Inefficient nitrogen transport to the lower mantle by sediment subduction

The fate of sedimentary nitrogen during subduction is essential for understanding the origin of nitrogen in the deep Earth. Here we study the behavior of nitrogen in slab sediments during the phengite to K-hollandite transition at 10–12 GPa and 800–1100 °C. Phengite stability is extended by 1–3 GPa in the nitrogen (NH4+)-bearing system. The phengite-fluid partition coefficient of nitrogen is 0.031 at 10 GPa, and K-hollandite-fluid partition coefficients of nitrogen range from 0.008 to 0.064, showing a positive dependence on pressure but a negative dependence on temperature. The nitrogen partitioning data suggest that K-hollandite can only preserve ~43% and ~26% of the nitrogen from phengite during the phengite to K-hollandite transition along the cold and warm slab geotherms, respectively. Combined with the slab sedimentary nitrogen influx, we find that a maximum of ~1.5 × 108 kg/y of nitrogen, representing ~20% of the initial sedimentary nitrogen influx, could be transported by K-hollandite to the lower mantle. We conclude that slab sediments may have contributed less than 15% of the lower mantle nitrogen, most of which is probably of primordial origin.

The manuscript "Inefficient nitrogen transport to the lower mantle by sediment subduction" by Huang et  al., presents the role of sediment subduction in the origins of deep Earth nitrogen and examines the behaviour of sedimentary nitrogen during the transition of phengite to K-hollandite under conditions of 10-12 GPa and temperatures ranging from 800-1100°C.The study investigates the nitrogen partitioning coefficients between K-hollandite and fluid (5 experiments), as well as phengite and fluid (1 experiment), revealing the trends with increasing pressure (and temperature).These findings offer new insights into how much nitrogen remains preserved at the phengite-hollandite transition depth and how much might be transported to the lower mantle by K-hollandite.However, the study may fall short on some fronts as detailed below.Most importantly, there are potential contradictions regarding the depths at which nitrogen-rich diamonds are found, especially in relation to the residual pressure of ice-VII inclusions in diamonds.While this research provides a new picture of phengite/K-hollandite transition in sediment subduction's contribution to mantle nitrogen, these weaknesses need further clarification.
Lines 159-162: The nitrogen content in K-Hollandite jumps from about 1000 ppm at 10 GPa to a high value of 8000 ppm at 11 GPa.That's quite the leap in just a small pressure window!I wonder if the lower 1000 ppm at 10 GPa is because it's near the Phe/K-Holl boundary?I'd be cautious about extending this trend to much higher pressures.And also, the K-hollandite with around 1000 ppm nitrogen was at the highest experimental temperature, while the one with higher nitrogen formed at a cooler temperature.Could temperature be playing a role here?Also since the change is so strong, it should be demonstrated with more experiments as it may be due to outliers.
Lines 169-172: But how much nitrogen actually gets to the depth where phengite transitions to Khollandite?Given that DN(mineral/fluid) is pretty low, at about 0.031 for phengite/fluid, and considering phengite's presence from the start of subduction to 10 GPa, it's possible most of the nitrogen is already out by 10 GPa.And with the slab heating up from the inside, there's likely a lot of fluid escaping from its core and moving up through the phengite-rich top layer.
Lines 196-199: Now, phengite interacts with fluid coming from within the slabs, especially as the serpentinized mantle rocks of the slab heat up.If this fluid isn't rich in nitrogen, phengite might lose its nitrogen to it, especially since DN(phengite/fluid) is quite low at 0.031.
Lines 200-203: This rapid nitrogen drop might hinge on the lower DN(K-hollandite/fluid), which seems to be increasing quickly within a tight pressure range of 1 GPa.This might be because it's close to the phengite/k-hollandite transition, as mentioned earlier in lines 159-162.
Lines 205-207: Unless it's reacting with the ultramafic surrounding mantle rocks, given that K-hollandite is significantly more siliceous.
Lines 281-287: This is based on the assumption that nitrogen degassing from the mantle (at 7.73 x10^7 kg/y) has been consistent throughout Earth's history.But, with Earth cooling down, there's been a decline in magmatism, as seen in the slowing rates of MORB spreading, reduced partial melting, and cooler upper mantle temperatures.So, it's likely that nitrogen degassing has been decreasing over time, which might make these calculations a bit off.
Lines 291-294: Some earlier research suggests that Earth's ancient atmosphere had a pressure pretty similar to what we have today.Just check out the studies by Som and colleagues in 2013 (Nature) and 2016 (Nature Geoscience), and the one by Marty and team in 2013 (Science).
Lines 307-310: It's not too surprising that nitrogen-rich diamonds are mainly found at shallower depths.After all, the subduction of nitrogen-rich materials tends to happen from the top down.
Lines 313-316: The Science study you cited, titled "Ice-VII inclusions in diamonds: Evidence for aqueous fluid in Earth's deep mantle", shows the current residual pressure of the ice-VII inclusions at 9 +-2 GPa.However, the diamonds containing these inclusions actually formed much deeper, around the mantle transition zone (14-22 GPa and even beyond 22 GPa).This seems a bit contradictory to your results, especially since this study's main takeaway is that diamonds primarily form at around 310-315 km or roughly 10 GPa (as shown in Fig. 4).At 9 +-2 GPa, ice-VII can only exist below 500 C, but even the coldest slabs are hotter than 800 C at this pressure.This might need some rethinking or further clarification.
Reviewer #3 (Remarks to the Author): Huang et al present new experimental data to constrain the partitioning of N during the mineralogical transition of phengite and K-hollandite.They find that N partitioning is weaker into K-hollandite than into phengite, and this implies that slabs could lose a large fraction of remaining N budget as they pass through 10 GPa (~300 km depth), potentially limiting the supply of N to deeper sections of the mantle.
While the essential data reported may provide an important constraint regarding how slabs work to redistribute N in Earth's interior, the manuscript needs to include a section that discusses evidence for equilibrium being closely approached for the experiments, with careful attention paid to N. Without this, N partition coefficients cannot be established, as partitioning is a reflection of an equilibrium chemical system.
Moreover, previous works have identified that oxygen fugacity is a major control on N partitioning, but this parameter is also not discussed.I think it is simply assumed that all N remains reduced, but this is not stated nor defended.
The mass balance calculations appear to assume that exactly 8 wt % of a fluid was added to oxide powders to generate the starting composition.It is not possible to add exactly 8 wt % of fluid to a capsule and then have 100 % retention with welding, and given the centrality of this number, discussion of the precision and accuracy of this number needs to be included.
The manuscript states that carbonates were used as sources of Ca, Na, and K. Typically these are fired in air to decarbonate, but firing will oxidize the FeO (potentially leading to oxidation of N in experiments).If not fired, then clearly CO2 will be a part of the system.More detail regarding starting composition preparation needs to be included.Was a LOI taken for the starting oxide composition to verify that it adds negligible water or CO2?I was lost in the section regarding diamonds and suggest it be removed to provide more focus on the essential data.Similarly, I had a hard time understanding the uncertainties regarding the N flux calculations.More robust number to focus on may be simply that fraction of N retained in the slab to the point of phengite breakdown is released.I commend the authors for their attempt to calculate the mass and composition of the supercritical fluid in their experiments, but insufficient details were given for the reader to evaluate this work in the manuscript.It may be helpful to publish this work as a separate manuscript to provide space and focus for this work to be understood and evaluated.
The comparison with the Ono phengite-out determination is important, but the conclusion that N (at relatively low concentrations) can shift this boundary by ~2 GPa is weak.A comparison of bulk system chemistries and experimental approaches need to be considered.What is the pressure calibration of the presses and assemblies used in these studies?A more firm conclusion could be derived if the same starting composition and same press+assembly was used for N-bearing and N-free experiments.
Please discuss the choice of functional form used for the Eq on line 163 (and I presume that R2 should be 0.92 not 92).
An important possibility to consider is that AOC and sediments may have water-rich fluid pass through them relating to the breakdown of serpentinites.The analysis of this paper appears to neglect this possibility.
Please discuss the K-alpha peak position of N in BN vs that in your samples.

