see Online Material1 for details) to assess the potential presence and abundance of these volatiles.


Previous gas-melt equilibrium experiments at IW-5.1 yielded N contents of 68.1 ± 6.0 and 35.6 ± 10.7 ppm for AND1 and MO2, respectively, and those at IW-8 yielded 2672 ± 40 ppm and 5987 ± 63 ppm, respectively, after 24 h (Boulliung et al. 2020). These experiments demonstrated that N solubility is highest in depolymerized melts under very reducing conditions.

The run products of diffusion experiments performed with platinum crucibles at IW-5.1 contain <5 ppm N, and concentrations are indistinguishable within analytical uncertainties. The glasses produced using vitreous graphite crucibles at IW-8 have homogeneous N concentrations (208 ± 10 ppm in AND1 and 400 ± 47 ppm in MO2) and lack any apparent diffusion profiles. Therefore, N diffusion coefficients could not be determined in experiments using platinum and vitreous graphite crucibles.

A significant loss of melt (~50%) and partial crystallization was observed in the experiment on the MO2 melt using a compacted graphite crucible at IW-8. Given its high degree of depolymerization (NBO/T = 2.1) and correspondingly low viscosity, this melt loss was likely caused by melt migration. We assume that minor evaporation of major oxides (mainly SiO2 and MgO) during the bubble elimination steps (at 1450 °C under an Ar flux), affected the liquidus temperature (initially estimated just below ~1400 °C) and promoted crystallization upon quenching. Due to these limitations, no nitrogen diffusion profiles were observed for the MO2 melt. In contrast, using the same experimental design, the AND1 melt was successfully quenched to a crystal-free glass, and N concentration gradients were determined along four profiles (A–D; Fig. 1). The N concentrations range from 1068 ± 41 to 4 ± 3 ppm, 142 ± 5 to 7 ± 4 ppm, 220 ± 9 to 8 ± 4 ppm, and 2001 ± 80 to 541 ± 22 ppm along profiles A, B, C, and D, respectively (Fig. 1; Table 2). Although the surface of the melt adopts the shape of a concave meniscus (Fig. 1e), N concentrations along the gas-melt interface are nearly homogeneous (906 ± 37 to 1068 ± 41 ppm; Online Material1 Fig. OM1).


The N contents of glasses produced in experiments using Pt crucibles are too low (<5 ppm) to detect concentration gradients by SIMS. Although the 1 h experimental duration was probably too short to dissolve a significant amount of N, even at low fO2 conditions (IW-5.1) under which N contents are expected to be relatively important at gas-melt equilibrium (i.e., tens of parts per million; Boulliung et al. 2020), longer experiments were not possible because Pt crucibles are prone to evaporative losses at such strongly reducing conditions. The run products of experiments using vitreous graphite are N-rich (208 ± 10 ppm in AND1, 400 ± 47 ppm in MO2), but were likely homogenized by convection induced by the bottom-up migration of silicate melts along the vitreous graphite crucible. We, therefore, conclude that platinum and vitreous graphite are not appropriate for experiments on N diffusion in silicate melt under reducing conditions.

On the other hand, the uniaxial diffusion experiment using compacted graphite yielded variable N concentration gradients in glass AND1 (Fig. 1). The occurrence of N gradients along profiles B, C, and D (Fig. 1) is surprising since no direct gas-melt interaction was expected at the edges or bottom of the glass cylinder. These gradients may be the result of N migration along or diffusion through the graphite crucible. Nevertheless, the central part of the glass cylinder is N-free (Table 2), which suggests that no or very limited convection movements occurred in the melt during the experiment. The N diffusion coefficients can be determined from each profile using the one-dimensional diffusion equation in a semi-infinite medium with a constant interface concentration (Crank 1975):


where C(x,t) is the concentration at distance x from the gas-melt interface after time t (the experimental duration), C0 is the initial concentration in the glass (here, C0 = 0), C1 is the concentration at the gas-melt interface (x = 0), and D is the diffusion coefficient. For profile A, we chose the starting point (x = 0) to be at the center of the meniscus, whereas the starting point for the other profiles was chosen arbitrarily. In each case, the concentration at the gas–melt interface was obtained by extrapolating the diffusion profile to x = 0. Finally, we linearized the left-hand side of Equation 1 by plotting the inverse error function against distance to extract the diffusion coefficient as (Van Orman et al. 1998):


