Abstract
Large Hesperian-aged (~3.7 Ga) layered deposits of sulfate-rich sediments in the equatorial regions of Mars have been suggested to be evidence for ephemeral playa environments. But early Mars may not have been warm enough to support conditions similar to what occurs in arid environments on Earth. Instead cold, icy environments may have been widespread. Under cryogenic conditions sulfate formation might be blocked, since kinetics of silicate weathering are typically strongly retarded at temperatures well below 0 °C. But cryo-concentration of acidic solutions may counteract the slow kinetics. Here we show that cryo-concentrated acidic brines rapidly chemically weather olivine minerals and form sulfate minerals at temperatures as low as −60 °C. These experimental results demonstrate the viability of sulfate formation under current Martian conditions, even in the polar regions. An ice-hosted sedimentation and weathering model may provide a compelling description of the origin of large Hesperian-aged layered sulfate deposits on Mars.
Sulphate-rich sediments have been taken as evidence of surface water on Mars. Here, the authors show that cryo-concentrated brines chemically weather olivine minerals forming sulfate minerals at up to −60 °C, showing that cryogenic weathering and sulfate formation can occur under current Martian conditions.
Introduction
The nature of the Martian climate through history remains an extremely important and unresolved question in planetary science. Despite huge amounts of data returned from orbiters and landers on Mars, there still remains uncertainty about whether the Martian surface environment ever supported an Earth-like climate and if so, for how long. Certainly, substantial geomorphological evidence has revealed that water has flowed across much of the Martian surface. However, this evidence is generally insufficient to further constrain the timescales involved, and many of the channels, deltas, lakes, and other features could represent only brief water activity1, 2.
Substantial oxidized sulfur in Martian soils was detected by the Viking landers and has been suggested to form via oxidation of sulfide minerals or via reactions with acidic aerosols in the atmosphere3–6. However, more recent rover and orbiter results have revealed the presence of large deposits of layered sulfate-rich sediments (up to 30% SO3) that largely occur within Hesperian-aged deposits on the Martian surface. On Earth, large deposits of sulfate-rich sediments typically form from bodies of liquid water and therefore their presence on Mars has been taken as evidence for widespread (though transient) lacustrine environments (~3.7 Ga)7. Yet, massive deposits of relatively young sulfates are also observed around the north pole8, in an environment that is very unlikely to have involved surface water. If it can be shown that sulfates can form under the cold, dry conditions in the Martian polar regions on Mars in the Amazonian, it should force a serious reconsideration of how equatorial sulfate-bearing sediments formed in the Hesperian. Understanding the aqueous environments which produce sulfate minerals on Mars is important to understand the evolution of the Martian climate.
In this paper we consider an alternate, more uniformitarian view of the ancient Martian climate, contending that prolonged warm temperatures were never present except in the earliest stages of its history, and that the atmosphere and climate have been similar to modern conditions throughout most of the planet’s history1, 9. In this model, the formation of layered sulfate deposits represents a period of intense volcanic outgassing in a cold, dry climate where outgassed sulfur was concentrated into icy ash/dust deposits10, 11. Mass balance calculations have shown that sufficient SO2 was degassed during this period to form massive sulfate-rich deposits11. In particular, it has not been clear how sulfate minerals could form at temperatures below 0 °C where the very low kinetics might effectively lower the weathering rate of basaltic minerals to a virtual standstill12, 13. Very slow dissolution rates have been measured during experimental dissolution of olivine and basaltic glass at temperatures as low as −19 °C in a CaCl2–NaCl–H2O brine13. However, at temperatures below 0 °C acidic solutions can become increasingly concentrated14 through ice formation, which may actually enhance acid-weathering despite the slower kinetics at such low temperatures suggesting that sulfate formation may be possible at temperatures below 0 °C. We have conducted a set of experiments to test this hypothesis and show that the weathering rates of olivine at temperatures below 0 °C are sufficient to form sulfates in this cold, liquid water limited environment over timescales < 1000 years.
