On the equilibrium limit of liquid stability in pressurized aqueous systems

Domain: earth_science
Published: 2024-12-18
Editorial outcome: major_revision

Abstract
Phase stability, and the limits thereof, are a central concern of materials thermodynamics. However, the temperature limits of equilibrium liquid stability in chemical systems have only been widely characterized under constant (typically atmospheric) pressure conditions, where under these limits are represented by the eutectic. At higher pressures, the eutectic will shift in both temperature and chemical composition, opening a wide thermodynamic parameter space over which the absolute limit of liquid stability, i.e., the limit under arbitrary values of the thermodynamic forces at play (here pressure and concentration), might exist. In this work, we use isochoric freezing and melting to measure this absolute limit for the first time in several binary aqueous brines, and nodding to the etymology of “eutectic”, we name it the “cenotectic” (from Greek “κοινός-τῆξῐς”, meaning “universal-melt”). We discuss the implications of our findings on ocean worlds within our solar system and cold ocean exoplanets; estimate thermodynamic limits on ice crust thickness and final ocean depth (of the cenotectic or “endgame” ocean) using measured cenotectic pressures; and finally provide a generalized thermodynamic perspective on (and definition for) this fundamental thermodynamic invariant point.

Introduction
Multiphase liquid-solid equilibrium ranks amongst the most fundamental concepts in thermodynamics and physical chemistry, providing the foundation of modern phase diagrams, grounding of thermodynamic analysis, and driving countless industrial processes. In multi-component systems, at constant pressure, the lowest temperature at which a liquid may remain stable at equilibrium is defined as the eutectic (from Greek “εὐ-τῆξῐς”, “easy-melt”), an invariant point in temperature-concentration (T-x) space at which the liquid will transition entirely into a mixture of solid phases. Eutectics are of crucial importance to a wide range of applications, from metallurgy to igneous rock formation, phase change thermal energy storage to cryopreservation, drug discovery to planetary science, etc. The canonical definition of the eutectic is often considered at a fixed pressure (typically 0.1 MPa/atmospheric pressure); however, increased states of compression may substantially affect the melting curves of solids, resulting in a change of eutectic T-x coordinates. When pressure is varied, the eutectic becomes an univariant curve in P-T-x space, the trajectory of which depends upon the geometry of the liquidus curves of the contributing solid phases.

For most materials, solid phases are denser than the liquid phase, meaning these materials possess positive Clapeyron melting slopes (dP/dT > 0). For systems containing such solids, univariant eutectic curve (also called cotectic) temperatures will increase with increasing pressures.

Select compounds in natural science and engineering, however, such as water, silicon, or gallium, have negative Clapeyron melting slopes at 0.1 MPa (i.e., select solid phases of these compounds are less dense than the liquid). In many binary systems containing these compounds, initial compression from 0.1 MPa leads to pressure-induced melting point depression, resulting in the univariant eutectic curve decreasing in temperature with increasing pressure1. However, for all of these systems, continued compression of the liquid will eventually result in the formation of a denser solid phase (e.g., ice III, Si-II, Ga-II), thereby reversing the Clapeyron slope. In this context, the negative-Clapeyron eutectic curve for the lower pressure range will intersect a positive-Clapeyron higher-pressure melting line at an invariant point in P-T-x space.

For aqueous solutions in which the eutectic in equilibrium with ice-Ih is the lowest-temperature eutectic in the phase diagram (including most solutions of salts, sugars, and other solutes that are solid at room temperature), this invariant point represents the lowest possible temperature at which a given aqueous liquid phase may remain stable at equilibrium under any P-T-x conditions and therefore represents a fundamental property of the system. While select previous works have inadvertently observed this fundamental invariant thermodynamic point in the study of high-pressure eutectics2–4, to our knowledge, no previous study has identified or measured the invariant point itself, nor defined it as an entity distinct from other univariant transitions.

Based on the etymology of eutectic (from Greek “εὐ-τῆξῐς”, “easy-melt”), we propose the name cenotectic (from Greek “κοινός-τῆξῐς”, “universal-melt”) for this invariant point, and we illustrate it in Fig. 1 as point κ (the Greek letter kappa), which presents a semi-quantitative P-T-x diagram for a binary system of water and a generic salt-like solute. Note that in most aqueous systems, given the geometries of the ices-liquid liquidus surfaces, this point is typically located on the ice Ih-ice III-liquid or ice Ih-ice II-liquid equilibrium boundary.

In this work, we describe first-of-their-kind experimental determinations of the precise P-T coordinates of the cenotectic points of major binary aqueous systems relevant to planetary sciences, medical sciences, and engineering. These results are acquired via an isochoric freezing and melting approach previously established by our group1 for the interrogation of univariant phase configurations, which we herein extend to the absolute temperature limit of aqueous liquid stability and furthermore use to identify several potentially new high-pressure hydrate phases. We discuss the implications of this data on our evolving understanding of low-temperature aqueous thermodynamics, detail implications in planetary science for icy ocean worlds, and provide a suggested roadmap toward rapid illumination of the yet-unexplored low-temperature high-pressure parameter space for aqueous solutions. In closing, we provide a generalized and complete definition of the cenotectic, applicable to arbitrary chemical systems under the influence of any arbitrary modes of thermodynamic work.

Results
Here, we use isochoric freezing and melting1 to measure the pressure-temperature evolution of the eutectic for eight aqueous binary solutions (Na2CO3, KCl, MgSO4, Na2SO4, Urea, NaCl, MgCl2, and NaHCO3) in the temperature range 203–273.15 K and the pressure range 250 to 0.1 MPa, identifying the P-T coordinates of the cenotectic point in five of them and pointing at new possible high-pressure hydrate phases in the remaining three (NaCl, MgCl2, NaHCO3). The eutectic P-T curves for all eight solutions studied are shown in Fig. 2.

In brief, the experimental methodology consists of confining each ~5.33 mL eutectic solution sample in a custom metallic isochoric chamber free of air and fitted with a high-accuracy pressure transducer; submerging the chamber in a calibration-grade programmable circulating bath; cooling the chamber continuously to a temperature at least 30 K beneath the 0.1 MPa eutectic temperature; allowing all crystallization processes to reach steady-state (after nucleation of ice III or ice II), as indicated by constancy of the pressure signal; then warming the chamber and melting its contents in 0.5 K increments, recording the steady pressure at each temperature. Isochoric conditions allow the pressure in the system to vary freely in response to the changing volumes of emerging or receding phases and couple the temperature and pressure according to Gibbs’ phase rule, which dictates that a univariant phase configuration (i.e., the three-phase eutectic in a binary solution) has only one intensive degree of freedom.

Cenotectic measurements
After total freezing of the solution, most experiments are observed to stabilize around 210 MPa (see, for example, Supplementary Fig. S2), coincident with the solid-solid phase transitions of ice Ih-ice III and ice Ih-ice II in the studied temperature range5,6. Upon warming, the pressure first remains approximately constant for some period, again consistent with the quasi-isobaric nature of the ice Ih-ice III/II phase boundary, and we then observe two varieties of isochoric pressure-temperature curves, monotonic (Na2CO3, KCl, MgSO4, Na2SO4, and Urea), and non-monotonic (NaCl, MgCl2, and NaHCO3).

For monotonic curves, shown in Fig. 2a, b, as temperature increases during warming, we first observe a clear discontinuity in the slope of the P-T curve upon the emergence of the liquid phase, and then a monotonic decrease in pressure as the liquid phase fraction increases along the eutectic curve. This first discontinuity is identified as the cenotectic point, the lowest temperature at which the liquid phase remains stable, and occurs at pressures consistent with the ice Ih-ice III or ice Ih-ice II transitions.

In order to precisely identify the cenotectic P-T coordinates, we fit polynomials to P-T eutectic curves colder and warmer than the apparent cenotectic point (the colder curve including ice Ih, ice II/III, and the salt-bearing solid phase; and the warmer curve including ice Ih, the salt-bearing solid phase, and the liquid) and calculated their intersection, at which all four phases may coexist. Average cenotectic pressures and temperatures across n = 3 trials per solution are listed in Table 1, alongside the initial concentration of the solution used, the eutectic temperature measured at atmospheric pressure, and the temperature delta between the eutectic and the cenotectic. Propagated uncertainties accounting for both experimental error and fit uncertainty are included in parentheticals (details in Supplementary Note 4).

In Fig. 2a, we also compare our eutectic curve P-T results for MgSO4 and Na2SO4 to those of Hogenboom and colleagues2,3, which agree well and represent the only other data we were able to identify on high-pressure, low-temperature eutectic equilibria for the systems studied here. Furthermore, although Hogenboom and co. did not measure the cenotectic points of these two solutions, we may estimate them by quadratically fitting the data clusters along the ice Ih eutectic and ice III eutectic curves and calculating the intersections of these fits. The cenotectic values calculated from the data of Hogenboom and co. (MgSO4: 211.74 MPa, 248.50 K; Na2SO4: 208.34 MPa, 249.95 K) stand in strong agreement with the measurements featured in Table 1.

These literature data also highlight the distinct enhancement in resolution afforded by the isochoric freezing and melting approach, which enables continuous generation and measurement of pressure in response to continuous variation of the temperature, as compared to isobaric techniques performed at discrete isothermal-isobaric pressure-temperature steps. The results herein furthermore confirm the suspicions of Hogenboom et al. that their measurements of water-Na2SO4 eutectic coordinates did not reflect the equilibrium state (i.e., entered a metastable configuration) at pressures above 200 MPa.

It should be noted that while we do not directly measure the evolution of the salt concentration in the aqueous liquid phase, based on our previous study of high-pressure binary eutectics1, we expect that it will continuously decrease with increasing pressure, beginning at approximately the eutectic concentration (me in Fig. 1; exact value listed in Table 1) and ending at the cenotectic concentration (mκ in Fig. 1). Using the cenotectic P-T coordinates shown in Table 1, future work should aim to characterize the cenotectic salt concentration in the liquid directly.

For NaCl, MgCl2, and NaHCO3, our ability to observe the stable ice III (or ice II below 238 K) transition and determine the cenotectic was confounded by the apparent emergence of high-pressure intermediates, some of which we anticipate may represent previously unknown phases. P-T coordinates measured for each of these systems under different cooling protocols (see “Methods”) are shown individually in Fig. 2c (with additional runs shown in Supplementary Note 3), and suggest that isochoric freezing and melting may prove an effective technique for screening for new phases in low-temperature aqueous systems.