The slope of the best-fit line, m, was derived using IsoplotR (Vermeesch 2018) with an uncertainty that takes into account the uncertainties on measured N concentrations and on x positions (5 μm). The diffusion coefficients are reported in Figure 1, and the inversion error function of diffusion profile A is presented as a representative example in Figure 2. Because of the meniscus shape of the gas-melt interface (Fig. 1e), N diffusion may not be strictly one-dimensional along profile A. Thus, the main source of uncertainty for profile A is related to the position of the origin of the diffusion profile (x = 0). The overall uncertainty was evaluated by comparing the diffusion coefficient for a starting point at the center (4.2 ± 0.4 × 10−12 m2 s−1) and at mid-height of the meniscus (6.2 ± 0.6 × 10−12 m2 s−1). By coupling the standard deviation related to the geometrical and the analytical uncertainties, the average diffusion coefficient is equal to 5.3 ± 1.5 × 10−12 m2 s−1 along profile A. The diffusion coefficients obtained for the four profiles differ significantly, with lower values for profiles B, C, and D (Fig. 1), likely due to distinct boundary conditions; given that N diffusion along profiles B, C, and D may have been controlled by delayed transport of nitrogen through the graphite container wall, these three values are excluded from further discussions.

To date, the diffusion of molecularly (N2) and chemically incorporated nitrogen (N3–) in silicate melts has only been studied in soda-lime silicate melts at atmospheric pressure and 1000–1400 °C (Frischat et al. 1978). The authors studied N2 diffusion by heating a pre-saturated glass slab under an oxygen atmosphere and chemical diffusion by heating a glass containing silicon nitride under an Ar-H2 atmosphere. Under these conditions, N diffuses faster as N2 than N3– in soda-lime silicate melts (Frischat et al. 1978; Behrens 2010). However, nitride diffusivity increases more rapidly than N2 diffusivity with increasing temperature because of its higher activation energy (244 kJ mol−1 for N3– vs. 161 kJ mol−1 for N2; Frischat et al. 1978). Indeed, N2 displays an intrinsic diffusivity resembling that of noble gases (Dingwell and Webb 1990; Dingwell 2006), whereas N3– diffusivity seems to be extrinsic, as it increases significantly with increasing temperature.

Under nominally anhydrous and very reducing conditions (i.e., IW-8), N is expected to dissolve predominantly as nitride species (Libourel et al. 2003), likely bonded as Si-N (Boulliung et al. 2020), whereas C-N and N-H species are inferred to represent a minor fraction of the total N budget (see Online Material1 for details). After extrapolation of the data from Frischat et al. (1978) to 1425 °C, N 3– diffusion in soda-lime silicate melts is two orders of magnitude higher (~6.0 × 10−10 m2 s−1) than in our melt AND1 (5.3 ± 1.5 × 10−12 m2 s−1). As soda-lime silicate melts are more depolymerized (NBO/T = 0.7) than basaltic andesite melts (NBO/T = 0.5), it appears that N3– diffusion increases with melt depolymerization. However, since the experimental conditions (e.g., fO2) of the study of Frischat et al. (1978) are not clearly indicated, it is difficult to ascertain that the NBO/T value is the only parameter responsible for this difference. Although additional experiments, including distinct melt compositions, are needed to better understand the effect of melt polymerization on N3– diffusion, we note here that similar behavior is observed for O2–, for which the activation energy decreases with increasing depolymerization (e.g., Lesher 2010). As in the case of oxygen, nitride diffusion requires the breaking of Si-O bonds, and the increased occurrence of Si-O-M (where M is a network-modifying cation and O is a non-bridging oxygen) compared to Si-O-Si bounds (with O as a bridging oxygen) in highly depolymerized melts enhances nitride diffusion by oxygen substitution (Boulliung et al. 2020). To compare the diffusivity of network formers (such as Si and Al) and O2– (e.g., Dingwell and Webb 1990) with that of nitride obtained for profile A, we used the Eyring equation:


where D is the diffusion coefficient in m2 s−1; k is the Boltzmann constant, T is the temperature in K, η is the melt viscosity in Pa s, and λ is the jump distance, which is fixed at 3 Å for the diffusion of network formers (e.g., Nowak et al. 2004). The melt viscosity (η) of AND1 at 1425 °C is 2.19 Pa s (calculated using the model of Giordano et al. 2008) (see Online Material1 for details). The Eyring diffusivity at 1425 °C, ~3.6 × 10−11 m2 s−1, is less than one order of magnitude higher than the diffusion coefficient obtained for N in this study (5.3 ± 1.5 × 10−12 m2 s−1; Online Material1 Fig. OM2). This similarity suggests that movements of network formers are involved in nitride diffusion, reinforcing the conclusion of Boulliung et al. (2020) that N diffuses as a Si-N species under highly reducing conditions in basaltic andesite melts.