A response to reviewers
Reply to the comments from Reviewer #1: I have been asked to review the machine learning component of the manuscript.My review will focus purely on the use of Extra Trees to calculate solute content in supercritical fluid.I must confess that domain of application and the high pressure-high temp experiments are outside my areas of expertise, so I will be very focused on the machine learning aspect of this work.
The main manuscript has barely any description of the machine learning method beyond the stated predictions in table 1.It would be useful to have some details beyond just the final predicted values in the main manuscript rather than relegate all the methods used to predict solute content to the supplementary material.
Reply：Thanks for your suggestions, we have moved the descriptions of machine learning method from supplementary materials to the main manuscript, and the methods used to predict solute content were detailed in this revised main manuscript (Lines 138-147; Methods lines 371-402).

Review Supplementary Text 3:
This section contains a good preliminary explanation of the machine learning process.
While the authors have used this method in previous papers as highlighted by the references, it would be ideal to add a few lines explaining the Extra Trees Algorithm and how it works.Additionally, there is no mention of why Extra-Trees was selected as the best algorithm for this data over more popular algorithms like Random Forest (which works similar to Extra Trees), or XGboost etc.It would be good to show that the choice of algorithm was based on Extra-Trees performing better than many of the commonly used regression models.
Reply：We have added the description about the principles of the Extra-Trees, Random Forest, and XGBoost algorithms in Supplementary Text 5. We have compared the performances of these three algorithms in this revision (Methods lines 381-402; Supplementary Fig. 6; Supplementary Table 3).
The Extra-Trees performs best with the lowest RMSEs for both fluid model and melt model (Table R1-1).This result is in good agreement with several recent studies [1][2][3] .The performance of the Extra-Trees is always a bit better than that of the Random Forest and XGBoost when solving regression problems with small data sets.It is possibly due to the Extra-Trees reduces overfitting through randomness, while for small data sets, overfitting is one of the most important factors that affect the performance of model.Reply: Thanks very much for your suggestion.We have compared the performance of different models based on RMSEs rather than R 2 in this revision (Methods lines 395-402; Supplementary Fig. 6; Supplementary Table 3).
Overall, it seems the machine learning component is mainly a step in their larger workflow and I hope my comments help add important information for readers and other researchers.But because most of my review focused on information in a specific section of the supplementary material, I do not feel comfortable making a recommendation to accept or reject the manuscript based on my review alone.
Reply： Thanks very much for your suggestions.We believe the revised manuscript has been much improved.

Reply to the comments from Reviewer #2:
The manuscript "Inefficient nitrogen transport to the lower mantle by sediment Reply：Thanks very much for your nice comments.Aimed at these shortcomings, we have added some experiments, deepened the discussion and revised the manuscript point-by-point.We have deleted the discussion of the formation of diamond according to the suggestion of Reviewer #3.
Lines 159-162: The nitrogen content in K-Hollandite jumps from about 1000 ppm at 10 GPa to a high value of 8000 ppm at 11 GPa.That's quite the leap in just a small pressure window!I wonder if the lower 1000 ppm at 10 GPa is because it's near the Phe/K-Holl boundary?I'd be cautious about extending this trend to much higher pressures.And also, the K-hollandite with around 1000 ppm nitrogen was at the highest experimental temperature, while the one with higher nitrogen formed at a cooler temperature.Could temperature be playing a role here?Also since the change is so strong, it should be demonstrated with more experiments as it may be due to outliers.Reply: Thanks for pointing out this.We have modified this description in this revised manuscript (Lines 163-168).