For the 23.3% NaCl solution, which begins in a eutectic configuration comprised of liquid, ice Ih, and hydrohalite (NaCl·2H2O, or SC2), an intermediate phase transition was observed at approximately 237 K/140 MPa, remarkably close to the temperature at which Journaux and colleagues estimate the recently discovered hyper-hydrate 2NaCl·17H2O (SC8.5) may form7. This second phase configuration continued without interruption to approximately 215 MPa across trials but achieved this pressure at between 216 and 224 K depending on the run. The P-T coordinates of the initial eutectic configuration agree well with previous data from Kanno & Angell (black triangles in Fig. 2c), who observed high-pressure eutectic phenomena whilst studying pressurized homogeneous ice nucleation via differential thermal analysis in emulsified H2O-NaCl samples4. They do not report an additional phase transition, however, which is likely a kinetic consequence of both emulsification and minuscule sample sizes (0.04–0.08 mL), which they deploy in order to hinder heterogeneous nucleation of new phases. The large sample sizes (here 5.33 mL) deployable in isochoric freezing and melting may provide a distinct advantage in this regard, helping to ensure timely heterogeneous nucleation of new phases.

In 6.15% NaHCO3 solution, which begins in a eutectic configuration comprised of liquid, ice Ih, and pure NaHCO3, a phase transition was observed at approximately 255 K/130 MPa, suggesting the existence of what may be the first reported hydrate for NaHCO3, at high-pressure or otherwise. Chamber-to-chamber P-T results grow less consistent after this first phase transition, with two runs eventually unifying in pressure at 210 MPa (albeit at 232 K and 238 K), and the third taking a much shallower approach in temperature. The transition at 210 MPa suggests that another phase transition may occur in this 232–238 K temperature range, be it within the salt-bearing solid phase or the ice phase. Future work should address the structure and stability range of these (potentially multiple) new hydrates and may provide fundamental new insight into the hydration dynamics of NaHCO3.

Finally, in 21.6% MgCl2 solution, which begins in a eutectic configuration comprised of liquid, ice Ih, and MgCl2·12H2O, discrete phase transitions were observed in multiple runs at approximately 233 K/75 MPa and 223 K/155 MPa, after which the behaviors of the different samples diverged significantly. MgCl2 is known for its diverse array of stable hydrate phases, with hydration numbers up to 12 observed at ambient pressure8. However, to our knowledge, the only hydrate reported to exist in equilibrium with ice Ih is MgCl2·12H2O, suggesting that the phase transitions observed here may represent previously unrealized phases.

Methods
Isochoric freezing and melting process
In order to identify the temperature limit of liquid stability in the aqueous solutions explored herein, we extended the isochoric freezing and melting technique reported previously by Chang et al.1 to deeper temperatures. In brief, 5.33 mL aqueous samples mixed at the atmospheric-pressure eutectic concentration were confined absent air within a custom Al7075 isochoric chamber fitted with a high-pressure transducer (ESI Technology Inc). By constraining the total volume of the binary system and allowing the pressure to vary freely, we create a thermodynamic environment in which the 3-phase equilibrium present in the eutectic configuration is prescribed by a single intensive thermodynamic degree of freedom. As such, temperature and pressure are coupled within the chamber, and simple control of the temperature enables simultaneous measurement of the equilibrium temperature and pressure. Further experimental details and chamber schematics are provided in Supplementary Notes 1–3, and described below, with full experimental procedures provided to ensure reproducibility.

Freezing process
Two high-accuracy recirculating cooling baths were employed for isochoric testing, a PolyScience AP15R-40 with a minimum working temperature of 243.15 K and a Fluke Calibration 7380 with a minimum working temperature of 193.15 K. The latter was utilized for solutions with phase transitions lower than 243.15 K (including all those exhibiting intermediate high-pressure hydrate phases), and the former for all others. For each solution, three replicate samples in identical chambers were studied, and the chambers were submerged completely within the cooling bath fluid to ensure uniformity of temperature. More details on the cooling methodology and equipment are available in Supplementary Note 1, and a sample cooling profile is shown in Supplementary Note 2.

For solutions without intermediate high-pressure hydrates phases (i.e., those with monotonic P-T trajectories), the chambers are plunged into a bath pre-cooled to at least 30 K beneath the 0.1 MPa eutectic temperature of the solution, monitored until the ice III/II transition is observed (indicated upon cooling by a precipitous collapse in pressure to approximately 210 MPa; see Supplementary Fig. S2), and then allowed to further equilibrate until the pressure stabilizes to <0.1 MPa/min variation (typically 1-2 h).

For solutions found to host intermediate high-pressure hydrate phases (NaCl, NaHCO3, and MgCl2, i.e., those with non-monotonic P-T trajectories), contrary to their less phase-diverse counterparts, preliminary testing showed broad varieties in behavior sample-to-sample, leading us to believe that metastable configurations were being produced and that a more gradual cooling approach may be necessary. As such, for the protocol identified as Slow Cooling in Fig. 2c, the chambers were pre-cooled only to 273.15 K, and the bath temperature was then decreased by 1 K every 10 min. The protocol identified as Fast Cooling follows the approach described above for solutions without high-pressure intermediates, wherein the chamber is submerged directly into liquid pre-cooled to the minimum temperature of the run, with the exception that pressure equilibration after the ice III/II transition typically required 6–8 h. In order to demonstrate the hallmark dependence of metastable configurations on thermal history, a combined slow-fast cooling approach was also tested, which incorporated a pseudo-annealing logic. In this process, the temperature was incrementally lowered at a rate of 1 K per 10 min until the intermediate hydrate was detected, then raised 5 K above the observed transition temperature and cooled once more at a rate of 0.5 K/min to the cenotectic point.

See Supplementary Note 2 for example time-series data on the freezing process, and Supplementary Note 3 for additional data on solutions with intermediate hydrates.

Melting process
For all solutions, after completion of the cooling process, the system is heated in discrete increments of 0.5 K, with time increments chosen based on the heat transfer characteristics of each bath to produce steady steady-state P-T data by the end of each step (at which point the data is sampled), as indicated by a <0.1 MPa/min evolution of the pressure. Additional equipment details are available in Supplementary Notes 1 and 2, and an example cooling-warming profile is shown in Supplementary Fig. S2. The steady pressure and temperature are recorded at the end of each step, and this pressure-temperature data provides the P-T curves shown in Fig. 2.

Eutectic and cenotectic point identification
In order to extract more precise cenotectic points from the P-T data shown in Fig. 2a, second-order polynomials were fitted to the data above and below the apparent cenotectic temperature (as indicated by the discontinuity in the slope of the P-T curve) using the polyfit() function in MATLAB 2023b, and their intersection provided the cenotectic temperatures/pressures reported in Table 1.

Similarly, following the approach of Chang et al.1, the intersection of the higher-temperature fitted polynomial curve with the 0.1 MPa isobar identifies the atmospheric pressure eutectic temperature of the system.