Results
Acid weathering experiments
We performed laboratory experiments to simulate weathering of olivine by thin films of acid fluids at temperatures between −40 and −60 °C. The experiments subjected fine grained (5–53 µm) olivine particles to small amounts of 0.5 M sulfuric acid mixed with 400 µm silica beads at −40 and −60 °C in order to form a 10 µm liquid film coating each bead. These experiments were intended to simulate the exposure of small dust grains to thin films of sulfuric acid at cryogenic temperatures inside ice deposits on the surface of Mars. The longest duration experiments (12 days) yielded sulfate minerals even at temperatures, as low as −60 °C (Fig. 1). While these experiments intentionally and artificially induce contact between the mineral grains and acidic fluids, it is likely that this will occur naturally on Mars, where dust grains in the atmosphere will serve as nucleation points for ice and acidic aerosols which will ensure close contact between the reactants15.
Olivine dissolution rates and activation energy
After quenching the experiment with a sodium acetate buffer, the concentrations of dissolved Mg2+ and Fe2+ were measured (Fig. 2, Supplementary Tables 1–4) and used to calculate dissolution rates by using a disappearing sphere model for a situation where substantial dissolution is expected and corrected with results from blank experiments16. Calculated rates of olivine dissolution from olivine in this work were 6.7(±1.2) × 10−13 mol cm−2 s−1 for −40 °C experiments, and 2.2(±0.7) × 10−13 mol cm−2 s−1 for the −60 °C experiments (Supplementary Figs. 1 and 2). The rate measured at −40 °C is comparable to forsterite dissolution rates in a pH 2.5 solution at 25 °C17 suggesting that acid weathering under subzero conditions may be quite efficient in dissolving olivine (Fig. 3). This rate can also be compared with other laboratory studies of olivine dissolution using the Arrhenius equation
1 |
where k T is the rate constant at temperature (233 K), k T,R is the rate constant at the reference temperature (T R = 298 K), E a is the activation energy, and R is the universal gas constant. There are substantial data available for all of these terms in the literature except for k T,R which is not well known at pH of −0.66 (expected pH of fluids at −40 °C, see materials and methods below). We can obtain a plausible k T,R by extrapolating the equation for forsterite dissolution rate formulated by Olsen and Rimstidt12 to pH of −0.66 (−40 °C) and pH −0.73 (−60 °C). This results in a k T,R of 2.62 × 10−11 mol cm−2 s−1 at −40 °C and 2.82 × 10−11 mol cm−2 s−1 at −60 °C. Finally, we calculate the activation energy of forsterite dissolution to be 33 kJ mol−1 (−40 °C) and 30 kJ mol−1 (−60 °C). This is lower than what has been observed in other studies who have a compiled ‘best estimate’ of 63 kJ mol−1 for forsterite dissolution12, 13. However this is very similar to values measured for fayalite dissolution under a range of temperatures (22.1 to −19.4 °C)13. The calculated activation energy of ~32 kJ mol−1 under our experimental conditions suggests that olivine dissolution at cryogenic temperatures and very low pH may be very different than dissolution reactions in more dilute solutions at warmer temperatures. The difference may also simply be a product of the difficulty in extrapolating k T,R values to the extremely low pH values expected.
The experimental results also show that the ratio of Mg/Fe leaching rates proceed in stoichiometric fashion similar to the results from previous experiments at higher temperatures, where acidic solutions are shown to leach cations from the structures of the minerals in nearly stoichiometric fashion18, 19, especially from finer grained material which is less susceptible to formation of weathering rinds19, 20. The observed stoichiometric release of Fe2+ into solution was observable despite the fact that the experiments were conducted with terrestrial air. This indicates that the experimental conditions inhibited exchange between the oxygen in the air and the Fe2+ in solution. This could have been the result of the low pH solutions or isolation from the air by ice formation. In this system, the dissolution capability of the acidic solution is maximized through eutectic freezing in an environment where the silicate minerals are extremely fine grained and have high surface areas. This provides an ideal environment for sulfate formation despite the very low temperatures which may be perceived to hinder dissolution rates.
Discussion
The weathering rates measured in this study suggest that fine grained olivine on Mars at the surface will be weathered over short timescales if it is exposed to H2SO4 aerosols at temperatures warmer than −40 °C. It is clear that even the extremely cold modern surface temperatures can typically exceed −40 °C21. In addition, we show evidence that this dissolution process, if followed by sublimation, would result in sulfate minerals (Fig. 1, Supplementary Fig. 3, Supplementary Table 5) as should be expected given the chemistry involved. Using the dissolution rate measured in this study at −40 °C, a 100 µm olivine grain would have a lifetime of ~5 yr12, however it is likely that this laboratory derived dissolution rate is much higher than one would expect to see in the field18. For example, salts may accumulate in the solutions which may hinder dissolution rates13. Nevertheless, even an decrease of several orders of magnitude ( > 1000) in the dissolution rate makes olivine unstable on 1000 to 10,000 year periods, which is short compared to the hundreds of millions of years available during the Hesperian.