Reply
Moreover, we have revised the discussion of nitrogen preservation in phengite and sedimentary nitrogen subduction efficiency passing through the phengite to Khollandite transition in this revision (Lines 203-239; Supplementary Table 4; Supplementary Fig. 3).
First, we give a max estimate assuming there is no fluid provided by other sources.
Previous study showed that ~49-89% of sedimentary nitrogen may pass through the sub-arc mantle for the cold IBM slab 4 .For the warm CA slab, we estimate that ~24-89% of sedimentary nitrogen may pass through the sub-arc depth, using available nitrogen influx and outflux [5][6][7][8] (Supplementary Text 3).For simplification in our cases for the cold IBM slab and warm CA slab, we use average values (~69% and ~56%) for the fractions of slab sedimentary nitrogen passing through the sub-arc depth, respectively.Assuming that after the sub-arc depth phengite is the only hydrous mineral in slab sediments that carries water and nitrogen down to the phengite to K-hollandite transition depth, and that its abundance does not significantly decrease along both cold and warm slab geothermal paths 9 , we can estimate that ~30% and ~15% of the initial sedimentary nitrogen can pass through the phengite to K-hollandite transition for the cold IBM slab and the warm CA slab, respectively.It should be noted that these should be maximum values.Any breakdown or dehydration of phengite at the depth before the phengite to K-hollandite transition 10 would decrease the estimated nitrogen deep subduction efficiency; and any reaction between phengite and fluids derived from the subducting slab, such as those from the serpentinite, would also decrease the estimated nitrogen deep subduction efficiency.
Then, we give an estimate considering fluid supplied from serpentinized slab mantle (Fig. R2-2).The amounts of fluid produced from serpentine dehydration depend on geotherms [11][12][13] .We take the cold Izu-Bonin-Mariana (IBM) slab and warm Central America (CA) slab as representative slabs in our discussion.In the cold IBM slab, serpentine-bearing peridotite transfers to the Phase A-bearing peridotite and almost no fluid released 11 , so that 100% nitrogen can be preserved in phengite and carried to the K-hollandite filter.On the other hand, serpentinized slab mantle completely dehydrates at ~6 GPa in the warm CA slab, which will cause a significant nitrogen loss from phengite.In this scenario, assuming a serpentinized slab mantle with a thickness of 2 km and water content of 2 wt% 14 , the nitrogen preservation in phengite is calculated to be only ~12.3% based on the reported value of D N Phe/Fluid at 5.5 and 6.3 GPa 15,16 .This results in only ~7% of slab sedimentary nitrogen transported to the phengite to Khollandite transition depth, and only ~2% of slab sedimentary nitrogen passing through the phengite to K-hollandite transition in the CA slab.If with fluid from other sources poor in nitrogen, such as the slab oceanic crust, the nitrogen preservation in phengite to the K-hollandite filter of both cold and warms labs can be even smaller, especially considering that D N Phe/Fluid at 10 GPa is much smaller.
In short, if considering fluid supplied from other sources, sedimentary nitrogen subduction to the lower mantle would be more inefficient, further strengthening our conclusion.

Fig. R2-2 Illustration of nitrogen preservation of phengite considering serpentinite dehydration. P-T path of the slab
Moho is from D80 model 12 .The phase relations of water saturated peridotite are displayed by black dashed lines 11 .In the cold slab (Izu-Bonin-Mariana, cyan line), antigorite directly transfers to Phase A and no fluid will be released up to the depth of mantle transition zone 11 .In the warm slab (Central American, orange line), antigorite completely dehydrates and significant fluid will be produced, which will cause nitrogen loss from phengite.100% and 12.3% are the estimated nitrogen preservations in phengite of the cold slab and warm slab, respectively.4; Supplementary Fig. 3).
As the response above, without considering fluid supplied from other sources, we estimate the maximum values of the initial sedimentary nitrogen that can pass through the phengite to K-hollandite transition for the cold IBM slab of 30% and the warm CA slab of 15%.It should be noted that any breakdown or dehydration of phengite at the depth before the phengite to K-hollandite transition 10 would decrease the estimated nitrogen deep subduction efficiency; and any reaction between phengite and fluids derived from the subducting slab, such as those from the serpentinite, would also decrease the estimated nitrogen deep subduction efficiency.It depends on the amount of fluid in the slabs, especially supplied by serpentine dehydration subject to geotherms [11][12][13] .We take the cold Izu-Bonin-Mariana (IBM) slab and warm Central America (CA) slab as representative slabs in our discussion.In the cold IBM slab, serpentine-bearing peridotite transfers to the Phase A-bearing peridotite and almost no fluid released 11 , so that 100% nitrogen can be preserved in phengite and carried to the K-hollandite filter.
On the other hand, serpentinized slab mantle completely dehydrates at ~6 GPa in the warm CA slab, which will cause a significant nitrogen loss from phengite.In this scenario, assuming a serpentinized slab mantle with a thickness of 2 km and water content of 2 wt% 14 , the nitrogen preservation in phengite is calculated to be only ~12.3% based on the reported value of D N Phe/Fluid at 5.5 and 6.3 GPa 15,16 .This results in only ~7% of slab sedimentary nitrogen transported to the phengite to K-hollandite transition depth, and only ~2% of slab sedimentary nitrogen passing through the phengite to Khollandite transition in the CA slab.If with fluid from other sources poor in nitrogen, such as the slab oceanic crust, the nitrogen preservation in phengite to the K-hollandite filter of both cold and warm slabs can be even smaller, especially considering that D N Phe/Fluid at 10 GPa is much smaller.
In short, if only considering fluid poor in nitrogen supplied from serpentine dehydration, nitrogen preservation in phengite from the sub-arc depth to the phengite to K-hollandite transition depth is estimated to be 100 % for clod slab, while 12.3% for the warm slab.Accordingly, sedimentary nitrogen subduction efficiency passing through the phengite to K-hollandite transition depth is ~30% for the cold slab, while ~2% for the warm slab.Obviously, sedimentary nitrogen subduction to the lower mantle would be more inefficient if considering fluid from the serpentinized slab mantle.As the above response, nitrogen content in K-hollandite increases with pressure but decreases with temperature, which results in the drop of D N K−holl/Fluid at 10 GPa-1100 ℃ compared with D N Phe/Fluid at 10 GPa-1000 ℃.D N K−holl/Fluid is thus strongly controlled by temperature and pressure (Fig. R2-3), which can be described as the Where temperature is in K, and pressure is in GPa.Lines 205-207: Unless it's reacting with the ultramafic surrounding mantle rocks, given that K-hollandite is significantly more siliceous.
Reply: Thanks for pointing out this.In order to evaluate the contribution of sedimentary nitrogen to the origin of nitrogen in the lower mantle, we have estimated a maximum nitrogen flux carried by K-hollandite to the lower mantle, assuming that all K-hollandite after the phengite to K-hollandite transition can be subducted into the lower mantle in the revised manuscript (Lines 259-260).
We agree that K-hollandite is more siliceous and may react with ultramafic surrounding mantle rocks.But recent studies suggest that the composition of mantle is inhomogeneous and may become more silica-rich than pyrolite in the deep mantle 17- 19 .Notably, K-hollandite inclusions have been observed in some diamonds from the lower mantle [20][21][22] .These evidences suggest that K-hollandite is possible to exist in the deep mantle, depending on the model mantle composition providing sufficient K, Si, and Al.In our study, in order to evaluate the contribution of sedimentary nitrogen to the origin of nitrogen in the lower mantle, we just estimate a maximum nitrogen flux carried by K-hollandite, assuming that K-hollandite does not react with the surrounding mantle rocks in the lower part of upper mantle and the mantle transition zone.
Lines 281-287: This is based on the assumption that nitrogen degassing from the mantle (at 7.73 x10^7 kg/y) has been consistent throughout Earth's history.But, with Earth cooling down, there's been a decline in magmatism, as seen in the slowing rates of MORB spreading, reduced partial melting, and cooler upper mantle temperatures.So, it's likely that nitrogen degassing has been decreasing over time, which might make these calculations a bit off.