Propagating uncertainty analysis was performed to account for uncertainty in both the experimental setup and the fitting procedure and is described in detail in Supplementary Note 4.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The manuscript “On the equilibrium limit of liquid stability in pressurized aqueous systems” presents the results of an experimental study, involving the isochoric freezing of binary aqueous brines, which demonstrates the existence of a “cenotectic” defined as the “invariant point occurring at the lowest temperature at which the liquid phase, for any value of concentration, pressure, or other thermodynamic forces acting on the system, remains in stable equilibrium”. Although this work was limited to binary aqueous brines, the manuscript highlights that the results can be extended more generally to other systems, where the location of the cenotectic will be governed by intersection of phase equilibrium lines with opposite Clapeyron slopes. The existence of a cenotectic is demonstrated to be significant to icy ocean worlds since it governs the depth at which the final remnant of a liquid ocean solidifies. Implications for cryopreservation are also highlighted.\nThe manuscript represents an important contribution to the scientific literature and introduces a key concept that has implications across a diverse range of fields. The results are compelling, and the methodology is well-founded. However, there are a few areas where the manuscript could be improved.\nSpecific recommendations for minor edits are included in the attachment, but more significant comments are summarized here. We recommend the manuscript be published after these comments are sufficiently addressed.\n-Figure 1:\n• Please label the concentration axis and include the appropriate limits. Currently the axis value is 0 at both ends (corresponding to the 0 value for temperature and pressure).\n• Since the variables P-T-x are used throughout the manuscript, I recommend including them in the label, Example: Pressure, P (GPa)\n• Please define me, mc, Pc in the figure caption\n• Consider including a 2D cutout (or multiple 2D cutouts) of the figure intersecting at point C\n• It’s not clear that me is different from mc given your experiments, please elaborate on this point somewhere in the manuscript\n-Discontinuity:\n• The term discontinuity is used to describe the conditions at which the cenotectic is reached. This is not formally a discontinuity in the eutectic curve itself but perhaps a “kink” or more explicitly a “discontinuity in the slope”?\n-Table 1:\n• Consider emphasizing that the initial concentration is the eutectic concentration at 1 atm, since it's not immediately apparent from the table.\n• For clarity, please write out \"Difference between Eutectic Temperature at 0.1 MPa and cenotectic temperature\" instead of or in addition to Delta T\n-Figure 2:\n• Please label plots with a, b, c\n• In addition to Delta T, please write out \"Difference between Eutectic and Cenotectic Temperature\"\n• Please include variables along with axis labels, Example: Temperature, T (K)\n-Table 2:\n• The gravitational accelerations and therefore depth of the cenotectic for Titan and Europa appear to be switched\n• Consider including the source for the gravitational acceleration, particularly for the exoplanets\n-Figure 4:\n• The gravitational accelerations and therefore depth of the cenotectic for Titan and Europa appear to be switched\n-Terminology\nOne recurring but minor issue throughout the manuscript is the lack of consistency and precision in terminology:\n• “eutectic line” vs. “eutectic curve” vs. “P-T curve” vs. “P-T trajectory” vs. “eutectic pressure-temperature profile”. To minimize confusion, I recommend adopting a single term for the “eutectic curve” and using it throughout the manuscript.\n• If using the term “P-T coordinates” specify if these are “P-T coordinates of the eutectic points” or “P-T coordinates of the cenotectic point”.\n• Similarly for atmospheric pressure 1 atm, 1 bar, 0.1 MPa?\n• T-P vs P-T (I recommend P-T)\n• P-T-X vs. P-T-x", "reviewer_2": "The manuscript “On the equilibrium limit of liquid stability in pressurized aqueous systems” presents the results of an experimental study, involving the isochoric freezing of binary aqueous brines, which demonstrates the existence of a “cenotectic” defined as the “invariant point occurring at the lowest temperature at which the liquid phase, for any value of concentration, pressure, or other thermodynamic forces acting on the system, remains in stable equilibrium”. Although this work was limited to binary aqueous brines, the manuscript highlights that the results can be extended more generally to other systems, where the location of the cenotectic will be governed by intersection of phase equilibrium lines with opposite Clapeyron slopes. The existence of a cenotectic is demonstrated to be significant to icy ocean worlds since it governs the depth at which the final remnant of a liquid ocean solidifies. Implications for cryopreservation are also highlighted.\nThe manuscript represents an important contribution to the scientific literature and introduces a key concept that has implications across a diverse range of fields. The results are compelling, and the methodology is well-founded. However, there are a few areas where the manuscript could be improved.\nSpecific recommendations for minor edits are included in the attachment, but more significant comments are summarized here. I recommend the manuscript be published after these comments are sufficiently addressed.\nFigure 1\n•Please label the concentration axis and include the appropriate limits. Currently the axis value is 0 at both ends (corresponding to the 0 value for temperature and pressure).\n•Since the variables P-T-x are used throughout the manuscript, I recommend including them in the label, Example: Pressure, P (GPa)\n•Please define me, mc, Pc in the figure caption\n•Consider including a 2D cutout (or multiple 2D cutouts) of the figure intersecting at point C\n•It’s not clear that me is different from mc given your experiments, please elaborate on this point somewhere in the manuscript\nDiscontinuity\n•The term discontinuity is used to describe the conditions at which the cenotectic is reached. This is not formally a discontinuity in the eutectic curve itself but perhaps a “kink” or more explicitly a “discontinuity in the slope”?\nTable 1\n•Consider emphasizing that the initial concentration is the eutectic concentration at 1 atm, since it's not immediately apparent from the table.\n•For clarity, please write out \"Difference between Eutectic Temperature at 0.1 MPa and cenotectic temperature\" instead of or in addition to Delta T\nFigure 2\n•Please label plots with a, b, c\n•In addition to Delta T, please write out \"Difference between Eutectic and Cenotectic Temperature\"\n•Please include variables along with axis labels, Example: Temperature, T (K)\nTable 2\n•The gravitational accelerations and therefore depth of the cenotectic for Titan and Europa appear to be switched\n•Consider including the source for the gravitational acceleration, particularly for the exoplanets\nFigure 4\n•The gravitational accelerations and therefore depth of the cenotectic for Titan and Europa appear to be switched\nTerminology\nOne recurring but minor issue throughout the manuscript is the lack of consistency and precision in terminology.\n•“eutectic line” vs. “eutectic curve” vs. “P-T curve” vs. “P-T trajectory” vs. “eutectic pressure-temperature profile”. To minimize confusion, I recommend adopting a single term for the “eutectic curve” and using it throughout the manuscript.\n•If using the term “P-T coordinates” specify if these are “P-T coordinates of the eutectic points” or “P-T coordinates of the cenotectic point”.\n•Similarly for atmospheric pressure 1 atm, 1 bar, 0.1 MPa?\n•T-P vs P-T (I recommend P-T)\n•P-T-X vs. P-T-x", "reviewer_3": "Zarriz et al. report first-of-their-kind experimental data on low-temperature (T) / high pressure (P) phase relations of aqueous salt systems, namely between the different ice polymorphs and salt-bearing solids. They claim to determine the T-P coordinates of the low-temperature endpoint of the cotectic between ice and a solute-bearing solid, which they name the “cenotectic” and suggest that this is the lowest possible temperature at which the respective aqueous salt solution can stably exist. They then explore implications for thermodynamics of such systems and applications to “icy moon” environments.\nThe experimental findings as such are very interesting and novel. Yet, I had a very hard time preparing this review as the organization of the manuscript is poor. In my opinion it requires a major re-write / thorough major revisions, followed by another round of reviewing, before it can be considered for publication in a leading peer-reviewed journal. Namely, a clear documentation of the experimental approach and its likely first-order interpretation is largely absent although it would be absolutely essential to make the text more readable and the work reproducible. Regarding discussion of the implications a much stronger and clearer connection to the experimental results should be made.\nSome of my concerns in detail are:\n• Perhaps my biggest criticism is that the authors do not clearly (and not even very briefly) document how they did the experiments and that the remaining descriptions and wording in the text are really misleading in this respect. If I understood it correctly – and it is really inacceptable that one has do read a previous publication (Chang et al.) to get to this point – the experiments are actually NOT freezing experiments but rather melting / heating experiments at very low temperatures. The experimental charge is first frozen and then slowly heated and phase transitions are recorded as changes of temperature/pressure slopes upon heating in the isochoric system. Unfortunately, this is never clearly spelled out (a “Methods” or “Experimental” section would have helped). In fact, much of what should be part of such an early-on description of what was done and observed comes as interpretation the discussion instead of reporting the experimental facts and then base some discussion on them.\n• Large parts of the results are then discussed as if these were cooling experiments, which is misleading. It would have been very, very helpful if Figures like 2a and c (btw: the a,b,c is missing from the actual figure and only available in the caption) would first have been used to explain how the signals are interpreted along the timeline of the experiment. I would assume that upon freezing, conceptually, Ice Ih + solute-bearing solid would crystallize until pressure is high enough that denser Ice II (or III) crystallization would be induced to buffer the expansion due to Ice II formation. This would be the pressure on the left of Fig 2a,c at which the heating experiments then commence and so, the near-horizontal curve parts in Fig 2 are actually representing heating the 3-solids assemblage before the formation of liquid upon heating (not last freezing of it is implied in line 123). Stating this concept in line with the actual experimental protocol would help the reader understand the reasoning and interpretation much better.\n• In fact, the data as such do not tell if the Ice II (III) / Ih boundary was reached, the authors should provide arguments for that (e.g., coincidence with previous T-P data on this phase transition). Otherwise, similar heating curves would be obtained for Ice Ih + solute-bearing solid systems, right?\n• In that sense, large parts of the (partly redundant/circular) discussion could be shortened if it would be made crystal-clear in the beginning that the “cenotectic” always is the intersection of the Ice II (or III) / Ih phase boundary with the cotectic (which is the proper IUPAC term rather than “eutectic line”). Then, large parts of the discussion would almost be obsolete and boil down to providing arguments that this boundary was indeed encountered in the experiment. Furthermore, it should be stated earlier on (and not be somewhat hidden late in the discussion) that the experiments do not provide any evidence on the T-P trajectory of next cotectic at pressures beyond the “cenotectic”, i.e., if the conceptual idea of Fig. 1 that it’ll have a different T-P dependence is correct (btw. arguing with a single-component Clapeyron slope for a two-component, two solids + liquid system is not very defendable if the assumptions are not spelled out).\n• Also, the discussion of the “22K” offset could be done much more rigorously. As the boundaries II/Ih and III/1h have slopes in P-T, the intersection of the Ih/L curve, shifted by the eutectic temperature at 0.1 MPa and intersected with the respective Ice phase boundaries (e.g., taking the parameterizations of Dunaeva et al., 2010; Solar System Research, 44, 202-222), would be much more useful than the simplistic approach of Fig. 2b. Within the uncertainty of the Dunaeva fits, the agreement is remarkably good.\n• Regarding the latter, in addition: indeed, the Ice-Ih melting behavior seems to control the P-T trajectory of the cotectic (no real surprise as it is associated with the largest volume change). However, the shape of the solute-bearing solid’s liquidus also plays a role in modulating that broad behavior, so the 22K are only approximate (in spite of the “remarkably good” when using Dunaeva) and may not be an as general rule as inferred from the rather small data base.