Sulphates have been found in ice deposits in Greenland and Antarctica on Earth that have been attributed to forming within the ice deposit22–25. Mg, Na, and Ca sulfates have all been found in micro-inclusions in the ice23. These have been attributed to interaction between acidic aerosols and sea salt or airborne dust23. The temperatures at which these reactions occurred are not well constrained. Likewise, weathering has been observed in soils in the Antarctic Dry Valleys indicating possible cryogenic silicate weathering processes26. While these terrestrial examples are promising, the active hydrological cycling on Earth makes it difficult to observe these processes on the larger scales on which it may have operated on Mars.
If cryogenic sulfate formation was active on Mars in the past, it should also be active in the polar regions of Mars today—although this process would be strongly controlled by the amount and rate of volcanic outgassing of sulfur. The modern polar regions of Mars have large deposits of ice and dust that have been deposited over long periods of time and have resulted in vast, layered sedimentary deposits. The results of this study suggest that this environment should be conducive to formation of sulfate minerals provided a sufficient amount of sulfur-rich volatiles were supplied during a given period.
Indeed, large regions of sulfate-rich material have been detected on and around the modern north polar region of Mars and there is evidence that the material is derived from the polar sediments themselves27. It has been shown that even in the polar regions, conditions could be warm enough to melt pure water ice around dark dust grains on steep equatorial facing slopes in the polar region28. Our experiments demonstrate that weathering occurs at even much lower temperatures than the 273 K, and therefore if H2SO4 aerosols are present we expect weathering to occur over an even larger area and for longer portions of the day. However, the dominant sulfate mineral identified in the polar regions is CaSO4, which would have been derived via weathering of minerals other than olivine, and Ca-bearing phases were not included in this work.
The experimental evidence combined with field evidence from both the Earth and Mars provides a compelling argument that cryogenic sulfate formation is not only possible, but would likely be unavoidable on Mars. The evidence clearly shows that cryogenic weathering can operate, even under the extremely cold current Martian conditions. Furthermore, the combination of extensive volcanic outgassing and obliquity variations in the Hesperian29, 30 provides a plausible mechanism for the deposition of large amounts of dust, ice, and sulfuric acid aerosols in the equatorial regions. During certain periods of high orbital obliquity the polar regions received greater solar insolation than the equatorial regions and would almost certainly result in deposition of ice at lower latitudes30. This provides a means for depositing ice/dust/sulfur deposits at equatorial latitudes in a process similar to that which deposits the polar layered deposits today10. Indeed there exists substantial geomorphic evidence of glacial activity in the equatorial regions in the areas, where the layered sulfate deposits are found31, 32. Given the frequency and magnitude of the obliquity variations, a substantial sedimentary record could have been produced by this process33. On the basis of the abundance of layered sediments in the equatorial regions, estimates for the amount of sulfur required to form these deposits is well within estimates of SO2 outgassing in the Noachian and Hesperian11. The source of the cations required to form these sulfate minerals may not have come exclusively from olivine weathering, but the preponderance of Mg-, Fe-rich sulfates in these deposits suggests that olivine was an important source. The scenario described here represents a completely different weathering regime from anything preserved in the terrestrial geologic record and it is enabled by volcanism in a subfreezing environment on a planet without an ocean.