As with N3– and O2–, noble gas diffusivity also increases with an increasing degree of melt depolymerization. For example, at 1400 °C, Amalberti et al. (2018) reported that the argon diffusion coefficient (DAr) in a synthetic basaltic melt with NBO/T = 1 (9.3 × 10−11 m2 s−1) is ~3 times higher than that in a synthetic Hawaiitic melt with NBO/T = 0.7 (2.9 × 10−11 m2 s−1; Nowak et al. 2004). The relative difference in NBO/T between the soda-lime silicate melt (NBO/T = 0.7) used by Frischat et al. (1978) and our melt AND1 (NBO/T = 0.5) is comparable to that between basaltic and Hawaiitic melts. However, DN is ~110 times higher in soda-lime silicate melts than in AND1, indicating that nitride diffusion is more dependent on the degree of melt polymerization than Ar diffusion in this temperature range. Furthermore, at the same degree of melt polymerization (NBO/T = 0.5), DAr = 1.5 × 10−11 m2 s−1 in andesitictholeiitic melts at 1400–1450 °C and 500 MPa (Nowak et al. 2004), is ~3 times higher than the DN value observed for our AND1 melt (5.3 × 10−12 m2 s−1). Since increased pressure slows down noble gas diffusion in silicate melts (Roselieb et al. 1996; Behrens and Zhang 2001; Zhang et al. 2007), DAr is expected to be even larger at 1 atm. This difference between DAr and DN suggests that under reducing conditions (i.e., N as N3–), diffusion during magmatic processes significantly fractionates the N/Ar ratio.


Our results imply the efficient transport of N as nitride under magma ocean conditions during the early stages of Earth's formation [i.e., fO2 between IW-3 and IW-5 for 70% of Earth's mass accreted (Rubie et al. 2011; Wade and Wood 2005); ~2000 K (Rubie 2007; Solomatov 2007); and NBO/T ~ 2 (Ringwood 1966; Javoy et al. 2010; Dasgupta and Grewal 2019)]. Under such conditions favorable to nitrogen diffusion as nitride, the N/Ar ratio may be kinetically fractionated during degassing and/or ingassing and melt migration. Therefore, the different N/Ar ratios of Earth's mantle and atmosphere (e.g., Marty 1995) may have resulted from an early stage of atmospheric formation when Earth's magma ocean was highly reducing. During later stages of magma ocean differentiation, for redox conditions between IW-3 and IW-1.5 [i.e., when Earth had accreted more than 70% of its final mass (Rubie et al. 2011)], N dissolves not only as N3–, but as other species such as N-H or C-N complexes, and, to a lesser extent, N2 (e.g., Dalou et al. 2019; Grewal et al. 2020; Boulliung et al. 2020) depending on fH2 and fO2. Since the speciation of volatile elements affects their diffusivity in silicate melts (e.g., Frischat et al. 1978; Zhang and Ni 2010), the diffusion and transport mechanism(s) of such species needs to be investigated through multi-component experiments over a range of P-T-fO2 conditions. With this respect, the experimental design (gas–melt interaction in compacted graphite crucibles), analytical protocol (in situ SIMS analysis), and first results presented here represent an important step toward improving our understanding of N behavior within planetary magma oceans.


This work was supported by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (grant agreement no. 715028). This is CRPG contribution 2733.


Delphine Lequin is thanked for her help during the diffusion experiments. Technical support by Cécile Deligny, Etienne Deloule, Nordine Bouden, and Johan Villeneuve (SIMS), and Olivier Rouer (electron microprobe), is gratefully acknowledged, and we thank Francois Faure and Mathieu Roskosz for constructive discussions. Robert Dennen is thanked for English editing. Constructive comments by associate editor Charles E. Lesher, Harald Behrens, and an anonymous reviewer helped to improve the manuscript.


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