\n• Besides the reader-unfriendly text- and argument-organization, often, the wording is not very accurate (eutectic line -> cotectic, “granularity” (line 144) -> resolution, and so on).\n• The parts on the findings with NaCl etc. that may indicate new hydrate phases dilute the overall results and discussion. These could easily go into the supporting material and just briefly be referenced in the main text. I also speculate that parts of the strange curve shapes may rather be the results of the presence of “normal” hydrate phases. The melting curve’s T-P trajectory would be influenced by the fact that starting with a 1bar near-eutectic composition would move the composition towards the solute-rich side of the eutectic in the case of NaCl at higher P (taking the Chang et al. results from the same group who reported a shift to lower NaCl-contents on the cotectic with increasing P), i.e., the melting behavior (which solid starts to melt first) will be different from starting on the water-rich side. Again, a thorough discussion of the behavior along the experimental time coordinate would be very helpful.\n• The section “Implications for materials thermodynamics and generalized definition of the cenotectic” is not adding a lot of value and can be left out.\n• In the section on “Implications for planetary science”, the reasoning and assumptions behind the structures displayed in Fig. 3 and their link to the experimental results are not really apparent and the authors should guide the reader. In that sense, in its current form, the text does not provide new insights based on the new experimental results.", "reviewer_4": "In this work, the authors experimentally explored the effect of pressure on the eutectic in aqueous systems. According to the authors’ findings, as the pressure increases, the eutectic point is transformed into an eutectic line, which ends in a “cenotectic” point, which is characterized by the cenotectic temperature and cenotectic pressure and depends on the solute type. The relevance of this work is that the discovery of the cenotectic point plays a central role in understanding complex multiphase equilibria and denotes the limits at which a liquid phase is stable invariantly. From a thermodynamic viewpoint, this point represents a new thermodynamical coordinate on the Clapeyron diagram for mixtures and also extends the application of thermodynamics to other sceneries.\nThe reported information (i.e., experimental details, data interpretation, etc.) is broadly explained and discussed, providing the information needed to reproduce the experiments.\nSome minor details to be considered to improve this work are:\n1. It suggests fitting the curves reported in Fig. 2 by using the glass transition temperature hyperbola proposed by Patrone et al. (P.N. Patrone, A. Dienstfrey, A.R. Browning, S. Tucker, S. Christensen, Uncertainty quantification in molecular dynamics studies of the glass transition temperature, Polymer 87 (2016) 246–259.) rather than polynomial functions. The advantage of the glass transition temperature hyperbola is that it provides more accurate transition coordinates.\n2. In the text, the authors use Tc and Pc as the cenotectic temperature and pressure and zc as the cenotectic depth. It is advised to replace them with other symbols because it causes confusion with fluids' critical temperature, pressure, and compressibility.\n3. It is important to discuss the effect of the initial concentration used in the experiments.\n4. According to the experimental results, the authors claim, “ We observe that when no solute-bearing high-pressure phases exist, the cenotectic occurs consistently 22±2K below the 1 bar eutectic and at approximately 213±3 MPa” This statement is valid for the explored systems but the authors need to provide more evidence to be generalized.", "reviewer_5": "The authors have submitted a manuscript where they considered the liquid limit of aqueous salt solutions at high pressures. The manuscript started with the measurement of experimental data followed by a discussion thereof and ended with implications of the measurements to various different fields.\nThe manuscript has been submitted to Nature Communications and therefore the intended audience is broader than that of a traditional thermodynamics/thermophysical journal. The authors tried to but at times struggled to present information to the wide audience but still show the scientific merits of the manuscript. The authors need to consider the main contribution of the manuscript and ensure that this comes through strongly. At times the manuscript is lacking in focus and therefore the impact is difficult to judge. The experimental measurements are not very well presented (see below) yet some of the discussions are at times superficial. Further, a significant amount of text is dedicated to the applications but I am not convinced these findings are a significant scientific contribution (I may be wrong as I am not an expert in many of the applications e.g. planetary science and cryopreservation).\nThe manuscript has potential but, in my opinion, needs some improvement before it can be published.\nGeneral comments:\nPlease define terms and abbreviations used at first use.\nWhat is the mathematical definition of the cenotectic point? Similar to the critical point of a pure component where ├ (∂^2 P)/(∂v^2 )┤|_(T=T_c )=0 and ├ ∂P/∂v┤|_(T=T_c )=0, how does one define the cenotectic point?\nThe thermodynamic basis is poorly explained. At times the Gibbs Phase Rule is mentioned but the underlying thermodynamics could have been better presented.\nHow do the results presented in Table 1 relate to know thermodynamic behaviour of the various systems? The authors allude to this in their discussion but a clearer explanation is needed, in my opinion.\nMethod used for measurements and presentation of experimental results is not fully clear and therefore there are some concerns regarding the credibility of the results.\nThe authors state that this is the first time these types of measurements have been conducted yet the experimental method essentially only referred to in the main manuscript and not described in detail in the supplementary information. I would recommend a more detailed exposition of the experimental method to illustrate the approach used, especially as part of the contribution of the manuscript is the ‘first-of-their-king’ measurements.\nEspecially considering the audience, the authors need to expand how their constant volume, constant bulk composition measurements will give an accurate description of the cenotectic point. Further, how does the accuracy of the composition loaded influence the measurements? The authors could project their measurement isochore on Figure 1. Part of this information can be provided in the supplementary information.\nFrom the experimental method how can the authors prove that the true cenotectic point is obtained?\nThe authors are requested to do a full uncertainty analysis as outlined by the “Guide to the expression of uncertainty in measurement” produced by Working Group 1 of the Joint Committee for Guides in Metrology (JCGM/WG 1). The uncertainty in the temperature, pressure and composition should be provided taking into account all factors influencing the results. It is standard practice for thermodynamic data to include these measurements. The standard deviation provided here are, according to my understanding, the standard deviations from the three repeat runs and do not constitute to experimental uncertainties."}, "author_response": "We sincerely thank all five reviewers for their diligent evaluations. We have responded to all of their comments and made substantial corresponding revisions to both the main text and the supplementary information. As a result, we believe the manuscript has been significantly improved, and we hope that the reviewers and editor will now find it suitable for publication.\nIn the text below, we reproduce each of the original reviews in black, and provide point-by-point responses in blue. Given the extensiveness of the edits, in the marked-up revised manuscript we have highlighted the areas of most significant revision. We thank the reviewers again for their time and consideration.\nReviewer #1 (Remarks to the Author):\nThe manuscript “On the equilibrium limit of liquid stability in pressurized aqueous systems”\npresents the results of an experimental study, involving the isochoric freezing of binary aqueous\nbrines, which demonstrates the existence of a “cenotectic” defined as the “invariant point\noccurring at the lowest temperature at which the liquid phase, for any value of concentration,\npressure, or other thermodynamic forces acting on the system, remains in stable equilibrium”.\nAlthough this work was limited to binary aqueous brines, the manuscript highlights that the results\ncan be extended more generally to other systems, where the location of the cenotectic will be\ngoverned by intersection of phase equilibrium lines with opposite Clapeyron slopes. The existence\nof a cenotectic is demonstrated to be significant to icy ocean worlds since it governs the depth at\nwhich the final remnant of a liquid ocean solidifies. Implications for cryopreservation are also\nhighlighted.\nThe manuscript represents an important contribution to the scientific literature and introduces a\nkey concept that has implications across a diverse range of fields. The results are compelling,\nand the methodology is well-founded. However, there are a few areas where the manuscript could\nbe improved.\nWe thank the reviewer for their close reading of the manuscript. We are pleased to hear they find\nthe results compelling, and are very happy to incorporate their suggested improvements.\nSpecific recommendations for minor edits are included in the attachment, but more significant\ncomments are summarized here. We recommend the manuscript be published after these\ncomments are sufficiently addressed.\n-Figure 1:\n• Please label the concentration axis and include the appropriate limits. Currently the axis value\nis 0 at both ends (corresponding to the 0 value for temperature and pressure).\n• Since the variables P-T-x are used throughout the manuscript, I recommend including them in\nthe label, Example: Pressure, P (GPa)\n• Please define me, mc, Pc in the figure caption\nWe have executed all the changes recommended above for Figure 1, thank you for the\nsuggestions!\n• Consider including a 2D cutout (or multiple 2D cutouts) of the figure intersecting at point C\nWe thank the reviewer for this suggestion, and we heavily considered the potential merit of 2D\nslices. However, we concluded that they may only introduce undue confusion– this is because\nthe cenotectic point of interest is a four-phase equilibrium invariant, and a 2D slice can only\neffectively convey up to three-phase equilibrium. In light of this, we elected to maintain only the\n3D visualization.\n• It’s not clear that me is different from mc given your experiments, please elaborate on this point\nsomewhere in the manuscript\nWe thank the Reviewer for identifying this oversight, and we have added a brief paragraph\nexplaining that, starting at the eutectic concentration m_e, we expect based on previous work that\nthe concentration of the liquid phase to continually decrease with increasing pressure until m_k\n(the cenotectic concentration as now marked) is reached.\n-Discontinuity:\n• The term discontinuity is used to describe the conditions at which the cenotectic is reached. This\nis not formally a discontinuity in the eutectic curve itself but perhaps a “kink” or more explicitly a\n“discontinuity in the slope”?\nWe thank the reviewer for this comment, and have updated the language to employ “discontinuity\nin the slope” throughout.\n-Table 1:\n• Consider emphasizing that the initial concentration is the eutectic concentration at 1 atm, since\nit's not immediately apparent from the table.\n• For clarity, please write out \"Difference between Eutectic Temperature at 0.1 MPa and cenotectic\ntemperature\" instead of or in addition to Delta T\nWe thank the reviewer for these Table comments, and have incorporated all of them.\n-Figure 2:\n• Please label plots with a, b, c\n• In addition to Delta T, please write out \"Difference between Eutectic and Cenotectic\nTemperature\"\n• Please include variables along with axis labels, Example: Temperature, T (K)\nWe thank the reviewer for these figure comments, and have incorporated all of them.\n-Table 2:\n• The gravitational accelerations and therefore depth of the cenotectic for Titan and Europa\nappear to be switched\nThanks for this good catch, the table has been corrected.\n• Consider including the source for the gravitational acceleration, particularly for the exoplanets\nThe gravitational accelerations are provided in the reference cited in the text (Ojha et al. 2022,\nNat. Comms). We added it in the caption as well for clarity. Thanks.\n-Figure 4:\n• The gravitational accelerations and therefore depth of the cenotectic for Titan and Europa\nappear to be switched\nThanks again, the figure has been corrected.\n-Terminology\nOne recurring but minor issue throughout the manuscript is the lack of consistency and precision\nin terminology:\n• “eutectic line” vs. “eutectic curve” vs. “P-T curve” vs. “P-T trajectory” vs. “eutectic pressure-\ntemperature profile”. To minimize confusion, I recommend adopting a single term for the “eutectic\ncurve” and using it throughout the manuscript.\nWe unified the description to “eutectic curve” throughout the manuscript for clarity. Thanks for the\nsuggestion.