Methods
Experimental materials and setup
In cryogenic experiments, 0.5 mL of 0.5 M H2SO4 was pipetted into 40-mL freezer-proof polycarbonate tubes containing 10 g of acid-washed 400-µm silica beads and frozen at a predetermined temperature (−40° and −60 °C) in a precisely temperature-controlled freezer. In total 50 mg of San Carlos olivine (Fo90) ground under acetone (5–53 µm) were then added on top of the acid-treated silica beads, and the tube was removed from the freezer and shaken vigorously using a vortex mixer for 1 min to mix the reactants and immediately transferred back to the freezer. The amount of dilute (0.5 M) acid was calculated to be just enough to coat the silica beads to a ~10 µm thickness. On the basis of modeling results by Marion14 we expect that at the experimental temperatures the films of acid solution would be mixtures of ice and cryo-concentrated acidic solutions of 4.8 molal at −40 °C (pH = −0.66) and 5.6 molal at −60 °C (pH = −0.73). The silica beads provided a matrix on which the reaction could take place providing surface area, which could be coated with a thin layer of solution, and could evenly distribute the olivine grains while maintaining low temperatures. If the beads were not used, then it would be very difficult to get olivine grains mixed with an icy acid solution at cryogenic temperatures. The glass beads provided the momentum to break up the semi-frozen solutions and to get reactants fully mixed. The beads also help provide contact between the acidic films and the olivine grains. By limiting the amount of time outside the freezer to only 1 min, temperatures were not allowed to increase substantially inside the tubes, although this could not be measured directly.
Quenching procedure and analysis
At the conclusion of each experiment, reaction products were collected by adding 10 mL of 0.1 M sodium acetate buffer (pH = 7) to neutralize remaining acidity and to melt all the ice. The quenched mixture was shaken for 30 s and filtered immediately using 0.2 μm Nalgene filter unit under vacuum to separate the supernatant. The elements Mg and Fe in buffered extracts were determined by using a Perkin Elmer Analyst 800 atomic absorption spectrometer with AS800 Autosampler using matrix matched reference standards. Si was not measured because of extremely high backgrounds provided by the Si-spheres. Experiments were run for different durations ranging from 1 h to 9 days. Select experiments were not quenched with NaOH solution, but were instead taken out of the freezer and immediately freeze dried. The products were then mounted for scanning electron microscope (SEM) imaging.
Dissolution rate calculation
The measured solution compositions were converted into dissolution rates by using a disappearing sphere model for a situation where substantial dissolution is expected16:
2 |
Where, n is the cumulative number of moles (Mg+Fe) released from a sphere of radius r, k is the rate of dissolution of the mineral in moles m−2 s−1, V is the molar volume of the mineral, t is the time of dissolution, S is the number of particles, and I is the correction factor to account for the atoms per formula unit (e.g., 0.5 for forsterite Mg2SiO4). Initial sphere radius (r o) for olivine was calculated to be 8 μm assuming a log-normal distribution of particle sizes between 5 and 53 µm34. S was calculated using the initial sphere radius (olivine particles) and the mass of the sample which did not include the silica spheres. Because Eq. (2) cannot be easily solved for k, a method of successive approximations was used to calculate the number of moles until it matched the experimental results to four significant digits. The final dissolution rate was calculated by averaging the rates calculated from the longest duration experiments (>3 days). The rates were also corrected for results from blank experiments conducted with no olivine present. The blank experiment consisted of adding all of the materials except for the olivine and immediately adding the buffer solution and collecting the product (<1 h total duration). The short duration blank did show a significant background level (above 1 µmol) of Mg and Fe (Supplementary Table 1). In addition, similar experiments run at 7 days length showed minimal additional contribution of Mg and Fe (~1 µmol) from silica spheres (Supplementary Table 4). Acid-free blanks (all materials except for acid) were also run using similar durations (Supplementary Table 3). Assuming 50 mg of olivine and 0.5 mL of 0.5 M H2SO4 solution, we can calculate 0.25 mmol of H2SO4 and 0.54 mol of olivine. As 2 mol of H2SO4 are neutralized by 1 mol of olivine, the amount of olivine in the experiments is double the amount needed to neutralize the acid. This is consistent with what would be expected in natural systems, where the amount of silicate should overwhelm the available acidity.
Data availability
All data generated or analyzed during this study are included in this published article (and its supplementary information files).
Electronic supplementary material
Acknowledgements
We would like to acknowledge funding from Johnson Space Center.
Author contributions
P.B.N. conceived of the study, helped reduce the data, and wrote most of the manuscript. J.M. and D.W.M. wrote some portions of the manuscript. D.C.G. performed the experiments and analyses and reduced the data.
Competing interests
The authors declare no competing financial interests.
Footnotes
Electronic supplementary material
Supplementary Information accompanies this paper at doi:10.1038/s41467-017-01227-7.
Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
References
- 1.Gaidos E, Marion G. Geological and geochemical legacy of a cold early Mars. J. Geophys. Res.-Planets. 2003;108:5055. doi: 10.1029/2002JE002000. [DOI] [Google Scholar]
- 2.Carr MH, Chuang FC. Martian drainage densities. J. Geophys. Res.-Planets. 1997;102:9145–9152. doi: 10.1029/97JE00113. [DOI] [Google Scholar]
- 3.Settle M. Formation and deposition of volcanic sulfate aerosols on Mars. J. Geophys. Res. 1979;84:8343–8354. doi: 10.1029/JB084iB14p08343. [DOI] [Google Scholar]
- 4.Burns RG, Fisher DS. Iron-sulfur mineralogy of Mars - magmatic evolution and chemical-weathering products. J. Geophys. Res.-Solid Earth Planets. 1990;95:14415–14421. doi: 10.1029/JB095iB09p14415. [DOI] [Google Scholar]
- 5.Dehouck E, et al. Evaluating the role of sulfide-weathering in the formation of sulfates or carbonates on Mars. Geochim. Cosmochim. Acta. 2012;90:47–63. doi: 10.1016/j.gca.2012.04.057. [DOI] [Google Scholar]
- 6.Tosca NJ, McLennan SM, Lindsley DH, Schoonen MAA. Acid-sulfate weathering of synthetic Martian basalt: the acid fog model revisited. J. Geophys. Res.-Planets. 2004;109:E05003. doi: 10.1029/2003JE002218. [DOI] [Google Scholar]
- 7.Andrews-Hanna JC, Lewis KW. Early Mars hydrology: 2. Hydrological evolution in the Noachian and Hesperian epochs. J. Geophys. Res. 2011;116:E02007. doi: 10.1029/2010JE003709. [DOI] [Google Scholar]
- 8.Langevin Y, Poulet F, Bibring J-P, Gondet B. Sulfates in the north polar region of mars detected by OMEGA/Mars express. Science. 2005;307:1584–1586. doi: 10.1126/science.1109091. [DOI] [PubMed] [Google Scholar]
- 9.Carr MH. Martian oceans, valleys, and climate. Astronomy Geophys. 2000;41:3.20–3.26. doi: 10.1046/j.1468-4004.2000.00320.x. [DOI] [Google Scholar]
- 10.Niles PB, Michalski J. Meridiani planum sediments on Mars formed through weathering in massive ice deposits. Nat. Geosci. 2009;2:215–220. doi: 10.1038/ngeo438. [DOI] [Google Scholar]
- 11.Michalski J, Niles PB. Atmospheric origin of Martian interior layered deposits: Links to climate change and the global sulfur cycle. Geology. 2012;40:419–422. doi: 10.1130/G32971.1. [DOI] [Google Scholar]
- 12.Olsen AA, Rimstidt JD. Using a mineral lifetime diagram to evaluate the persistence of olivine on Mars. Am. Min. 2007;92:598–602. doi: 10.2138/am.2007.2462. [DOI] [Google Scholar]
- 13.Hausrath EM, Brantley SL. Basalt and olivine dissolution under cold, salty, and acidic conditions: What can we learn about recent aqueous weathering on Mars? J. Geophys. Res. 2010;115:E12001. doi: 10.1029/2010JE003610. [DOI] [Google Scholar]
- 14.Marion GM. A molal-based model for strong acid chemistry at low temperatures (<200 to 298 K) Geochim. Cosmochim. Acta. 2002;66:2499–2516. doi: 10.1016/S0016-7037(02)00857-8. [DOI] [Google Scholar]
- 15.Halevy I, Head III JW. Episodic warming of early Mars by punctuated volcanism. Nat. Geosci. 2014;7:865–868. doi: 10.1038/ngeo2293. [DOI] [Google Scholar]
- 16.Lasaga AC. Chemical kinetics of water-rock interactions. J. Geophys. Res. 1984;89:4009–4025. doi: 10.1029/JB089iB06p04009. [DOI] [Google Scholar]
- 17.Pokrovsky OS, Schott J. Kinetics and mechanism of forsterite dissolution at 25 degrees C and pH from 1 to 12. Geochim. Cosmochim. Acta. 2000;64:3313–3325. doi: 10.1016/S0016-7037(00)00434-8. [DOI] [Google Scholar]
- 18.Brantley, S. L. in Treatise on Geochemistry (eds. Holland, H. D. & Turekian, K. K.) 73–117 (Pergamon, 2003).