Reply:
Yes.With Earth cooling down, it's likely that nitrogen degassing has been decreasing over time.But we here provide a maximum estimation of nitrogen accumulation to the lower mantle applying the current values of influx and degassing flux, in order to evaluate the contribution of sedimentary nitrogen to the origin of the lower mantle nitrogen.We have stated this in this revised manuscript (Lines 258-263).
Assuming that plate tectonics started ~3 Ga ago 23 with a steady nitrogen net influx, and all K-hollandite after the phengite to K-hollandite transition can be subducted into the lower mantle 21,24 , we can estimate that ~4.6×10 17 kg nitrogen from slab sediments has been subducted to the lower mantle, which corresponds to ~0.15 ppm nitrogen in the lower mantle.The estimated nitrogen amount to the lower mantle should be a maximum value, because the ancient slab geothermal could be warm to hot 25 , which could readily increase outgassing and decrease the net nitrogen influx by slab sediments to the lower mantle.
Based on this maximum estimation, sedimentary nitrogen contributes 2.5-15% nitrogen in the present lower mantle.As a result, the origin of nitrogen in the lower mantle from sedimentary nitrogen should be very limited, less than ~15% considering the higher outgassing flux in the past.Reply: Thanks for your suggestion.We have read studies by Som and colleagues in 2013 (Nature) and 2016 (Nature Geoscience), and the one by Marty and team in 2013 (Science).We noted that Som et al. 26,27 and Marty et al. 28 provided nitrogen partial pressure of Archean atmosphere at 2.7-3.5 Ga ago.But Yoshioka et al. 29 suggested the nitrogen partial pressures of a primordial atmosphere coexisting with the crystallizing magma ocean.
To evaluate the contribution of sedimentary nitrogen to the origin of the lower mantle nitrogen, we do not apply the initial mantle nitrogen budget of Yoshioka et al. 29 , but have chosen the present mantle nitrogen budget obtained from N2/Ar ratios [30][31][32] in this revised manuscript (Lines 263-267).
Lines 307-310: It's not too surprising that nitrogen-rich diamonds are mainly found at shallower depths.After all, the subduction of nitrogen-rich materials tends to happen from the top down.
Reply: Yes.We have deleted the discussion of formation of diamond in this revised manuscript.
Lines 313-316: The Science study you cited, titled "Ice-VII inclusions in diamonds: Evidence for aqueous fluid in Earth's deep mantle", shows the current residual pressure of the ice-VII inclusions at 9 +-2 GPa.However, the diamonds containing these inclusions actually formed much deeper, around the mantle transition zone (14-22 GPa and even beyond 22 GPa).This seems a bit contradictory to your results, especially since this study's main takeaway is that diamonds primarily form at around 310-315 km or roughly 10 GPa (as shown in Fig. 4).At 9 +-2 GPa, ice-VII can only exist below 500 C, but even the coldest slabs are hotter than 800 C at this pressure.This might need some rethinking or further clarification.
Reply: Yes.We have removed this part and mainly paid attention to the contribution of sedimentary nitrogen to the origin of nitrogen in the lower mantle, following the suggestion of reviewer #3.

Reply to the comments from Reviewer #3:
Huang et al present new experimental data to constrain the partitioning of N during the mineralogical transition of phengite and K-hollandite.They find that N partitioning is weaker into K-hollandite than into phengite, and this implies that slabs could lose a large fraction of remaining N budget as they pass through 10 GPa (~300 km depth), potentially limiting the supply of N to deeper sections of the mantle.
While the essential data reported may provide an important constraint regarding how slabs work to redistribute N in Earth's interior, the manuscript needs to include a section that discusses evidence for equilibrium being closely approached for the experiments, with careful attention paid to N. Without this, N partition coefficients cannot be established, as partitioning is a reflection of an equilibrium chemical system.
Reply: Yes, thanks very much for the nice comment and suggestion.To evaluate equilibrium, we have added two experiments for different durations, i.e., 48 h and 72 h.
Based on the homogenous distribution of nitrogen and major elements, and excellent P-T dependence of nitrogen content of K-hollandite and D N K−holl/Fluid , we have added a section to discuss the attainment of equilibrium in this revised manuscript (Lines 170-