\n• If using the term “P-T coordinates” specify if these are “P-T coordinates of the eutectic points”\nor “P-T coordinates of the cenotectic point”.\nThank you, we have done so.\n• Similarly for atmospheric pressure 1 atm, 1 bar, 0.1 MPa?\nThank you, we have unified the description of atmospheric pressure as 0.1 MPa.\n• T-P vs P-T (I recommend P-T)\nThank you, we now use P-T throughout.\n• P-T-X vs. P-T-x\nThank you, we now use P-T-x throughout.\nReviewer #2 are duplicates of Reviewer #1. We thank both reviewers again for their consideration\nand suggestions.\nReviewer #3 (Remarks to the Author):\nZarriz et al. report first-of-their-kind experimental data on low-temperature (T) / high pressure (P)\nphase relations of aqueous salt systems, namely between the different ice polymorphs and salt-\nbearing solids. They claim to determine the T-P coordinates of the low-temperature endpoint of\nthe cotectic between ice and a solute-bearing solid, which they name the “cenotectic” and suggest\nthat this is the lowest possible temperature at which the respective aqueous salt solution can\nstably exist. They then explore implications for thermodynamics of such systems and applications\nto “icy moon” environments.\nThe experimental findings as such are very interesting and novel. Yet, I had a very hard time\npreparing this review as the organization of the manuscript is poor. In my opinion it requires a\nmajor re-write / thorough major revisions, followed by another round of reviewing, before it can be\nconsidered for publication in a leading peer-reviewed journal. Namely, a clear documentation of\nthe experimental approach and its likely first-order interpretation is largely absent although it\nwould be absolutely essential to make the text more readable and the work reproducible.\nRegarding discussion of the implications a much stronger and clearer connection to the\nexperimental results should be made.\nWe are very grateful for the in-depth review provided, and we have reorganized various aspects\nof the manuscript to enhance clarity, with particular regard to the method employed. We hope that\nthe Reviewer now finds the manuscript easier to digest, and thank them again for their close\nreading of the work.\nSome of my concerns in detail are:\n• Perhaps my biggest criticism is that the authors do not clearly (and not even very briefly)\ndocument how they did the experiments and that the remaining descriptions and wording in the\ntext are really misleading in this respect. If I understood it correctly – and it is really inacceptable\nthat one has do read a previous publication (Chang et al.) to get to this point – the experiments\nare actually NOT freezing experiments but rather melting / heating experiments at very low\ntemperatures. The experimental charge is first frozen and then slowly heated and phase\ntransitions are recorded as changes of temperature/pressure slopes upon heating in the isochoric\nsystem. Unfortunately, this is never clearly spelled out (a “Methods” or “Experimental” section\nwould have helped). In fact, much of what should be part of such an early-on description of what\nwas done and observed comes as interpretation the discussion instead of reporting the\nexperimental facts and then base some discussion on them.\n• Large parts of the results are then discussed as if these were cooling experiments, which is\nmisleading. It would have been very, very helpful if Figures like 2a and c (btw: the a,b,c is missing\nfrom the actual figure and only available in the caption) would first have been used to explain how\nthe signals are interpreted along the timeline of the experiment. I would assume that upon\nfreezing, conceptually, Ice Ih + solute-bearing solid would crystallize until pressure is high enough\nthat denser Ice II (or III) crystallization would be induced to buffer the expansion due to Ice II\nformation. This would be the pressure on the left of Fig 2a,c at which the heating experiments\nthen commence and so, the near-horizontal curve parts in Fig 2 are actually representing heating\nthe 3-solids assemblage before the formation of liquid upon heating (not last freezing of it is\nimplied in line 123). Stating this concept in line with the actual experimental protocol would help\nthe reader understand the reasoning and interpretation much better.\nThe following answer addresses the last 2 points:\nWe agree with the reviewer entirely that the experimental details were not sufficiently documented\nand that the way it was previously described could have been left unclear that these were\nisochoric freezing AND warming/melting experiments, in which final equilibrium data is recorded\nduring the melting process.\nWe have addressed these important concerns by rephrasing the entire manuscript accordingly;\nclarifying aspects of the methods section; providing much more comprehensive example time-\nseries data of the entire freezing-melting process in the Supplementary Information; and adding\na comprehensive uncertainty analysis in the Supplementary Information.\nWe thank the reviewer for flagging this– the manuscript has been substantially improved as a\nresult.\n• In fact, the data as such do not tell if the Ice II (III) / Ih boundary was reached, the authors should\nprovide arguments for that (e.g., coincidence with previous T-P data on this phase transition).\nOtherwise, similar heating curves would be obtained for Ice Ih + solute-bearing solid systems,\nright?\nWe thank the reviewer for this comment. The cenotectic points measured in this work always\noccur around 210MPa, which corresponds to the ice Ih-II and Ih-III solid-solid phase transition. It\nis reasonable to believe that ice II and III grow pure, as ice Ih and ice VI partition coefficients for\nsalts have been measured to be below 5E-3 (Journaux et al. 2017, EPSL 463, 36–47). Therefore\nit is reasonable to explain the location of the cenotectic transition to be along the quasi-isobaric\nIh-III or Ih-II transitions around 209 MPa (Journaux et al. 2020, Journal of Geophysical Research:\nPlanets 125 (1), e2019JE006176). We added discussion to the manuscript to clarify this point.\nAdditionally, to aid interpretation, we have plotted the pure-water ice Ih - ice II and ice Ih - ice III\nphase boundaries in Figures 2a and 2b. We thank the reviewer again for this comment.\n• In that sense, large parts of the (partly redundant/circular) discussion could be shortened if it\nwould be made crystal-clear in the beginning that the “cenotectic” always is the intersection of the\nIce II (or III) / Ih phase boundary with the cotectic (which is the proper IUPAC term rather than\n“eutectic line”). Then, large parts of the discussion would almost be obsolete and boil down to\nproviding arguments that this boundary was indeed encountered in the experiment. Furthermore,\nit should be stated earlier on (and not be somewhat hidden late in the discussion) that the\nexperiments do not provide any evidence on the T-P trajectory of next cotectic at pressures\nbeyond the “cenotectic”, i.e., if the conceptual idea of Fig. 1 that it’ll have a different T-P\ndependence is correct (btw. arguing with a single-component Clapeyron slope for a two-\ncomponent, two solids + liquid system is not very defendable if the assumptions are not spelled\nout).\nWe thank the reviewer for these comments. We have added a line in the beginning of the\nmanuscript clarifying that, for the systems studied here, the cenotectic will occur at the\nintersection of the ice Ih / ice II (or III) phase boundary and the eutectic curve / cotetic. We have\nalso significantly expanded our discussion of the data in Figure 2 in general to reflect these points.\n• Also, the discussion of the “22K” offset could be done much more rigorously. As the boundaries\nII/Ih and III/1h have slopes in P-T, the intersection of the Ih/L curve, shifted by the eutectic\ntemperature at 0.1 MPa and intersected with the respective Ice phase boundaries (e.g., taking\nthe parameterizations of Dunaeva et al., 2010; Solar System Research, 44, 202-222), would be\nmuch more useful than the simplistic approach of Fig. 2b. Within the uncertainty of the Dunaeva\nfits, the agreement is remarkably good.\nWe agree with the reviewer, and for clarity have added the relevant boundaries of the pure-water\nphase diagram to Figures 2a and 2b. We used the SeaFreeze derived phase diagram (Journaux\net al. 2020, Journal of Geophysical Research: Planets 125 (1), e2019JE006176), as it combines\nthe self-consistent Gibbs energy descriptions for ice II and III from recent XRD data with the Ih\nGibbs description from Feistel and Wagner (2006), which all reproduce well experimental data for\nthe Ih-II and Ih-III phase transitions. We also rewrote the related part of the discussion accordingly.\nThanks very much for the comment.\n• Regarding the latter, in addition: indeed, the Ice-Ih melting behavior seems to control the P-T\ntrajectory of the cotectic (no real surprise as it is associated with the largest volume change).\nHowever, the shape of the solute-bearing solid’s liquidus also plays a role in modulating that broad\nbehavior, so the 22K are only approximate (in spite of the “remarkably good” when using\nDunaeva) and may not be an as general rule as inferred from the rather small data base.\nWe thank the reviewer for this comment, and have added additional discussion to the end of this\nsection stating more clearly that this 22K offset is simply a rule of thumb, with applicability only to\nsystems for which the ice Ih phase boundary is much more pressure sensitive than the solute-\nbearing solid phase boundaries.\n• Besides the reader-unfriendly text- and argument-organization, often, the wording is not very\naccurate (eutectic line -> cotectic, “granularity” (line 144) -> resolution, and so on).\nWe thank the reviewer for calling these out. We have corrected “granularity” to be “resolution”. At\nthe advice of other reviewers, we have unified our language as “eutectic curve”, as opposed to\n“eutectic line”, “eutectic trajectory”, etc. We now also mention in the introduction that here the\neutectic curve is equivalent to a cotectic.\n• The parts on the findings with NaCl etc. that may indicate new hydrate phases dilute the overall\nresults and discussion. These could easily go into the supporting material and just briefly be\nreferenced in the main text. I also speculate that parts of the strange curve shapes may rather be\nthe results of the presence of “normal” hydrate phases. The melting curve’s T-P trajectory would\nbe influenced by the fact that starting with a 1bar near-eutectic composition would move the\ncomposition towards the solute-rich side of the eutectic in the case of NaCl at higher P (taking\nthe Chang et al. results from the same group who reported a shift to lower NaCl-contents on the\ncotectic with increasing P), i.e., the melting behavior (which solid starts to melt first) will be\ndifferent from starting on the water-rich side. Again, a thorough discussion of the behavior along\nthe experimental time coordinate would be very helpful.\nWe thank the reviewer for this comment, but must very respectfully disagree with them on the\nvalue of the NaCl findings. We believe the discussion of possible new hydrates to be integral to a\ncomprehensive understanding of the cenotectic concept, and believe further that the distinct\ndifferences between the P-T curves exhibiting potential intermediate hydrates and the simpler\ncurves shown in Figure 2a highlight the diversity of potential phase behaviors that future\npractitioners of isochoric freezing and melting may encounter. We have tried to enhance the level\nof discussion in this section in order to increase clarity.\n• The section “Implications for materials thermodynamics and generalized definition of the\ncenotectic” is not adding a lot of value and can be left out.\nWe thank the Reviewer for this comment, but again feel that this section broadens the impact of\nthe results and also provides the definition/logic necessary for the cenotectic concept to be\nrigorously understood and applied in the future. In fact, this section in particular was requested\nby previous reviewers, who argued to us that without a rigorous discussion of the possible\nmanifestations of the cenotectic, the risk that it may be misinterpreted and misapplied in the future\nis much higher. In order to supplement the rigor of this section however, we have added an\nadditional Supplementary Note (#5) further clarifying formal aspects of the cenotectic within the\ncontext of Gibbs’ Phase Rule.\n• In the section on “Implications for planetary science”, the reasoning and assumptions behind the\nstructures displayed in Fig. 3 and their link to the experimental results are not really apparent and\nthe authors should guide the reader. In that sense, in its current form, the text does not provide\nnew insights based on the new experimental results.\nWe thank the reader for flagging this, and have rephrased the planetary science section to better\nguide the reader. We sincerely hope that reviewer will now find it both clearer and more\ncompelling, as we believe these (simple!) applications of the cenotectic concept to planetary\nscience to be very impactful.\nReviewer #4 (Remarks to the Author):\nIn this work, the authors experimentally explored the effect of pressure on the eutectic in aqueous\nsystems. According to the authors’ findings, as the pressure increases, the eutectic point is\ntransformed into an eutectic line, which ends in a “cenotectic” point, which is characterized by the\ncenotectic temperature and cenotectic pressure and depends on the solute type. The relevance\nof this work is that the discovery of the cenotectic point plays a central role in understanding\ncomplex multiphase equilibria and denotes the limits at which a liquid phase is stable invariantly.