- 19.Burns RG. Rates and mechanisms of chemical-weathering of ferromagnesian silicate minerals on Mars. Geochim. Cosmochim. Acta. 1993;57:4555–4574. doi: 10.1016/0016-7037(93)90182-V. [DOI] [Google Scholar]
- 20.Brantley SL, Chen Y. Chemical weathering rates of pyroxenes and amphiboles. Rev. Min. 1995;31:119–172. [Google Scholar]
- 21.Mellon MT, Jakosky BM. Geographic variations in the thermal and diffusive stability of ground ice on Mars. J. Geophys. Res.-Planets. 1993;98:3345–3364. doi: 10.1029/92JE02355. [DOI] [Google Scholar]
- 22.Iizuka Y, Hondoh T, Fujii Y. Na2SO4 and MgSO4 salts during the Holocene period derived by high-resolution depth analysis of a Dome Fuji ice core. J. Glaciol. 2006;52:58–64. doi: 10.3189/172756506781828926. [DOI] [Google Scholar]
- 23.Ohno H, Igarashi M, Hondoh T. Characteristics of salt inclusions in polar ice from Dome Fuji, East Antarctica. Geophys. Res. Lett. 2006;33:08501. doi: 10.1029/2006GL025774. [DOI] [Google Scholar]
- 24.Iizuka Y, et al. A relationship between ion balance and the chemical compounds of salt inclusions found in the greenland ice core project and Dome Fuji ice cores. J. Geophys. Res. 2008;113:D07303. [Google Scholar]
- 25.Ohno H, Igarashi M, Hondoh T. Salt inclusions in polar ice core: Location and chemical form of water-soluble impurities. Earth Planet. Sci. Lett. 2005;232:171–178. doi: 10.1016/j.epsl.2005.01.001. [DOI] [Google Scholar]
- 26.Wentworth SJ, Gibson EK, Velbel MA, McKay DS. Antarctic dry valleys and indigenous weathering in Mars meteorites: implications for water and life on Mars. Icarus. 2005;174:383–395. doi: 10.1016/j.icarus.2004.08.026. [DOI] [Google Scholar]
- 27.Masse M, et al. Martian polar and circum-polar sulfate-bearing deposits: Sublimation tills derived from the North Polar Cap. Icarus. 2010;209:434–451. doi: 10.1016/j.icarus.2010.04.017. [DOI] [Google Scholar]
- 28.Losiak A, Czechowski L, Velbel MA. Ephemeral liquid water at the surface of the martian North Polar Residual Cap: Results of numerical modelling. Icarus. 2015;262:131–139. doi: 10.1016/j.icarus.2015.08.025. [DOI] [Google Scholar]
- 29.Head JW, Kreslavsky MA, Pratt S. Northern lowlands of Mars: Evidence for widespread volcanic flooding and tectonic deformation in the Hesperian Period. J. Geophys. Res.-Planets. 2002;107:5003. doi: 10.1029/2000JE001445. [DOI] [Google Scholar]
- 30.Jakosky BM, Carr MH. Possible precipitation of ice at low latitudes of Mars during periods of high obliquity. Nature. 1985;315:559–561. doi: 10.1038/315559a0. [DOI] [Google Scholar]
- 31.Gourronc M, et al. One million cubic kilometers of fossil ice in Valles Marineris: Relicts of a 3.5 Gy old glacial landsystem along the Martian equator. Geomorphology. 2014;204:235–255. doi: 10.1016/j.geomorph.2013.08.009. [DOI] [Google Scholar]
- 32.Mège D, Bourgeois O. Equatorial glaciations on Mars revealed by gravitational collapse of Valles Marineris wallslopes. Earth Planet Sci. Lett. 2011;310:182–191. doi: 10.1016/j.epsl.2011.08.030. [DOI] [Google Scholar]
- 33.Tanaka KL. Dust and ice deposition in the Martian geologic record. Icarus. 2000;144:254–266. doi: 10.1006/icar.1999.6297. [DOI] [Google Scholar]
- 34.Brantley SL, Mellott NP. Surface area and porosity of primary silicate minerals. Am. Miner. 2015;85:1767–1783. doi: 10.2138/am-2000-11-1220. [DOI] [Google Scholar]
Associated Data
This section collects any data citations, data availability statements, or supplementary materials included in this article.
Supplementary Materials
Data Availability Statement
All data generated or analyzed during this study are included in this published article (and its supplementary information files).