179).
All products have closely approached the equilibrium of nitrogen based on the following reasons: (1) As the only nitrogen-bearing minerals in the run products, phengite and K-hollandite of each run have homogeneous nitrogen content with relatively small standard deviations less than 15%.Besides, their homogeneous major element compositions display the same P-T dependence to those observed in previous studies with volatile-rich pelite (Fig. R3-1a, b). ( 2) For the runs ranging from 48 h to 72 h, the nitrogen content of K-hollandite shows a strong temperature dependence at 11 GPa (Fig. R3-1c) and similar pressure dependences at different temperatures (800, 1000 and 1100 ℃; Fig. R3-1d).( 3) The variation of D N K−holl/Fluid can also be explained by the variation of the experimental P-T conditions (Fig. R3-1e).Moreover, previous works have identified that oxygen fugacity is a major control on N partitioning, but this parameter is also not discussed.I think it is simply assumed that all N remains reduced, but this is not stated nor defended.
Reply: Thanks for pointing out this.Oxygen fugacity should be an important parameter that influence nitrogen partitioning.To evaluate potential impact of oxygen fugacity on the nitrogen partitioning behavior in our study, we have added two experiments at 11 GPa and 1000 o C with NH3 solution and NH4NO3 as the source of nitrogen, respectively.We have evaluated the oxygen fugacity of our experimental systems in this revised manuscript (Lines 165-168; lines 180-187; Methods lines 347-370).
(1) Oxygen fugacity evaluation.The oxygen fugacity in our experiments is not controlled by buffer, but it can be roughly constrained by the phase assemblages and the compositions of phases.In the NH4NO3-bearing run, the decomposition reaction of NH4NO3 = N2 + 2H2O + 1/2O2 should occur at 1000 o C and cause an oxidized condition.
Indeed, the observation of hematite in this run indicates that the oxygen fugacity is at least higher than Fe2O3-Fe3O4 (HM) buffer.As shown in the following Fig.R3-2, the oxidized condition is also evidenced by the abnormal mineral compositions.Garnet in this run is lack of almandine composition (Fig. R3-2a), while the enrichments of iron in kyanite and clinopyroxene are observed.The composition of clinopyroxene is similar to jadeite (NaAlSi2O6), with a minor diopside composition (CaMgSi2O6), but has obvious lower Al content.It indicates that iron is mainly Fe 3+ which replaces the Al 3+ (Fig. R3-2b).On the contrary, in the NH3-bearing runs, negligible iron is detected in clinopyroxene and kyanite, suggesting that most of Fe is still ferrous iron.
Clinopyroxene formed, at 10-12 GPa and 1000-1100 o C, in a Ni-NiO (NNO) buffered pelite system with ~4.12 wt% iron contains ~1.18-1.68wt% iron 33 , much higher than the Fe content of our clinopyroxene formed in a pelite system with ~7 wt% iron.This comparison suggests that the oxygen fugacity of the NH3-bearing runs should be at least lower than NNO buffer.On the other hand, the absence of metal iron indicates that the oxygen fugacity of the NH3-bearing runs is higher than Fe-FeO (IW) buffer.Therefore, the oxygen fugacity of the NH3-bearing runs can be limited between NNO and IW buffers.
(2) Influence of oxygen fugacity on D N K−holl/Fluid .In the NH4NO3-bearing run, no nitrogen is detected in the K-hollandite based on the EPMA and Raman spectroscopy, in contrast to the high nitrogen content of 6553±813 ppm in the K-hollandite of the NH3-bearing run at the same P-T condition (Fig. R3-2 c).This suggests that high oxygen fugacity in the NH4NO3-bearing run, as indicated by the presence of hematite, stabilizes N2 over reduced nitrogen species, and nitrogen is stored in K-hollandite mainly as ammonium (Fig. R3-2 c).This contrast indicates that high oxygen fugacity may reduce the nitrogen partition coefficient between K-hollandite and fluid, depending on N species in fluid.
Anyway, our study provides nitrogen partition coefficient between K-hollandite and fluid of the NH3-bearing runs corresponding to the oxygen fugacity between NNO and IW buffers similar to the subduction zone redox conditions 34 .The mass balance calculations appear to assume that exactly 8 wt% of a fluid was added to oxide powders to generate the starting composition.It is not possible to add exactly 8 wt % of fluid to a capsule and then have 100 % retention with welding, and given the centrality of this number, discussion of the precision and accuracy of this number needs to be included.
Reply: Thanks for the pointing out this.We have corrected this and discussed the precision and accuracy in the revision (Methods lines 287-293; Supplementary Text 4; Supplementary Table 1), and we used the corrected the fluid mass fractions of each NH3-bearing run in the following Table R3-1 to calculate nitrogen partition coefficients for the NH3-bearing runs.
For the NH3-bearing runs, a NH3 (25 wt%)-H2O solution was used as the water and nitrogen source.The added volume of NH3 solution was calculated by the ideal mass of NH3 solution and its density (0.9).The difference between the capsule weight before the addition of NH3 solution and that after the gas-tightness test is considered as the mass of NH3 solution in the capsule.By comparison with the ideal mass of NH3 solution that should be loaded in, we can estimate the maximum uncertainty induced by the loading and welding processes.The fluid retention in the capsule ranges from ~77 to 94%.This indicates that ~6.2-7.5 wt% fluid has been added to the system.
However, the concentration of NH3 in fluid should not change greatly due to the consistent P-T dependence of the nitrogen content in K-hollandite, despite variations in fluid retention among different runs.For example, the 10 GPa-1100 °C run with a fluid retention of 94% has the lowest nitrogen content in K-hollandite, while the 12 GPa-1000 °C run with a fluid retention of 77% has the second highest nitrogen content in Khollandite.Therefore, the fluid mass fraction of each run (Table R3-1) was concurrently corrected for both water and NH3 during the calculation of partition coefficients.The manuscript states that carbonates were used as sources of Ca, Na, and K. Typically these are fired in air to decarbonate, but firing will oxidize the FeO (potentially leading to oxidation of N in experiments).If not fired, then clearly CO2 will be a part of the system.More detail regarding starting composition preparation needs to be included.
Was a LOI taken for the starting oxide composition to verify that it adds negligible water or CO2?
Reply: Thanks for the suggestion.We have dried the carbonates to remover water and decarbonate.To avoid being oxidized, the FeO was added to the mixture after decarbonation.We did not take a LOI, but the whole preparation process is generally applied in this field and should remove CO2 and absorbed water.We have added the detailed descriptions about the preparation of starting materials in this revision