\nFrom a thermodynamic viewpoint, this point represents a new thermodynamical coordinate on the\nClapeyron diagram for mixtures and also extends the application of thermodynamics to other\nsceneries.\nThe reported information (i.e., experimental details, data interpretation, etc.) is broadly explained\nand discussed, providing the information needed to reproduce the experiments.\nSome minor details to be considered to improve this work are:\n1. It suggests fitting the curves reported in Fig. 2 by using the glass transition temperature\nhyperbola proposed by Patrone et al. (P.N. Patrone, A. Dienstfrey, A.R. Browning, S. Tucker, S.\nChristensen, Uncertainty quantification in molecular dynamics studies of the glass transition\ntemperature, Polymer 87 (2016) 246–259.) rather than polynomial functions. The advantage of\nthe glass transition temperature hyperbola is that it provides more accurate transition coordinates.\nWe thank the reviewer for this comment and their interesting suggestion. After reading the\nsuggested work, we respectfully conclude that the method described in there would not quite be\njustifiable for our application here, because that method targets a smooth and continuous second-\norder transition (the glass transition), whereas we target here the discrete intersection of liquidus\nor cotectic curves (both of which mark first-order transitions). However, we agree with the reviewer\nthat more robust uncertainty quantification is needed, as was also suggested by Reviewer 5\nbelow. As such, we have added a comprehensive new uncertainty analysis to the SI, according\nto the “Guide to the expression of uncertainty in measurement”, produced by Working Group 1 of\nthe Joint Committee for Guides in Metrology (JCGM/WG 1). We have accordingly updated the\nuncertainty values in all of the tables where temperature-pressure coordinates are reported. We\nthank the reviewer again for highlighting the need for a more robust uncertainty analysis.\n2. In the text, the authors use Tc and Pc as the cenotectic temperature and pressure and zc as\nthe cenotectic depth. It is advised to replace them with other symbols because it causes confusion\nwith fluids' critical temperature, pressure, and compressibility.\nWe thank the reviewer for this comment. We agree that this might cause confusion and have\nchanged them to Tκ, Pκ, etc., to avoid confusion with the critical properties.\n3. It is important to discuss the effect of the initial concentration used in the experiments.\nWe thank the reviewer for this note. We have enhanced the discussion of our choice to use 0.1\nMPa eutectic concentration as our initial concentration, and further clarified the chosen\nconcentration in Table 1. We have also added commentary in Supplementary Note 1 on the\nrelative insensitivity of the eutectic curve’s T-P trajectory to experimental uncertainty in starting\nconcentration.\n4. According to the experimental results, the authors claim, “We observe that when no solute-\nbearing high-pressure phases exist, the cenotectic occurs consistently 22±2K below the 1 bar\neutectic and at approximately 213±3 MPa” This statement is valid for the explored systems but\nthe authors need to provide more evidence to be generalized.\nWe thank the reviewer for this comment, and have added additional discussion to the end of this\nsection stating more clearly that this 22K offset is simply a rule of thumb, with applicability only to\nsystems for which the ice Ih phase boundary is much more pressure sensitive than the solute-\nbearing solid phase boundaries.\nReviewer #5 (Remarks to the Author):\nThe authors have submitted a manuscript where they considered the liquid limit of aqueous salt\nsolutions at high pressures. The manuscript started with the measurement of experimental data\nfollowed by a discussion thereof and ended with implications of the measurements to various\ndifferent fields.\nThe manuscript has been submitted to Nature Communications and therefore the intended\naudience is broader than that of a traditional thermodynamics/thermophysical journal. The authors\ntried to but at times struggled to present information to the wide audience but still show the\nscientific merits of the manuscript. The authors need to consider the main contribution of the\nmanuscript and ensure that this comes through strongly. At times the manuscript is lacking in\nfocus and therefore the impact is difficult to judge. The experimental measurements are not very\nwell presented (see below) yet some of the discussions are at times superficial. Further, a\nsignificant amount of text is dedicated to the applications but I am not convinced these findings\nare a significant scientific contribution (I may be wrong as I am not an expert in many of the\napplications e.g. planetary science and cryopreservation).\nThe manuscript has potential but, in my opinion, needs some improvement before it can be\npublished.\nWe thank the reviewer for their time and consideration here – we are very happy to incorporate\nthe suggested improvements in order to bring the manuscript to Nature Communications quality.\nRegarding text spent discussing other applications, in order to enhance narrative clarity, at the\nsuggestion of the other reviewers and the editor, we have expanded our discussion of planetary\nscience applications to better guide the reader, and removed the brief section on\ncryopreservation.\nGeneral comments:\n● Please define terms and abbreviations used at first use.\nThank you, we have done so.\n● What is the mathematical definition of the cenotectic point? Similar to the critical point of\na pure component where ├ (∂^2 P)/(∂v^2 )┤|_(T=T_c )=0 and ├ ∂P/∂v┤|_(T=T_c )=0,\nhow does one define the cenotectic point?\nThe cenotectic does not lend itself to straightforward mathematical definition in the same way that\nthe critical point does, because at the critical point, only one phase exists, whereas at the\ncenotectic point, depending on the composition of the solution and the modes of thermodynamic\nwork affecting it, many phases co-exist.\nWe have thus in the manuscript described it phenomenologically, rather than mathematically. We\nnote that this too is how the eutectic is typically defined, for the same reason.\nHowever, in an effort to clarify formal aspects of the cenotectic definition, we have added a new\nSupplementary Note 5 that gives a more rigorous technical definition within the context of Gibbs’\nPhase Rule. We anticipate that between the extensive discussion and definition in the manuscript\nand this new Supplementary Note, the definition of the cenotectic should now be clear to the\nreader. We thank the reviewer for this note.\n● The thermodynamic basis is poorly explained. At times the Gibbs Phase Rule is mentioned\nbut the underlying thermodynamics could have been better presented.\nWe thank the reviewer for this comment, and have worked to clarify the underlying thermodynamic\nbasis. As mentioned in the previous response, we have also included Supplementary Note 5\nfurther clarifying the relationship between the Phase Rule and cenotectic.\n● How do the results presented in Table 1 relate to known thermodynamic behaviour of the\nvarious systems? The authors allude to this in their discussion but a clearer explanation\nis needed, in my opinion.\nWe thank the reviewer for this comment, and agree that the heading labeling in Table 1 was\ninsufficiently clear. We have amended this for clarity. We now list the initial brine concentration in\nthe experimental system, which is the known eutectic concentration at 0.1 MPa; the according\neutectic temperature at 0.1 MPa; our measured cenotectic temperatures and pressures; and the\ndifference in temperature between our measured cenotectic temperature and the known 0.1 MPa\neutectic temperature. Thank you again.\n● Method used for measurements and presentation of experimental results is not fully clear\nand therefore there are some concerns regarding the credibility of the results.\n● The authors state that this is the first time these types of measurements have been\nconducted yet the experimental method essentially only referred to in the main manuscript\nand not described in detail in the supplementary information. I would recommend a more\ndetailed exposition of the experimental method to illustrate the approach used, especially\nas part of the contribution of the manuscript is the ‘first-of-their-king’ measurements.\nWe agree with these last two comments, and have added various additional methodological\ndetails throughout the manuscript (in the main text, the methods, and the Supplementary\nInformation alike) that provide more in-depth description of the experimental techniques and\nanalysis. We also provide a new supplementary note dedicated to uncertainty analysis, and we\nbelieve this information in sum should allow other groups to fully reproduce the experiments. We\nthank the reviewer for flagging this.\n● Especially considering the audience, the authors need to expand how their constant\nvolume, constant bulk composition measurements will give an accurate description of the\ncenotectic point. Further, how does the accuracy of the composition loaded influence the\nmeasurements? The authors could project their measurement isochore on Figure 1. Part\nof this information can be provided in the supplementary information.\nWe thank the reviewer for this comment, and have worked throughout the main text and\nSupplementary Information to clarify how and why the isochoric freezing and melting method\nleads us to the cenotectic point. We believe that with better description of the methods/approach\nthroughout, and new details in Supplementary Notes 1, 2 and 5, it should now be sufficiently clear.\nWe have also explicitly addressed in Supplementary Note 1 that experimental uncertainty in\nconcentration can generally affect the phase fractions of the phases involved in the eutectic\nassemblage, but not the P-T trajectory of the equilibrium eutectic curve, because the system has\nonly one intensive thermodynamic degree of freedom per Gibbs’ Phase Rule.\nWe have furthermore highlighted in the Figure 1 caption that the P-T trajectory of the measured\nisochore is given by the thick magenta eutectic curve between points (e) and (𝜅) in the Figure 1\nphase diagram.\n● From the experimental method how can the authors prove that the true cenotectic point is\nobtained?\nAs mentioned in the text, our confidence that the measured invariant points truly represent\nthe cenotectic is ultimately limited by our understanding of the phase behavior of the\nsystem as a whole. If indeed the isochoric trajectory is originating from the lowest-\ntemperature eutectic point that exists at atmospheric pressure, based on our\nthermodynamic arguments, we reason that our confidence in interpreting the cenotectic\ncorrectly is high. However, if, for a given system, a different atmospheric-pressure eutectic\nwas to be discovered in the future at lower temperatures, starting the isochoric trajectory\nfrom that eutectic concentration would lead to the cenotectic. As such, we operate here\nwith the best information available, but acknowledge that (as in most aspects of materials\nscience and discovery), future research may either support, update, or change our\nconclusions.\n● The authors are requested to do a full uncertainty analysis as outlined by the “Guide to\nthe expression of uncertainty in measurement” produced by Working Group 1 of the Joint\nCommittee for Guides in Metrology (JCGM/WG 1). The uncertainty in the temperature,\npressure and composition should be provided taking into account all factors influencing\nthe results. It is standard practice for thermodynamic data to include these measurements.\nThe standard deviation provided here are, according to my understanding, the standard\ndeviations from the three repeat runs and do not constitute to experimental uncertainties.\nWe thank the reviewer for this comment, and agree with the need for more extensive uncertainty\nanalysis. We now include an extensive uncertainty analysis in the SI, following the JCGM\nguidelines, and we have updated all tables reporting temperature-pressure data accordingly.\nThanks again for the suggestion."}, {"round": 2, "reviewer_comments": {"reviewer_2": "I thank the authors for thoroughly addressing my comments and recommend that the manuscript be accepted for publication in its current form.", "reviewer_3": "The revision has clarified many things that I criticized in the earlier version; namely, the much clearer documentation of experimental procedures and interpretation of the experimental curves now allows readers for form an own opinion on the results. All further critique that I could raise now (e.g., regarding style and clarity of writing as well as clarity of scientific details, such as why a thicker ice crust would enhance fluid circulation and hwo much) would be rather subjective / express my personal preferences, so I refrain from suggesting these points for minor revisions. In my opinion the manuscript can be accepted now.", "reviewer_4": "In this revised version, the authors carried out all the questions and queries", "reviewer_5": "The authors have submitted an improved manuscript as well as a detailed description of the changes made to address the concerns of the reviewers. The resubmitted manuscript is an improvement of the previous submission but in my opinion the manuscript still requires improvement before it can be considered for publication.\n1. The authors need to be clear in the manuscript that they are consider aqueous salt solutions. Throughout they talk about liquids but the liquid considered is water. This needs to be clearer in the text. Also, throughout the authors need to refer to the liquid as water and be specific when they refer to the salt e.g. line 191 ‘it’ is indeed a the salt.\n2. The authors have attempted to improve the clarity of the manuscript by including the methodology. This is however given at the end of the text with no reference to it in the results section that starts immediately after the introduction. One of the main contributions of the manuscript is the establishment of a new method. Therefore, I strongly feel that the methodology section should be before the results; the reader needs to know how the experiments were conducted before the outcomes of the experiments are discussed.\n3. The cooling and subsequent heating profiles have been given in the experimental section. How do the authors know that they are at equilibrium, especially at the start of the experiment. If the mixture is cooled down for only 45 min, is this enough to get to equilibrium? Personal experience suggests that equilibrium, especially those including a phase change where there is no mixing can take very long to attain, hours, sometimes even days, not just minutes. Figures S3 and S5 do not start at the same pressure when heated; is this not an indication that the experiments were not at equilibrium? I am not convinced regarding the results for the salts in Figure 2(c).\nSome minor comments\n4. Please add page numbers and give figures and tables as soon as possible after first mention.\n5. The figure captions are very long. Be careful of including descriptions and interpretations in the captions."}, "author_response": "RESPONSE TO REVIEWERS\nWe sincerely thank all five reviewers for re-evaluating our manuscript. We have\nresponded to all of their comments and made substantial corresponding revisions to both\nthe main text and the supplementary information. As a result, we believe the manuscript\nhas been significantly improved, and we hope that the reviewers and editor will now find\nit suitable for publication.\nIn the text below, we reproduce each of the original reviews in black, and provide point-\nby-point responses in blue. Given the extensiveness of the edits, in the marked-up revised\nmanuscript we have highlighted the areas of most significant revision. We thank the\nreviewers again for their time and consideration.\nReviewer #2 (Remarks to the Author):\nI thank the authors for thoroughly addressing my comments and recommend that the\nmanuscript be accepted for publication in its current form.\nWe thank the Reviewer for their time and consideration, and agree with their assessment.\nReviewer #3 (Remarks to the Author):\nThe revision has clarified many things that I criticized in the earlier version; namely, the\nmuch clearer documentation of experimental procedures and interpretation of the\nexperimental curves now allows readers for form an own opinion on the results. All\nfurther critique that I could raise now (e.g., regarding style and clarity of writing as well\nas clarity of scientific details, such as why a thicker ice crust would enhance fluid\ncirculation and how much) would be rather subjective / express my personal\npreferences, so I refrain from suggesting these points for minor revisions. In my opinion\nthe manuscript can be accepted now.\nWe thank the Reviewer for their time and consideration, and agree with their assessment.\nReviewer #4 (Remarks to the Author):\nIn this revised version, the authors carried out all the questions and queries\nWe thank the Reviewer for their time and consideration, and agree with their\nassessment.\nReviewer #5 (Remarks to the Author):\nThe authors have submitted an improved manuscript as well as a detailed description of\nthe changes made to address the concerns of the reviewers. The resubmitted\nmanuscript is an improvement of the previous submission but in my opinion the\nmanuscript still requires improvement before it can be considered for publication.\nWe thank the Reviewer for their time and consideration here, and are happy to make\nfurther modifications in response to their new comments. Please see below.\n1. The authors need to be clear in the manuscript that they are consider aqueous salt\nsolutions. Throughout they talk about liquids but the liquid considered is water. This\nneeds to be clearer in the text. Also, throughout the authors need to refer to the liquid as\nwater and be specific when they refer to the salt e.g. line 191 ‘it’ is indeed a the salt.\nWe thank the reviewer for this comment, and have modified the text throughout to\nenhance clarity. We will note that we mention “liquid” in several contexts: 1) in the\ncontext of the general thermodynamic theory of the cenotectic, wherein we are referring\nto an arbitrary liquid phase; 2) in the context of our experiments, where we are referring\nto an aqueous liquid phase; and 3) in the context of planetary science/the oceans of icy\nmoons, where we are referring to an aqueous liquid phase. We have clarified this\nthroughout, and made sure that, in the select instances wherein we discuss pure water\nas the liquid phase, that too is clear.\nWith regard to clarifying that the solutes considered in our experiments here are\nexclusively salts, we have updated “solute-bearing solid phase” to “salt-bearing solid\nphase” as appropriate, and otherwise worked to clarify this topic throughout.\n(DONE)\n2. The authors have attempted to improve the clarity of the manuscript by including the\nmethodology. This is however given at the end of the text with no reference to it in the\nresults section that starts immediately after the introduction. One of the main\ncontributions of the manuscript is the establishment of a new method. Therefore, I\nstrongly feel that the methodology section should be before the results; the reader\nneeds to know how the experiments were conducted before the outcomes of the\nexperiments are discussed.\nWe thank the reviewer for this comment. In our presentation of the methodology, we\nhave sought to follow the formatting guidelines of Nature Communications\n(https://www.nature.com/ncomms/submit/article), which recommend that the text be\norganized as Introduction  Results  Discussion  Methods. The Methods section is\nalso considered separate from the Main Text, subject to a separate word limit, etc. The\norganization of our manuscript is also consistent with other recent Nature\nCommunications publications (token example: https://www.nature.com/articles/s41467-\n024-50839-3). As such, we suggest respectfully that we must keep the Methods section\nwhere it is at present. However, we have modified the initial paragraphs following the\nIntroduction both to introduce the methodology at a high level and to emphasize to the\nreader that the complete methodology is available in the Methods section. We hope this\nstrikes an appropriate balance, and thank the reviewer for their comment here.\n3. The cooling and subsequent heating profiles have been given in the experimental\nsection. How do the authors know that they are at equilibrium, especially at the start of\nthe experiment. If the mixture is cooled down for only 45 min, is this enough to get to\nequilibrium? Personal experience suggests that equilibrium, especially those including a\nphase change where there is no mixing can take very long to attain, hours, sometimes\neven days, not just minutes. Figures S3 and S5 do not start at the same pressure when\nheated; is this not an indication that the experiments were not at equilibrium? I am not\nconvinced regarding the results for the salts in Figure 2(c).\nWe very much appreciate the reviewer’s comment here, which identified some\ntypographical errors in our main-text Methods section that were inconsistent with the\ndata and description we provide in Supplementary Note.\nCritically, the solutions are cooled for much longer than 45 min. This was\nshown/described in Supplementary Note 2, but our according description in the main-\ntext Methods section contained some confusing language that obscured this fact, which\nwe have now corrected. We wholeheartedly agree with the reviewer that 45 minutes on\ncooling would nigh-certainly be insufficient initial equilibration time, especially for so\nlarge a system (~5mL). As shown in Fig S2, upon cooling, we monitor the pressure\nsignal to ensure that the ice II/III transition occurs (as indicated by a precipitous collapse\nin the pressure), then leave the system to equilibrate for several additional hours before\ninitiating the warming protocol. We have modified the Methods section text\naccordingly—most importantly, the description of the freezing and melting process has\nbeen modified to include the following, consistent with our Supplementary notes and\nfigures:\n“Freezing process\nTwo high-accuracy recirculating cooling baths were employed for isochoric testing, a\nPolyScience AP15R-40 with a minimum working temperature of 243.15K and a Fluke\nCalibration 7380 with a minimum working temperature of 193.15K. The latter was utilized\nfor solutions with phase transitions lower than 243.15K (including all those exhibiting\nintermediate high-pressure hydrate phases), and the former for all others. For each\nsolution, three replicate samples in identical chambers were studied, and the chambers\nare submerged completely within the cooling bath fluid to ensure uniformity of\ntemperature. More details on the cooling methodology and equipment are available in\nSupplementary Note 1, and a sample cooling profile is shown in Supplementary Note 2.\nFor solutions without intermediate high-pressure hydrates phases (i.e. those with\nmonotonic P-T trajectories), the chambers are plunged into a bath pre-cooled to at least\n30K beneath the 0.1 MPa eutectic temperature of the solution, monitored until the ice III/II\ntransition is observed (indicated upon cooling by a precipitous collapse in pressure to\napproximately 210 MPa; see Fig. S2), and then allowed to further equilibrate until the\npressure stabilizes to <0.1 MPa/min variation (typically 1-2 hours).\nFor solutions found to host intermediate high-pressure hydrate phases (NaCl, NaHCO ,\n3\nand MgCl , i.e. those with non-monotonic P-T trajectories), contrary to their less phase-\n2\ndiverse counterparts, preliminary testing showed broad varieties in behavior sample-to-\nsample, leading us to believe that metastable configurations were being produced and\nthat a more gradual cooling approach may be necessary. As such, for the protocol\nidentified as “Slow Cooling” in Figure 2c., the chambers were pre-cooled only to 273.15K,\nand the bath temperature was then decreased by 1K every 10 minutes. The protocol\nidentified as “Fast Cooling” follows the approach described above for solutions without\nhigh-pressure intermediates, wherein the chamber is submerged directly into liquid pre-\ncooled to the minimum temperature of the run, with the exception that pressure\nequilibration after the ice III/II transition typically required 6-8 hours. In order to\ndemonstrate the hallmark dependence of metastable configurations on thermal history, a\ncombined slow-fast cooling approach was also tested, which incorporated a pseudo-\nannealing logic. In this process, the temperature was incrementally lowered at a rate of\n1K per 10 minutes until the intermediate hydrate was detected, then raised 5K above the\nobserved transition temperature, and cooled once more at a rate of 0.5K/min to the\ncenotectic point.\nSee Supplementary Note 2 for example time-series data on the freezing process, and\nSupplementary Note 3 for additional data on solutions with intermediate hydrates.\nMelting process\nFor all solutions, after completion of the cooling process, the system is heated in discrete\nincrements of 0.5K, with time increments chosen based on the heat transfer\ncharacteristics of each bath to produce steady steady-state P-T data by the end of each\nstep (at which point the data is sampled), as indicated by a <0.1 MPa/min evolution of the\npressure. Additional equipment details are available in Supplementary Notes 1 and 2,\nand an example cooling-warming profile is shown in Figure S2. The steady pressure and\ntemperature are recorded at the end of each step, and this pressure-temperature data\nprovides the P-T curves shown in Figure 2.”\nWith regard to the results shown in Fig. 2(c), and supplementary Figs. S3 and S5:\nThese figures all show examples of the “non-monotonic” T-P profiles we observed, i.e.\nresults that suggest the formation of intermediate high-pressure hydrate phases that may\nbe metastable and confound the thermodynamic path towards the cenotectic. As\ndescribed in the text, we are confident that we have not observed the cenotectic in these\nsystems, because of the cooling-rate dependent formation of metastable\nassemblages. The different pressures observed at the initiation of warming and the\ndifferences in T-P profile between like samples are both consequences of this\nmetastability, as is the acute effect of cooling protocol. These observations both convince\nus that these non-monotonic profiles have likely not reached global equilibrium, and that,\nby virtue of contrast, the other monotonic profiles have reached equilibrium. For more\ndiscussion of these intermediate hydrate phases and metastable phenomena, please see\nthe section “Intermediate salt-based phase transitions along the eutectic curve”. We\nhave also added a statement to the end of this section highlighting additional kinetic\naspects of the systems that may be interrogated to explore their potential metastability\nfor deeply.