(Methods lines 278-288).
To remove absorbed water, SiO2, TiO2, Al2O3, and MgO powders were heated at 1000 °C for 12 h, Na2CO3 and K2CO3 powders were fired at 100 °C for 5 h, and CaCO3 powder was held at 200 °C for 5 h.These chemical powders were mixed and ground in ethanol in an agate mortar for at least 1 h and subsequently dried at room temperature, after which the dried mixture was decarbonated at 1000 °C for 10 h.Finally, the FeO powder was mixed with the decarbonated mixture and ground in ethanol in an agate mortar for at least 1 h, after which the final mixture was dried at room temperature.All the dried starting materials were stored in a vacuum oven at 100 °C for at least 24 h before being loaded into the Au capsules.NH3 (25 wt%)-H2O solution and NH4NO3 were used as nitrogen sources for the eight NH3-bearing runs and one NH4NO3-bearing run, respectively.
I was lost in the section regarding diamonds and suggest it be removed to provide more focus on the essential data.Similarly, I had a hard time understanding the uncertainties regarding the N flux calculations.More robust number to focus on may be simply that fraction of N retained in the slab to the point of phengite breakdown is released.
Reply: Thanks for your suggestion.We have removed the section about diamond formation.We have adjusted the paragraphs, and focused more on sedimentary nitrogen subduction efficiency passing through the phengite to K-hollandite transition (Lines 188-239).To make the nitrogen flux calculation clearer, we have re-organized language and paragraphs in this revision (Lines 241-257).We also modified Fig. 4b by adding the values of sedimentary nitrogen subduction efficiency.
I commend the authors for their attempt to calculate the mass and composition of the supercritical fluid in their experiments, but insufficient details were given for the reader to evaluate this work in the manuscript.It may be helpful to publish this work as a separate manuscript to provide space and focus for this work to be understood and evaluated.
Reply: Thanks very much for your recommendation.We applied machine learning to calculate the mass and composition of the supercritical fluid in our experiments.This method part was in the original Supplementary Text 3 (now Lines 138-147; Methods lines 371-402; Supplementary Text 5), which was specifically reviewed by Reviewer #1.
According to the suggestion of Reviewer #1, we have added some descriptions about datasets, the processes for building the models, uncertainties of the models, and the performances of different algorithms in the revised manuscript (Lines 138-147; lines 371-402).We also have provided the description about the principles of the algorithms in the revised Supplementary Text 5.
The comparison with the Ono phengite-out determination is important, but the conclusion that N (at relatively low concentrations) can shift this boundary by ~2 GPa is weak.A comparison of bulk system chemistries and experimental approaches need to be considered.What is the pressure calibration of the presses and assemblies used in these studies?A more firm conclusion could be derived if the same starting composition and same press+assembly was used for N-bearing and N-free experiments.
Reply: Yes, we have discussed the bulk system chemistry and experimental approaches of our study and Ono.(1998) 35 in this revision (Lines 92-100; Methods lines 304-308; Supplementary Fig. 4).
The compositions of the starting materials we used is the same as that used by Ono.
(1998), and the only difference is that we added nitrogen in the system.Therefore, the impact of compositions except nitrogen can be excluded.The relationships between the press load and the sample pressure were calibrated following phase transformations  Please discuss the choice of functional form used for the Eq on line 163 (and I presume that R2 should be 0.92 not 92).
Reply: Yes, it was 0.92.In this revision, we use the equation of Y= a/T + b*P/T +c to fit the P-T dependence of log(D N K−holl/Fluid ) (Lines 157-162).
The equilibrium constant (K) of nitrogen partitioning between mineral and fluid can be expressed as An important possibility to consider is that AOC and sediments may have water-rich fluid pass through them relating to the breakdown of serpentinites.The analysis of this paper appears to neglect this possibility.
Reply: Thanks for the comment.In this revision, we have discussed the nitrogen preservation in phengite considering fluid existing, and thereby revised the discussion about sedimentary nitrogen subduction efficiency passing through the phengite to Khollandite transition in this revision (Lines 228-239; Supplementary Table 4; Supplementary Fig. 3).
Without considering fluid supplied from other sources, we estimate the maximum values of the initial sedimentary nitrogen that can pass through the phengite to Khollandite transition for the cold IBM slab of 30% and the warm CA slab of 15%.It should be noted that any breakdown or dehydration of phengite at the depth before the phengite to K-hollandite transition 10 would decrease the estimated nitrogen deep subduction efficiency; and any reaction between phengite and fluids derived from the subducting slab, such as those from the serpentinite, would also decrease the estimated nitrogen deep subduction efficiency.It depends on the amount of fluid in the slabs, especially supplied by serpentine dehydration subject to geotherms [11][12][13] .We take the cold Izu-Bonin-Mariana (IBM) slab and warm Central America (CA) slab as representative slabs in our discussion (Fig. R3-4).In the cold IBM slab, serpentinebearing peridotite transfers to the Phase A-bearing peridotite and almost no fluid released 11 , so that 100% nitrogen can be preserved in phengite and carried to the Khollandite filter.On the other hand, serpentinized slab mantle completely dehydrates at ~6 GPa in the warm CA slab, which will cause a significant nitrogen loss from phengite.
In this scenario, assuming a serpentinized slab mantle with a thickness of 2 km and water content of 2 wt% 14 , the nitrogen preservation in phengite is calculated to be only ~12.3% based on the reported value of D N Phe/Fluid at 5.5 and 6.3 GPa 15,16 .This results in only ~7% of slab sedimentary nitrogen transported to the phengite to K-hollandite transition depth, and only ~2% of slab sedimentary nitrogen passing through the phengite to K-hollandite transition in the CA slab.If with fluid from other sources poor in nitrogen, such as the slab oceanic crust, the nitrogen preservation in phengite to the K-hollandite filter of both cold and warm slabs can be even smaller, especially considering that D N Phe/Fluid at 10 GPa is much smaller.
Fig. R3-4 Illustration of nitrogen preservation of phengite considering serpentinite dehydration.P-T path of the slab Moho is from D80 model 12 .The phase relations of water saturated peridotite are displayed by black dashed lines 11 .In the cold slab (Izu-Bonin-Mariana, cyan line), antigorite directly transfers to Phase A and no fluid will be released up to the depth of mantle transition zone 11 .In the warm slab (Central American, orange line), antigorite completely dehydrates and significant fluid will be produced, which will cause nitrogen loss from phengite.100% and 12.3% are the estimated nitrogen preservations in phengite of the cold slab and warm slab, respectively.
Please discuss the K-alpha peak position of N in BN vs that in your samples.