\nWe sincerely thank the reviewer again for their comments here, which, in both this review\nand the previous, have no doubt strengthened the manuscript. We hope that these\nclarifications of the methodology and interpretation satisfy their remaining concerns.\nSome minor comments\n4. Please add page numbers and give figures and tables as soon as possible after first mention. We have done so—thank you for noting.\n5. The figure captions are very long. Be careful of including descriptions and interpretations in the captions. Thanks again for the flag—we have cut ~4 lines from the\nFigure 2 caption (removing interpretational elements), and tightened up each of the\nothers."}, {"round": 3, "reviewer_comments": {"reviewer_3": "Please see attached pdf"}, "author_response": "RESPONSE TO REVIEWERS\nWe would like to sincerely thank Dr. Driesner for examining our manuscript once more, and\nespecially within the context of evaluating our response to the concerns of Reviewer #5, and we’re\npleased to hear that he has found those concerns sufficiently addressed. Regarding his new\ninsights into Figure 1, we reproduce his comments below in black and respond to them in blue.\nREVIEWER 3\nI (Reviewer 3) was asked for a final check if another reviewer’s (5, who was not available) points\nwere properly addressed in the revision. I am happy to say that a careful inspection of the\nrevision lets me conclude that this is the case.\nPleased to hear it, thank you for taking the time to do that.\nHowever, when re-reading the manuscript with all the new clarification I felt that a few things\nremained unclear to me. If you combine Fig. 2 with Fig. 1 you get the following: [image not\nshown]\nClearly, this looks as if something is wrong with the interpretation as the melting paths (arrows)\nstart way off any possible cenotectic of the kind drawn. It would also not explain the near-\nhorizontal initial pressure curves as those should be along the variable-pressure Ice Ih/II\nboundary.\nAfter thinking and trying out possible explanations (2 – 3 hours, something you don’t want a\nreader to spend to understand your results) I finally mean to have understood that Fig. 1 is\nactually misleading. In fact, the “solubility surfaces” of your systems are located much higher up,\nat low to very low solute mole fractions (please convert your wt% to mole fraction to see\nyourself).\nSo, I think what you want to draw is rather something like my second figure (of course nicer and\nmore accurate than my quick sketch). Also, the cenotectic pressures now make sense as they\nare related to Ih/III without any Ih/II influence. When you convert to mole fraction (perhaps\ntaking into account ion dissociation for the salts vs. urea) and consider the 0 bar ice melting\ncurve as a generic, colligative property-based curve, then this also nicely explains why you have\ntwo groups of curves in Fig. 2a, and perhaps also the “22K rule of thumb”.\nI would strongly recommend to think this through and – if you think I am right – consider revising\nthe manuscript accordingly, including possible newly gained insights. After such a revision the\nmanuscript is very likely ready for publication.\nWe thank the reviewer tremendously for this analysis and insight, and wholeheartedly agree that\nthe figure was unnecessarily confusing-- because indeed none of the systems shown in Fig. 2a/b\nHAVE their cenotectic in equilibrium with ice II! We have modified the figure to take the valuable\nnoted insights into account. We have shifted the representation to a higher range where only ice\nIII is present at the cenotectic, consistent with the data shown in Fig. 2a/b, and we have revised\nthe figure caption to enhance clarity (see the new figure and caption at end of this document).\nWe note further that this figure is only a schematic aimed at illustrating the principle of the\ncenotectic concept, not an empirically accurate representation of the liquidus and solubility curves\nof any particular system investigated herein-- hence the use of the a.u. in the composition space.\nTo clarify this further, and remove any potential misconceptions related to units or scale of\nconcentration (mass % vs. mol %), we have also removed “1” at the right-hand side of the\nconcentration axis.\nWe have also combed the manuscript to ensure that this edited figure is in no way inconsistent\nwith other written aspects of our interpretation, and have found that it is not. Throughout the results\nsection, we discuss the cenotectic point for the systems at hand as either occurring at the liquid /\nice Ih / ice III intersection (as is certainly the case in the uncomplicated binaries shown in Fig\n2a/b), or possibly at the liquid / ice Ih / ice II intersection for the systems displaying intermediate\nhydrate phases in Figure 2.c. As such, the Figure 1 now reflects the case for which we have the\nmost (and most definitive) data, and should accurately prepare the reader for the data presented\nin Figure 2.\nWe hope that these edits makes the figure (and manuscript!) considerably less confusing, and we\nwould like to sincerely thank Dr. Driesner again for this suggestion. In light of his above-and-\nbeyond reviewer input here, we would also like to credit him in the acknowledgment of this\nmanuscript (with his and the editor’s permission).\nAs a final remark (also to the editor, given the response on paper format in the rebuttal): you\nmay now see why it is so important to really clearly document your experimental approach well\nand right from the beginning.\nSincerely, Thomas Driesner\nWe thank the reviewer for this comment as well, and certainly agree that better organization\nupon initial submission could no doubt have saved us (all) significant time and effort—we will\nbear it mind going forward! Thanks again for a very valuable review."}, {"round": 4, "reviewer_comments": {"reviewer_3": "Thanks for the positive feedback on my previous comments, and I'd be happy to be acknowledged.\nObviously the revised figure fits the data and text doesn't contradict the new Figures, but: I wonder if you dont't give away an opportunity to show the (claimed) generality and to make even some predictions. Sorry for bringing that up as the quick response seemed to indicate some pressure to get the paper out. Yet, I think for a \"high impact\" journal also the content should make as much out of the content as possible with the insights obtained during the study. And, I like the results and would find it a pity if you let the chance pass to make this more \"seminal\".\nSo, my previous suggestion with three surfaces on Fig. 1 showed that the experimental curves could align differently (quite significantly, actually, your Figure 2) with the ice diagram with the mole fraction of solute particles. Assuming full dissociation of electrolytes and none of urea, these are MgSO4 0.03, Na2SO4 0.016, Na2CO 30.03 and KCl 0.11, urea 0.127, if I didn't miscalculate that. One sees easily, that these numbers align nicely with the positions on Fig 2a and I think there is quite some benefit from adding this insight to Fig 1.\nOne can now speculatively predict that there may be cases (with high eutectic molar factions of solute particles) for which one would predict a cenotectic with ice II stability (you original Fig. 1) and according possible variations in cenotectic pressure etc.\nI attach a slightly changed suggestion for what could be modified in Fig 1 to highlight this (and it needs a disclaimer that it is schematic; yet, all salts except MgCl2 seem to follow a +/- similar eutectic curve at 0.1 MPa if plotted in mole fraction space and assuming full dissociation, so it seems very acceptable to stick to the suggested design). Please consider this seriously as a starting point for a revision of Fig. 1 given the points above (and a few minor explanations added to the text and maybe in the results).\nOf course, it is your paper; if you feel that the above thoughts are misleading or likely/possibly \"too wrong\" to be considered, then please reject the suggestion but with a good explanation why."}, "author_response": "RESPONSE TO REVIEWER\nWe thank Dr. Driesner once more for his sustained effort in reviewing and improving our manuscript. We\nhave addressed his remaining comments in the final version of our manuscript. For the editor’s ease, we\nreproduce Dr. Driesner’s comments below (blue) and the according changes we’ve made to the\nmanuscript (black). These changes are also highlighted in the “marked-up” version of the revised\nmanuscript file. We thank the editor and reviewer again for their terrific effort here.\nReviewer #3 (Remarks to the Author):\nThanks for the positive feedback on my previous comments, and I'd be happy to be acknowledged.\nObviously the revised figure fits the data and text doesn't contradict the new Figures, but: I wonder if you\ndont't give away an opportunity to show the (claimed) generality and to make even some predictions.\nSorry for bringing that up as the quick response seemed to indicate some pressure to get the paper out.\nYet, I think for a \"high impact\" journal also the content should make as much out of the content as\npossible with the insights obtained during the study. And, I like the results and would find it a pity if you let\nthe chance pass to make this more \"seminal\".\nSo, my previous suggestion with three surfaces on Fig. 1 showed that the experimental curves could align\ndifferently (quite significantly, actually, your Figure 2) with the ice diagram with the mole fraction of solute\nparticles. Assuming full dissociation of electrolytes and none of urea, these are MgSO4 0.03, Na2SO4\n0.016, Na2CO 30.03 and KCl 0.11, urea 0.127, if I didn't miscalculate that. One sees easily, that these\nnumbers align nicely with the positions on Fig 2a and I think there is quite some benefit from adding this\ninsight to Fig 1.\nOne can now speculatively predict that there may be cases (with high eutectic molar factions of solute\nparticles) for which one would predict a cenotectic with ice II stability (you original Fig. 1) and according\npossible variations in cenotectic pressure etc.\nI attach a slightly changed suggestion for what could be modified in Fig 1 to highlight this (and it needs a\ndisclaimer that it is schematic; yet, all salts except MgCl2 seem to follow a +/- similar eutectic curve at 0.1\nMPa if plotted in mole fraction space and assuming full dissociation, so it seems very acceptable to stick\nto the suggested design). Please consider this seriously as a starting point for a revision of Fig. 1 given\nthe points above (and a few minor explanations added to the text and maybe in the results).\nOf course, it is your paper; if you feel that the above thoughts are misleading or likely/possibly \"too wrong\"\nto be considered, then please reject the suggestion but with a good explanation why.\nResponse:\nWe agree completely with Dr. Driesner that the “expanded” version of Figure 1 he suggests will deepen\nthe impact and clarity of the work. As such, we have elected to capture the best of all worlds in the final\nrevision and include both our Figure 1 from the previous revision (which the Reviewer notes is now\nconsistent with our data in Figure 2) and the “expanded” version suggested by Dr. Driesner, which we\ninclude as Figure 3 in the revised text. That figure and the according descriptive text added is reproduced\nbelow:\nFigure 3: Conceptual pressure-temperature-concentration phase diagram depicting binary solutions of water and generic\nsalt-like solutes of varying solubilities. A generic low solubility surface is shown in red, a generic medium solubility surface is shown\nin yellow, and a generic high solubility surface is shown in green. The 0.1 MPa eutectic points corresponding to each surface are\nmarked by (e, e, e), and the cenotectics are marked by (𝜅 𝜅 𝜅), where increasing subscript indices correspond to increasing\n1 2 3 1, 2, 3\nsolubility. All other markings retain the meanings indicated in Figure 1.\nFor clarity, in Figure 3, we have extended the conceptual phase diagram presented in Figure 1 to include\nprototypical examples of solute solubility surfaces that may correspond to these differing cenotectics,\norganizing them by molar solubility. Examples of low solubility (e.g. aqueous Na SO or MgSO ) and\n2 4 4\nmedium solubility (e.g. aqueous KCl or Urea) cenotectics are represented within the experimental data in\nFig. 2a/b, and marked conceptually in Fig. 3 by 𝜅 and 𝜅 . Examples of high solubility cenotectics\n1 2\n(occurring at the ice ih-ice II-liquid triple point and marked by 𝜅 ) have not been experimentally confirmed\n3\nin this work, but we suggest that aqueous perchlorates may be good candidates, as they often possess\nvery low 0.1 MPa eutectic temperatures (e.g. 236 K for NaClO and 206 K for MgClO ). For aqueous\n4 4\nNaCl and MgCl , while we observe signs of new hydrate species at high pressures that may increase the\n2\ntemperature of the cenotectic, it appears likely that they will yet fall beneath 238K (along the Ih-ice II-\nliquid triple point), considering the trends of their eutectic curves (Fig.2c).\nWe agree with Dr. Driesner that this figure best conveys the broadness of the possibility space, and will\nhelp the reader to understand the wide array of cenotectic possibilities presented by different aqueous\nsystems."}]

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