Reply:
The N Kα peak positions of BN (147.56 ± 0.01 mm) and our sample (147.19 ± 0.29 mm) are similar within the error range (Fig. R3-5).We have provided the detailed introduction of nitrogen measurement and the accuracy in this revised manuscript (Methods lines 327-342; Supplementary Fig. 5).As stated in my review of the previous version of this manuscript, I have been asked to review the machine learning component of the manuscript.My review will focus purely on the machine learning methods, their application, and reviewing the accurate representation of the results of fluid and melt predictive models.I must confess that domain of application and the high pressure-high temp experiments are outside my areas of expertise, so I will be very focused on the machine learning aspect of this work.
As per suggestions on the previous version of the manuscript, the authors have included more details on the machine learning method in the main manuscript.The authors have also addressed all of my previous suggestions to improve the accuracy and clarity of the machine learning component of this manuscript.
One minor point: Line 392-394: It is unclear to me what this sentence is stating.I assume the authors mean that since their dataset is small, the final fluid and melt models made available to researchers will be trained on all the data.If this is the correction interpretation, then I recommend modifying the sentence to make it a bit clearer to the reader.
Overall, the machine learning component of the manuscript has improved and the authors have taken reviewer suggestions to provide key details about the machine learning method, the results, and the reproducibility of the model.I still do not feel entirely comfortable providing an accept or reject because the domain of application and the high pressure-high temp experiments are outside my areas of expertise.I will however state that the machine learning component of this paper is well described and the authors have provided sufficient information on the choice of algorithm, the comparison of accuracy of results between models, and the reproducibility of the machine learning algorithm.
Reviewer #1 (Remarks on code availability): I was able to download and run the code in my local machine.The authors provide enough instruction to install and run the code.
Reviewer #2 (Remarks to the Author): I read the manuscript again and I am happy with all the improvements and the detailed responses to my concerns.I recommend publication now!Reviewer #3 (Remarks to the Author): Huang et al present a revised draft of their manuscript focused on the partitioning of N in sediment-fluid systems containing phengite and K-hollandite.I commend the authors on completing new experiments, additional analysis regarding their peak centers, and discussion regarding oxygen fugacity.
I still have issues with the following: 1) The additional experiment conducted with a more oxidized starting fluid (NH4NO3) now demonstrates that oxygen fugacity likely plays a role in N partitioning at ~10 GPa in slab system, and yet the effect of redox remains unaccounted for in the parameterization of the data or application of the parameterization to modeling the fate of N in slab systems.Constraining oxygen fugacity to a 4 orders-ofmagnitude range (IW to NNO) is not sufficient when developing predictions to natural systems.In short, the treatment of redox remains insufficient.
2) Nitrogen is shown to be incompatible to similar degrees in both phengite and K-hollandite (both minerals incorporate ~1000 ppm N in experiments), but it is argued that the preferential incorporation of N into phengite stabilizes it over K-hollandite by 2 GPa.Please further discuss this observation and seek support for other elements providing a similar degree of stabilization at these low concentrations.
Perhaps the impact of N on the phengite/K-Hollandite boundary relates to changes in fluid chemistry?Although, the simple effect of adding N to a fluid should be to dilute H2O and destabilize hydrous minerals over anhydrous ones.
3) Wavescans are now reports for the standard and an experimental mineral (K-hollandite).The peak center is provided for the K-hollandite, along with an uncertainty, but I cannot find any description of how the uncertainty was derived.The peak center depends on the background model, and it is stated that an exponential model is used, but the red line subduction" by Huang et al., presents the role of sediment subduction in the origins of deep Earth nitrogen and examines the behaviour of sedimentary nitrogen during the transition of phengite to K-hollandite under conditions of 10-12 GPa and temperatures ranging from 800-1100°C.The study investigates the nitrogen partitioning coefficients between K-hollandite and fluid (5 experiments), as well as phengite and fluid (1 experiment), revealing the trends with increasing pressure (and temperature).These findings offer new insights into how much nitrogen remains preserved at the phengitehollandite transition depth and how much might be transported to the lower mantle by K-hollandite.However, the study may fall short on some fronts as detailed below.Most importantly, there are potential contradictions regarding the depths at which nitrogenrich diamonds are found, especially in relation to the residual pressure of ice-VII inclusions in diamonds.While this research provides a new picture of phengite/Khollandite transition in sediment subduction's contribution to mantle nitrogen, these weaknesses need further clarification.

:
Thanks very much for the suggestion.In this revision, we have added two new experiments at 11 GPa-1000 o C and 11 GPa-1100 o C to investigate the role of temperature in nitrogen content in K-hollandite.We have demonstrated the P-T dependence of nitrogen content in K-hollandite in the revised manuscript (Lines 114-120).As shown in the following Fig.R2-1a, the nitrogen content of K-hollandite indeed depends on temperature and shows a decrease with increasing temperature at 11 GPa.Besides, at each investigated temperature, it increases with enhancing pressure following the same slope (Fig. R2-1b).Linear regression of the experimental data yields the following equation to predict N content in K-hollandite: log(C N K−holl , ppm) = −2481.25(±1539.39) + 482.05(±127.99) + 1.42(±0.57)(R 2 =0.82, p-value=0.01)(Eq.1)Therefore, the excellent P-T dependence can exclude the possible effect of Phe/Kholl boundary.Based on Eq. 1, the high values of ~8000-9000 ppm at 11 GPa-800/900 o C, and low value of ~1000 ppm at 10 GPa-1100 o C are expected.Thus, the drastic decrease of nitrogen content in K-hollandite of the 10 GPa-1100 o C run should be caused by the lower pressure and higher temperature.

Fig. R2- 1
Fig. R2-1 (a) The temperature and (b) pressure dependence of the nitrogen content in K-hollandite.Lines 169-172: But how much nitrogen actually gets to the depth where phengite transitions to K-hollandite?Given that DN(mineral/fluid) is pretty low, at about 0.031 for phengite/fluid, and considering phengite's presence from the start of subduction to 10 GPa, it's possible most of the nitrogen is already out by 10 GPa.And with the slab heating up from the inside, there's likely a lot of fluid escaping from its core and moving up through the phengite-rich top layer.
Lines 196-199: Now, phengite interacts with fluid coming from within the slabs, especially as the serpentinized mantle rocks of the slab heat up.If this fluid isn't rich in nitrogen, phengite might lose its nitrogen to it, especially since DN(phengite/fluid) is quite low at 0.031.Reply: Yes.We have discussed the nitrogen preservation in phengite considering fluid existing, and thereby revised the discussion about sedimentary nitrogen subduction efficiency passing through the phengite to K-hollandite transition in this revision (Lines 228-239; Supplementary Table

Lines 200- 203 :
This rapid nitrogen drop might hinge on the lower DN(Khollandite/fluid), which seems to be increasing quickly within a tight pressure range of 1 GPa.This might be because it's close to the phengite/k-hollandite transition, as mentioned earlier in lines 159-162.Reply: It is mainly caused by the temperature effect, which is demonstrated by the data from our added experiments.We have discussed the P-T dependence of D N K−holl/Fluid in this revised manuscript (Lines 157-165).We have also modified the comparison between D N Phe/Fluid and D N K−holl/Fluid at the same P-T condition, 0.031 versus 0.013 at 10 GPa-1000 ℃ (Lines 196-198).

Lines 291- 294 :
Some earlier research suggests that Earth's ancient atmosphere had a pressure pretty similar to what we have today.Just check out the studies by Som and colleagues in 2013 (Nature) and 2016 (Nature Geoscience), and the one by Marty and team in 2013 (Science).

Fig. R3- 1
Fig. R3-1 (a) Pressure dependence of major elements in phengite.(b) Temperature dependence of major elements in K-hollandite.(c) Temperature dependence of nitrogen content in K-hollandite.(d) Pressure and temperature dependences of nitrogen content in K-hollandite.(e) Pressure and Temperature effects on D N K−holl/Fluid .

Fig. R3- 2
Fig. R3-2 (a) Fe contents in garnet in different systems.(b) Pressure dependence of the substitution of NaAlSi2O6 to CaMgSi2O6 compositions, and the substitution of NaFe 3+ Si2O6 to NaAlSi2O6 occurring in NH4NO3-bearing run.(c) Raman spectroscopy of K-hollandite with different nitrogen contents.Peaks in the range of 2700-3400 cm -1 are the signal of ammonium.Asterisks indicate that the peaks are influenced by the contamination of resin.

(
Fig. R3-3a): Bi (I-II, 2.55 Pa), Bi (III-V, 7.7 Pa), Pb (13.6 Pa), ZnS (15.6 GPa) at room temperature and quartz-coesite (3.5 GPa), coesite-stishovite (9.9 GPa), olivinewadsleyite (14.5 GPa) at 1400 o C.Under our experimental conditions, the difference between the calibrations at 1400 o C and room temperature is within 0.4 GPa.The phase transitions used for pressure calibration in Ono.(1998) are as follow: SiO 2 (quartzcoesite) at 3.2 GPa at 1200 o C, Fe2SiO4 (α-γ) at 5.8 and 6.3 GPa at 1200 o C and 1400 o C, SiO 2 (coesite-stishovite) at 9.7 GPa at 1400 o C, and Mg 2 SiO 4 (α-β) at 14.3 GPa and 15.1 GPa at 1400 o C and 1600 o C.There are three same phase transitions in pressure range of ~3-15 GPa used for pressure calibration in our study and Ono.(1998).Therefore, uncertainty induced by pressure calibration should be small.In addition, the substitution of (Mg, Fe 2+ ) + Si = Al IV + Al VI in phengite displays good correlation with pressure in the pelitic system (Fig.R3-3b), and the Si, Al, Mg, and Fe contents of phengite in our work and Ono's work almost display the same pressure dependence.It further demonstrates that the uncertainty of pressure induced by pressure calibration is negligible and should not influence our conclusions.

Fig. R3- 5
Fig. R3-5 Comparison of the N K-alpha peak between BN and K-hollandite.Baseline correction for the N K-alpha peak of (a) BN and (b) K-hollandite (NH-8).Peakfitting of the N K-alpha peak of (c) BN and (d) K-hollandite with Gaussian + Lorentzian function.The N K-alpha peak positions of BN and K-hollandite are 147.56±0.01mmand 147.19±0.29 mm, respectively.
Fig S5 B seems to have a different functional form than described in the text.Backgrounds are extremely important here as signals are highly impacted by the background, as down in Fig S5.

and explained in this revised manuscript (Methods lines 384- 392).
It is good to see the use of RMSE to evaluate the error of the extra trees model.